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Article From:https://www.cnblogs.com/profession/p/9969753.html
```1、Root mean square (RMS) is sometimes called root mean square (RMS) and validity. It is written in English as: RootMean Square (RMS).The definition of American traditional dictionary is: The square root of the average of squareEs of aset of numbers.
That is, the square sum of N terms divided by N is the result of square root of mean square.#include<iostream>#include "math.h"using namespace std; double calcRMS(double* Data, int Num){ double fSum = 0; for (int i = 0; i < Num; ++i) { fSum += Data[i] * Data[i]; } return sqrt(fSum/Num);} int main(){ double data[10] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}; double a = calcRMS(data, 10); cout << "the rms of data is:" << a << endl; return 0;}
2、The root mean square error is the square root of the square deviation between the observed value and the true value and the ratio of the observed number n. In practical measurement, the observed number n is always limited, and the true value can only be replaced by the most reliable (best) value. The root square error is very sensitive to a group of very large or very small errors in measurement, so the root mean square error is very sensitive.The difference can well reflect the precision of measurement. The root mean square error (RMS) is defined as the standard deviation, expressed in_, when a quantity is measured many times. _reflects the degree to which the measured data deviate from the true value, and the smaller_is._can be used as a standard to evaluate the accuracy of this measurement process.double calcRMSE(double* Data,double *Data2,int Num){ double fSum = 0; for (int i = 0; i < Num; ++i) { fSum += (Data[i] - Data2[i]) *(Data[i] - Data2[i]); } return sqrt(fSum / Num);}int main(){ double dataReal[10] = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}; double dataCheck[10] = { 1.02, 2.1, 2.95, 3.98,5.1, 6.05, 7.1, 7.95, 8.98, 10.1 }; double a = calcRMSE(dataReal,dataCheck,10); cout << "the rmse of dataREAL and check is:" << a << endl; return 0;}
3、Standard Deviation is the arithmetic square root of variance, also known as mean square error. It is the average of the distance from the mean of each data. It is the square root after the square and average of the mean difference. It is expressed in_.Precision can reflect the degree of dispersion of a data set.double calcMSR(double* DataR,double *DataC,int Num){ double fSum = 0; double meanValue = 0; for (int i = 0; i < Num; ++i) { meanValue += DataR[i]; } meanValue = meanValue / Num; for (int i = 0; i < Num; ++i) { fSum += (DataC[i] - meanValue) *(DataC[i] - meanValue); } return sqrt(fSum / Num); //MSR}
--------------------- ```
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+0
# Ant 101
+2
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In the graph below, each grid line counts as one unit. The line shown below passes through the point $$(1001,n)$$ (not shown on graph). Find n .
ant101 Mar 24, 2017
#1
+88871
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Note that the line passes through the points (0,3) and (7,7)
So.....the slope if this line is [7 -3 ] / [7 - 0] = 4/7
And using the point (0,3) the equation of the line is
y = (4/7)x + 3
And when x = 1001
y = (4/7)(1001) + 3 = 573
So (1001, n) = (1001, 573)
CPhill Mar 24, 2017
#2
+20009
+2
In the graph below, each grid line counts as one unit.
The line shown below passes through the point (not shown on graph).
Find n .
The line passes through the points (0,3) and (-7,-1)
$$\begin{array}{|rcll|} \hline \text{slope } = \frac{3-(-1)}{0-(-7)} &=& \frac{n-3}{1001-0} \\ \frac{3-(-1)}{0-(-7)} &=& \frac{n-3}{1001-0} \\ \frac{4}{7} &=& \frac{n-3}{1001} \\ 1001\cdot \frac{4}{7} &=& n-3 \\ 3+ 1001\cdot \frac{4}{7} &=& n \\ \mathbf{575} & \mathbf{=} & \mathbf{n} \\ \hline \end{array}$$
heureka Mar 24, 2017
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https://www.physicsforums.com/threads/simple-optics-being-stupid.214888/
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# Homework Help: Simple Optics - being stupid?
1. Feb 12, 2008
### mikehibbert
[SOLVED] Simple Optics - being stupid?!!!
1. The problem statement, all variables and given/known data
There's an object 1.5m from a white screen. What is the focal length of a lens needed to form a real and inverted image on the screen with magnification of 4.0?
How far from the object should the lens be placed?
2. Relevant equations
-M=S'/S
1/f=1/S'+1/S
3. The attempt at a solution
My problem is the first part of the question, what to use for S and S', surely there are an infinite number of possibilities?
2. Feb 12, 2008
### mgb_phys
You have a couple of extra constraints.
1, the lens to image_distance is the focal length
2, magnification = f / (f - object_distance)
3, object_distance + image_distance = 1.5m
3. Feb 12, 2008
### mikehibbert
I don't see how point 1 helps me sorry?
I understand that objectdistance + imagedistance = 1.5m
but that gives the distances sooo many possibilities?
4. Feb 12, 2008
### mgb_phys
image distance i = f, object distante = o
i + o = 1.5m
o = 1.5m - i = 1.5m -f
m = f / ( f - o ) = 4
subsitute o and solve for f
5. Feb 12, 2008
### mikehibbert
right,
if i follow that through i get f=8/3
but then putting f back into m=f/(f-o) to find o,
i get o=2, which cant be right because the object is only 1.5m from the screen?
6. Feb 12, 2008
### mgb_phys
Sorry my fault, image distance is only f if the object is at infinity (i'm an astronomer - objects are always at infinity!) I meant to say:
1/f = 1/o + 1/i and o+i=1.5
m = f / (f - o) = 4
Rearrangement is a little trickier
7. Feb 12, 2008
### mikehibbert
i'm really struggling with this... i cant seem to get f out of the maths?!
8. Feb 12, 2008
### kdv
maybe I am missing something here but S'/S = -M = 4 so S'= 4S, right? And S+S' = 1.5 meter so a simple substitution gives you both S and S'!!
Then you may find the focal length using 1/f = 1/S + 1/S'. Iam probably missing something because it seems straightforward to me.
9. Feb 12, 2008
### mikehibbert
You're right.... i feel like SUCH an idiot haha.
Thanks!
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https://calculator.academy/wholesale-margin-calculator/
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Enter the wholesale sell price ($) and the wholesale purchase price ($) into the Wholesale Margin Calculator. The calculator will evaluate and display the Wholesale Margin.
## Wholesale Margin Formula
The following formula is used to calculate the Wholesale Margin.
WM = (WSP – WPP) / WSP * 100
• Where WM is the Wholesale Margin (%)
• WSP is the wholesale sell price ($) • WPP is the wholesale purchase price ($)
## How to Calculate Wholesale Margin?
The following example problems outline how to calculate Wholesale Margin.
Example Problem #1:
1. First, determine the wholesale sell price ($). • The wholesale sell price ($) is given as: 50.
2. Next, determine the wholesale purchase price ($). • The wholesale purchase price ($) is provided as: 30.
3. Finally, calculate the Wholesale Margin using the equation above:
WM = (WSP – WPP) / WSP * 100
The values given above are inserted into the equation below and the solution is calculated:
WM = (50 – 30) / 50 * 100 = 40 (%)
Example Problem #2:
For this problem, the variables required are provided below:
wholesale sell price ($) = 60 wholesale purchase price ($) = 10
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https://www.univerkov.com/according-to-the-rules-of-the-road-the-braking-system-of-a-car-is-considered-to-be-in-good-working-order/
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# According to the rules of the road, the braking system of a car is considered to be in good working order
According to the rules of the road, the braking system of a car is considered to be in good working order if it provides braking on a dry and flat road with an acceleration of 5 m / s ^ 2. Determine the braking distance and deceleration time corresponding to this standard for the vehicle, which is moving at a speed of 54 km / h.
Data: a (acceleration when braking a working braking system) = 5 m / s2; V (initial vehicle speed) = 54 km / h (in SI V = 15 m / s).
1) Normal deceleration time: t = (V0 – V) / a = (15 – 0) / 5 = 3 s.
2) Braking distance corresponding to the norm: S = (V0 ^ 2 – V ^ 2) / 2a = (15 ^ 2 – 0) / (2 * 5) = 225/10 = 22.5 m.
Answer: The standard corresponds to a braking distance of 22.5 m and a braking time of 3 s.
One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.
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https://educatorpages.com/site/jibanez/pages/14094
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# FAQs
Q: What can my second grader expect to learn in Math this year?
Mathematics in grade two builds on what the child has already learned; experience in using math is a process of continuous growth. Although second graders are introduced to new, more complex forms of math, the study of mathematics remains far more concrete than abstract -- numbers stand for something that the children can see.
Children are encouraged to see that mathematics is something logical, not merely a random collection of facts, and that numbers are linked together by relationships that can be grasped. Second graders use math in the course of working with science, cooking, health, social studies, reading, and writing. They are able to read numbers into the hundreds, both as numerals and as words. Their conceptions of ordinal numbers will reach to "twentieth."
The idea of zero will become clearer, and children will use it in their computations. Second graders learn the position of 1s, 10s, and 100s; they gain an understanding of fractions such as 1/4, 1/8, 1/3, 2/3, and 1/10 and their relationship to wholes; they begin to estimate more confidently; they conduct precise measurements in inches, feet, yards, ounces, and pounds; they learn about the calendar -- days, weeks, months, years; they begin using graphs to represent numerical comparisons; and they gain more understanding of money, learning the value of all coins and of one-dollar and five-dollar bills. In grade two, children become increasingly aware of the patterns of mathematics. They also do more computations in the form of word or story problems.
Q: What can my second grader expect to learn in Science this year?
The natural world is the basis of most science study in the second grade, just as it was during kindergarten and the first grade. The teacher's primary goal is to foster the children's sense of curiosity about the world and their skills of inquiry. Teachers will make frequent use of questions that stimulate the critical thinking of the children: Why is that? How does that happen? What if...?
Science study should be very active in the early primary years. Whenever possible, children interact directly with science materials and observe phenomena firsthand. They learn about pollution and the problems it causes; they become familiar with the relationships between oceans, seas, rivers, and ponds; they study animals and plants in increasing detail; they learn about the different planets and the solar system; they use simple machines; they experiment with electricity, principally through batteries and bulbs; they begin to understand the history of life on earth, primarily through studying the dinosaurs; and they add scientific terms -- matter, environment, machine, heat, electricity, extinction, and experiment -- to their vocabularies.
Q: What can my second grader expect to learn in Social Studies this year?
A large part of the social studies curriculum throughout the primary grades consists of learning about families, neighborhoods, cities and towns, and countries. Second graders focus their attention on the own neighborhoods - on landmarks, architecture, history, changes over time, commerce, distinctive features, and similarity to other neighborhoods. They also learn about and celebrate various local, state, and national holidays and festivals. They read biographies of important Americans.
The concept of citizenship is emphasized, usually in ways that promote responsibility, such as helping others and learning about rules and how rules are used to resolve conflict. Children will be asked to talk with their parents about voting and governmental functions. They will also interview their parents and grandparents about their cultural heritage. Maps will become more familiar, and children will be able to use map coordinates, read map symbols, and locate oceans, rivers, cities, and towns. One key aspect of second grade social studies is that children will show increased understanding of historical time.
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# Continuous function proof help
Let $f : [a, b]\to R$ be a continuous function such that $[a,b] \subset [f(a), f(b)]$. Prove that there exists $x\in [a,b]$ such that $f(x) = x$.
My attempt: I said let there be a $\delta > 0$and defined $c$ and $d$ to be $x + \delta$ and $x-\delta$ respectively. From here since $f$ is continuous $[f(c), f(d)]\subset [f(a), f(b)]$. Then I assumed by definition $[c,d]$ is also a subset of $[f(c), f(d)]$. Then I claimed $\delta$ can be arbitrarily small so that $f(c) = f(d) = f(x)$.
Is this correct or is there a better approach?
-
If $[a,b]\cap [f(a),f(b)]=\emptyset$ then for any function $f:[a,b]\to \mathbb{R}$ (with this property) there is no such $x^*$. – vesszabo Nov 16 '12 at 13:23
It's not necessarily true that $[f(c),f(d)]$ is a subset of $[f(a),f(b)]$. Consider a function where $f(0) = 0$, $f(1) = (1)$ where $f(x)$ starts decreasing at $0$. – Jason DeVito Nov 16 '12 at 13:28
Your approach is not correct, since you are assuming what you are supposed to show. You cannot define $c$ and $d$ to be something which depends on $x^*$ before you have shown that there is such a number as $x^*$.
A better approach would be to consider the function $g(x)=f(x)-x$. Argue that $g$ is continuous, that $g(a)\leq 0$, and that $g(b)\geq 0$. Then there should be a result available that you can use.
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I see. I'm trying to show $g(a)\leq 0$ but I'm having a hard time seeing how knowing $[a,b] \subset [f(a), f(b)]$ will help. I only know it is a subset and can't say much about their values. – Vincent Nov 16 '12 at 13:56
Try to draw the two intervals along a real line. What must the order of the four points be? What does that tell you about the size of $a$ and $f(a)$? – Per Manne Nov 16 '12 at 14:00
I know that $a < b$ and that $f(a) < f(b)$. But isn't it still possible for either $a$ to be greater than $f(a)$ or vice versa? – Vincent Nov 16 '12 at 14:08
Did you draw the two intervals with one being contained in the other? Try to find a numerical example where $[a,b]\subset [f(a),f(b)]$ and $a<f(a)$. (Hint: It can't be done.) – Per Manne Nov 16 '12 at 14:32
In $\mathbb R^2$ draw the straight line $y=x$ and consider any interval at the positive part of $x$-axis, you'll get some intuition. Your problem is saying that under some conditions the graph of your function is going to intersept the straight line $y=x$ in some point. Think about the conditions for it to happen..
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Physics
# What is positive acceleration?
###### Wiki User
Positive Acceleration refers to the force acting on an object whose speed increases as it moves away from its original starting position.
If the velocity is increasing along with time it is called positive acceleration, and if the velocity decreases it is negative acceleration.
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## Related Questions
positive acceleration helps to increase the velocity for positive direction while negative acceleration resists the motion.
Positive acceleration = speeding up. Negative acceleration = slowing down.
Yes, acceleration can be positive and negative because acceleration is a vector. It has both direction and magnitude. The direction is what makes it positive or negative. Negative acceleration is usually called deceleration.
The velocity has to increase in a positive direction. The increase in velocity in a positive direction is a positive acceleration.
No. "Positive acceleration" means increasing speed. The acceleration is usually constantin typical Physics examples and applications.
Positive acceleration is an increased speed, i.e. acceleration acts in the same direction that the object is moving.
Positive acceleration is an increase in velocity in the direction in which motion is being measured.
Positive acceleration could be called "speeding up" if you felt like it.
Actually, it depends on how you define the coordinate axes, but usually when moving forward, negative acceleration decreasesspeed, positive acceleration increasesit.
no a body can only have positive velocity .sometimes it have negative acceleration
Positive acceleration ==> speeding up Negative acceleration ==> slowing down
In this case, acceleration is positive. Negative acceleration would cause the object to slow down (decelerate.)
Yes. An object slowing down but still moving in a positive direction has a positive velocity but a negative acceleration.
If you define the positive direction as pointing down, then the falling object has positive acceleration.Its magnitude is 9.8 m/s2.
when the acceleration of the body is positive its mean that its velocity is increasing and the speed of the motion also increases and speed will decrease when acceleration is negative.
Yes, it just depends on how you define which way is "positive". If you define the "backwards" direction to be the positive direction, acceleration will be positive when going "backwards". Note that if we define the axes like this, going "forwards" will give the car a negative acceleration.
Acceleration is a vector. It has both a magnitude and a direction. So you first have to choose which direction is positive. Lets say we choose "left" as negative and "right" as positive. If an object is increasing speed (positive magnitude) while moving Right (positive direction) its acceleration is Positive' If an object is decreasing speed (negative magnitude) while moving Right (positive direction) its acceleration is Negative. If an object is increasing speed (positive) while moving Left (negative direction) its acceleration is Negative. If an object is decreasing speed (negative) while moving Left (negative) its acceleration is Positive. For vertical motion you would probably choose "up" as positive and "down" as negative.
positive acceleration is when things speed up; negative acceleration is when things slow down; and zero acceleration is when things do not speed up or slow down, this is called constant speed, or no change in velocity.
If you define the "up" direction as "positive", then the acceleration is negative, because it is downward. If you define "down" as positive, then acceleration is negative. You can use any convention; just be sure to be consistent within a particular calculation, to avoid errors.
Either of these is referred to as positive acceleration: A) the object's velocity is increasing in the frame of reference B) the object is being moved in a positive direction in a coordinate plane
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# Venn diagrams for 11 sets
Ask most people about set theory and you will get a blank look, but ask them about a Venn diagram and they are much more likely to understand: indeed Venn diagrams are so well grasped that Mitt Romney’s campaign for the US Presidency recently attempted to make use of them (though I am not sure it was much of a success, but that’s another story…)
So called 2-Venn (two circles) and 3-Venn diagrams are very familiar. But higher dimension Venn diagrams that are (relatively) easy to grasp (I’ll explain what I mean by that below) are actually difficult to produce – and until last month nobody had managed to get beyond 7.
So, let’s state a few basic properties of any Venn diagram (here is a good general survey of Venn diagrams)- firstly – each region (face) is unique – there is only one region where the bottom curve intersects with the right curve alone, and only one where it intersects with the left curve alone and only one where all three curves intersect (the grey region) and so on.
This image (taken from that survey, apologies) – shows a series of set intersections which are not a Venn diagram:
For instance, we can see the two shaded areas both represent intersections of the ‘blue’ and ‘red’ sets.
A second point is that there is a finite number of intersections. In other words segments of curves cannot lie on top of one another (in fact this rule means the intersections must be in the form of Eulerian points of zero length – as, following on from the last post about Aristotle’s Wheel Paradox, any segment of a curve is continuous and has an uncountable infinite number of points).
The 3-Venn example above illustrates some of the key points about easier to understand Venn diagrams – firstly it is simple: no intersection is of more than two curves and secondly it is symmetric. In fact, if we are willing to ignore these points we can draw Venn diagrams of any number of sets, each with less intelligibility than the last.
Drawing higher number simple and symmetric Venn diagrams is exceptionally difficult and it has been proved that such $n-Venn$ diagrams only exist when $n$ is a prime.
So we have 2-Venns and 3-Venns, and mathematicians have managed 5-Venns:And 7-Venns:
But, until now, simple symmetric 11-Venns have been elusive. Certainly 11-Venn’s have been around – as the example below shows:
This example is symmetric but it is not simple.
Now, though, a breakthrough has been made. Named newroz – the Kurdish name for the new year – the first simple, symmetric 11-Venn has come from Khalegh Mamakani and Frank Ruskey, both of the Department of Computer Science at the University of Victoria, Canada.
And it is beautiful:
That said, I don’t think it will be featuring in any presidential campaigns just yet – by definition there are $2^{11} - 1= 2047$ intersecting regions, probably a bit more than even the keenest voter would care for.
1. andy x says:
can’t scroll the page on the iPad. Can you disable whatever overcomplicated “mobile” template/skin you have? Stock WordPress works best on the iPad.
• Sorry about that – have switched off the special iPad interface that wordpress recommend – hope it works now.
• d says:
iPad, haha you suck!
• Emilio Koutani says:
he can’t scroll low enough to see that remark..
haha, what a looser
• Bobby says:
Works perfectly on my Nexus 7. lolz
2. Someone make a .svg of that pic so we can see it with full detail? :3
3. non-linear says:
I can smell interesting fractals coming with higher dimensions ….
4. […] Venn diagrams for 11 sets (Cartesian Product) […]
5. Mike Blackburn says:
can this be extended to 3 dimensions – does it form a cell boundary?
6. jsbiff says:
Where can I get this on a t-shirt?
7. […] [via Cartesian Product] […]
8. […] sent me a link to a Venn Diagrams post, so that got me thinking. A Venn Diagram with \$n\$ atoms has to represent […]
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# Search by Topic
#### Resources tagged with Visualising similar to Turning Cogs:
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### Turning Cogs
##### Age 7 to 11 Challenge Level:
What happens when you turn these cogs? Investigate the differences between turning two cogs of different sizes and two cogs which are the same.
##### Age 7 to 11 Challenge Level:
How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!
### Right or Left?
##### Age 7 to 11 Challenge Level:
Which of these dice are right-handed and which are left-handed?
### World of Tan 10 - Butterflies
##### Age 7 to 11 Challenge Level:
Can you fit the tangram pieces into the outline of the butterfly?
### World of Tan 19 - A Circular Problem
##### Age 7 to 11 Challenge Level:
Can you fit the tangram pieces into the outline of this teacup?
### Making Maths: Rolypoly
##### Age 5 to 11 Challenge Level:
Paint a stripe on a cardboard roll. Can you predict what will happen when it is rolled across a sheet of paper?
### Coin Cogs
##### Age 7 to 11 Challenge Level:
Can you work out what is wrong with the cogs on a UK 2 pound coin?
### World of Tan 13 - A Storm in a Tea Cup
##### Age 7 to 11 Challenge Level:
Can you fit the tangram pieces into the outlines of the convex shapes?
### Ten Hidden Squares
##### Age 7 to 11 Challenge Level:
These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?
### The Development of Spatial and Geometric Thinking: the Importance of Instruction.
##### Age 5 to 11
This article looks at levels of geometric thinking and the types of activities required to develop this thinking.
### Twice as Big?
##### Age 7 to 11 Challenge Level:
Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.
### World of Tan 16 - Time Flies
##### Age 7 to 11 Challenge Level:
Can you fit the tangram pieces into the outline of the candle?
### Painted Faces
##### Age 7 to 11 Challenge Level:
Imagine a 3 by 3 by 3 cube made of 9 small cubes. Each face of the large cube is painted a different colour. How many small cubes will have two painted faces? Where are they?
### Fractional Triangles
##### Age 7 to 11 Challenge Level:
Use the lines on this figure to show how the square can be divided into 2 halves, 3 thirds, 6 sixths and 9 ninths.
### World of Tan 3 - Mah Ling
##### Age 7 to 11 Challenge Level:
Can you fit the tangram pieces into the outline of Mah Ling?
### World of Tan 21 - Almost There Now
##### Age 7 to 11 Challenge Level:
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
### World of Tan 25 - Pentominoes
##### Age 7 to 11 Challenge Level:
Can you fit the tangram pieces into the outlines of the people?
### Dicey
##### Age 7 to 11 Challenge Level:
A game has a special dice with a colour spot on each face. These three pictures show different views of the same dice. What colour is opposite blue?
### Green Cube, Yellow Cube
##### Age 7 to 11 Challenge Level:
How can you paint the faces of these eight cubes so they can be put together to make a 2 x 2 x 2 cube that is green all over AND a 2 x 2 x 2 cube that is yellow all over?
### Three Squares
##### Age 5 to 11 Challenge Level:
What is the greatest number of squares you can make by overlapping three squares?
### More Building with Cubes
##### Age 7 to 11 Challenge Level:
Here are more buildings to picture in your mind's eye. Watch out - they become quite complicated!
### How Would We Count?
##### Age 5 to 11 Challenge Level:
An activity centred around observations of dots and how we visualise number arrangement patterns.
### World of Tan 29 - the Telephone
##### Age 7 to 11 Challenge Level:
Can you fit the tangram pieces into the outline of the telephone?
### Square to L
##### Age 7 to 11 Challenge Level:
Find a way to cut a 4 by 4 square into only two pieces, then rejoin the two pieces to make an L shape 6 units high.
### World of Tan 5 - Dragon
##### Age 7 to 11 Challenge Level:
Can you fit the tangram pieces into the outline of the dragon?
### World of Tan 7 - Golden Goose
##### Age 7 to 11 Challenge Level:
Can you fit the tangram pieces into the outline of the plaque design?
### World of Tan 6 - Junk
##### Age 7 to 11 Challenge Level:
Can you fit the tangram pieces into the silhouette of the junk?
### World of Tan 18 - Soup
##### Age 7 to 11 Challenge Level:
Can you fit the tangram pieces into the outlines of Mah Ling and Chi Wing?
### World of Tan 28 - Concentrating on Coordinates
##### Age 7 to 11 Challenge Level:
Can you fit the tangram pieces into the outline of the playing piece?
### World of Tan 24 - Clocks
##### Age 7 to 11 Challenge Level:
Can you fit the tangram pieces into the outline of the clock?
### World of Tan 1 - Granma T
##### Age 7 to 11 Challenge Level:
Can you fit the tangram pieces into the outline of Granma T?
### World of Tan 12 - All in a Fluff
##### Age 7 to 11 Challenge Level:
Can you fit the tangram pieces into the outlines of the rabbits?
### World of Tan 20 - Fractions
##### Age 7 to 11 Challenge Level:
Can you fit the tangram pieces into the outlines of the chairs?
### World of Tan 4 - Monday Morning
##### Age 7 to 11 Challenge Level:
Can you fit the tangram pieces into the outlines of Wai Ping, Wu Ming and Chi Wing?
### World of Tan 8 - Sports Car
##### Age 7 to 11 Challenge Level:
Can you fit the tangram pieces into the outline of the sports car?
### World of Tan
##### Age 5 to 11 Challenge Level:
Read about the adventures of Granma T and her grandchildren in this series of stories, accompanied by interactive tangrams.
### World of Tan 9 - Animals
##### Age 7 to 11 Challenge Level:
Can you fit the tangram pieces into the outlines of the camel and giraffe?
### World of Tan 30 - Logical Thinking
##### Age 7 to 11 Challenge Level:
Can you logically construct these silhouettes using the tangram pieces?
### Square Surprise
##### Age 5 to 11 Challenge Level:
Why do you think that the red player chose that particular dot in this game of Seeing Squares?
### World of Tan 15 - Millennia
##### Age 7 to 11 Challenge Level:
Can you fit the tangram pieces into the outlines of the numbers?
### World of Tan 14 - Celebrations
##### Age 7 to 11 Challenge Level:
Can you fit the tangram pieces into the outlines of Little Ming and Little Fung dancing?
### World of Tan 2 - Little Ming
##### Age 7 to 11 Challenge Level:
Can you fit the tangram pieces into the outline of Little Ming?
### World of Tan 27 - Sharing
##### Age 7 to 11 Challenge Level:
Can you fit the tangram pieces into the outline of Little Fung at the table?
### World of Tan 11 - the Past, Present and Future
##### Age 7 to 11 Challenge Level:
Can you fit the tangram pieces into the outlines of the telescope and microscope?
### Counter Roundup
##### Age 7 to 11 Challenge Level:
A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.
### World of Tan 17 - Weather
##### Age 7 to 11 Challenge Level:
Can you fit the tangram pieces into the outline of the house?
### Reef and Granny
##### Age 7 to 11 Challenge Level:
Have a look at what happens when you pull a reef knot and a granny knot tight. Which do you think is best for securing things together? Why?
### World of Tan 22 - an Appealing Stroll
##### Age 7 to 11 Challenge Level:
Can you fit the tangram pieces into the outline of the child walking home from school?
### Go Moku
##### Age 7 to 11 Challenge Level:
A game for two players on a large squared space.
### World of Tan 26 - Old Chestnut
##### Age 7 to 11 Challenge Level:
Can you fit the tangram pieces into the outline of the brazier for roasting chestnuts?
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Cody
# Problem 12. Fibonacci sequence
Solution 1661094
Submitted on 28 Oct 2018 by Sohrab Karamroudi
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.
### Test Suite
Test Status Code Input and Output
1 Pass
n = 1; f = 1; assert(isequal(fib(n),f))
a = 1 a = 1 1
2 Pass
n = 6; f = 8; assert(isequal(fib(n),f))
a = 1 a = 1 1 a = 1 1 2 a = 1 1 2 3 a = 1 1 2 3 5 a = 1 1 2 3 5 8
3 Pass
n = 10; f = 55; assert(isequal(fib(n),f))
a = 1 a = 1 1 a = 1 1 2 a = 1 1 2 3 a = 1 1 2 3 5 a = 1 1 2 3 5 8 a = 1 1 2 3 5 8 13 a = 1 1 2 3 5 8 13 21 a = 1 1 2 3 5 8 13 21 34 a = 1 1 2 3 5 8 13 21 34 55
4 Pass
n = 20; f = 6765; assert(isequal(fib(n),f))
a = 1 a = 1 1 a = 1 1 2 a = 1 1 2 3 a = 1 1 2 3 5 a = 1 1 2 3 5 8 a = 1 1 2 3 5 8 13 a = 1 1 2 3 5 8 13 21 a = 1 1 2 3 5 8 13 21 34 a = 1 1 2 3 5 8 13 21 34 55 a = 1 1 2 3 5 8 13 21 34 55 89 a = 1 1 2 3 5 8 13 21 34 55 89 144 a = 1 1 2 3 5 8 13 21 34 55 89 144 233 a = 1 1 2 3 5 8 13 21 34 55 89 144 233 377 a = 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 a = 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 a = Columns 1 through 15 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 Columns 16 through 17 987 1597 a = Columns 1 through 15 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 Columns 16 through 18 987 1597 2584 a = Columns 1 through 15 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 Columns 16 through 19 987 1597 2584 4181 a = Columns 1 through 15 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 Columns 16 through 20 987 1597 2584 4181 6765
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# Question: What Is A Real Root Example?
## What type of number is 0?
0 is a rational, whole, integer and real number.
Some definitions include it as a natural number and some don’t (starting at 1 instead)..
## What are real and non real roots?
The difference between real and imaginary roots: Real roots are the values of x where the graph of the function actually crosses the x-axis. Real roots are any roots that don’t have an “i” term. Imaginary roots are values of x that make the function equal zero, but the graph doesn’t actually cross the x-axis.
## What if b2 4ac is negative?
The discriminant is the expression b2 – 4ac, which is defined for any quadratic equation ax2 + bx + c = 0. … If you get 0, the quadratic will have exactly one solution, a double root. If you get a negative number, the quadratic will have no real solutions, just two imaginary ones.
## What does a healthy root system look like?
Healthy roots should be white or tan, succulent, and numerous and long enough to hold the soil in the shape of the pot. … If any root tips are visible, they should be white. If the roots are brown and crumbly, that means the plant is unhealthy.
## How do you know how many roots a graph has?
1 Answer. The points at which the graph crosses or touches x- axis, give the real roots of the function (or zeros of the function) represented by the graph. If the graph touches x-axis and turns back, then it would be a double root at that point.
## How do you find roots on a graph?
A root is a value for which a given function equals zero. When that function is plotted on a graph, the roots are points where the function crosses the x-axis. For a function, f(x) , the roots are the values of x for which f(x)=0 f ( x ) = 0 .
## What is a real root?
The terms solutions/zeros/roots are synonymous because they all represent where the graph of a polynomial intersects the x-axis. The roots that are found when the graph meets with the x-axis are called real roots; you can see them and deal with them as real numbers in the real world.
## What is a real root in a quadratic equation?
For an equation ax2+bx+c = 0, b2-4ac is called the discriminant and helps in determining the nature of the roots of a quadratic equation. If b2-4ac > 0, the roots are real and distinct. If b2-4ac = 0, the roots are real and equal. If b2-4ac < 0, the roots are not real (they are complex).
## What does an imaginary root look like on a graph?
The roots belong to the set of complex numbers, and will be called “complex roots” (or “imaginary roots”). These complex roots will be expressed in the form a + bi. … The graph of this quadratic function shows that there are no real roots (zeros) because the graph does not cross the x-axis.
## Who invented the 0?
MayansThe first recorded zero appeared in Mesopotamia around 3 B.C. The Mayans invented it independently circa 4 A.D. It was later devised in India in the mid-fifth century, spread to Cambodia near the end of the seventh century, and into China and the Islamic countries at the end of the eighth.
## What does it mean to find all roots?
A function has a root when it crosses the x-axis, i.e. . A function can have more than one root, when there are multiple values for that satisfy this condition. The goal is to find all roots of the function (all values). In general we take the function definition and set to zero and solve the equation for .
## What is real and distinct roots?
If the discriminant is greater than zero, this means that the quadratic equation has two real, distinct (different) roots. … If the discriminant is equal to zero, this means that the quadratic equation has two real, identical roots.
## How do you find real roots?
You can find the roots, or solutions, of the polynomial equation P(x) = 0 by setting each factor equal to 0 and solving for x. Solve the polynomial equation by factoring. Set each factor equal to 0. 2×4 = 0 or (x – 6) = 0 or (x + 1) = 0 Solve for x.
## What are real roots on a graph?
Nature of the Roots The roots of a quadratic equation are called real roots if the graph crosses or touches the x-axis. These roots are real numbers. If the graph does NOT cross the x-axis the equation has no real roots.
## What are 4 types of roots?
Types of RootsFibrous Roots. Fibrous roots are found in monocot plants. … Taproots. Taproots are found in the majority of dicot plants. … Adventitious Roots. Adventitious roots are similar to the fibrous roots. … Creeping Roots. … Tuberous Roots. … Water Roots. … Parasite Roots.
## Is zero a real number?
What Are Real Numbers? Edit. Real numbers consist of zero (0), the positive and negative integers (-3, -1, 2, 4), and all the fractional and decimal values in between (0.4, 3.1415927, 1/2). Real numbers are divided into rational and irrational numbers.
## Is 0 real or imaginary?
The real numbers are a subset of the complex numbers, so zero is by definition a complex number ( and a real number, of course; just as a fraction is a rational number and a real number). If we define a pure real number as a complex number whose imaginary component is 0i, then 0 is a pure real number.
## Are roots and zeros the same?
The rule of thumbs: zero refers to the function (e.g. polynomial) and root refers to the equation.
## Is negative a real root?
Negative numbers don’t have real square roots since a square is either positive or 0. The square roots of numbers that are not a perfect square are members of the irrational numbers. This means that they can’t be written as the quotient of two integers.
## What are 2 types of roots?
Root systems are mainly of two types (Figure 1). Dicots have a tap root system, while monocots have a fibrous root system. A tap root system has a main root that grows down vertically, and from which many smaller lateral roots arise.
## What type of root is Onion?
fibrous rootsOnion plants possess fibrous roots. A bundle of fibrous roots are present at the base of the bulb.
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January 22, 2021, 01:58:29 PM
Forum Rules: Read This Before Posting
### Topic: Half-Life (Read 6854 times)
0 Members and 1 Guest are viewing this topic.
#### Scholar98
• Regular Member
• Posts: 15
• Mole Snacks: +1/-0
##### Half-Life
« on: January 11, 2015, 02:55:01 PM »
21. A first-order reaction is 45% complete at the end of 35 minutes. What is the length of the half-life of this reaction?
a) 41 min
b) 39 min
c) 30. min
d) 27 min
ne of these
ANS: a) 41 min PAGE: 12.4
How do you solve this. I think you have to use the integrated rate law but I'm not sure how.
#### mjc123
• Chemist
• Sr. Member
• Posts: 1837
• Mole Snacks: +256/-12
##### Re: Half-Life
« Reply #1 on: January 11, 2015, 05:06:56 PM »
The integrated rate law gives you concentration as a function of time. Rearrange to give time as a function of conc., and insert the data given to find the rate constant. Then calculate the time for 50% reaction.
#### Scholar98
• Regular Member
• Posts: 15
• Mole Snacks: +1/-0
##### Re: Half-Life
« Reply #2 on: January 11, 2015, 07:38:57 PM »
21. A first-order reaction is 45% complete at the end of 35 minutes. What is the length of the half-life of this reaction?
a) 41 min
b) 39 min
c) 30. min
d) 27 min
ne of these
ANS: a) 41 min PAGE: 12.4
How do you solve this. I think you have to use the integrated rate law but I'm not sure how.
ln(55)-ln(100)/(35)=41
« Last Edit: January 11, 2015, 09:14:52 PM by Scholar98 »
#### mjc123
• Chemist
• Sr. Member
• Posts: 1837
• Mole Snacks: +256/-12
##### Re: Half-Life
« Reply #3 on: January 12, 2015, 05:10:01 AM »
Quote
ln(55)-ln(100)/(35)=41
That's not correct. Even if you meant {ln(55)-ln(100)}/35, that's not 41 either.
{ln(55)-ln(100)}/35 = -k
Once you know k, you can work out the half-life.
#### Scholar98
• Regular Member
• Posts: 15
• Mole Snacks: +1/-0
##### Re: Half-Life
« Reply #4 on: January 13, 2015, 11:32:13 PM »
.693/0.01708=41
#### mjc123
• Chemist
• Sr. Member
• Posts: 1837
• Mole Snacks: +256/-12
##### Re: Half-Life
« Reply #5 on: January 14, 2015, 04:36:30 AM »
That's it.
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# Math
posted by .
Solve the problem. Round to the nearest unit.
584 is 12.2% of what?
I got 47.868852459016 (on the calculator) Just wanted to know if I rounded to the nearest unit correctly. When I rounded I got 4787?
• Math -
You're right! :-)
• Math -
47.87, I think you mean. Doesn't nearest unit mean to round to the nearest whole number though? (48)
• Math -
Jen, I think you misread the problem.
• Math -
584/0.122 = 4786.8852
• Math -
thx ms.sue
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Find the simple interest. Round your answer to the nearest cent. Principal = \$900 Rate = 4% Time in years = 3 Is this correct: 900*0.04=36 36*3=108.00 Then my next question is when you round to the nearest unit is it the same as regular …
A Number rounded to the nearest tenth is 6.1. The same number rounded to the nearest hundredth is 6.08 and rounded to the nearest thousandth is 6.083. What is the original number?
5. ### Rounding Decimals
Use the digits 0,2,5 and 8. Write a decimal that will round up if rounded to the nearest whole number, round down if rounded to the nearest tenth, and round up if rounded to the nearest hundredth.
6. ### math aig
Tyrone rounded 23.94 to 24.How did he round?
7. ### Math
Math Problem: Find the area of a circle that has a radius of 14 feet. Round your answer to the nearest hundredth. Would someone please check the way I worked this and let me know if I did it correct or not?
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Hi I am putting the questions that don't have pictures with the problem from my Measurement Unit Test I need my answers checked because as of now I have a D in math and I want to raise it so I need to make sure my answers are correct! …
9. ### Math
Plot points on the number line to represent all values that round to 500 when rounded to the nearest hundred and 450 when rounded to the nearest ten
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Hi I am putting the questions that don't have pictures with the problem from my Measurement Unit Test I need my answers checked because as of now I have a c in math and I want to raise it so I need to make sure my answers are correct! …
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# Graphing polynomial functions
posted by .
Given f(x)= 4x^2=9x+2 and g(x)=3x-2, find and simplify the following:
(f+g)(x)
(fg)(x)
(f-g)(3)
I have a few other problems i need help with too so if you want to lend me a hand let me know.
• Graphing polynomial functions -
We will be happy to critique your thinking.
• Graphing polynomial functions -
the standard definition of
(f+g)(x) = f(x) + g(x)
(f+g)(x) = (4x^2+9x+2) + (3x-2)
simplify this and then
follow the same technique for the other two questions, and let me know what you got
## Similar Questions
1. ### Algebra Functions
I don't know how to simplify the following functions (I get the asnwer right, but I don't know the steps!) f(x) = 4x^2 - 12x / x^2 + x - 12 Please e-mail me: [email protected] if you can help me with a few more problems, too. …
2. ### Algebra
I have some problems that I need help with please. Thanxs! Find the domain of the function. 1. f(x)=-8x-2 Given fuctions f and g, perform the indicated operations. 2. f(x)=4x-9 g(x)=7x-3 find f - g. Given the functions f and g, determine …
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8. ### Grammar
Could you say... lend a hand in helping... or is it just..lend a hand... Because lend a hand and help both mean the same thing.
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0
# How do you make the number 16 with only the numbers 1 2 3 and 4?
Updated: 9/18/2023
Wiki User
12y ago
3-1=2
2x2=4
4x4=16
or
3-1=2
2*4=8
8*2=16
Wiki User
12y ago
Earn +20 pts
Q: How do you make the number 16 with only the numbers 1 2 3 and 4?
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Related questions
(1+3+4) * 2 = 16
### What 3 numbers equal 16?
There is only one number that equals 16. That number is 16.
### What are some prime numbers in 16?
The only prime number that divides 16 evenly is 2.
### What are the square numbers 14 to 20?
16 is the only square number.
### What are two whole numbers of 16?
By te uniqueness of integers, there is only one whole number for 16 and that is 16.
16
There's only 4.
### What numbers can go into 16 25 27 equally?
Only the number 1.
### What is the only prime number that has a factor of 16?
Small words make a difference. No prime number "has" a factor of 16. But 2 is the only prime number that "is" a factor of 16.
24 = 16
### Are any prime numbers also square numbers?
No. That is impossible. A prime number is defined as a number that factors only to itself and the number one. A prime number MUST only be "divisible" by 1 and itself to get an integer number. For example, 7 only has 2 factors - 1 and 7. Square numbers are divisible by a number other than 1 and itself. For example, 16 has the factors 1, 2, 4, 8, and 16. 4 squared = 16
### What number goes in to 7 and 16?
The HCF of both numbers is 1
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## What are the dots on a die called?
On dice, pips are small dots on each face of a common six-sided die. These pips are typically arranged in patterns denoting the numbers one through six.
## How many dots are in die?
A traditional die is a cube, with each of its six faces showing a different number of dots (pips) from 1 to 6. When thrown or rolled, the die comes to rest showing on its upper surface a random integer from one to six, each value being equally likely. There are 21 dots on one dice: 6+5+4+3+2+1= 21.
Is it a die or dice?
Die is the singular form of dice. It comes from the French word des, a plural word for the same objects. In English, the most common way to make nouns plural is to add an S. If die followed that rule, its plural form would be dies.
### How many spots does a dice have?
The most common form of die is the cube, with each side marked with from one to six small dots (spots). The spots are arranged in conventional patterns and placed so that spots on opposite sides always add up to seven: one and six, two and five, three and four.
### What PIP means?
Pip is an acronym for “percentage in point” or “price interest point.” A pip is the smallest price move that an exchange rate can make based on forex market convention. Most currency pairs are priced out to four decimal places and the pip change is the last (fourth) decimal point.
Are the dots on dice called eyes?
They are pips and shall ever be called pips.
#### How many dots are there in 2 dice?
1 + 2 + 3 + 4 + 5 + 6 = 21 dots on one die. So 2 dice will have 42 dots.
#### How many dots are there on a dice opposite?
How many dots are there on the dice face opposite the one with three dots? Explanation: From figures (i), (ii) and (iv), we conclude that 6, 4,1 and 2 dots appear adjacent to 3 dots. Clearly, there will be 5 dots on the face opposite the face with 3 dots….Exercise :: Cubes and Dice – Section 2.
A. 2
B. 3
C. 4
D. 5
What is rolling a die?
A compound event is an event with more than one outcome. For example, in rolling one six-sided die, rolling an even number could occur with one of three outcomes: 2, 4, and 6. When you roll a six-sided die many times, you should not expect any outcome to happen more often than another (assuming that it is a fair die).
## What are dice made of?
Most dice are made with a thermoset plastic. One plastic that meets all of these requirements is polymethyl methacrylate (PMMA). Cellulose based plastics are also used. Since the polymer, which makes up the bulk of the plastic is typically colorless, colorants are added to make the dice more appealing.
## What is opposite 2 on a dice?
The sum of the number on the opposite faces will be equal to ‘7’ always. The number 1 will be opposite to number 6. The number 2 is opposite to 5 and 3 is opposite to 4.
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# Partitioning a set of size n to k-subsets of at most size b
I want to count the number of possibilities that one can produce $k$-subsets of a larger set $V$ with size $n$ such that 1) each subset $X_i$ has size at most $b$, 2) subsets do not have a common element, and 3) subsets altogether cover the elements in the larger set $V$.
More specifically, given a set $V$ where $|V|=n$, how many possibilities is there to choose subsets $X_1, ..., X_k \subseteq V$ such that
1) $|X_i| \leq b$,
2) $\forall_{i \neq j} X_i,X_j :$ $X_i \cap X_j = \emptyset$,
3) $\bigcup_{i \in \{1,...,k\}} X_i = V$,
Two possibilities are different if they do not have exactly same subsets. The order of subsets doesn't matter.
If finding the exact number of possibilities is hard, an upper bound suffices.
Can anyone suggest an approach to counting such possibilities?
An exponential generating series is a formal sum $f(x) = \sum_{n \ge 0} a_n \frac{x^n}{n!}$. We denote the relationship between $f(x)$ and $a_n$ by saying that $n![x^n]f(x) = a_n$. Here $[x^n]f(x)$ is the coefficient in front of $x^n$ in the formal sum.
This is $$\frac{n!}{k!} [x^n] \left( x + \frac{x^2}{2} + \frac{x^3}{3!} + \dots + \frac{x^b}{b!} \right)^k$$ by basic exponential generating function theory.
Here $$x + \frac{x^2}{2} + \frac{x^3}{3!} + \dots + \frac{x^b}{b!}$$ is the generating function for non-empty sets of size at most $b$ and so $$\frac{\left( x + \frac{x^2}{2} + \frac{x^3}{3!} + \dots + \frac{x^b}{b!} \right)^k}{k!}$$ is the generating function for a partitions of a set into $k$ sets of size between $1$ and $b$.
For example, $$\frac{(2n)!}{n!} [x^{2n}]\left( \frac{x^2}{2} \right)^n = \frac{(2n)!}{n!2^n}$$ is the number of ways to partition a $2n$-element set into $n$ sets of size $2$.
• Look up generating functions (also called generating series). They are a convenient way of encoding data. For instance, the sequence $(1,1,1,\dots)$ is encoded in $\frac{1}{1-x} = 1 + x + x^2 + x^3 + \dots$ via the coefficients. Another example is $\frac{1}{(1-x)^2} = 1 + 2x + 3x^2 + 4x^3 + \dots$ which is the generating function for the sequence $(1,2,3,\dots)$. The operator $[x^n]$ picks up the coefficient in front of $x^n$. – Trevor Gunn Mar 26 '18 at 22:42
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## PHYS208 Fundamentals of Physics II
The binomial theorem is useful in determining the leading-order behavior of expressions with n negative or fractional when x is small. Of course when n is a positive integer, it reduces to the familiar expressions for polynomials with which you are familiar from your study of algebra.
### Derivation:
You may derive the binomial theorem as a Maclaurin series. Recall that a Taylor series relates a function f(x) to its value at any arbitrary point x=a by
where f', f'', and f^(n) are derivatives with respect to x. A Maclaurin series is the special case of a Taylor series with a=0
The function (1+x)^n may be expressed as a Maclaurin series by evaluating the following derivatives:
Thus the Maclaurin series for (1+x)^n is the binomial theorem:
"http://www.physics.udel.edu/~watson/phys208/binomial.html"
Last updated Sept. 21, 1997.
Copyright George Watson, Univ. of Delaware, 1997.
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# a scuba diver is 30 feet below the surface of water 10 seconds after he entered the water and 100 feet below the surface after 40 seconds. Find the rate of change including units.
2 months ago
## Solution 1
Guest #9219
2 months ago
Here, we can make 2 points
30 feet below the surface of water 10 seconds after he entered the water
100 feet below the surface of water after 40 seconds
So, we have (10,30) and (40,100)
Slope = y2-y1 / x2-x1
So, lets substitute the values of the slope
m = (100-30)/ (40-10)
= 70/30
= 7/3
m = 2 1/3 or 2.33
## 📚 Related Questions
Question
Which angle is coterminal with 153°
Solution 1
It will be:
Positive Cotermintal Angles - 513 & 873
and
Negative Coterminal Angles - -207 -567
Question
Evaluate the expression. If necessary, round to the nearest hundredth. log 2.8
Solution 1
the answer is 0.447158 and rounded it is 0.45
Solution 2
I got .45, I'm not sure if this is right but I hope it helps!
Question
Find the value of x in each of the following: Please explain how you got your answer(s), thanks!
Solution 1
The first one: x is 3 because 3 x 3 x 3 is 27
the second one: x is 1/64 because the denominator, 4, to the power of 3 is 64. Anything rad 1 will always be 1, ∛64 is 4.
the third one: x is 1/8 because 8 x 8 x 8 which is the same thing as 8^3 is 512.
∛1/512 (1 divided or multiplied by 1 is always going to be 1)
the fourth one: x is 1331, I know this because I did, 11 x 11 x 11 to get 1331.
Let me know if this doesn't make sense
Question
Write your question here (Keep it simple and clear to get the best answer)the medal zena won for athletics consists of silver and brass in the ratio 3:5.if the medal has a mass of 200g how do i calculate the mass of the silver?
Solution 1
Silver : brass = 3 : 5
Lets take the value as x
Therefore, 3x+5x = 200 ( since the mass of the medal is 200 g )
8x = 200
x = 200/8
= 25
The mass of silver = 3x
= 3*25
= 75 g
Solution 2
Silver : brass = 3 : 5
Lets take the value as x
Therefore, 3x+5x = 200 ( since the mass of the medal is 200 g )
8x = 200
x = 200/8
= 25
The mass of silver = 3x
= 3*25
= 75 g
Question
Robert drove at an average speed of 60 miles per hour for 6 hours. Nancy drove for 7 hours at an average speed of 56 miles per hour. Which method shows a way to calculate the difference in the distances they drove? A.Step 1 Divide: 60 ÷ 6.Step 2 Divide: 56 ÷ 7. Step 3 Subtract the two quotients. B.Step 1 Divide: 60 ÷ 6. Step 2 Divide: 56 ÷ 7. Step 3 Add the two quotients. C.Step 1 Multiply: 60 × 6. Step 2 Multiply: 56 × 7. Step 3 Add the two products. D.Step 1 Multiply: 60 × 6. Step 2 Multiply: 56 × 7. Step 3 Subtract the two products.
Solution 1
A)1. 60/6=10
2. 56/7=8
3. 10-8=2
B)1.10
2.8
3.10+8=18
C)1. 360
2.392
3. 360+392=752
D)1. 360
2. 392
3. 360-392=-32
Question
PLEASE HELP! In college, you earn credits for courses taken. For each semester, tuition at a local college is \$2400, plus \$184 per credit. You have financial aid that will cover \$5,160 for the semester. How many credits can you take without spending any of our own money?
Solution 1
15 because 5,160-2400=2,760, then 2760/184
Question
A car can go 310 on 20 gallons gas. What’s your cars gas mileage ( miles per gallon). How far could you drive on 55 gallons of gas
Solution 1
Your gas mileage is 15.5 miles to the gallon. On 55 gallons of gas, you could drive 852.5 miles
Question
A rectangular prism has length x+2, width x+1, height 4, and volume 24. Find the length and the width.
Solution 1
The length is 3 and the width is 2. 3 × 2 × 4 = 24
Question
The half-life of carbon-14 is 5600 years. If a piece of charcoal made from the wood of a tree shows only 66% of the carbon-14 expected in living matter, when did the tree die?
Solution 1
The tree died 3696 years ago because 66x5600=369600/10=3696.
Question
SOME ONE PLEASE HELP Determine the sum: (9r3s2t − 4r2s2t2 − 6rs2t3) + (−4r3s2t + 8rs2t3). A. 3r10s10t10 B. −r3s2t + 4rs2t3 C. 5r6s4t2 − 4r2s2t2 + 2r2s4t6 D. 5r3s2t − 4r2s2t2 + 2rs2t3
Solution 1
5r3s2t4r2s2t2+2rs2t3
2647929
842281
748681
586256
406852
368373
348603
324927
199835
130075
112100
106146
77164
23213
22589
19607
17108
13966
10987
3389
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## Intermediate Algebra (6th Edition)
1. Factor the expression. $z^{2}$/6 - z/2 - 3 = (z/3 + 1)(z/2 - 3) 2. Apply the zero factor property. a) z/3 + 1 = 0 b) z/2 - 3 = 0 3. Solve each linear equation. a) z = -3 b) z = 6 The solutions are {-3, 6}.
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Farsley Farfield Class 6S blog
Decimals, Biographies and Chronology
Friday 11th January | No comments yet
3
HOMEWORK:
Learning Log: children have been asked to create a timeline of someone they know well – a friend or a relative. The timeline should focus on a particular theme. For example, a timeline on Usain Bolt would focus on his running career. This homework is due on Wednesday 23rd January and will be used to help plan a piece of writing. An example can be found later on in this blog.
Spelling: school are trialling the spelling website Spelling Shed. This can be accessed at spellingshed.com and children can use their Mathletics usernames and passwords to help login. Children have practised using the site in school briefly but are encouraged to practise further at home. I can check whether children have accessed the practice mode by monitoring how many points a child accrues whilst on the site. There will be an assessment on the Years 5 and 6 spelling list words next week.
Maths: children have re-capped multiplying and dividing by multiples of 10 this week. Homework allows children to practise this further. This is due on Friday 18th January.
In maths this week, children have been looking at decimal numbers. Children who are able to identify the 7 in the number 6.987 as 7 thousandths are deemed to be meeting the standard; children who can identify the 8 as equalling 8 hundredths or 80 thousandths can be said to be exceeding the standard. Children then began to multiply decimal numbers by 10, 100 and 1,000. Children understand that the digits move along the place value chart depending on which number they are multiplying by.
Children, at the end of the week, have multiplied integers (whole numbers) by decimal numbers, using their knowledge of place value to help them. 4 x 1.5, for example, would equal 6; 15 x 6.1 would equal 91.5. Children are expected to be able to multiply numbers with two decimal places by two-digit integers.
In literacy, children have begun work on biographies. The children began the week by identifying key features of a biography using a text on William Shakespeare:
Children identified quickly that the sub-headings used were far from engaging – a question would be much better! Children then went on to look at a timeline of Charles Dickens and saw how it could be helpful in writing a biography.
In History, children have begun learning about the Industrial Revolution. They began with a chronology lesson: children were asked to sort the following images in time-order. Which image shows the oldest village? Why do you think this?
In music, children begun learning their song of the half-term – A New Year Carol by Benjamin Britten. In PSHE, children did some work around e-safety and social media. In PE, children enjoyed the first week of their modules: tchoukball, tag rugby or climbing at the depot.
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Homework 1 Answers Back You are encouraged to run PSpice and look at web sites during this homework quiz. The questions review some things you should have learned in experiment 1 and help prepare you for experiment 2. TO GET BACK FROM A LINK TO A WEBPAGE, RIGHT CLICK AND CHOOSE BACK. Question 1 (1 point) Question 1-1 Which equation will give you the combined resistance in the circuit below? Student response: Percent Value Correct Response Student Response Answer Choices 0.0% a. RT = ((R1+R2)*(R3+R4))/((R1+R2)+ (R3+R4)) 0.0% b . RT = R1 + R4 + (R2*R3/(R2+R3)) 0.0% c. RT = R1 + (R3*(R2+R4))/(R3+(R2+R4)) 0.0% d . (1/RT) = R1+ R3 + (1/R2) + (1/R4) 100.0% e. RT = R1 + R3 + (R2*R4/(R2+R4)) 0.0% f. RT = R1 + R3 + (R2+R4/(R2*R4)) 0.0% g . RT = R1 + R2 + R3 + R4 0.0% h (1/RT) = (1/R1) + (1/R2) + (1/R3) +
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. (1/R4) General feedback: Use the laws for combining resistances to reduce the resistors to a single resistor with a value equal to the combined resistance. Score: 1 / 1 Question 2 (1 point) Question 1-2 What is the current in the circuit if V1=9V, R1=59 ohms, R2=4K ohms, R3=1K ohms and R4=9MEG ohms? Express your answer in milliamps. . (Answer tolerance is 2% and decimal places is 3) Student response: 1.78 Correct answer: 1.780 General feedback: You can find the current in the circuit by calculating the combined resistance and using ohms law (I=V/R). Score: 1 / 1 Question 3 (1 point) Question 1-3 In the circuit below, what is the voltage across resistor R1 if V1=10V, R1=41 ohms, R2=3K ohms, R3=2K ohms and R4=9MEG ohms? Express your answer in volts. (Answer tolerance is 2% and decimal places is 3).
Student response: 0.081 Correct answer: 0.081 General feedback: You can use ohms law to find the voltage across a resistor, once you know the current through the resistor. (Answer tolerance is 2% and decimal places is 3) Score: 1 / 1 Question 4 (1 point) Question 1-4 In the circuit below, what is the voltage across resistor R2 if V1=7V, R1=51 ohms, R2=1K ohms, R3=4K ohms and R4=10MEG ohms? Express your answer in volts. (Answer tolerance is 2% and decimal places is 3). Student response: 1.386 Correct answer: 1.386 General feedback: You can use ohms law to find the voltage across a resistor, once you know the current through the resistor. (Answer tolerance is 2% and decimal places
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is 3). Note that since R4 is so much bigger than R2, almost all the current goes through R2. If R2 and R4 are closer in value, this is not true. Score: 1 / 1 Question 5 (1 point) Question 1-5 In the circuit below, what is the current through R4 if V1=10V, R1=60 ohms, R2=1K ohms, R3=2K ohms and R4=11MEG ohms? Express your answer in microamps. (Answer tolerance is 2% and decimal places is 3). Student response: 0.297 Correct answer: 0.297 General feedback: Since R3 and R4 are in parallel, the current will divide between them. The voltage across each resistor, however, will be the same. Find the voltage first, using the total current and parallel resistance, then apply Ohm's law to calculate the portion of current through R4. Score:
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# Visualizing 3 D In 2 D Solution of TS & AP Board Class 8 Mathematics
###### Exercise 13.1
Question 1.
Draw the following 3-D figures on isometric dot sheet.
(i)
(ii)
(iii)
(iv)
(i)
(ii)
(iii)
(iv)
Question 2.
Draw a cuboid on the isometric dot sheet with the measurements 5 units × 3 units × 2 units.
Question 3.
Find the number of unit cubes in the following 3-D figures.
A unit cube is drawn by joining 2 adjacent dots in the isometric sheet.
Here in the vertical bar, there are 2 unit cubes
In the horizontal bar, there are 3 unit cubes
∴ Total no of unit cubes in given figure is: 5
Question 4.
Find the number of unit cubes in the following 3-D figures.
Here, in each bar there are 2 unit cubes
∴ 2× 4(bars) = 8 unit cubes
And also there is a unit cube in center
∴ Total no. of unit cubes in given figure are: 8 + 1 = 9
Question 5.
Find the number of unit cubes in the following 3-D figures.
Here, there are 4 unit cubes in the top layer
In bottom layer, there are 4 + 12 = 16 unit cubes
∴ Total no. of unit cubes in the given figure are:20
Question 6.
Find the number of unit cubes in the following 3-D figures.
Here, there is 1 cube at the top
In the middle layer, there are 4 cubes
In the bottom layer, there are 9 cubes
∴ Total no. of cubes = 1 + 4 + 9 = 14 unit cubes
Question 7.
Consider the distance between two consecutive dots to be 1 cm and draw the front view, side view and top view of the following 3-D figures.
(a)
(b)
(C)
Question 8.
Find the areas of the shaded regions of the 3-D figures given in question number 3.
(i)
In the figure we can clearly see that there are 3 shaded squares with 1 sq. unit area
∴ total shaded area = 3×1 sq. units = 3 sq. units
(ii)
Here, we can clearly see that all upper faces of the cubes in the figure are shaded and there are 9 unit cubes in the figure.
∴ area of the shaded region = 9×1 sq. unit = 9 sq units
(iii)
Here, we can see that whole upper face of top layer unit cubes is shaded, that is 4 unit cubes and in bottom layer, we can see that upper face of 12 unit cubes are shaded.
∴ Total shaded area = (4 + 12)× 1 sq. unit = 16 sq. units
(iv)
Here, we can see that upper face of the unit cube in the top layer is shaded and in middle layer 4 unit cubes are shaded and in the bottom layer, 5 unit cubes are shaded.
∴ total shaded area = (1 + 3 + 5)× 1 sq. unit = 8 sq. units
###### Exercise 13.2
Question 1.
Count the number of faces , vertices , and edges of given polyhedra and verify Euler’s formula.
Here,
No. of Faces (F):5
No. of Vertices (V):6
No. of Edges (E):9
Euler’s formula: F + V = E + 2
⇒ 5 + 6 = 9 + 2
⇒ 11 = 11
∴ Euler’s formula satisfies for the shape.
Question 2.
Count the number of faces , vertices , and edges of given polyhedra and verify Euler’s formula.
Here,
No. of Faces (F):7
No. of Vertices (V):10
No. of Edges (E):15
Euler’s formula: F + V = E + 2
⇒ 7 + 10 = 15 + 2
⇒ 17 = 17
∴ Euler’s formula satisfies for the shape.
Question 3.
Count the number of faces , vertices , and edges of given polyhedra and verify Euler’s formula.
Here,
No. of Faces (F):8
No. of Vertices (V):12
No. of Edges (E):18
Euler’s formula: F + V = E + 2
⇒ 8 + 12 = 18 + 2
⇒ 20 = 20
∴ Euler’s formula satisfies for the shape.
Question 4.
Count the number of faces , vertices , and edges of given polyhedra and verify Euler’s formula.
Here,
No. of Faces (F):6
No. of Vertices (V):6
No. of Edges (E):10
Euler’s formula: F + V = E + 2
⇒ 6 + 6 = 10 + 2
⇒ 12 = 12
∴ Euler’s formula satisfies for the shape.
Question 5.
Count the number of faces , vertices , and edges of given polyhedra and verify Euler’s formula.
Here,
No. of Faces (F):5
No. of Vertices (V):5
No. of Edges (E):8
Euler’s formula: F + V = E + 2
⇒ 5 + 5 = 8 + 2
⇒ 10 = 10
∴ Euler’s formula satisfies for the shape.
Question 6.
Count the number of faces , vertices , and edges of given polyhedra and verify Euler’s formula.
Here,
No. of Faces (F):8
No. of Vertices (V):12
No. of Edges (E):18
Euler’s formula: F + V = E + 2
⇒ 8 + 12 = 18 + 2
⇒ 20 = 20
∴ Euler’s formula satisfies for the shape.
Question 7.
Count the number of faces , vertices , and edges of given polyhedra and verify Euler’s formula.
Here,
No. of Faces (F):8
No. of Vertices (V):6
No. of Edges (E):12
Euler’s formula: F + V = E + 2
⇒ 8 + 6 = 12 + 2
⇒ 14 = 14
∴ Euler’s formula satisfies for the shape.
Question 8.
Count the number of faces , vertices , and edges of given polyhedra and verify Euler’s formula.
Here,
No. of Faces (F):7
No. of Vertices (V):10
No. of Edges (E):15
Euler’s formula: F + V = E + 2
⇒ 7 + 10 = 15 + 2
⇒ 17 = 17
∴ Euler’s formula satisfies for the shape.
Question 9.
Is a square prism and cube are same? explain.
No, Every Square prism is not a Cube (∵ All faces in a square prism need not be identical), but conversely all cubes are Square prisms.
Question 10.
Can a polyhedra have 3 triangular faces only? explain.
No, a polyhedra with 3 triangular faces does not exist,
∵For a polyhedra with 3 triangular faces, there exist another triangular face.
Question 11.
Can a polyhedra have 4 triangular faces only? explain.
Yes, a polyhedra with exactly 4 triangular faces can exist,
A polyhedra with 4 triangular faces is triangular Pyramid.
Question 12.
Complete the table by using Euler’s formula.
(i) Given: Faces = 8
Vertices = 6
Edges = ?
According to Euler’s formula, we know that : F + V = E + 2
∴ 8 + 6 = E + 2
⇒ 14 = E + 2
⇒ E = 14—2 = 12
∴ No. of Edges = 12
(ii) Given: Faces = 5
Vertices = ?
Edges = 9
According to Euler’s formula, we know that : F + V = E + 2
∴ 5 + V = 9 + 2
⇒ 5 + V = 11
⇒ V = 11—5 = 6
∴ No. of Vertices = 6
(iii) Given: Faces = ?
Vertices = 12
Edges = 30
According to Euler’s formula, we know that : F + V = E + 2
∴ F + 12 = 30 + 2
⇒ F + 12 = 32
⇒ E = 32—12 = 20
∴ No. of faces = 20
Question 13.
Can a polyhedra have 10 faces, 20 edges and 15 vertices?
Given: No. of face(F):10
No. of edges(E):20
No. of vertices(V):15
According to Euler formula, we know that
F + V = E + 2
That is, here
10 + 15 = 20 + 2
⇒ 25 = 22
This is not true.(That is, 25≠22 )
∴ A polyhedra with 10 faces, 20 edges and 15 vertices is not possible.
Question 14.
Complete the following table
1) A cuboid has 8 vertices and 12 edges.
2) A square pyramid has 5 vertices and 8 edges.
3) A triangular prism has 6 vertices and 9 edges.
∴
Question 15.
Name the 3-D objects or shapes that can be formed from the following nets.
No. of faces in the net: 7 (1 hexagon + 6 triangles)
No. of vertices in the net: 7
No. of edges in the net: 12
∴The possible shape we get from the net is hexagonal pyramid.
Question 16.
Name the 3-D objects or shapes that can be formed from the following nets.
No. of faces in the net: 6 (2 squares + 4 rectangles)
No. of vertices in the net: 8
No. of edges in the net: 12
∴The possible shape we get from the net is Cuboid.
Question 17.
Name the 3-D objects or shapes that can be formed from the following nets.
No. of faces in the net:6(1 pentagon + 5 triangles)
No. of vertices in the net: 6
No. of edges in the net: 10
∴The possible shape we get from the net is pentagonal pyramid.
Question 18.
Name the 3-D objects or shapes that can be formed from the following nets.
No. of faces in the net: 3 (2 circles + 1 rectangle)
No. of vertices in the net: 0
No. of edges in the net: 2
∴The possible shape we get from the net is Cylinder.
Question 19.
Name the 3-D objects or shapes that can be formed from the following nets.
No. of faces in the net: 6(6 squares)
No. of vertices in the net: 8
No. of edges in the net: 12
∴The possible shape we get from the net Cube.
Question 20.
Name the 3-D objects or shapes that can be formed from the following nets.
No. of faces in the net:6(1 hexagon + 6 triangles)
No. of vertices in the net: 7
No. of edges in the net: 12
∴The possible shape we get from the net is hexagonal pyramid.
Question 21.
Name the 3-D objects or shapes that can be formed from the following nets.
No. of faces in the net:6(2 trapezium + 4 rectangles)
No. of vertices in the net: 8
No. of edges in the net: 12
∴The possible shape we get from the net is trapezoid.
Question 22.
Draw the following diagram on the check ruled book and find out which of the following diagrams makes cube?
(a)
i. Fold Square-2, 90° downwards
ii. Fold Square-3, 90° downwards
iii. Fold Square-4, 90° downwards
iv. Now, fold Square-5, 90° left upward
v. Now, fold Square-6, 90° upward
Hence, by the above procedure, we can form a cube with the given net.
(b)
i. Fold Square-2, 90° downwards
ii. Fold Square-3, 90° downwards
iii. Fold Square-4, 90° right
iv. Now, fold Square-5, 90° downward
v. Now, fold Square-6, 90° left upward
Hence, by the above procedure, we can form a cube with the given net.
(c)
i. Fold Square-2, 90° downwards
ii. Fold Square-3, 90° downwards
iii. Fold Square-4, 90° downwards
iv. Now, fold Square-5, 90° right upward
v. Now, fold Square-6, 90° right
Hence, by the above procedure we can form a cube with the given net.
(d)
i. Fold Square-2, 90° downwards
ii. Fold Square-3, 90° left
iii. Fold Square-4, 90° downwards
iv. Now, fold Square-5, 90° right upward
v. Now, fold Square-6, 90° right
Hence, by the above procedure we can form a cube with the given net.
(e)
i. Fold Square-2, 90° downwards
ii. Fold Square-3, 90° downwards
iii. Fold Square-4, 90° downwards
iv. Fold Square-5, 90° downward
v. Now, fold Square-6, 90° left upward
Hence, by the above procedure we can form a cube with the given net.
(f)
i. Fold Square-3, 90° downwards
ii. Fold Square-4, 90° downwards
iii. Fold Square-5, 90° downwards
iv. Now, fold Square-2 90° left
v. Now, fold Square-6 90° left upward
Hence, by the above procedure we can form a cube with the given net.
(g)
i. Fold Square-2, 90° downwards
ii. Fold Square-3, 90° right
iii. Fold Square-4, 90° downwards
iv. Now, fold Square-5 90° left
v. Now, fold Square-6 90° straight upward
Hence, by the above procedure we can form a cube with the given net.
(h)
i. Fold Square-2, 90° downwards
ii. Fold Square-3, 90° downwards
iii. Fold Square-4, 90° downwards
iv. Now, fold Square-5 90° left
v. Now, fold Square-6 90° straight upward
Hence, by the above procedure we can form a cube with the given net.
(i)
i. Fold Square-2, 90° downwards
ii. Fold Square-3, 90° downwards
iii. Fold Square-4, 90° left of square-3
iv. Now, fold Square-5 90° downwards
v. Now, fold Square-6 90° right upward
Hence, by the above procedure we can form a cube with the given net.
(j)
i. Fold Square-2, 90° downwards
ii. Fold Square-3, 90° downwards
iii. Fold Square-4, 90° right to square-3
iv. Now, fold Square-5 90° right to square-4
v. Now, fold Square-6 90° left upward
Hence, by the above procedure we can form a cube with the given net.
(k)
i. Fold Square-6, 90° downwards
ii. Fold Square-5, 90° downwards
iii. Fold Square-4, 90° downwards
iv. Now, fold Square-3 90° downwards
v. Now, fold Square-1 90° downwards
Hence, by the above procedure we can form a cube with the given net.
Question 23.
(a) Name the polyhedron which has four vertices, four faces?
(b) Name the solid object which has no vertex?
(c) Name the polyhedron which has 12 edges?
(d) Name the solid object which has one surface?
(e) How is a cube different from cuboid?
(f) Which two shapes have the same number of edges, vertices, and faces?
(g) Name the polyhedron which has 5 vertices and 5 faces?
(a) A polyhedron with 4 vertices and 4 faces is tetrahedron.
(b) The only Solid object with no vertex is Sphere.
(c) The possible polyhedrons with 12 edges are a cube, cuboid, Hexagonal Pyramid.
(d) The Only solid object with 1 face is Sphere.
(e) Cube is a Regular Polyhedron (All faces are identical)
Whereas Cuboid is not a Regular Polyhedron (All faces are not identical)
(f) Cube and Cuboid have a same number of faces, edges, vertices.
That is 6 faces, 12 edges, 8 vertices.
(g) A Polyhedron with 5 vertices and 5 faces is square Pyramid.
Question 24.
Write the names of the objects given below.
(a) (b) (c) (d)
(a) The given Object is Octagonal prism.
(b) The given Object is Hexagonal prism.
(c) The given Object is triangular prism.
(d) The given Object is Pentagonal Pyramid.
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# Inference for Regression Multiple Choice Practice Problems for AP Statistics
(not rated)
By — McGraw-Hill Professional
Updated on Feb 4, 2011
Review the following concepts if necessary:
### Problems
1. Which of the following statements is (are) true?
1. In the computer output for regression, s is the estimator of σ, the standard deviation of the residuals.
2. The t-test statistic for the H0: b = 0 has the same value as the t-test statistic for H0: r = 0.
3. The t-test for the slope of a regression line is always two sided (HA: β ≠ 0).
1. I only
2. II only
3. III only
4. I and II only
5. I and III only
2. Use the following output in answering questions 2–4:
A study attempted to establish a linear relationship between IQ score and musical aptitude. The following table is a partial printout of the regression analysis and is based on a sample of 20 individuals.
3. The value of the t-test statistic for H0: β = 0 is
1. 4.05
2. –1.72
3. 0.4925
4. 6.143
5. 0.0802
4. A 99% confidence interval for the slope of the regression line is
1. 0.4925 ± 2.878(6.143)
2. 0.4925 ± 2.861(0.1215)
3. 0.4925 ± 2.861(6.143)
4. 0.4925 ± 2.845(0.1215)
5. 0.4925 ± 2.878(0.1215)
5. Which of the following best interprets the slope of the regression line?
1. For each increase of one IQ point, the Musical Aptitude score increases by 0.4925 points.
2. As IQ score increases, so does the Musical Aptitude score.
3. For each increase of one IQ point, the Musical Aptitude score is predicted to increase by 0.4925 points.
4. For each additional point of Musical Aptitude, IQ is predicted to increase by 0.4925 points.
5. There is a strong predictive linear relationship between IQ score and Musical Aptitude.
6. The two screens shown below were taken from a: TI-83/84 LinRegTTest. What is the standard error of the slope of the regression line (sb)?
1. 17033.53
2. 6953.91
3. 2206.98
4. 9225.16 ± 17033.53
5. 3115.84
7. A group of 12 students take both the SAT Math and the SAT Verbal. The least-squares regression line for predicting Verbal Score from Math Score is determined to be Verbal Score = 106.56 + 0.74(Math Score). Further, sb = 0.11. Determine a 95% confidence interval for the slope of the regression line.
1. 0.74 ± 0.245
2. 0.74 ± 0.242
3. 0.74 ± 0.240
4. 0.74 ± 0.071
5. 0.74 ± 0.199
### Solutions
1. The correct answer is (d). II is true since it can be shown that . III is not true since, although we often use the alternative HA: β ≠ 0, we can certainly test a null with an alternative that states that there is a positive or a negative association between the variables.
2. The correct answer is (a). .
3. The correct answer is (e). For n = 20, df = 20 – 2 = 18 t* = 2.878 for C = 0.99.
4. The correct answer is (c). Note that (a) is not correct since it doesn't have "predicted" or "on average" to qualify the increase. (b) Is a true statement but is not the best interpretation of the slope. (d) Has mixed up the response and explanatory variables. (e) Is also true (t = 4.05 P-value = 0.0008) but is not an interpretation of the slope.
5. The correct answer is (c). The TI-83/84 does not give the standard error of the slope directly. However,
6. The correct answer is (a). A 95% confidence interval at 12 – 2 = 10 degrees of freedom has a critical value of t* = 2.228 (from Table B; if you have a TI-84 with the invT function, invT(0.975,10)= 2.228). The required interval is 0.74 ± (2.228)(0.11) = 0.74 ± 0.245.
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Found in: Page 528
### Abstract Algebra: An Introduction
Book edition 3rd
Author(s) Thomas W Hungerford, David Leep
Pages 608 pages
ISBN 9781111569624
# Let r be a real number, $r\ne 1$. Prove that for every integer $n\ge 1$ , $1+r+{r}^{2}+{r}^{3}+....+{r}^{n-1}=\frac{{r}^{n}-1}{r-1}$.
It is proved that for every integer $n\ge 1$:
$1+r+{r}^{2}+{r}^{3}+....+{r}^{n-1}=\frac{{r}^{n}-1}{r-1}$
See the step by step solution
## Consider the given parameters
Assume that $r\ne 1$ is a real number. The objective is to show that for each integer $n\ge 1$ .
$1+r+{r}^{2}+{r}^{3}+....+{r}^{n-1}=\frac{{r}^{n}-1}{r-1}$
## Obtain the equation for Sr
Let $S=1+r+{r}^{2}+{r}^{3}+...+{r}^{n-1}$ …. (1)
Then multiply both the sides of the sum S by the real number r and get the equation as follows:
role="math" localid="1648726203258" $Sr=r\left(1+r+{r}^{2}+{r}^{3}+....{r}^{n-1}\right)\phantom{\rule{0ex}{0ex}}Sr=r+{r}^{2}+{r}^{3}+.....+{r}^{n-1}+{r}^{n}.....\left(2\right)$
## Solve the equations (1) and (2)
Subtract equation (1) from equation (2) and solve in the following manner:
$\begin{array}{rcl}rS-S& =& r+{r}^{2}+{r}^{3}+....+{r}^{n-1}+{r}^{n}-\left(1+r+{r}^{2}+{r}^{3}+....{r}^{n-1}\right)\\ \left(r-1\right)S& =& r+{r}^{2}+{r}^{3}+....+{r}^{n-1}+{r}^{n}-1-r-{r}^{2}-{r}^{3}-.....-{r}^{n-1}\\ \left(r-1\right)S& =& {r}^{n}-1\\ S& =& \frac{{r}^{n}-1}{r-1}\end{array}$
$S=1+r+{r}^{2}+{r}^{3}+....+{r}^{n-1}$; therefore, $1+r+{r}^{2}+{r}^{3}+.......+{r}^{n-1}=\frac{{r}^{n}-1}{r-1}$ .
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# Important Quadratic Equation Formulas for JEE and NEET
Page 1
Page # 22
x
2
+ b
x + c = 0, a ? 0
x =
a 2
c a 4 b b
2
? ? ?
, The expression b
2
? 4 a
c ? D is called
If ?, ? are the roots, then (a) ? + ? = ?
a
b
(b) ? ? ? ? =
a
c
A quadratic equation whose roots are ? & ?, is (x ? ? ?) (x ? ? ?)
= 0 i.e. x
2
? ( ? + ? ) x + ? ? ? = 0
2. Nature of Roots:
x
2
+ b
x + c = 0 having ?
,
? as its roots;
D ? b
2
? 4 a
c
D = 0 D ? 0
Roots are equal ? = ? = ? b/2a Roots are unequal
a, b, c ? R & D > 0 a, b, c ? R & D < 0
Roots are real Roots are imaginary ? = p + i
q, ? = p ? i
q
a, b, c ? Q & a, b, c ? Q &
D is a perfect square D is not a perfect square
? Roots are rational ? Roots are irrational
? i.e. ? = p +
q
, ? = p ?
q
a = 1, b, c ? ? & D is a perfect square
? Roots are integral.
Page 2
Page # 22
x
2
+ b
x + c = 0, a ? 0
x =
a 2
c a 4 b b
2
? ? ?
, The expression b
2
? 4 a
c ? D is called
If ?, ? are the roots, then (a) ? + ? = ?
a
b
(b) ? ? ? ? =
a
c
A quadratic equation whose roots are ? & ?, is (x ? ? ?) (x ? ? ?)
= 0 i.e. x
2
? ( ? + ? ) x + ? ? ? = 0
2. Nature of Roots:
x
2
+ b
x + c = 0 having ?
,
? as its roots;
D ? b
2
? 4 a
c
D = 0 D ? 0
Roots are equal ? = ? = ? b/2a Roots are unequal
a, b, c ? R & D > 0 a, b, c ? R & D < 0
Roots are real Roots are imaginary ? = p + i
q, ? = p ? i
q
a, b, c ? Q & a, b, c ? Q &
D is a perfect square D is not a perfect square
? Roots are rational ? Roots are irrational
? i.e. ? = p +
q
, ? = p ?
q
a = 1, b, c ? ? & D is a perfect square
? Roots are integral.
Page # 23
3. Common Roots:
1
x
2
+ b
1
x + c
1
= 0 & a
2
x
2
+ b
2
x + c
2
= 0.
(i) If two quadratic equations have both roots common, then
2
1
a
a
=
2
1
b
b
=
2
1
c
c
.
(ii) If only one root ? is common, then
? =
1 2 2 1
1 2 2 1
b a b a
a c a c
?
?
=
1 2 2 1
1 2 2 1
a c a c
c b c b
?
?
4. Range of Quadratic Expression f (x) = a
x
2
+ b
x + c.
Range in restricted domain: Given x ? [x
1
, x
2
]
(a) If ?
a 2
b
? [x
1
, x
2
] then,
f(x) ? ? ? ? ? ? ? ) ( ) ( ) ( ) (
2 1 2 1
x f , xf max , xf , xf min
(b) If ?
a 2
b
? [x
1
, x
2
] then,
f(x) ?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
a 4
D
, xf , xf max ,
a 4
D
, xf , xf min ) ( ) ( ) ( ) (
21 21
Page 3
Page # 22
x
2
+ b
x + c = 0, a ? 0
x =
a 2
c a 4 b b
2
? ? ?
, The expression b
2
? 4 a
c ? D is called
If ?, ? are the roots, then (a) ? + ? = ?
a
b
(b) ? ? ? ? =
a
c
A quadratic equation whose roots are ? & ?, is (x ? ? ?) (x ? ? ?)
= 0 i.e. x
2
? ( ? + ? ) x + ? ? ? = 0
2. Nature of Roots:
x
2
+ b
x + c = 0 having ?
,
? as its roots;
D ? b
2
? 4 a
c
D = 0 D ? 0
Roots are equal ? = ? = ? b/2a Roots are unequal
a, b, c ? R & D > 0 a, b, c ? R & D < 0
Roots are real Roots are imaginary ? = p + i
q, ? = p ? i
q
a, b, c ? Q & a, b, c ? Q &
D is a perfect square D is not a perfect square
? Roots are rational ? Roots are irrational
? i.e. ? = p +
q
, ? = p ?
q
a = 1, b, c ? ? & D is a perfect square
? Roots are integral.
Page # 23
3. Common Roots:
1
x
2
+ b
1
x + c
1
= 0 & a
2
x
2
+ b
2
x + c
2
= 0.
(i) If two quadratic equations have both roots common, then
2
1
a
a
=
2
1
b
b
=
2
1
c
c
.
(ii) If only one root ? is common, then
? =
1 2 2 1
1 2 2 1
b a b a
a c a c
?
?
=
1 2 2 1
1 2 2 1
a c a c
c b c b
?
?
4. Range of Quadratic Expression f (x) = a
x
2
+ b
x + c.
Range in restricted domain: Given x ? [x
1
, x
2
]
(a) If ?
a 2
b
? [x
1
, x
2
] then,
f(x) ? ? ? ? ? ? ? ) ( ) ( ) ( ) (
2 1 2 1
x f , xf max , xf , xf min
(b) If ?
a 2
b
? [x
1
, x
2
] then,
f(x) ?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
?
a 4
D
, xf , xf max ,
a 4
D
, xf , xf min ) ( ) ( ) ( ) (
21 21
Page # 24
5.
Let f
(x) = ax²
+ bx
+ c, where a > 0 & a
,
b
,
c ? R.
(i) Conditions for both the roots of f
(x) = 0 to be greater than a
specified number‘x
0
’ are b² ? 4ac ? 0; f
(x
0
) > 0 & ( ?
b/2a) > x
0
.
(ii) Conditions for both the roots of f
(x) = 0 to be smaller than a
specified number ‘x
0
’ are b² ? 4ac ? 0; f
(x
0
) > 0 & ( ?
b/2a) < x
0
.
(iii) Conditions for both roots of f
(x) = 0 to lie on either side of the
number ‘x
0
’ (in other words the number ‘x
0
’ lies between the roots
of f
(x) = 0), is f
(x
0
) < 0.
(iv) Conditions that both roots of f
(x) = 0 to be confined between the
numbers x
1
and x
2
, (x
1
< x
2
) are b²
? 4ac ? 0; f
(x
1
) > 0 ; f
(x
2
) > 0 &
x
1
< ( ?
b/2a) < x
2
.
(v) Conditions for exactly one root of f
(x) = 0 to lie in the interval (x
1
, x
2
)
i.e. x
1
< x < x
2
is f
(x
1
).
f
(x
2
) < 0.
## Mathematics (Maths) for JEE Main & Advanced
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## Mathematics (Maths) for JEE Main & Advanced
209 videos|443 docs|143 tests
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This membership plan is closed for the session. Mister Spex Fake, CBSE NCERT Solutions for Class 12 Maths Chapter 9 Differential Equations PDF – is designed and prepared by the best teachers across India. ���qLTHv8��m?�8�n����v� i� @]*�/�����)�tסb���:ư(�7�m-�����NQ�B�;xEv��zG�y�%�l�{��R�,LJ�^h�~�t���vXԫ���ȑhX���3R�'�!+1�LLyR!+ ۑ��0�j�td �i�[M ��X"|�L�l1υ��@�� �\$����*P�d����O1�y����}/��&����� ����I����R"'oɹQn,��~�А����Y���_PQxL�hjB��B���Η��"��z��I����!�P��e����%��h�!�;�)#�0N�G6 C�u�=Y�,hwƞ9ݱ�l��8�XO��w�L���Ԙ�' � These equations arise in a variety of applications, may it be in Physics, Chemistry, Biology, Anthropology, Geology, Economics etc. Differentiating both sides with respect to x, we get. 9.4 Formation of a Differential Equation whose General Solution is given CBSE Class 12 Maths Notes Chapter 9 Differential Equations. Atum D Arby, Substituting the values of y’ in the given differential equations, y′ + sin x = 0, we get; Therefore, y = cos x + C is a solution of y′ + sin x = 0. 332 0 obj <> endobj For example, if …
e.g. 0 Eset Smart Security Premium License Key 2020, Postcode 3752, The topics and sub-topics covered in Differential Equations Class 12 Formulas are: 9.1 Introduction. Chapter-9 To form a differential equation from a given function we differentiate the function successively as many times as the number of arbitrary constants in the given function and then eliminate the arbitrary constants. The given differential equation is, y’’’ + 2y’’ + y’ = 0, Order = 3 (Highest order derivative is y”’). !��D�3�om-�] NCERT Books for Class 12 Maths Chapter 9 Differential Equations can be of extreme use for students to understand the concepts in a simple way.Class 12th Maths NCERT Books PDF Provided will help you during your … “There are no impossible dreams, just our limited perception of what is possible.”. Windows Defender Windows 8,
Differential equations are called partial differential equations (pde) or or-dinary differential equations (ode) according to whether or not they contain partial derivatives.
A di erential equation is an equation (i.e. New California Voting Laws,
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https://researchdatapod.com/how-to-solve-r-warning-longer-object-length-is-not-a-multiple-of-shorter-object-length/
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Select Page
# How to Solve R Warning: longer object length is not a multiple of shorter object length
by | Programming, R, Tips
In R, if you perform an operation on objects with different lengths, you will get the warning message: longer object length is not a multiple of shorter object length.
This warning happens specifically if the length of the longer object is not a multiple of the shorter object
In the case of vectors, you can append zeros to the end of the shorter vector using a for loop, for example:
```for(i in ((length(y)+1):length(x)))
{y = c(y,0)}```
This tutorial will go through the warning in detail and how to solve it with code examples.
## Example #1
Consider two vectors, which we want to add together:
```x <- c(1, 3, 4, 9, 10)
y <- c(2, 4, 5)
x + y```
When we run the code we get a warning message:
```[1] 3 7 9 11 14
Warning message:
In x + y : longer object length is not a multiple of shorter object length```
If the R objects are of different lengths, R will still perform the operation but will replicate the elements from the shorter vector to continue.
The last two elements of the resultant vector is 11, which is the fourth element of x (9) plus the first element of y (2), and 14, which is the fifth element of x (10) plus the second element of y (4). R will auto-replicate objects so that they are the same length if they differ. However, if the length of the shorter vector is not a factor of the length of the longer vector, R will raise the warning message.
It is a warning message instead of an error because R can still perform the operation, but the data may be mismatched.
We can verify the vectors are of different lengths by using the length() function:
```length(x)
length(y)```
```[1] 5
[1] 3```
### Solution
We can solve this error by making sure that the vectors have the same length. We can use a for loop to append zeroes to the shorter vector. Let’s look at the revised code:
```x <- c(1, 3, 4, 9, 10)
y <- c(2, 4, 5)
for(i in ((length(y)+1):length(x)))
{y = c(y,0)}
x
y
length(x)
length(y)```
```[1] 1 3 4 9 10
[1] 2 4 5 0 0
[1] 5
[1] 5
```
The vectors are the same length. Let’s try to perform the addition operation again:
`x + y`
`[1] 3 7 9 9 10`
This time we do not get a warning because the vectors are of equal length.
## Example #2
Let’s look at a second example where the shorter vector is only short by one. W
```x <- c(1, 3, 4, 9, 10)
y <- c(2, 4, 5, 7)
x + y```
If we run the code, we will get the same warning message:
```[1] 3 7 9 16 12
Warning message:
In x + y : longer object length is not a multiple of shorter object length```
We can verify the lengths of the vectors using the length() function.
```length(x)
length(y)```
```[1] 5
[1] 4```
### Solution
As the vector y is shorter than x by one, we can append one zero to the end as follows:
```x <- c(1, 3, 4, 9, 10)
y <- c(2, 4, 5, 7)
y <- c(y, 0)
x + y```
Let’s run the code to see what happens:
`[1] 3 7 9 16 10`
## Example #3
Note that if the length of the shorter vector is a factor of length of the longer vector, we will not get the error message. Let’s look at an example:
```x <- c(3, 6, 9, 12, 15, 18)
y <- c(2, 4)
length(x)
length(y)```
```[1] 6
[1] 2```
The length of y is 2 and the length of x is 6, of which 2 is a factor. Let’s try to add the two vectors together:
`x + y`
`[1] 5 10 11 16 17 22`
Note that R does not raise the warning message and auto-replicates the shorter vector y to complete the addition operation.
### Solution
If you do not want R to auto-replicate the shorter vector you can add an if-statement to only perform the operation if the vectors are equal in length.
```x <- c(3, 6, 9, 12, 15, 18)
y <- c(2, 4)
if(length(x)==length(y)){
x + y} else {
print('vectors are not of equal length:')
}```
Let’s run the code to see the result:
```[1] "vectors are not of equal length"
```
With the if-statement we can control when to perform the addition operation.
## Summary
Congratulations on reading to the end of this tutorial!
For further reading on R related errors, go to the articles:
Go to the online courses page on R to learn more about coding in R for data science and machine learning.
Have fun and happy researching!
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Home / Electric Current / Ampere’s Circuital Law [Explained]
# Ampere’s Circuital Law [Explained]
Ampere’s circuital law states that the line integral of magnetic field intensity about any closed path is exactly equal to the direct current enclosed by that path. In the figure below, the integral of H about closed paths a and b gives the total current I, while the integral over path c gives only that portion of the current that lies within c.
James Clerk Maxwell had derived that ampere’s circuital law. It alternatively says, the integral of magnetic field intensity (H) along an imaginary closed path is equal to the current enclosed by the path.
In another way we can define Ampere’s Circuital Law as the relationship between the current and the magnetic field created by the current. This law says, the integral of magnetic field density (B) along an imaginary closed path is equal to the product of current enclosed by the path and permeability of the medium.
## Ampere’s Circuital Law applied to long straight wires
The value of the magnetic field near a long straight wire is directly to proportional to the current in the wire. The magnetic field is inversely proportional to the distance from the wire.
Therefore we get two equations i.e. B α I and B α 1/r
In order to make this an equation multiply to the proportionality constant.
B= kI/r & K = μo/2π where μo = 4π x 10-7 T . m/A
Now we shall get B= μoI/2πr and the most general form is B= μoI / l
Note that it really isn’t the distance from the wire, but the circumference of the circle that the magnetic field circumvents.
### Ampere’s Circuital Law and Solenoids
A solenoid can be considered to be a set of circular loops placed side by side that carry the same current. It produces a uniform magnetic field inside it. We can place this into Ampere’s Law equation as number of loops per unit length.
B= N μoI / l
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# Physics
posted by on .
A typical laboratory centrifuge rotates at 4100 rpm. Test tubes have to be placed into a centrifuge very carefully because of the very large accelerations.
(a) What is the acceleration at the end of a test tube that is 11 cm from the axis of rotation?
dropped from a height of 1.2 m and stopped in a 1.0 ms long encounter with a hard floor?
• Physics - ,
acceleration in the centifruge
w^2r=(4100rpm*1min/60 sec * 2PIrad/sec)^2*.11m = appx 275 g's. Work it out. check my math.
Now dropping it,
1/2 mv^2=mgh
v=sqrt(2gh)=sqrt(2*9.8*1.2)=4.95m/s
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• Dec 6th 2010, 03:34 PM
bat
Hey guys I need a little help with this problem.
A rocket is fired from the ground into the air. After 10 seconds, the rocket is 150 feet in the air. After 50 seconds, the rocket is back down to 90 feet, and after 112 seconds, 30 feet.
1. Write the equation in standard form. This one I put it into a matrix and got: y = .005x^2-1.813x+167.609
2. how many seconds will the rocket be back to the ground?
No idea how to solve this.
• Dec 6th 2010, 04:15 PM
skeeter
Quote:
Originally Posted by bat
Hey guys I need a little help with this problem.
A rocket is fired from the ground into the air. After 10 seconds, the rocket is 150 feet in the air. After 50 seconds, the rocket is back down to 90 feet, and after 112 seconds, 30 feet.
1. Write the equation in standard form. This one I put it into a matrix and got: y = .005x^2-1.813x+167.609
2. how many seconds will the rocket be back to the ground?
No idea how to solve this.
where did this problem come from?
• Dec 6th 2010, 04:29 PM
bat
Quote:
Originally Posted by skeeter
where did this problem come from?
From my exam review. Is this a problem? (Surprised)
• Dec 6th 2010, 04:35 PM
skeeter
Quote:
Originally Posted by bat
From my exam review. Is this a problem? (Surprised)
never had a rocket problem where the trajectory is an open-upwards parabola ...
• Dec 6th 2010, 04:44 PM
bat
Quote:
Originally Posted by skeeter
never had a rocket problem where the trajectory is an open-upwards parabola ...
You're right... Neither have I, am I doing something wrong?
I keep on getting an upwards parabola.
• Dec 6th 2010, 04:59 PM
skeeter
you're not doing anything wrong ... as far as the math goes, your calculated quadratic fits all three given points.
set y = 0 and use your calculator to find the time for the zero height.
ask about it when you go over it in class ... bogus problem imho.
• Dec 7th 2010, 12:42 AM
jgv115
mmm.. sorry for going off topic but how come this is in the precalculus forum?
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Topic: Matheology § 152
Replies: 53 Last Post: Nov 19, 2012 4:49 PM
Messages: [ Previous | Next ]
LudovicoVan Posts: 4,165 From: London Registered: 2/8/08
Re: Matheology § 152
Posted: Nov 16, 2012 2:42 PM
"WM" <[email protected]> wrote in message
> "LudovicoVan" <[email protected]> wrote:
>
> >> What is the limit of the sequence of the sets of indexes on the left
> >> hand side?
>
> > {oo}
>
> oo is not a natural number but indices are natural numbers because
> they determine a position. oo is not a position.
Was that an objection? We are just using limits as usual.
Let's make it formal, with the original balls and vase problem where at each
step we simply put 10 new balls in and remove the oldest one.
That translates to a sequence of sets, in fact a sequence of intervals of
natural numbers so defined:
s(n) := { i in N | n+1 <= i <= 10*n } =
= [ n+1; 10*n ]
For example, that gives:
s(0) := { } // empty
s(1) := [ 2; 10 ]
s(2) := [ 3; 20 ]
s(2) := [ 4; 30 ]
etc.
The limit of that sequence is:
lim_{n->oo} s(n) =
= lim_{n->oo} [ n+1; 10*n ] =
= [ lim_{n->oo} n+1; lim_{n->oo} 10*n ] =
= [ oo; oo ] =
= { oo }
> >> What is the limit of the decimal numbers?
>
> > oo
>
> > By the same basic arithmetic: note that if you disallow the first,
> > you should disallow the second on exactly the same grounds.
>
> Talking about the limit oo does not mean that it is assumed. It means
> that the sequence grows beyond every finite positive number.
>
> Also the sequence (1/n) does never assume its limit 0. Only the
> difference between 1/n and 0 shrinks below every positive number.
Just the same as above.
-LV
Date Subject Author
11/16/12 [email protected]
11/16/12 William Hughes
11/16/12 [email protected]
11/16/12 LudovicoVan
11/16/12 [email protected]
11/16/12 Uirgil
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11/16/12 LudovicoVan
11/16/12 Uirgil
11/16/12 William Hughes
11/16/12 Uirgil
11/17/12 [email protected]
11/17/12 LudovicoVan
11/17/12 LudovicoVan
11/17/12 Uirgil
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11/17/12 [email protected]
11/17/12 LudovicoVan
11/17/12 William Hughes
11/17/12 trj
11/17/12 LudovicoVan
11/17/12 William Hughes
11/17/12 LudovicoVan
11/17/12 Uirgil
11/17/12 LudovicoVan
11/17/12 Uirgil
11/17/12 William Hughes
11/17/12 [email protected]
11/17/12 William Hughes
11/18/12 [email protected]
11/18/12 William Hughes
11/18/12 [email protected]
11/18/12 William Hughes
11/18/12 [email protected]
11/18/12 William Hughes
11/18/12 [email protected]
11/18/12 Vurgil
11/18/12 Vurgil
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11/19/12 [email protected]
11/19/12 Vurgil
11/18/12 Vurgil
11/19/12 [email protected]
11/19/12 Vurgil
11/17/12 Uirgil
11/17/12 Uirgil
11/17/12 trj
11/17/12 Uirgil
11/17/12 Uirgil
11/17/12 [email protected]
11/17/12 Virgil
11/18/12 gus gassmann
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# How to calculate your hourly wage
GettyImages-51481254.jpg
(Photo Illustration by Alex Wong/News/Getty Images)
On December 1, if you're a salaried employee who makes less than \$47,476 a year, there's a good chance that your pay structure will change. That's because on that day a new federal rule goes into effect that will change the minimum amount that employers can pay salaried employees without giving them overtime.
Employers have choices. If your salary is below \$47,476 a year or \$913 a week, they can increase your salary to that level and keep you as a salaried employee who is exempt from overtime. They can also re-classify you as hourly and pay you overtime for any hours you work over 40 hours a week. Another option is to keep you as a salaried employee, not give you a raise, and pay you overtime if you work over 40 hours a week.
Kerry Lear, Director of HR Content at Mammoth HR in Portland also talks about a variation on re-classifying and paying hourly: employers could make you hourly and change your hourly wage to reflect the number of hours they want you to work a week. This means that if you are now salaried and expected to work over 40 hours a week, they will factor overtime pay--time and a half--into your hourly salary so they aren't paying you more and you are working the same number of hours.
So, how do you find out how much you would make hourly if your employer chose this option? You use algebra!
Here's the equation:
40w + ([hours over 40]w X 1.5)=[your salary]/52
Step 1: Figure out how many hours you would be getting paid for.
In this equation, w is the unknown hourly wage. For 40 hours, you will be paid w. Hours over 40, you will be paid w X 1.5 (time and a half).
So, if you work 50 hours a week that means you work 40 hours at regular pay and 10 at time and a half and that would look like this: 40w + (10w X 1.5) or 40w + 15w or 55w.
Step 2: Figure out your weekly wage.
This one's easy. Take your annual salary and divide it by 52, the number of weeks a year. So, if you make \$30,000 a year, your weekly salary is \$576.92.
Step 3: Solve for w.
So, here's what you have now, in the above example:
55w = \$576.92 or w = \$576.92/55 or w = \$10.49
So, if your boss wanted to keep you working the same amount of hours at the same cost, you would be making \$10.49 an hour.
Of course, then you would also be taking a pay cut if, for a week, you worked less than 50 hours.
In the coming weeks, I'll be writing more about this new rule. Do you have specific questions you want answered? Send them to me!
-- Lizzy Acker
503-221-8052
[email protected], @lizzzyacker
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# LOCATION OF THE VANISHING, VIEW AND DEPTH POINTS IN PARALLEL PERSPECTIVE
First of all, draw the three parallel and horizontal lines:
— support line
— horizon line
— distance line.
Work to a scale and perform the following operations:
A) — Draw a perfectly geometric square on the support line with the vertical and horizontal lines in parallel.
B) — Locate the vanishing and view points as follows: find the middle of the square and with a vertical line starting at the support line and going up to the horizon line (which is the viewer’s view) you will find where to mark the vanishing point. From the support line, starting at the same vertical line downwards, determine the visual distance of 17cm and locate the view point. Work always to a scale. 17cm is equal to 8.5mm in 1:20 scale.
C) — Now sketch a diagonal within the square, from one vertex to the other. Then, sketch a line parallel to this diagonal; from the view point to the distance line (we do not construct the square out of focus in order to facilitate the process of carrying out the structure). From this point, sketch a perpendicular line up to the horizon line and you will find the depth point. This operation is shown in figure nº 7.
After obtaining the vanishing, view and depth points, you will construct a flat surface to draw in perspective.
Note in figure nº 8 that the distance between the view point and the distance line is always equal to the distance between the vanishing point and the depth point. Therefore, in order to work on parallel perspective it will not be necessary to perform the whole operation shown in figure nº 7 to find the three points. You have only to place the depth point at the horizon line, far from the vanishing point in the same proportion that the view point is located at the distance line.
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Length of shortest possible knot - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T12:32:55Z http://mathoverflow.net/feeds/question/53824 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/53824/length-of-shortest-possible-knot Length of shortest possible knot fastforward 2011-01-30T21:29:37Z 2011-02-10T17:25:02Z <p>Consider a line L in R^3 in the shape of a trefoil knot. Consider the surface S that is the union of all unit circles that have centers on this line and whose tangent vectors are all perpendicular to the tangent vector of L at the cirle's center. S does not intersect itself. </p> <p>What is the shortest possible length of L?</p> http://mathoverflow.net/questions/53824/length-of-shortest-possible-knot/53828#53828 Answer by Oliver for Length of shortest possible knot Oliver 2011-01-30T21:57:59Z 2011-01-31T05:27:18Z <p>The invariant you are talking about is usually called the "ropelength" of the knot. You can find some basic stuff at the wikpedia page <a href="http://en.wikipedia.org/wiki/Ropelength" rel="nofollow">http://en.wikipedia.org/wiki/Ropelength</a> which also gives some good references. (Note that some people use unit circles, while other people use circles of diameter 1, so the reported ropelength differs by a factor of 2.)</p> <p>The exact value of the ropelength is not known for any nontrivial knot. However in the case of the trefoil, there are some pretty good bounds. It is between 15.66 and 16.372 if we define ropelength using circles of diameter 1. The upper bound is believed to be tighter.</p>
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# Calculus 3 : Vector Addition
## Example Questions
### Example Question #51 : Vector Addition
Find the sum of the vectors and
Explanation:
To find the sum between the vectors and , we use the following formula:
Using the vectors from the problem statement, we get
### Example Question #52 : Vector Addition
Find the sum of the vectors and
Explanation:
To find the sum between the vectors and , we use the following formula:
Using the vectors from the problem statement, we get
### Example Question #53 : Vector Addition
Find the sum of the vectors and
Explanation:
To find the sum between vectors and , we use the following formula:
Using the vectors from the problem statement, we get
### Example Question #261 : Vectors And Vector Operations
Find the sum of the vectors and
Explanation:
To find the sum between vectors and , we use the following formula:
Using the vectors from the problem statement, we get
### Example Question #262 : Vectors And Vector Operations
Find the sum of the vectors and
Explanation:
To find the sum of two vectors and , we use the following formula:
Applying to the vectors from the problem statement, we get
### Example Question #263 : Vectors And Vector Operations
Find the sum of the vectors and
Explanation:
To find the sum of two vectors and , we use the following formula:
Applying to the vectors from the problem statement, we get
### Example Question #264 : Vectors And Vector Operations
Find the sum of the vectors , and
Explanation:
To find the sum of three vectors , and , we use the following formula:
Using the two vectors from the problem statement and applying, we get
### Example Question #265 : Vectors And Vector Operations
Find the sum of the vectors and
Explanation:
To find the sum of two vectors and , we use the following formula:
Using the two vectors from the problem statement and applying, we get
### Example Question #266 : Vectors And Vector Operations
Find the sum of the vectors and
Explanation:
To find the sum of two vectors and , we apply the following formula:
Using the vectors from the problem statement, we get
### Example Question #267 : Vectors And Vector Operations
Find the sum of the vectors and
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# What is the energy of a 420 nm photon?
## What is the energy of a 420 nm photon?
KEe=hν–Φ=2.96eV–2.71eV=0.246eV. The energy of this 420-nm photon of violet light is a tiny fraction of a joule, and so it is no wonder that a single photon would be difficult for us to sense directly—humans are more attuned to energies on the order of joules.
## What would be the energy associated with a wave that has a wavelength of 420 nm?
A light wave has a wavelength of 420nm, calculate the energy of this wave in joules. E = ((6.63 x 10-34)x(3.0 x 108))/(420 x 10-9)E = 4.74 x 10-19J leaving the answer as this is in Joules already.
What is the frequency of a photon with a wavelength of 420 nm?
The violet light has a frequency of 7.14×1014 Hz.
What is the energy of light with a wavelength of 400 nm?
Solution: From the previous problem, the energy of a single 400 nm photon is 3.1 eV.
### How do you find the energy of a photon?
The energy of a single photon is: hν or = (h/2π)ω where h is Planck’s constant: 6.626 x 10-34 Joule-sec.
### What is the formula of de Broglie wavelength?
Apply the de Broglie wave equation λ=hmv λ = h m v to solve for the wavelength of the moving electron.
What is the difference between a wave and a medium?
There is a big difference between what the wave does and what the particles in the medium do. As the wave travels through the medium, the particles of the medium oscillate in response to the wave. In a uniform medium, the wave travels at constant speed; each particle, however, has a speed that is constantly changing.
What is the relationship between wavelength and frequency?
The shorter the wavelength, the higher the frequency. Hence, frequency and wavelength are inversely proportional to each other. Because all light waves move at the same speed in a vacuum, the number of wave crests passing at a given spot in one second is determined by the wavelength.
3×10−19J.
#### What is the energy in eV of a light wave with a wavelength of 700 nm?
The energy of a photon is often expressed in units of electron volts (1 eV = 1.602 × 10−12 erg); it is directly proportional to frequency and inversely proportional to wavelength….The visible spectrum.
colour* red (limit) 700 4.29 1.77
Which two wavelengths have the highest frequencies?
Gamma rays have the highest energies, the shortest wavelengths, and the highest frequencies. Radio waves, on the other hand, have the lowest energies, longest wavelengths, and lowest frequencies of any type of EM radiation.
How to calculate the energy of light by wavelength?
Formula: Energy of Light = (6.626 × 10 -31 × c) / w (m) Where, e = Energy c = Speed Of Light (300000000 m/s) w = Wavelength.
## How much energy does a photon of green light have?
The energy of a single photon of green light of a wavelength of 520 nm has an energy of 2.38 eV. You can use the photon energy calculator to further explore the relationship between the photon energy and its frequency or wavelength.
## How to calculate the energy of a photon?
Photon energy refers to the energy of a single photon with a particular amount of wavelength and frequency. Use our wavelength to energy calculator to find the energy of light. Online energy of light with wavelength calculator to calculate energy in Joules, Kilojoules, eV, kcal.
Which is the wavelength and frequency of a photon?
λ is the wavelength of a photon, f is the frequency of a photon. This equation gives us an energy of a single, indivisible, quanta of light and we can think of light as a collection of particles. The opposite is also true.
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Discord
Community
DARK THEME
# 3D tutorial (by this_name_is_taken)!
So, I was considering making a tutorial about this using the new tutorial functions for projects. But making an article sounded more interesting! If you have any comments, questions or feedback (feedback would be greatly appreciated!) feel free to let me know down below! Also, would you me to make a raytracing tutorial? Last of all, remember to press the like button if you approve of this tutorial!
Anyway, this article will be covering a method of 3d, called `3d projection`. The basic idea of 3d projection is that you get a starting set of 3d points, rotate them around the camera, and then finally project the 2d points onto the screen.
## Overview
This tutorial aims to:
• Teach how to make first person 3d through the method of 3d projection
• Give examples of what the code would look like.
• Give a basic understanding of the concepts and why everything works
• Give some areas for improvement (eg. shape filling)
## Part 1: 3d to 2d projection.
3d to 2d projection is the formula we use to project a set of 3d points onto a 2d screen. The formula for this is outlined below (please note that FOV stands for the field of view, which is how wide your vision is. This should be set from ~100-300):
``````3dprojection=function(x,y,z) //X is side to side, Y is up and down, z is depth
outputx=FOV*x/z //Divide both x and y by z and multiply by FOV
outputy=FOV*y/z
end
``````
Basically, this works because things further away are smaller. As objects get further away the z position (depth) will be higher, and the difference between the point and the centre of the screen will become smaller and smaller. The FOV bit is basically just to adjust.
## Part 2: 2d rotation.
The next step is learning 2d rotation (we will implement this into our 3d rotation later). Basically, we will use sine and cosine to do this, as they have an interesting property which allows them to rotate points in a circle. See the `unit circle` for an example of this. Here is the code to rotate two 2d points by the angle 'rot'
``````rotate=function(x,y,rot) //Rotate two points x and y by the angle 'rot'
rotx=cosd(rot)*x-sind(rot)*y
roty=sind(rot)*x+cosd(rot)*y // I use cosd and sind instead of cos because I prefer to work in degrees
end
``````
Now that we know 2d rotation, how to we apply that into 3d rotation?
## Part 3: 3d rotation
How we use 2d rotation to get 3d rotation is by rotating the x with the z by the x-rotation, and then the y with the z by the y-rotation. So basically this:
``````3drotation=function(x,y,z)
rotate(z,x,camxrot) // camxrot is your x-rotation
outputx=roty // Final x-value
rotate(y,rotx,camyrot) // Use the updated z-value. Just to save space
outputy=rotx // Final values
outputz=roty
``````
And that's our 3d rotation done!
## Part 4: Drawing a line
Our last step in the rendering process is finally drawing a line. With all of the scripts already in place, it is surprisingly simple! We also have to remember to subtract the camera position as our first step. What this does is it allows the camera to move and also means that we are rotating the points `around the camera` instead of `around a point`. This is the difference between seeing a cube rotate around it's centre on the screen and first person 3d. So here is the code:
``````drawline=function(x1,y1,z1,x2,y2,z2) //Draws a line between these two 3d points
//Rotation
3drotation(x1-camx,y1-camy,z1-camz) //Camx,camy and camz are our camera position
X1=outputx
Y1=outputy
Z1=outputz
//Point 2
3drotation(x2-camx,y2-camy,z2-camz)
X2=outputx
Y2=outputy
Z2=outputz
//3d to 2d projection
if Z1>zclipdist or Z2>zclipdist then //Both points are behind the camera, don't render.
//If only one point is, then we z-clip (covered later)
3dprojection(X1,Y1,Z1) //Get final 2d coordinates
X1=outputx
Y1=outputy
3dprojection(X2,Y2,Z2)
X2=outputx
Y2=outputy
screen.drawLine(X1,Y1,X2,Y2,"rgb(0,0,255)") // Draws a line between the final points, with a blue RGB colour
end
end
``````
Phew, that was a massive script! Now we only have three steps to go (bear with me here). The third last step is z-clipping.
## Part 5: Z-clipping
Z-clipping is necessary when one point is behind the camera (has a negative z-value) and the other isn't. This makes lines wrap around the screen (as the x/y value swaps when the z is negative/positive). We fix this through `interpolating` the x and y and between the two points using our z-clipping distance value, and setting the z position to the z-clipping distance. Basically, we change shorten the line if part of it is behind the camera to where it should be. The z-clipping distance should be anywhere from 4-10. This is the code:
``````zclip=function()
percent=(zclipdist-Z1)/(Z2-Z1) //Decimal number from 0-1 representing how much line is behind camera
if Z1<zclipdist then
X1=X1+(X2-X1)*percent //Interpolate back up the line
Y1=Y1+(Y2-Y1)*percent
Z1=zclipdist // Set z position to the z clipping distance
end
if Z2<zclipdist then //Same thing but for second point
X2=X1+(X2-X1)*percent //Position will be the same as it would have for Z1
Y2=Y1+(Y2-Y1)*percent
Z2=zclipdist
end
``````
Now we put that into our draw line script!
``````drawline=function(x1,y1,z1,x2,y2,z2)
//Rotation
3drotation(x1-camx,y1-camy,z1-camz)
X1=outputx
Y1=outputy
Z1=outputz
//Point 2
3drotation(x2-camx,y2-camy,z2-camz)
X2=outputx
Y2=outputy
Z2=outputz
//3d to 2d projection
if Z1>zclipdist or Z2>zclipdist then
zclip() //Z-clipping goes here!
3dprojection(X1,Y1,Z1)
X1=outputx
Y1=outputy
3dprojection(X2,Y2,Z2)
X2=outputx
Y2=outputy
screen.drawLine(X1,Y1,X2,Y2,"rgb(0,0,255)")
end
end
``````
Now that we have a successful draw line script, we can (finally) get to drawing our cube!
## Part 6: Drawing our cube!
This is our second last step, drawing a cube. This is a very basic 3d shape and definitely has room for improvement. How we are going to do it is by rendering the front face, back face, and then the connecting lines. So here is the code:
``````cube=function()
//Front face (note that cube is centred at 0,0,0)
drawline(50,50,-50,-50,50,-50)
drawline(50,-50,-50,-50,-50,-50)
drawline(50,50,-50,50,-50,-50)
drawline(-50,50,-50,-50,-50,-50)
//Back face (same thing but with further z-position)
drawline(50,50,50,-50,50,50)
drawline(50,-50,50,-50,-50,50)
drawline(50,50,50,50,-50,50)
drawline(-50,50,50,-50,-50,50)
// Connecting lines (change z in each line but not x and y)
drawline(50,50,-50,50,50,50)
drawline(-50,50,-50,-50,50,50)
drawline(-50,-50,-50,-50,-50,50)
drawline(50,-50,-50,50,-50,50)
end
``````
And now we are done with our code! Now we are finally at our last step, which is realtime movement! This is perhaps the best part of the whole scripts.
## Part 7: Movement
Movement is relatively simple. We will use WASD for moving forward and backward, and we will use arrow keys to rotate the camera. So here is the code:
``````movement=function()
//First we will use arrow keys and rotate the camera
if keyboard.ARROW_RIGHT then //Right arrow key pressed
camxrot+=4 // You can change the number '4' for faster or slower movement
end
if keyboard.ARROW_LEFT then
camxrot-=4
end
if keyboard.ARROW_UP then
camyrot+=4
end
if keyboard.ARROW_DOWN then
camyrot-=4
end
//Now we will do movement (WASD). This movement is dependent on the camera direction.
//We account for this by using the rotate script from earlier!
if keyboard.W then
rotate(0,5,camxrot) //Rotate 5 units in the forward direction by camera x direction
camx+=rotx //Change camx and z by outputs
camz+=roty
end
if keyboard.S then
rotate(0,-5,camxrot)
camx+=rotx
camz+=roty
end
if keyboard.A then
rotate(5,0,camxrot)
camx+=rotx
camz+=roty
end
if keyboard.D then
rotate(-5,0,camxrot)
camx+=rotx
camz+=roty
end
end
``````
Now we are finally done with all of our scripts! All we have to do now is to put them in our init, update and draw blocks!
``````init=function()
camx=0 //Play around with the values to check if it works!
camy=0
zclipdist=5 //Can be anywhere from ~4-10
camz=-400
FOV=200
camxrot=0
camyrot=0
end
update=function()
movement()
end
draw=function()
screen.clear() //Clear screen (necessary for movement, as otherwise the screen would be filled with all our different outcomes)
cube() //Draws our cube
end
``````
So that's it for this tutorial! Finally! Remember, If you have any comments, questions, feedback (feedback would be greatly appreciated!),or it's not working, feel free to let me know down below!
Should I make a ray tracing tutorial? Also, down below should be some improvements that advanced coders can try!
## Poly filling
The first step to a more advanced 3d engine is poly filling. So instead of using the `screen.drawLine` function we use the `screen.fillPoly` function. I would suggest filling triangles (polygons with three points) because you can fill a lot of different shapes by out of triangles. Basically, you do the same thing as in the tutorial except with three points and filling a polygon between them.
If you do this however, the z-clipping method has to be different. How I do it is this: if one point is behind the camera, line clip it with one of the other points. Then fill a quad between those three points and then the point behind the camera and the point you haven't clipped it with yet. If two points are behind the camera you just have to clip the two points behind the camera with the point not behind the camera.
## Colours
If you really want to improve your 3d engine, adding colours is the way to go. Colours make a 3d engine much more exciting and realistic. Unfortunately, the problem with colours is that the last thing rendered on screen is always on top of everything else, and things are not rendered in order of what is closest to the camera. So we have to re-order them if we want to do colours. This is called `z-sorting`. Basically, how most programs do it is by finding the distance to the midpoint of a triangle and then sort the distances. You then use the sorted list to decide what you render first or last.
As they would say here in NZ,
### You da Man
Well done, looking forward to see more articles =)
`like`
Great article!
``````// I use cosd and sind instead of cos because I prefer to work in radians
``````
You mean you prefer to work in degrees?
@tinkersmith Thanks a lot :). Is that an image you posted at the bottom of your text? It isn't loading for me.
@gilles Thank you! And there's the mistake I knew would be in here somewhere, thanks for letting me know!
Nice! I think I could try and work on this myself (although it would take me a loooong time)
Yeah, it is a bit of a long tutorial. But that's the sacrifice for making something complex like 3d I guess... A raytracer is much longer as well LOL.
This tutorial shouldn't really take over an hour (I hope). I haven't tested it myself to be completely honest, I need some test subjects XD.
Yes @this_name_is_taken , that is an image link.
Let me try a different syntax...
##### ... another try
Syntax is now: ``
Does that work? Might be helpful for your article if it does.
Sorry to interrupt it with this :)
##### P.S. the syntax for separator lines like this is `##### blah blah blah`
Oh, I see. Thanks a lot,
##### Smith of tinkering!
I won't add any images yet but that should help! Also, what kind of links would the image syntax work on? Is there any way to link files or the like? What kind of website links would I need to go to?
I'm gonna see if it works, so does that mean i'm a test subject now `name of takening`??
Sorry for the late reply `taken one` , weekend kept me busy (... had to work actually)..
About the image syntax, should work on anything that's somewhere hosted on the web.
I mostly use (https://imgur.com/) to upload&share my images. Used other ones, but there I sometimes had problems with animated gifs.
anim test
And linking to files? Should work, let me test:
In theory that should link to a PDF file .. let me know if it does.
So, as long as it is online somewhere it should work. Haven't tried with Dropbox or Google Drive though. Someone else can test :)
The markup syntax is (nearly) the same as for images `[Alt text](web link)` ... just without the exclamation mark in the front `!`
In part 5 you say `if Z1>Nearplane or Z2>Nearplane`
Is that instead meant to be Zclipdist? It would make more sense
Also, I think you need to define zclipdist, as well
Oh, right! I fixed that, thanks for spotting the mistake :).
Edit: Did you have any other major feedbacks?
Lol, I love how you always say work on it `tomorrow` for the advanced stuff and the next day it's still tomorrow. I don't have any major feedbacks, I might release it as to show it works once I finish the movement and cube stuff because I'm lazy
By the way, I'm pretty sure the movement script might be wrong (messed up keys). It works for me correctly with the code like this:
`````` rotate(5, 0, camyrot)
camx += rotx
camz += roty
end
if keyboard.D then
rotate(-5, 0, camyrot)
camx += rotx
camz += roty
end
if keyboard.W then
rotate(0, 5, camxrot)
camx += rotx
camz += roty
end
if keyboard.S then
rotate(0, -5, camxrot)
camx += rotx
camz += roty
end
end
``````
Okay, thanks! Fixing that now :)
Edit: Is it fixed now? Can you see the fix?
This is the first one 3d projection post I found across the internet that accounts for z clipping, and with such an easy fix too! Well done!
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# 1 mole of methane in grams of salt?
Date created: Mon, Apr 26, 2021 3:15 AM
Date created: Mon, Apr 26, 2021 10:02 AM
›› Methane molecular weight. Molar mass of CH4 = 16.04246 g/mol. Convert grams Methane to moles or moles Methane to grams. Molecular weight calculation: 12.0107 + 1.00794*4 ›› Percent composition by element
Date created: Mon, Apr 26, 2021 6:50 PM
molecular weight of Methane or mol. The molecular formula for Methane is CH4. The SI base unit for amount of substance is the mole. 1 grams Methane is equal to 0.062334579609362 mole. Note that rounding errors may occur, so always check the results. Use this page to learn how to convert between grams Methane and mole.
Date created: Tue, Apr 27, 2021 3:33 AM
mass = molecular weight * mole. As 1.626×10 23 molecules of NaOH is also equal to 0.27 moles, and we know that the molecular weight of NaOH is 40, we can use these numbers to get: mass = 40 * 0.27 = 10.8 g. So we now know we need 10.8 g of NaOH to exactly neutralise our amount of hydrochloric acid. We hope this grams to moles calculator (or ...
Date created: Wed, Apr 28, 2021 11:46 AM
Calculate the mass of 1 mole of CH 4: mass of 1 mole CH 4 = M r (CH 4) expressed in grams mass of 1 mole CH 4 = 16.042 g State your answer: The mass of 1 mole of methane, CH 4, is 16.042 g Worked Example of Mole Definition: Molar Volume of Gas (V m)
Date created: Wed, Apr 28, 2021 3:38 PM
CH 101 Spring 2019 Grams, Moles, and Molecular Mass Review 1. A sample contains 3.4 g of methane (CH 4). A. What is the molar mass of methane?
Date created: Thu, Apr 29, 2021 11:10 PM
Converting grams to moles involves 2 steps: Step 1: Find the molecular mass of the compound. Step 2: Divide the number of grams of the compound by its molecular mass. In order to determine the number of moles of a given compound, the first thing you need to do is find the molecular mass (or molecular weight) of the compound in question.
Date created: Sat, May 1, 2021 11:49 AM
= 23.00 + 16.00 + 1.01 = 40.01 grams/mol Therefore: 40.01g NaOH = 1 mol NaOH = 6.022 x 1023 NaOH units = 6.022 x 1023 Na+ ion plus 6.022 x 1023 OH-ions 5. Example: Molar Mass of H 2 O. = 2 x 1.008 + 16.00 = 18.02 grams/mol Thus, 18.02g H 2 O = 1 mole H 2 O = 6.022 x 10 23 H 2 O molecules. And contains 6.022 x 1023 oxygen atoms 12.04 x 1023 hydrogen atoms 6.
Date created: Mon, May 3, 2021 5:13 AM
The total number of atoms in 1 mol 1 m o l of methane can be obtained as follows: N = Number of atoms in one molecule×Number of molecules per mole = 5×6.022×1023 mol−1 = 3.011×1024 mol−1 N ...
Date created: Tue, May 4, 2021 1:18 PM
Nevertheless, the mole still works: a mole of salt or sugar means 6.02 × 10 23 molecules of them. The molecular weights of salt and sugar are 58.45 and 342.3, respectively. Thus, 2.05 oz (58.45 g) of salt and 11.98 oz (342.3 g) of sugar contain the same number of molecules: 6.02 × 10 23. Robert L. Wolke.
Date created: Thu, May 6, 2021 2:52 AM
add 20.0 grams of sodium hydroxide to 1 L of water. How would you prepare a 0.5 M solution of sodium hydroxide? C^6H^8O^7. A 5.91 g unknown sample analyzed by elemental analysis revealed a composition of 37.51 % C. In addition, it was determined that the sample contains 1.4830 x 1023 hydrogen atoms and 1.2966 x 1023 oxygen atoms.
FAQ
⚡️
Methane is a one-carbon compound in which the carbon is attached by single bonds to four hydrogen atoms. It is a colourless, odourless, non-toxic but flammable gas (b.p. -161℃). It has a role as a fossil fuel, a member of greenhouse gas and a bacterial metabolite.
Compound formula for methane?
⚡️
However, methane that is released into the atmosphere before it is burned is harmful to the environment. Because it is able to trap heat in the atmosphere, methane contributes to climate change. Although methane’s lifespan in the atmosphere is relatively short compared to those of other greenhouse gases, it is more efficient at trapping heat than are those other gases.
⚡️
Methane is a one-carbon compound in which the carbon is attached by single bonds to four hydrogen atoms.It is a colourless, odourless, non-toxic but flammable gas (b.p. -161℃). It has a role as a fossil fuel, a member of greenhouse gas and a bacterial metabolite.
30 methane balloon chain reaction?
⚡️
Methane is a far more potent greenhouse gas than CO2, even though it only lasts about a decade in the atmosphere, whereas CO2 persists for a couple of centuries. A continued rise in the amount of methane in the air could easily cancel out any near-term progress we make in reducing CO2 emissions.
http://gas-lease.org/co2-vs-methane-global-warming-potential
⚡️
Methane (US: / ˈ m ɛ θ eɪ n /, UK: / ˈ m iː θ eɪ n /) is a chemical compound with the chemical formula CH 4 (one atom of carbon and four atoms of hydrogen).It is a group-14 hydride and the simplest alkane and is the main constituent of natural gas.The relative abundance of methane on Earth makes it an economically attractive fuel, although capturing and storing it poses technical ...
Is methane ch4?
⚡️
Reduction of methane emissions through feed additives, such as fats and oils, can reduce methane production by about 18% and offer energy and protein to the animal. For a 600 cow dairy herd (producing 100kg of methane per head per year) methane emissions could be reduced by 372 tonnes of carbon dioxide equivalent per year.
http://gas-lease.org/cow-with-methane-bag-on-skin
⚡️
• Methane is nontoxic on its own but can become lethal when it combines with another gas. Methane causes asphyxiation by displacing oxygen. It may produce symptoms of dizziness and headache, but these often go unnoticed until the brain signals the body to gasp for air. This happens too late, and the individual collapses.
How is methane bad for us?
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Methane, by contrast, is mostly removed from the atmosphere by chemical reaction, persisting for about 12 years. Thus although methane is a potent greenhouse gas, its effect is relatively...
### Biogas methane generator?
Biogas is primarily methane (CH4) and carbon dioxide (CO2) and may have small amounts of hydrogen sulfide (H2S), moisture and siloxanes. The gases methane, hydrogen, and carbon monoxide (CO) can be combusted or oxidized with oxygen. This energy release allows biogas to be used as a fuel for power generation.
### What are the uses of methane?
The main uses of methane natural gas are to generate electricity and make energy. It can power homes and other buildings. Methane natural gas can also provide heat.
### Methane element?
Methane (US: / ˈ m ɛ θ eɪ n /, UK: / ˈ m iː θ eɪ n /) is a chemical compound with the chemical formula CH 4 (one atom of carbon and four atoms of hydrogen). It is a group-14 hydride and the simplest alkane and is the main constituent of natural gas.
### Small methane digester for sale craigslist?
Digester and gas holder located in one plant component, Designed for 100 to 400 cows (or equivalent), Codigestion of co-substrates. View More. EUCOlino. Small scale (1000 à 6500 tons per year) dry digestion system for any organic substrates with over 25% TS. Easy installation and startup:….
### Electron dot structure for methane?
What is the electron dot structure of methane? Methane is a colorless, odourless and highly flammable gas which is the main component of natural gas. Electron dot structure of methane is- (Image attached) The covalent bonds are present in between four hydrogen atoms and the single carbon atom at the centre of the molecule.
### Methane contamination of drinking water due to rising sea levels?
Methane contamination of drinking water accompanying gas-well drilling and hydraulic fracturing Stephen G. Osborna, Avner Vengoshb, Nathaniel R. Warnerb, and Robert B. Jacksona,b,c,1 aCenter on Global Change, Nicholas School of the Environment, bDivision of Earth and Ocean Sciences, Nicholas School of the Environment, and cBiology Department, Duke University, Durham, NC 27708
### Half life of methane vs co2 and climate change correlation table?
Methane has a large effect but for a relatively brief period, having an estimated mean half-life of 9.1 years in the atmosphere, whereas carbon dioxide is currently given an estimated mean lifetime of over 100 years.
### Compost to methane gas?
Yes, composting does create methane. Any time organic materials (like food scraps) decompose, they can be expected to produce methane and carbon dioxide. There are several commonly used methods of aerobic composting that keep the production of methane to a minimum while composting.
### Methane sources in nature?
Natural sources Rice cultivation. The frequently waterlogged soils common to many rice fields can provide the anoxic, carbon-rich... Landfills. Landfill sites can provide ideal conditions for methanogenesis, with the plentiful supply of substrate held... Recommended.
### Hydrogen from methane?
Natural gas contains methane (CH 4) that can be used to produce hydrogen with thermal processes, such as steam-methane reformation and partial oxidation. Although today most hydrogen is produced from natural gas, the Hydrogen and Fuel Cell Technologies Office is exploring a variety of ways to produce hydrogen from renewable resources.
### Ethanoic acid to methane chemical?
Then, sodium ethanoate is heated with sodalime (NaOH + CaO) to get methane. CH 3.. COON aS odiumethanoate.. + Sodiumhydroxide(f romsodalims)N aOH..
### Gas gas motos salt lake city?
Paraguay. Oceania. Australia. New Zealand. Asia. Japan. Motorcycles Dealer search Technical Accessories Apparel Promotions Get on the brand Enduro Motocross Cross Country Trial Electric Balance Bikes 2-stroke EC 250 2022 EC 300 2022 Electric 2-stroke 4-stroke MC-E 5 2022 MC 50 2022 MC 65 2022 MC 85 17/14 2022 MC 85 19/16 2022 MC 125 2022 MC 250...
CH4
Natural gas
### Methane atmosphere percentage of earth?
Methane is an important trace gas in Earth’s atmosphere. Even though it only makes up 0.00017% (1.7 parts per million by volume) of the the atmosphere, methane traps a significant amount of heat, helping the planet remain warm and habitable.
### What are 5 uses of methane?
Used in cooking. Methane is a hydrocarbon and lighter than air.... Residential Uses.... Used to provide lighting.... Used in production of other compounds.... Used to run industrial machinery.... Used to produce carbon black.... It is a fertilizer ingredient.... Used as rocket fuel.
### Cons of methane?
Methane is nontoxic on its own but can become lethal when it combines with another gas. Methane causes asphyxiation by displacing oxygen. It may produce symptoms of dizziness and headache , but these often go unnoticed until the brain signals the body to gasp for air.
### How to liquify methane gas in well?
Methane gas can occur in water wells from natural processes or from nearby drilling activity. Methane may occur in a water well due to natural conditions or it may enter a well due to human activities including coal mining, gas well drilling, pipeline leaks and from landfills. Methane is a colorless, odorless, tasteless, and combustible gas.
### Impact of methane on climate change in africa?
The Intergovernmental Panel on Climate Change (IPCC) has indicated a GWP for methane between 84-87 when considering its impact over a 20-year timeframe (GWP20) and between 28-36 when considering its impact over a 100-year timeframe (GWP100).
### 1 mole of methane in grams calculator?
Molar mass of CH4 = 16.04246 g/mol. Convert grams Methane to moles or moles Methane to grams. Molecular weight calculation: 12.0107 + 1.00794*4.
### How much methane does a cow produce per day?
A dairy cow can produce up to 400 litres of methane per day! When burned, this is enough energy to power a small fridge for a day.
### How is methane gas produced naturally?
Methane (a gas composed of carbon and hydrogen) is produced two ways. The first is through biologic decomposition of organic matter at shallow depths. Swamps, landfills, and even shallow bedrock are some settings where this occurs.
### How long does methane remain in the atmosphere for earth?
Methane, by contrast, is mostly removed from the atmosphere by chemical reaction, persisting for about 12 years. Thus although methane is a potent greenhouse gas, its effect is relatively short-lived.
### Curiosity methane detector?
The finding suggests last week's methane detection — the largest amount of the gas Curiosity has ever found — was one of the transient methane plumes that have been observed in the past. While scientists have observed the background levels rise and fall seasonally, they haven't found a pattern in the occurrence of these transient plumes.
### Hydrogen from methane gas?
Most hydrogen produced today in the United States is made via steam-methane reforming, a mature production process in which high-temperature steam (700°C–1,000°C) is used to produce hydrogen from a methane source, such as natural gas. In steam-methane reforming, methane reacts with steam under 3–25 bar pressure (1 bar = 14.5 psi) in the presence of a catalyst to produce hydrogen, carbon monoxide, and a relatively small amount of carbon dioxide.
### 3d model of methane?
3D Model of Methane. Chemistry in Context December 2, 2019. MolView. Source: PubChem. This is a three-dimensional rendering of methane. Click on the structure to rotate it and view it from various angles.
### Cattle farming methane?
Feeding one type of seaweed at 3% of the diet has resulted in up to 80% reduction in methane emissions from cattle. Fats and oils show the most potential for practical application to farming systems and have shown methane emission reductions of 15–20%.
### How do cattle emit methane?
As grass and other vegetation ferments in the rumen, it produces the greenhouse gas, methane, as well as a host of other byproducts. (Incidentally, decomposing food in landfills does the same thing). The methane is then expelled by the cow, mainly through belching.
### Methane ppm to lel conversion equation?
The meaning and conversion of ppm, LEL and VOL I. Meaning of ppm, LEL and VOL 1. ppm: gas volume percentage per million, it is a dimensionless unit. i.e.: 5ppm carbon monoxide means that the air contains 5 per million of carbon monoxide. 2.
### Melting point methane temperature?
Melting point: −182.456 °C (−296.421 °F; 90.694 K) Boiling point: −161.5 °C (−258.7 °F; 111.6 K) Critical point (T, P) 190.56 K, 4.5992 MPa
### Phase - what color is solid methane?
Methane "snow" would be white. (Due to scattering of light). Solid methane under sufficient pressure would form a clear colorless solid. Methane "snow" (which would be on surface" of some celestial body) could be any color if contaminated by even small amounts of other hydrocarbons. A reddish color seems to be typical.
### Cow farts methane?
Let’s get this out of the way: when some people hear the word “methane,” they immediately think about cow farts. (Hence stories like this , this and this ). But in reality, cow burps are much more problematic: 90 to 95 percent of the methane released by cows comes out of their mouths, while 5 to 10 percent is released in the form of manure and flatulence.
### Methane pollution sources?
Main sources of methane emissions Methane Emissions: Human Sources. Since the Industrial Revolution, human sources of methane emissions have been growing. Fossil fuel production, distribution and use. The largest human source is from the production, distribution and... Livestock farming. An...
### Methane origin?
Methane comes from natural sources , such as wetlands and animal digestion, along with thermogenic sources, including oil and gas production. Natural gas is approximately 90% methane.
Yes
### Methane atmosphere percentage of the sun?
The new interpretations reveal methane emissions may account for a whopping third of the climate warming from well-mixed greenhouse gases between the 1750s and today. The IPCC report states that methane increases in our atmosphere account for only about one sixth of the total effect of well-mixed greenhouse gases on warming.
### How methane contributes to global warming?
While methane is a more potent greenhouse gas than CO2, there is over 200 times more CO2 in the atmosphere. Eg - CO2 levels are 380 ppm (parts per million) while methane levels are 1.75ppm. Hence the amount of warming methane contributes is calculated at 28% of the warming CO2 contributes.
### How do we get methane?
Methane Capture and Use Trash decomposes (or rots) in landfills, creating methane gas. Methane rises to the top of the landfill and is collected in pipes. The methane is burned to produce heat or generate electricity.
### How to make methane gas at home?
Hello today i am going to show How To Make Bio Gas Plant At Home ,Make a Methane Gas From Waste RicePlease don't forget to life share and Subscriber to our c...
### Atmospheric methane levels?
Changes in past atmospheric methane concentrations are determined by measuring the composition of air trapped in ice cores from Antarctica. So far, the Antarctic Vostok and EPICA Dome C ice cores have provided a composite record of atmospheric methane levels over the past 800,000 years. Credits: Loulergue, L., A.
### Annual methane emissions?
Estimates of methane emissions are subject to a high degree of uncertainty, but the most recent comprehensive estimate suggests that annual global methane emissions are around 570 million tonnes (Mt).
### Methane and oxygen combustion reaction?
Methane with oxygen – combustion reaction. The process of the combustion of methane is the interaction of methane with oxygen. As a result of the reaction, water, carbon dioxide and a great deal of energy are formed. The reaction equation of methane combustion:
### Fracking and methane gas?
How much methane leaks during fracking? Emissions of methane (CH4) from oil and natural gas development – including fracking – have been declining in recent years, thanks in large part to technological innovation. The current leakage rate for petroleum and natural gas systems is estimated at about 1.2 percent, according to the U.S. EPA.
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# Factoring Trinomials Calculator
Factoring Trinomials Calculator is a free online tool that identifies the factors of a given trinomial. STUDYQUERIES’s online calculator for factoring trinomials makes the calculation faster, and it displays the factors of a trinomial in a matter of seconds.
## How to Use the Factoring Trinomials Calculator?
To use the factoring trinomials calculator, follow these steps:
• Step 1: Enter the trinomial function into the input field
• Step 2: To get an answer, click “FACTOR”
• Step 3: In the new window, you will see the factors of the trinomial
## How to Factoring Trinomials?: 3 Easy Methods
Trinomials are algebraic expressions made up of three terms. Most likely, you’ll learn how to factor quadratic trinomials, which are trinomials written as $$ax^2 + bx + c$$. Using these tricks will improve your ability to factor quadratic trinomials, but it will take some practice.
Polynomials with terms like $$x^3$$ or $$x^4$$ are not always solvable by the same methods, but you can factor or substitute them into quadratic formulas just like any other polynomial.
### Factoring Trinomials Method 1: Factoring x² + bx + c
Become familiar with FOIL multiplication.
Using the FOIL method, or “First, Outside, Inside, Last,” you can multiply expressions like $$(x+2)(x+4)$$. Before we factor, it is useful to understand how this strategy works:
Multiply the $$\color{red}{First}$$ two terms:
$$(\color{red}{x} + 2)(\color{red}{x} + 4)=\color{red}{x^2} + {\_}$$
The $$\color{red}{Outside}$$ terms are multiplied as follows:
$$(\color{red}{x}+2)(x+\color{red}{4}) = x^2+\color{red}{4x} + {\_}$$
Multiply the $$\color{red}{Inside}$$ terms:
$$(x+\color{red}{2})(\color{red}{x}+4) = x^2+4x+\color{red}{2x} +{\_}$$
Multiply the $$\color{red}{Last}$$ terms:
$$(x+\color{red}{2})(x+\color{red}{4}) = x^2+4x+2x+\color{red}{8}$$
Simply write $$x^2+\color{red}{4x}+\color{red}{2x}+8\ as\ x^2+6x+8$$
Understand factoring.
Multiplying two binomials together in $$FOIL$$ produces a trinomial (an expression with three terms) in the form $$ax^2+bx+c$$, where $$a, b,\ and\ c$$ are ordinary numbers. You can factor back an equation in the same form into two binomials if you start with the same form.
• If the terms aren’t written in this order, arrange them so they are. For example, rewrite $$3x – 10 + x^2 as x^2 + 3x – 10$$.
• As the highest exponent is $$2$$, this type of expression is $$“quadratic.”$$
Write a space for the answer in FOIL form.
For now, just write $$(\_)(\_)$$ in the space where the answer is going to be written. We’ll fill this in as we go.
Please don’t write $$+$$ or $$-$$ between the blank terms yet, since we don’t know which one it will be.
Fill out the First terms.
Where the first term of your trinomial is just $$x^2$$, the terms in the First position will always be $$x$$ and $$x$$. These are the factors of the term $$x^2$$, since $$x \times x) = x^2$$.
The example $$x^2 + 3x – 10$$ starts with $$x^2$$, so we can write: $$(x\_)(x\_)$$.
In the next section, we’ll look at more complicated problems, including trinomials that start with a term like $$6x^2$$ or $$-x^2$$. For now, just follow the example problem.
Use factoring to guess at the Last terms.
When you read the $$FOIL\ method$$ step again, you’ll see that multiplying the Last terms together gives you the final term in the polynomial (the one with no x). To the factor, we need to find two numbers that multiply to create the last term.
In our example $$x^2 + 3x – 10$$, the last term is $$-10$$.
What are the factors of $$-10$$? What two numbers multiplied together equal $$-10$$?
A few possibilities are: $$-1 \times 10$$, $$1 \times -10$$, $$-2 \times 5$$, or $$2 \times -5$$. Write these pairs down somewhere to remember them.
We won’t change our answer yet. It still looks this way: $$(x\_)(x\_)$$.
Test which possibilities work with Outside and Inside multiplication.
The Last terms have been narrowed down to a few options. Test each possibility by multiplying the $$Outside$$ and $$Inside$$ terms and comparing the result to our trinomial. For example:
Within this test, we want to end up with an $$“x”$$ term of $$3x$$, as this is what we had in our original problem.
Test -1 and 10:
The $$Outside$$ + $$Inside$$ = $$10x – x = 9x$$. Nope.
Test 1 and -10:
$$-10x + x = -9x$$. This isn’t right. Once you test $$-1$$ and $$10$$, you know that $$1$$ and $$-10$$ will be just the opposite of the answer above: $$-9x$$ instead of $$9x$$.
Test -2 and 5:
$$5x – 2x = 3x$$. That matches the original polynomial, so the correct answer is $$(x-2)(x+5)$$.
If you don’t have a constant in front of the $$x^2$$ term, you can simply add the two factors together and then put an $$“x”$$ after it $$(-2+5 \longrightarrow 3x)$$. It won’t work for more complex problems, so it’s a good idea to remember the “long way” described above.
### Factoring Trinomials Method 2: Factoring More Complicated Trinomials
Use simple factoring to make more complicated problems easier.
Let’s say that you need to factor $$3x^2 + 9x – 30$$. Find the most common element (the “greatest common factor” or GCF). In this case, it’s 3:
$$3x^2 = (3)(x^2)$$
$$9x = (3)(3x)$$
$$-30 = (3)(-10)$$
Therefore, $$3x^2 + 9x – 30 = (3)(x^2+3x-10)$$. We can factor out the new trinomial by following the steps in the previous section. The final answer will be $$(3)(x-2)(x+5)$$.
Be on the lookout for trickier factors.
Factoring may require variables, or you may need to factor several times to find the simplest expression. Here are some examples:
$$2x^2y + 14xy + 24y = (2y)(x^2 + 7x + 12)$$
$$x^4 + 11x^3 – 26x^2 = (x^2)(x^2 + 11x – 26)$$
$$-x^2 + 6x – 9 = (-1)(x^2 – 6x + 9)$$
Don’t forget to factor the new trinomial further using method 1. Please check your work and find similar examples near the bottom of this page.
Solve problems with a number in front of the x².
In some cases, quadratic trinomials cannot be simplified down to the simplest form. Learn how to solve problems like $$3x^2 + 10x + 8$$, then practice on your own with the examples at the bottom of the page:
Let’s set up our answer: $${(\_\ \_)}{(\_\ \_)}$$
“First” terms will have an $$x$$ and will multiply together to make $$3x^2$$. The only option here is $${(3x\ \_\ \_)}{(x\ \_\ \_)}$$.
List the factors of $$8$$. Our options are $$1 \times 8$$, or $$2 \times 4$$.
Use the Outside and Inside terms to test them. Since the Outside term is being multiplied by $$3x$$ instead of $$x$$, the order of the factors matters. You need to try every possible solution until you get an $$Outside+Inside$$ result of $$10x$$ (from the original problem):
$$(3x+1)(x+8)\longrightarrow 24x+x = 25x\longrightarrow no$$
$$(3x+8)(x+1)\longrightarrow 3x+8x = 11x\longrightarrow no$$
$$(3x+2)(x+4)\longrightarrow 12x+2x=14x\longrightarrow no$$
$$(3x+4)(x+2)\longrightarrow 6x+4x=10x\longrightarrow Yes,\ this\ is\ correct$$
Use substitution for higher-degree trinomials.
Despite using simple factoring to make the problem easier, your math book might present an equation with a high exponent, such as $$x^4$$. Try substituting a new variable that turns it into a problem you can solve. Using this example:
$$x^5+13x^3+36x=(x)(x^4+13x^2+36)$$
Let’s invent a new variable. We’ll say $$y = x^2$$, and plug it in:
$$(x)(y^2+13y+36)$$
$$=(x)(y+9)(y+4)$$ Now switch back to using the original variable:
$$=(x)(x^2+9)(x^2+4)$$
$$=(x)(x\pm 3)(x\pm 2)$$
### Factoring Trinomials Method 3: Factoring Special Cases
Check for prime numbers.
Check to see if the constant in either the first or third term of the trinomial is a prime number. A prime number can be divided evenly only by itself and 1, so there is only one possible pair of binomial factors.
For example, in $$x^2 + 6x + 5$$, “$$5$$ is a prime number, so the binomial must be in the form $${(\_\ \_ 5)}{(\_\ \_ 1)}$$
In the problem $$3x^2+10x+8$$, $$3$$ is a prime number, so the binomial must be in the form $${(3x\ \_\ \_)}{(x\ \_\ \_)}$$
For the problem $$3x^2+4x+1$$, the only possible solution is $$(3x+1)(x+1)$$.
Check to see if the trinomial is a perfect square.
A perfect square trinomial can be factored into two identical binomials, and the factor is usually written $$(x+1)^2$$ instead of $$(x+1)(x+1)$$. Here a few common ones that tend to show up in problems:
$$x^2+2x+1=(x+1)^2,\ and\ x^2-2x+1=(x-1)^2$$
$$x^2+4x+4=(x+2)^2,\ and\ x^2-4x+4=(x-2)^2$$
$$x^2+6x+9=(x+3)^2,\ and\ x^2-6x+9=(x-3)^2$$
A perfect square trinomial in the form $$ax^2 + bx + c$$ always has a and c terms that are positive perfect squares (such as 1, 4, 9, 16, or 25), and a b term (positive or negative) that equals $$2(\sqrt{a} \times \sqrt{c})$$.
Check whether no solution exists.
Factoring trinomials is not possible for all trinomials. When you’re stuck on quadratic trinomials $$(ax^2+bx+c)$$, use the quadratic formula. When all the answers are the square root of a negative number, there are no real solutions, so there are no factors.
Use Eisenstein’s Criterion, which is described in the Tips section, for non-quadratic trinomials.
## Important Tips To Factoring Trinomials
Rather than factoring a quadratic trinomial $$(ax^2+bx+c)$$, you can solve for $$x$$ using the quadratic formula.
Eisenstein’s Criteria can be used to determine quickly if a polynomial is irreducible and cannot be factored, even if you don’t know how to do it. For trinomials, this criteria works well, but it is particularly useful for polynomials. The polynomial is irreducible if there is a prime number $$p$$ that evenly divides the last two terms and meets the following conditions:
The constant term (with no variable) is a multiple of $$p$$ but not of $$p^2$$.
The leading term (for instance, $$a$$ in $$ax^2+bx+c$$) is not a multiple of $$p$$.
For example, $$14x^2 + 45x + 51$$ is irreducible because there is a prime number $$3$$ that evenly divides both $$45$$ and $$51$$ but not $$14$$, and $$51$$ cannot be evenly divided by $$3^2$$.
## Conclusion
Trinomials of the form $$x^2 + bx + c$$ can be factored by finding two integers $$r$$ and $$s$$, whose sum is $$b$$ and whose product is $$c$$. Rewrite the trinomial as $$x^2 + rx + sx + c$$ and then factor the polynomial using the distributive property.
Look first for common factors for all three terms in a trinomial that takes the form $$ax^2 + bx + c$$, where $$a$$ is a coefficient other than $$1$$. The first factor out the common factor, then factor the simpler trinomials. In the case where the remaining trinomial is still of the form $$ax^2 + bx + c$$, find two integers, $$r$$, and $$s$$, whose sum is $$b$$ and whose product is $$ac$$. Rewrite the trinomial as $$ax^2 + rx + sx + c$$, and factor the polynomial using grouping and the distributive property.
When $$ax^2$$ is negative, you can factor $$−1$$ out of the whole trinomial before continuing.
## FAQs
How do you factor Trinomials step by step?
• Step 1: Identify the values for $$b$$ and $$c$$. In this example, $$b=6$$ and $$c=8$$.
• Step 2: Find two numbers that $$ADD$$ to $$b$$ and $$MULTIPLY$$ to $$c$$. This step can take a little bit of trial and error.
• Step 3: Use the numbers you picked to write out the factors and check.
What is trinomial and example?
A trinomial is an algebraic expression with three terms that are not zero. $$x + y + z$$ is a trinomial in three variables $$x, y,\ and\ z$$.
What is a basic trinomial?
A polynomial with three terms is called a trinomial. Trinomials often (but not always!) have the form $$x^2 + bx + c$$.
How do you write a trinomial in factored form?
Factoring Trinomials of the Form $$x^2 + bx + c$$ and $$x^2 – bx + c$$
• Write out all the pairs of numbers which can be multiplied to produce $$c$$.
• Add each pair of numbers to find a pair that produce $$b$$ when added.
• If $$b > 0$$, then the factored form of the trinomial is $$(x + d )(x + e)$$.
What is a cubic trinomial example?
Cubic Trinomials of the Form $$Ax^3 + Bx+^2 + Cx$$. For example, the greatest common factor of the trinomial $$3x^3 – 6x^2 – 9x$$ is $$3x$$, so the polynomial is equal to $$3x$$ times the trinomial $$x^2 – 2x -3$$, or $$3x(x^2 – 2x – 3)$$.
How do you break down a trinomial?
To the factor, a trinomial is to decompose an equation into the product of two or more binomials. This means that we will rewrite the trinomial in the form $$(x + m) (x + n)$$. Your task is to determine the value of m and n. In other words, we can say that factoring a trinomial is the reverse process of the foil method.
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SOLVED
# How to find the max value corresponding to a date range
Copper Contributor
# How to find the max value corresponding to a date range
Hello,
hope you are all doing good.
I have to work on some Excel report and ...i'm not good in Excel so i hope someone could help me a bit :p ...and i guess i will come back several other times :D
ok so... I have a worksheet where are multiple dates and I have to extract a maximum value for each separate date range but make it correspond to the first day of the month. i mean ...
16/02/2022 3 16/02/2022 1 16/02/2022 2 19/03/2022 5 20/04/2022 2 20/04/2022 1
for 16/02/2022 max would be 3
19/03/2022 max would be 5
20/04/2022 max would be 2
On another sheet, i would need to get the final max value from the previous sheet and make it correspond to
01/02/2022 which would be 3
01/03/2022 which would be 5
01/04/2022 which would be 2
Would someone please be able to help me do this ? :(
Thanks a lot for your time
6 Replies
best response confirmed by Kaddrik (Copper Contributor)
Solution
# Re: How to find the max value corresponding to a date range
Let's say your data is in Sheet1 (e.g Column A and B).
And the formula you want to write is "B1" in the sheet below and your formula is calculated based on the 1st day of the month. If so, you can try as below.
A B
1 1/2/2022 =MAXIFS(Sheet1!B:B, Sheet1!A:A,">="&A1, Sheet1!A:A,
"<="&eomonth(A1,0)
2 1/3/2022 drag down formula above
3 1/4/2022 drag down formula above
Or, do you want the max of exactly the first date occured in the month?
For e.g if there are 5/2/2022, 16/2/2022 and 20/2/2022 in Feb 2022, what you want is max of 5/2/2022. Please let me know.
# Re: How to find the max value corresponding to a date range
hello @Starrysky1988
hmm...not sure it's like this...
in fact i would have in sheet1 , column A and B, this
A B
16/02/2022 3 16/02/2022 1 16/02/2022 2 19/03/2022 5 20/04/2022 2 20/04/2022 1
and then in Sheet2 this ...
A
01/02/2022 and i have to populate column B with 3
01/03/2022 5
01/04/2022 2
In the meantime i see my colleague created an intermediate sheet... let's call it Sheet3 ... where he shows only 1 occurence of the date
A B
16/02/2022
19/03/2022
20/04/2022
so i created in column B of Sheet3 a formula like MAXIFS(Sheet1!A:A,Sheet1!B:B,\$A1)
Where A1 is date 16/02/2022. and this seems to give me the maximum value when i have several times the same date. I end up with
A B
16/02/2022 3
19/03/2022 5
20/04/2022 2
but then in sheet 3, imagining for 1 month i have several weeks that are reported with their maximum like this
09/02/2022 23
16/02/2022 3
23/02/2022 10
I still don't understand how i can have in sheet2 , the maximum value corresponding to 1 month
01/02/2022
01/03/2022
01/04/2022
which for 01/02/2022 (if i take the previous example) would be 23
is it clearer ?
Thanks a lot for your time
# Re: How to find the max value corresponding to a date range
What you want is maximum value for the whole month, then please see my previous reply.
It is for the whole month.
For individual date in the month, you can use your formula. Thanks
# Re: How to find the max value corresponding to a date range
Hello @Starrysky1988 ,
I just tested what you explain and it works ! :)
Thanks a lot for your time !!
# Re: How to find the max value corresponding to a date range
Other functions that could be used are MAXIFS or FILTER
``````"Month"
= 1+EOMONTH(UNIQUE(Date),-1)
"Maximum count"
= MAXIFS(Count, Date, UNIQUE(Date))``````
or, using Lambda functions and FILTER,
``````"Maximum count"
= MAP(UNIQUE(Date),
LAMBDA(d,
MAX(FILTER(Count, Date=d))
)
)``````
# Re: How to find the max value corresponding to a date range
Hello, I need to do something very similar but my date range is finding the max every 3 days. Do you know how I could adapt your formula to attempt this?
1 best response
Accepted Solutions
best response confirmed by Kaddrik (Copper Contributor)
Solution
# Re: How to find the max value corresponding to a date range
Let's say your data is in Sheet1 (e.g Column A and B).
And the formula you want to write is "B1" in the sheet below and your formula is calculated based on the 1st day of the month. If so, you can try as below.
A B
1 1/2/2022 =MAXIFS(Sheet1!B:B, Sheet1!A:A,">="&A1, Sheet1!A:A,
"<="&eomonth(A1,0)
2 1/3/2022 drag down formula above
3 1/4/2022 drag down formula above
Or, do you want the max of exactly the first date occured in the month?
For e.g if there are 5/2/2022, 16/2/2022 and 20/2/2022 in Feb 2022, what you want is max of 5/2/2022. Please let me know.
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Bank PO Important Questions MCQ – Practice Set 3
1. The weight of an object will be minimum when it is placed at ?
2. The length of a rectangular hall is 5m more than its breadth. The area of the hall is 750 m. The length of the hall is
3. The percentage increase in the area of a rectangle, if each of its sides is increased by 20%
4. Which region in India is known as the ''Rice Bowl of India''?
5. The first Law Officer of the Government of India is the
6. One side of a rectangular field is 15m and one of its diagonal is 17m. Find the area of field?
7. How many cubes of 3cm edge can be cut out of a cube of 18cm edge
8. Find the angle between the hour hand and the minute hand of a clock when the time is 3.25
9. Find the ratio of the areas of the incircle and circumcircle of a square.
10. At what time between 2 and 3 o'clock will the hands of a clock be together?
11. The length of a rectangle is halved, while its breadth is tripled. What is the percentage change in area?
12. Find the odd man out? 396, 462, 572, 427, 671, 264.
13. A salesman gets commission on total sales at 9%. If the sale is exceeded Rs.10,000 he gets an additional commission as bonus of 3% on the excess of sales over Rs.10,000. If he gets total commission of Rs.1380, then the bonus he received is:
14. The dimensions of a room are 10m x 7m x 5m. There are 2 doors and 3 windows in the room. The dimensions of the doors are 1m x 3m. One window is of size 2m x 1.5m and the other 2 windows are of size 1m x 1.5m. The cost of painting the walls at Rs. 3 per sq m is
15. The cost of fencing a square field @ Rs. 20 per metre is Rs.10.080.How much will it cost to lay a three meter wide pavement along the fencing inside the field @ Rs. 50 per sq m
16. At what angle the hands of a clock are inclined at 15 minutes past 5?
17. By default, your documents print in ________ mode
18. The altitude drawn to the base of an isosceles triangle is 8cm and the perimeter is 32cm. Find the area of the triangle?
19. The length of a rectangle is twice its breadth if its length is decreased by 5cm and breadth is increased by 5cm, the area of the rectangle is increased by 75 sq cm. Find the length of the rectangle.
20. At what time between 7 and 8 o'clock will the hands of a clock be in the same straight line but,not together?
21. The reflex angle between the hands of a clock at 10.25 is
22. The ratio between the perimeter and the breadth of a rectangle is 5 : 1. If the area of the rectangle is 216 sq. cm, what is the length of the rectangle?
23. If the length of the diagonal of a square is 20cm,then its perimeter must be a. 402–√cm b. 302–√cm c. 10cm d. 152–√cm
24. What was the day of the week on 17th June, 1998 ?
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### Three Cubes
Can you work out the dimensions of the three cubes?
### Euler's Formula and Topology
Here is a proof of Euler's formula in the plane and on a sphere together with projects to explore cases of the formula for a polygon with holes, for the torus and other solids with holes and the relationship between Euler's formula and angle deficiency of polyhedra.
### Magnetic Personality
60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?
# Investigating Solids with Face-transitivity
##### Stage: 4 and 5
Published October 2009,February 2011.
If you have access to a set of equilateral triangles which fit together, such as Polydron, you may wish to make some of the models discussed while reading this article. If you have not met the Platonic and Archimedean solids before, start by reading the article Classifying Solids using Angle Deficiency, which provided the inspiration for Edward's ideas discussed here.
Having read the NRICH article Classifying Solids using Angle Deficiency, I wondered what would happen if, instead of relaxing the requirement that all the faces be the same (which leads to the Archimedean solids), I relaxed the requirement that all the vertices be the same. I also removed the requirement that the solids be convex.
I constructed solids which consisted of identical, regular faces where the number of faces meeting at a vertex was a characteristic of that vertex, and each face had to have the same pattern of 'vertex numbers' around its vertices.
For example, the first shape I constructed had triangular faces, with three faces meeting at one vertex and six faces meeting at the other two vertices of each triangle.
I assembled the triangles in such a way that the pattern for every face was $V_{3,6,6}$.
This resulted in a peculiar shape with 12 faces, 18 edges, and 8 vertices. It looked like four tetrahedra stuck to the faces of a fifth.
Can you work out from the picture of the solid which vertices are $V_3$ and which are $V_6$? See the notes for the solution, and labelled vertices for other pictures in this article. Perhaps you could try making Edward's $V_{3,6,6}$ solid for yourself.
The $V_6$ vertices of the solid were not flat, as might be expected because six equilateral triangles can meet at a point to form a tessellation of the plane. Instead they folded around the vertex. The solid is concave and cannot rest on any face; only two edges at a time may rest on a plane.
I worked out the total angle deficiency which is $720^\circ$, because there are four $V_3$ vertices each with a deficiency of $180^\circ$, and four $V_6$ vertices which have zero angle deficiency.
From my analysis of the model I made, I think it has the same set of symmetries as the tetrahedron, being essentially a tetrahedron with each face replaced by another tetrahedron.
I then produced two more shapes with triangular faces, which I described as $V_{5,4,4}$ and $V_{3,4,4}$. Both of these consisted of two identical pyramids joined at their bases (pentagonal pyramids and tetrahedra respectively), and were convex. These were not so interesting as the first shape I made.
Two views of $V_{5,4,4}$
I then tried some other configurations, such as $V_{3,5,5}$ and quickly found that, for triangular faces, if you have an odd vertex number and the other two numbers are not equal to each other, the solid cannot be constructed. If I start with 5 triangles meeting at a point so that each has a $V_5$ vertex, this creates a pentagon. As each face already has one $V_5$ vertex, the remaining two vertices on each face must be one $V_3$ and one $V_5$, so around the pentagon I must alternate between $V_3$ and $V_5$ vertices. But as 5 is an odd number I cannot match the pattern when I get back to the beginning - I am forced to have either two $V_3$ or two $V_5$ vertices together. The same argument can apply to any odd vertex number, as alternating around an n-gon when n is odd will always result in two adjacent vertices needing to be the same.
I noticed that any configuration of the form $V_{a,4,4}$ for $a$< 6 will, if constructable, produce a pair of joined pyramids (see $V_{5,4,4}$ above). If $a$=4 this will, in fact, be an octahedron. However, the case $a$=6 cannot be constructed since this would produce two flat hexagons in the same plane. I don't think values of $a$ above 6 can work either, but I'm not sure.
I then tried to construct $V_{4,6,6}$. This produced a shape with 24 faces, 36 edges, and 14 vertices. It consists of a cube with each face replaced by a square pyramid; it is another concave figure, which seems to have the same symmetries as the cube from which it is formed. The angle deficiency comes from the six $V_4$ vertices (as the $V_6$ vertices have zero angle deficiency), each being deficient by $120^\circ$, so the total angle deficiency is $6\times 120^\circ = 720^\circ$.
Two views of $V_{4,6,6}$
I attempted also to construct $V_{5,6,6}$; this should have produced a figure formed from a dodecahedron with faces replaced by pentagonal pyramids, but I found it very difficult to physically construct. It might be easier to produce a computer model.
After further thought, it occurred to me that it was possible to replace the faces of any Platonic solid with pyramids, which meant that figures based on the octahedron and icosahedron could also be constructed. These would have configurations of $V_{3,8,8}$ and $V_{3,10,10}$ respectively, and would in each case share the symmetries of their 'parent' solid. Constructing $V_{3,8,8}$ produced the Stellated Octahedron (also called the Stella Octangula).
$V_{3,8,8}$ - the Stella Octangula
I believe that the vertex number configuration uniquely specifies the solid, so if you are given $V_{a,b,c}$ and lots of triangles, there is at most one solid you can make for a given set of values $a,b$ and $c$. I also think that the rule that all faces should have the same pattern of vertices around them is sufficient to ensure 'face-transitivity', by which I mean any face can be mapped onto any other by some symmetry of the solid. The Platonic solids are the convex solids which satisfy this rule as well as the rule for the Archimedean solids that all vertices should have the same pattern of faces around them.
One way to think about the face-transitive property is this: imagine a planet in the shape of one of the face-transitive polyhedra shown above, and imagine that you are given one of the faces as a piece of land to farm. Because the polyhedron is face-transitive, it makes no difference which face you are given, because they are all identical. Also, you cannot work out from the 'geography' of the planet where on its surface you are, since all faces are the same.
Having created solids by replacing the faces of Platonic solids with pyramids, I attempted to construct a solid from one of the Archimedean solids in the same way. I found that for each type of face on the original solid, there is a type of face on the new solid. For example, if we take the cuboctahedron and replace its triangular faces with tetrahedra and its square faces with square pyramids (using equilateral triangles), the faces which produce the tetrahedra will be $V_{3,8,8}$ and the faces which produce the square pyramids will be $V_{4,8,8}$, so it breaks my rule about every face having the same vertex numbers around it, so is not one of my face-transitive solids. However, the shape retains the symmetry of the cuboctahedron.
A mixture of $V_{3,8,8}$ and $V_{4,8,8}$ based on the cuboctahedron
I began to investigate the solids formed from other regular faces besides triangles. I tried to construct $V_{3,3,3,4,4}$ from pentagons, and found that it produces an infinite tunnel of dodecahedra:
A (finite) section of the infinite $V_{3,3,3,4,4}$
A view along the inside of $V_{3,3,3,4,4}$
There is no obvious upper limit on the polygons that can be used, nor on how large the vertex numbers may become, since a nonconvex vertex may have a negative angle deficiency.
Edward is about to embark on a degree in Mathematics at the University of Cambridge.
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# Missouri - Grade 1 - Math - Relationships and Algebraic Thinking - Number Sentences - 1.RA.A.3, 1.RA.A.4
### Description
1.RA.A.3 Develop the meaning of the equal sign and determine if equations involving addition and subtraction are true or false. 1.RA.A.4 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers.
• State - Missouri
• Standard ID - 1.RA.A.3, 1.RA.A.4
• Subjects - Math Common Core
### Keywords
• Math
• Relationships and Algebraic Thinking
## More Missouri Topics
Solve problems that call for addition of three whole numbers whose sum is within 20.
1.NBT.A.1 Understand that 10 can be thought of as a bundle of 10 ones – called a “ten”.
1.NBT.A.2 Understand two-digit numbers are composed of ten(s) and one(s).
Add or subtract a multiple of 10 from another two-digit number, and justify the solution.
1.GM.B.5 Order three or more objects by length.
1.GM.B.6 Compare the lengths of two objects indirectly by using a third object.
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# Find the perimeter of the triangle.[Graph]
Find the perimeter of the triangle.
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hosentak
The perimeter of a triangle is the sum of its side lengths so we first need to find the three side lengths of the triangle.
Since the side from (−3,−1) to (2,−1) is a horizontal segment, we can count the number of units between the two points to find its length. Since 2−(−3)=5, then the length of this side is 5.
Since the side from (2,−1) to (2,3) is a vertical segment, we can count the number of units between the two points to find its length. Since 3−(−1)=4, then the length of this side is 4.
The side between from (-3,-1) to (2,3) is not a horizontal or vertical segment so we need to use the distance formula $d=\sqrt{{\left(x2-x1\right)}^{2}+{\left(y2-y1\right)}^{2}}$ to find the lenght of this side:
$d=\sqrt{{\left(-3-2\right)}^{2}+{\left(-1-3\right)}^{2}}$ Substitute.
$=\sqrt{{\left(-5\right)}^{2}+{\left(-4\right)}^{2}}$ Substract.
$=\sqrt{\left(25+16\right)}$ Evaluate the powers.
$=\sqrt{41}$ Add.
The length of the third side is then $\surd 41\approx 6.4.$
The perimeter of the triangle is then about 5+4+6.4=15.4. The exact perimeter is $5+4+\sqrt{41}=9+\sqrt{41}$
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# 30278 (number)
30278 is an even five-digits composite number following 30277 and preceding 30279. In scientific notation, it is written as 3.0278 × 104. The sum of its digits is 20. It has a total of 2 prime factors and 4 positive divisors. There are 15,138 positive integers (up to 30278) that are relatively prime to 30278.
## Basic properties
• Is Prime? no
• Number parity even
• Number length 5
• Sum of Digits 20
• Digital Root 2
## Name
Name thirty thousand two hundred seventy-eight
## Notation
Scientific notation 3.0278 × 104 30.278 × 103
## Prime Factorization of 30278
Prime Factorization 2 × 15139
Composite number
Distinct Factors Total Factors Radical ω 2 Total number of distinct prime factors Ω 2 Total number of prime factors rad 30278 Product of the distinct prime numbers λ 1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ 1 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ 0 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0
The prime factorization of 30278 is 2 × 15139. Since it has a total of 2 prime factors, 30278 is a composite number.
## Divisors of 30278
1, 2, 15139, 30278
4 divisors
Even divisors 2 2 1 1
Total Divisors Sum of Divisors Aliquot Sum τ 4 Total number of the positive divisors of n σ 45420 Sum of all the positive divisors of n s 15142 Sum of the proper positive divisors of n A 11355 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G 174.006 Returns the nth root of the product of n divisors H 2.66649 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors
The number 30278 can be divided by 4 positive divisors (out of which 2 are even, and 2 are odd). The sum of these divisors (counting 30278) is 45420, the average is 11355.
## Other Arithmetic Functions (n = 30278)
1 φ(n) n
Euler Totient Carmichael Lambda Prime Pi φ 15138 Total number of positive integers not greater than n that are coprime to n λ 15138 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π ≈ 3276 Total number of primes less than or equal to n r2 0 The number of ways n can be represented as the sum of 2 squares
There are 15,138 positive integers (less than 30278) that are coprime with 30278. And there are approximately 3,276 prime numbers less than or equal to 30278.
## Divisibility of 30278
m n mod m
2 0
3 2
4 2
5 3
6 2
7 3
8 6
9 2
The number 30278 is divisible by 2.
## Classification of 30278
• Arithmetic
• Semiprime
• Deficient
### Expressible via specific sums
• Polite
• Non hypotenuse
• Square Free
## Base conversion 30278
Base System Value
2 Binary 111011001000110
3 Ternary 1112112102
4 Quaternary 13121012
5 Quinary 1432103
6 Senary 352102
8 Octal 73106
10 Decimal 30278
12 Duodecimal 15632
20 Vigesimal 3fdi
36 Base36 nd2
## Basic calculations (n = 30278)
### Multiplication
n×y
n×2 60556 90834 121112 151390
### Division
n÷y
n÷2 15139 10092.7 7569.5 6055.6
### Exponentiation
ny
n2 916757284 27757577044952 840443917767056656 25446960942150941430368
### Nth Root
y√n
2√n 174.006 31.168 13.1911 7.87454
## 30278 as geometric shapes
### Circle
Diameter 60556 190242 2.88008e+09
### Sphere
Volume 1.16271e+14 1.15203e+10 190242
### Square
Length = n
Perimeter 121112 9.16757e+08 42819.6
### Cube
Length = n
Surface area 5.50054e+09 2.77576e+13 52443
### Equilateral Triangle
Length = n
Perimeter 90834 3.96968e+08 26221.5
### Triangular Pyramid
Length = n
Surface area 1.58787e+09 3.27126e+12 24721.9
## Cryptographic Hash Functions
md5 1d7c91037101cce725efa1fe469232a5 b2f24245e063f4eac6831d1f464d1ffa3b4f9d0a baa1d10a4e38a30ec0653c8e2184e7f753dbf2ddb8363b0bd45dfbcf2216cb6d e9859eff249c6e16a0ed3b62872882222150616e5c13776c77a0075719ff1df52929c922621273cda28ad0c44a6576a8cc51a8edf428ce8a7ba7e3ed49b5bc88 0985298c6d583aedb97cfef47b12512811c2cbf0
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# HEAT TRANSFER
INTRODUCTION
Heat transfer is defined as the form of energy that is transferred between two systems (or a system and its surroundings) by virtue of a temperature difference.
convection.Mechanisms of Heat Transfer Heat can be transferred in three different ways: conduction. . All modes of heat transfer are from the hightemperature medium to a lower temperature one. All modes of heat transfer require the existence of a temperature difference. and radiation.
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The better the conductor. . the more rapidly heat will transfer.CONDUCTION Conduction is the transfer of heat between substances that are in direct contact with each other.
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FOURIER’S LAW OF HEAT CONDUCTION .
72 W/mK. The right face temperature of the brick is 900C. .Example 1 : A flat wall is composed of 20 cm of brick having a thermal conductivity kt = 0. and the left face temperature of the brick is 20C. Determine the rate of heat conduction through the wall per unit area of wall.
72 A x m K 0.Tright = 900C Tleft = 20C 20 cm T Qcond kt A x Q T W (900 20)K cond kt 0.2m W 3168 2 m .
Exercise 1 : .
52 W/mK. . Calculate the rate of heat transfer per unit area through the wall if the wall thickness is 300mm with the thermal conductivity 12.Exercise 2 : The temperature at the surface in and out of a stone wall are respectively 50 ° C and 30 ° C.
If it is determined that heat is transferred through the plate at a rate of 500 W/m2. respectively. .Exercise 3 : Two surfaces of a 2-cm-thick plate are maintained at 0°C and 100°C. determine its thermal conductivity.
Convection heat transfer is the mode of energy transfer between a solid surface and the adjacent liquid or gas that is in motion. .CONVECTION Convection is the up and down movement of gasses and liquids caused by heat transfer. and it involves the combined effects of conduction and fluid motion.
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Example: A cup of hot coffee left to cool by itself.FREE CONVECTION Fluid movement caused by buoyancy forces that occur from differences in density due to fluid temperature difference. Example: A cup of hot coffee quickly blown to cool . FORCED CONVECTION Fluid motion caused by an external source.
NEWTON’S LAW OF COOLING .
Example 2 : Consider a person standing in a breezy room at 20°C. respectively. and the convection heat transfer coefficient is 6 W/ m2 · °C .6 m2 and 29°C. Determine the total rate of heat transfer from this person if the exposed surface area and the average outer surface temperature of the person are 1.
If the convection heat transfer coefficient is 55 W/ m2 · °C.Exercise 4 : Hot air at 80°C is blown over a 2-m X 4-m flat surface at 30°C. . determine the rate of heat transfer from the air to the plate.
. Determine the rate of heat loss from the pipe by convection. 10-m-long hot-water pipe at 80°C is losing heat to the surrounding air at 5°C by natural convection with a heat transfer coefficient of 25 W/m2 · °C.Exercise 5: A 5-cm-external-diameter.
. The radiative energy transferred is proportional to the difference in the fourth power of the absolute temperatures of the bodies exchanging energy.RADIATION Radiative heat transfer is energy in transition from the surface of one body to the surface of another due to electromagnetic radiation.
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HEAT FLOW THROUGH THE DIFFERENT MEDIA value of heat transfer rate per unit area is same for each media .
Then calculate the temperature at the outer surface of the tank. Calculate the rate of heat loss of the tank when the atmospheric temperature is 30 ° C. The thermal conductivity of steel is 50 W / mK and the coefficient of heat transfer inside and outside of each tank is 2800 W/ m2 K and 25 W/ m2 K. .Example 3 : A steel tank with a wall thickness of 5mm containing water temperature of 90 ° C.
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STAT
2.3-2.4 solutions
# They are using machine time to estimate the cost so x
• Notes
• 9
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They are using machine time to estimate the cost, so X = machine time and Y = cost. 27. Interpret the correlation in the context of this problem. What additional variables might be related to electric bills besides hours of machine time? The correlation is .7375 which is moderate, positive, and linear(assuming we looked at the scatterplot). This means as time goes up, electricity does too, in a moderately predictable linear pattern. Other variables might include power needed for each machine, etc. 5
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28. What is the equation of the best-fitting regression line? Justify your answer. Slope = = 71.67 Y-intercept = =263.21 Cost = 263.21 + 71.67 (hours of machine time) 29. How many weeks of data were included in this study? 52 30. For each additional hour of machine time, how much does the cost increase (in dollars) on average? 71.67 dollars 31. For what machine times would you feel comfortable using your best fitting regression line to make predictions about electricity cost? Use the statistical information given in the problem to answer. 6 (minimum time in the data set) to 15 (maximum time in the data set) 32. What is the Y-intercept in this problem? Can it be interpreted in the context of this problem? If yes, interpret it. If no, explain why not. \$263.21 dollars in electric costs for 0 hours machine time. You could describe this as fixed cost before the machines are being used. But since time for this data set started at 6 hours so we can’t make a close prediction here with confidence. Suppose the increase in blood pressure (Y) is estimated by dosage of a drug (X mg). The equation of the best fitting regression line is Y = 0.05X. The correlation was found to be +0.80 *33. If the dosage increases by 10 mg how many units is BP expected to increase by? 0.05 * 10 = .5 units of BP increase 34. Explain why the Y-intercept should be 0 for this problem. there is no increase to measure yet since there is no drug given. 6
A jeweler in Singapore advertises the prices of 48 diamonds in her showroom. You record the weight of each diamond, along with the price, to see whether you can predict weight using price. The analysis is shown below. Weight is measured in carats (1 carat = .2 grams). Price is measured in Singapore dollars. (Note: some numbers have been replaced with question marks.) Descriptive Statistics: Weight, Price Total Variable Count Mean St Dev Minimum Q1 Median Q3 Maximum Weight 48 0.20417 ???? 0.12000 0.16000 0.18000 0.25000 0.35000 Price 48 500.1 213.64 223.0 336.5 428.5 661.0 1086.0 Predictor Coef SE Coef T P Constant -259.63 17.32 -14.99 0.000 Weight 3721.02 81.79 45.50 0.000 Pearson’s Correlation: 0.959. 35. Which of the statements below describes the correlation for this problem? a. As weight increases, price tends to also increase. b. There is a strong positive linear relationship between weight and price. c. You can use weight to predict price using a regression line and it would fit well. d. All of the above.
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# Factors Multiples Prime Composite Numbers Equivalent Fractions Comparing
• Slides: 55
Factors & Multiples Prime & Composite Numbers Equivalent Fractions Comparing Fractions \$100 \$100 \$200 \$200 \$300 \$300 \$400 \$400 \$500 \$500 Ordering
C 1 final FINAL JEOPARDY Josh says that 2/3 is the same as 4/6. Megan says that 2/3 and 4/6 are equivalent fractions, but they could be different amounts. Which student is correct? EXPLAIN.
C 1 final Megan is correct. 2/3 and 4/6 are equivalent fractions, which are the same. However, the wholes could be different amounts/sizes.
C 1 \$100 Find all the factors of the number 32.
C 1 \$100 1, 32, 4, 8, 2, 16
C 1 \$200 What are the factors of 12?
C 1 \$200 1, 12, 2, 6, 3, 4,
C 1 \$300 Write 5 multiples of the number 8.
8 x 1=8 8 x 2=16 8 x 3=24 8 x 4=32 8 x 5=40 C 1 \$300
C 1 \$400 How many factors are there in the number 48?
C 1 \$400 1, 48, 2, 24, 6, 8, 16, 3, 12, 4 10 factors
C 1 \$500 Tell whether the first number is a multiple of the second number. 44, 6
C 1 \$500 6 x 1=6, 6 x 2=12, 6 x 3=18, 6 x 4=24, 6 x 5=30, 6 x 6=36, 6 x 7=42, 6 x 8=48 44 is NOT a multiple of 6.
C 2 \$100 Is 11 a prime or composite number?
C 2 \$100 Prime
C 2 \$200 Give an example of a composite number.
C 2 \$200 Answers will vary… Teacher will determine.
C 2 \$300 Which of these numbers is prime? 4, 12, 17, 21, 28, 30
C 2 \$300 17
C 2 \$400 Is the number 300 prime or composite? Explain why.
C 2 \$400 300 is a composite number, because it has other factors besides 1 and itself (300). For example, 3 and 100 are both factors of 300.
C 2 \$500 What number is neither prime or composite?
C 2 \$500 1
C 3 \$100 Which of the following is an equivalent fraction to 5/6? a) 4/8 b) 10/12 c) 5/12 d) 15/30
C 3 \$100 b) 10/12
C 3 \$200
C 3 \$200 d) 7/8
C 3 \$300 Complete the equivalent fraction… 8/12 = ? /3
C 3 \$300 8/12 = 2/3
C 3 \$400 True or False… 1/2 and 15/30 are equivalent fractions.
C 3 \$400 True
C 3 \$500 Name 3 equivalent fractions for the part of the circle that is shaded.
C 3 \$500 Answers will vary. Teacher will determine.
C 4 \$100 Is 3/8 <, >, = 2/3
C 4 \$100 3/8 < 2/3
C 4 \$200 Which is greater, 3/5 or 7/8?
C 4 \$200 7/8
C 4 \$300 7/12 3/4
C 4 \$300 <
C 4 \$400 2/3 5/12
C 4 \$400 >
C 4 \$500 A melon was divided into 8 equal slices. Joe ate 3 slices. Sam and Stacy ate the rest. What fraction of the melon did Sam and Stacy eat?
C 4 \$500 5/8
C 5 \$100 Order the fractions from least to greatest. 5/12, 2/3, 1/4
C 5 \$100 1/4, 5/12, 2/3
C 5 \$200 Put these fractions in order from greatest to least. 1/2, 3/5, 2/10
C 5 \$200 3/5, 1/2, 2/10
C 5 \$300 What common denominator would you use to compare these fractions? 1/4, 1/6, 1/2
C 5 \$300 12
C 5 \$400 Order these fractions from least to greatest. 2/4, 3/12, 2/3
C 5 \$400 3/12, 2/4, 2/3
C 5 \$500 True or false… This is the correct way to order the fractions least to greatest. 2/3, 5/6, 7/12
C 5 \$500 False
Now use this information to study for your test!!!
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## 4. Find the common difference of the following A.P:1, -2, -5,-8,….
Question
4. Find the common difference of the following A.P:1, -2, -5,-8,….
in progress 0
2 years 2021-07-08T05:26:57+00:00 2 Answers 0 views 0
t1 = 1
t2 = -2
t3 = -5
t4 = -8
common difference (d) = t2 – t1 = -2-1 = -3
= t3-t2= -5 – (-2) = -3
hence, the common difference is -3
2. To find the common difference
Formula is :-
D= a2-a1
-2-1 = -3
So -3 is the common difference between A1 and a2
Do the same prossece with A3 and a2
D= a3-a2 = -5-(-2)=-3
So the difference between all the A.p is -3
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# ILP Part 62 – Maximally attacking chessboard
This is the sixtieth second part of the ILP series. For your convenience you can find other parts in the table of contents in Part 1 – Boolean algebra
Today we are going to solve a chess problem variation. We want to generate a chess board (with regular pieces for each player) with maximal attacking score. An attack is the same as in chess — a position in which one piece can capture another one in subsequent move.
We are interested in any position, it doesn’t need to be a legal one (so both kings can be under check, pawns can be in any rank or file etc) nor achievable (so we don’t care if there is a sequence of legal moves leading to a given position). We need to use all 32 pieces, no promotions are allowed.
The code is rather trivial, however, it is pretty hard to maximize the function:
In lines 13-32 we define binary flags describing what piece a field is. Next, in lines 34-48 we define some helper variables (to avoid recalculation) and then in lines 50-57 we make sure each field is of an exactly one type (or is empty). Finally, in lines 59-71 we make sure we have correct number of pieces on the board.
Then we define our goal. We start with some helper functions in lines 73-90 and then start adding rules for each piece. Pawns in lines 91-102 are rather trivial, we just check if a pawn attacks one of two neighbours (notice that we number rows from top to bottom so white pawns would move form higher ranks to lower ones). Similarly for knights in lines 104-127 (knight is essentially a pawn attacking some different fields).
Bishops, rooks, queens and kings are based on the same approach. We move farther and farther away from the starting position (whether in rank/file for rooks or diagonally for bishops), calculate a variable if given direction is still allowed (as we cannot “jump over” pieces) and update the state. For queens and kings it’s essentially the same.
Finally, we save the model, solve it and print the solution. Below is an example of some (non-optimal) result:
This is after running for 10 minutes on my machine using CPLEX. However, I ran it through Neos for 8 hours and found solution of value 98 which is presented below:
I actually don’t know if this is the optimal one but according to Gurobi it cannot be higher than 116. Maybe one day I’ll run it for more time to explore all nodes.
We can use this snippet to set a lower bound for the solution:
This allows for getting any solution as soon as possible or improving above something we know is possible.
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# Define discrete mathematics symbols to express the idea of discrete numbers.
The purpose should be to teach students that not all numbers in math are integers, and that they have to be capable to recognize that some numbers have already been modified by addition or subtraction. Some numbers in math are continuous and may be written out devoid of fractional digits.
Discrete signifies one thing that can't be summed. essay writer You usually do not need to use the word "integers" when dealing with discrete numbers mainly because they cannot be added together. Once you have complications with recognizing that you'll find distinct variations of a continuous quantity, you may need to understand the meaning of a single digit and its relationship to a different digit. A continuous quantity is called a simplex when all the digits are one, as an example, three.
All the digits of a continuous quantity will have to possess the exact same values, otherwise the outcome will likely be a series of zero digits. Nonetheless, there are actually some discrete numbers which can be multiples of 1. For example, each quantity with one particular plus one particular is called a numerous of one, but each of the numbers with two, 3, 4, five, and six are named multiples of one.
There are two symbols for any quantity which has a fractional aspect. The very first symbol is called a fraction plus the second is called a fractional component. In an effort to ascertain the value of a fraction, divide the number by 10. In the event the resulting worth is equal to ten, then it is actually a fraction.
The symbols together with the fraction are usually not applied. Most math students understand from instruction that the worth of any quantity may be the sum of its parts. It is actually effortless to remember the definition of a fraction when it is all you'll need to perform to multiply numbers.
The numerator is normally the very first number inside a series of numbers. homework help The denominator is definitely the second quantity within the series. You may see the numerator divided by one in front of a quantity which has a fraction. The difference among the numerator and also the denominator could be written as an integer. A single can also write the fraction in its decimal kind and use the proper symbol.
This number might be written in each of the digits in the all-natural numbers. The final digit would be the symbol for zero. In the event the fraction will not possess a zero, the symbol will likely be a single vertical bar. Several math teachers will instruct their students to create the fraction with no trailing zero as 1. They may be employing the traditional notation within a new way.
The symbols with all the fractions have the symbols for plus or minus. If a fraction has three sides, then there is an additional symbol for the side which is positive. These symbols are just a visual substitute for the conventional notation.
Sometimes it really is hard to know what the meaning of a number is. By way of example, in the event you add two fractions, you can notice that the numbers in each sides add up to 1. The combined number is what exactly is getting spoken about in the phrase, "the sum in the two fractions."
Mathematicians study the meaning of numbers in order that they can resolve issues and create models. They spend numerous years studying numbers, and they're a far cry from having the ability to draw on an empty board or use a ruler. If they have been only taught tips on how to draw a zero, lots of math students will be frustrated.
Students ought to start with simple concepts of calculus. In their minds, they'll not be able to draw the symbols, and can not recognize why it takes two to tango. Then they can take a few courses in differential equations and continue to enhance their understanding of your idea of two to tango.
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# Unit 1- Mr. Hunt
### Operations with Rational Numbers
TermDefinition
Zero Pairs The name for two values that add to make zero or cancel each other out
Additive Inverse The opposite (or negative) of a value that sums to zero
Absolute Value a value's distance from zero on a number line
Opposite another word for the negative of a certain value
Distance how long a vector is for a certain value on a number line
Integer A number with no fractional part
Rational Number A number that can be made by dividing two integers. The word comes from "ratio".
Commutative Property The law that says you can swap numbers around and still get the same answer when you add. Or when you multiply.
Associative Property it doesn't matter how we group the numbers (i.e. which we calculate first) ...when we add... or when we multiply.
Distributive Property The law says that multiplying a number by a group of numbers added together is the same as doing each multiplication separately
Positive Contexts cash, above, gain, over, right
Negative Contexts debt, below, loss, under, left
Charged Particle The model where you separate values on a T-chart with negative on the left and positive on the right
Vector Diagram/Number Line The model where you use arrows that have a certain direction and a certain length based on whether they are positive or negative and how large the value is.
Net Worth The final value when all debt and all cash are combined
Decomposing Strategy The act of breaking a single value into multiple values
Composing Stractegy The act of building a single value out of smaller values
Reciprocal The number you can multiply a value by to make it equal 1. (e.g.- 4 x 1/4 = 1, or 3/4 x 4/3 = 1)
Created by: mrhunt
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My Math Forum Find all values for x where function is differentiable
Calculus Calculus Math Forum
October 10th, 2011, 05:22 PM #1 Member Joined: Aug 2011 From: Alabama Posts: 93 Thanks: 0 Find all values for x where function is differentiable I am given the function ƒ(x) = ((3x-6)^?) + 5 How do I find all of the values of x where the function is differentiable?
October 10th, 2011, 05:24 PM #2 Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4 Re: Find all values for x where function is differentiable You could start by taking the derivative, and see where that is undefined.
October 10th, 2011, 05:30 PM #3 Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,155 Thanks: 463 Math Focus: Calculus/ODEs Re: Find all values for x where function is differentiable We are given: $f(x)=$$3x-6$$^{\small{\frac{1}{3}}}+5$ thus: $f'(x)=$$3x-6$$^{-\small{\frac{2}{3}}}$ Thus, we find f(x) is not differentiable for: $3x-6=0$ $x=2$
October 10th, 2011, 05:36 PM #4 Member Joined: Aug 2011 From: Alabama Posts: 93 Thanks: 0 Re: Find all values for x where function is differentiable Makes perfect sense. Thank you.
Tags differentiable, find, function, values
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# find all values of f for which the function is differentiable
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# math
posted by .
This year Ben is 4/7 as old as Glen. Fifteen years from now, Ben will be ¾ as old as Glen. At that time, the sum of their ages will be 63. How old are Ben and Glen now?
• math -
G = Glen's present age
B = Ben's present age
B = 4/7 G
G + 15 + B + 15 = 63
substitute, B = 4/7 G
G + 15 + 4/7 G + 15 = 63
Solve for G
## Similar Questions
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5. ### Math
the sum of the ages of rex, ben and alfred is 36 years, two years ago, ben was 3 times as old as rex was then, 8 years from now, alfred will be twice as old as ben will be then. find their present age.
6. ### math
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Elementary Algebra
Introduction to Algebra Linear Equations and Inequalities Functions and Graphs I Lines and thier Graphs Linear Systems Exponents & Polynomials
Intermediate Algebra
Factoring Rational Expressions Rational Equations and Applications Radical Expressions Nonlinear Equations and Applications Functions and Graphs II Exponential and Logarithmic Functions
Precalculus I / College Algebra
Equations and Inequalitites Functions and Graphs Polynomial and Rational Functions Exponential and Logarithmic Functions Systems and Matrices Geometry Basics Conic Sections Sequences and Series
Precalculus II / Trigonometry
The Six Trigonometric Functions Right Triangle Trigonometry Circular Functions Graphs of Trigonometric Functions Trigonometric Identities Trigonometric Equations Oblique Triangles and the Laws Vectors Complex, Parametric, and Polar Forms
Calculus I
Limits and Continuity Derivatives Analysis of Curves Antiderivatives
Calculus II
Transcendental Functions
Geometry Physics Integration Techniques Calculus of Infinity Parametric, Polar, and Conic Curves
Calculus III
Course: Intermediate Algebra
Topic: Rational Expressions
Subtopic: Operations III - Add & Subtract (same denominators)
Overview
In this lesson we add rational expressions where the fractions have the same denominator. To do so we simply add the numerators, simplify, and that result will be over the common denominator. When subtracting be careful to distribute the minus sign through the entire numerator of the fraction it precedes. Not doing so is a common error!
Objectives
By the end of this topic you should know and be prepared to be tested on:
• 8.3.1 Add rational expressions that have the same denominator
• 8.3.2 Subtract rational expressions that have the same denominator without making a sign error
Terminology
Terms you should be able to define: "like" (same) denominators, "unlike" (different) denominators
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1. ## Another Ellipse Problem
The Earth's orbit is an ellipse with the sun at one focus. The length of the major axis is 186,000,000 miles and the eccentricity 0.0167. Find the distances from the ends of the major axis to the sun. These are the greatest and least distances from the earth to the sun.
The Earth's orbit is an ellipse with the sun at one focus. The length of the major axis is 186,000,000 miles and the eccentricity 0.0167. Find the distances from the ends of the major axis to the sun. These are the greatest and least distances from the earth to the sun.
Hello,
the foci have the distance e (called linear eccentricity (literally translated from German)) from the centre of the ellipse. The proportion $\displaystyle \epsilon=\frac{e}{a}$ is called numerical eccentricity (translated ... as you now know) and that's the value you are given here.
Thus you can calculate the distance e:
$\displaystyle 0.0167 = \frac{e}{93,000,000} \Longleftrightarrow e \approx 1,553,100 \text{ miles}$
If you subtract this value from the half axis you'll get the shortest distance (it is called perihel) p = 91,446,900 miles
If you add this value to the half axis you'll get the greatest distance (it is called aphel) ap = 94,553,100 miles
EB
PS: Make a sketch of an ellipse and mark the lines a, b, e, p and ap.
The Earth's orbit is an ellipse with the sun at one focus. The length of the major axis is 186,000,000 miles and the eccentricity 0.0167. Find the distances from the ends of the major axis to the sun. These are the greatest and least distances from the earth to the sun.
Umm, eccentricity in a conic section.
Eccentricity, e, is the ratio of the distances of a point on the curve from the focus and from the directrix. If f = distance from focus, and d = distance from directrix, then e = f/d.
Also, e = c/a -----------(ii)
where
c = distance of focus from the center of ellipse
a = distance of end (vertex) of ellipse from the center along the major axis, or it is half of the major axis.
Given:
2a = 186M miles.
e = 0.0167 ----------very small. So the ellipse is almost like a circle.
Using (ii),
0.0167 = c/(186/2)
c = (0.0167)(93) = 1.5531M mi.
The focus is along the major axis, so,
f = 93 -1.5531 = 91.4469M mi.
Meaning, the nearest vertex of the ellipse to sun is 91.4469 million miles.
The other vertex is 186M -91.4469M = 94.5531M miles from the sun.
Therefore, the least distance of the Earth to the sun is about 91,446,900 miles, and the Earth's greatest distance from the sun is about 94,553,100 miles. -----------answer.
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# the earths orbit is ellipse, with the sun at the focus
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# x = sec^2 3y differentiate
How do i differentiate x = sec^2 3y?
I dont understand if i'm supposed to be using the chain rule or product rule. I've been looking at answers but i just dont understand it
Original post by TomokoRainMaker
How do i differentiate x = sec^2 3y?
I dont understand if i'm supposed to be using the chain rule or product rule. I've been looking at answers but i just dont understand it
What have you tried?
Original post by Muttley79
What have you tried?
i did
U = 3y du/dx = 3
y = sec^2U dy/dx = ksec^2UtanU
idk if thats even right. thats all i have bc idk what rule to use
Find dx/dy. Then use that to find dy/dx.
(You're on the right track for dx/dy)
Original post by TomokoRainMaker
i did
U = 3y du/dx = 3
y = sec^2U dy/dx = ksec^2UtanU
idk if thats even right. thats all i have bc idk what rule to use
dx/dy = dx/du * du/dy
Can't follow your method.
Which of those can you find?
Original post by Muttley79
dx/dy = dx/du * du/dy
Can't follow your method.
Which of those can you find?
How am i meant to know to put it into the chain rule? Thats what i dont get
Original post by TomokoRainMaker
How am i meant to know to put it into the chain rule? Thats what i dont get
You wrote:
U = 3y [du/dx] that is dU/dy as you have an equation between two variables U and y
y = sec^2U [dy/dx] here you have an equation between y and U, so it'd be dy/dU
(edited 1 month ago)
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# Search by Topic
#### Resources tagged with Mental addition & subtraction similar to Tricky Track:
Filter by: Content type:
Stage:
Challenge level:
### There are 19 results
Broad Topics > Calculations and Numerical Methods > Mental addition & subtraction
### Flip Flop - Matching Cards
##### Stage: 1, 2 and 3 Challenge Level:
A game for 1 person to play on screen. Practise your number bonds whilst improving your memory
### Fifteen
##### Stage: 2 and 3 Challenge Level:
Can you spot the similarities between this game and other games you know? The aim is to choose 3 numbers that total 15.
### Subtraction Squares
##### Stage: 1 and 2 Challenge Level:
A game for 2 players. Using 2 dice, some counters and a games board, can you form a line of counters from one side of the board to the other?
### Connect Three
##### Stage: 3 and 4 Challenge Level:
Can you be the first to complete a row of three?
### Dicey Operations for Two
##### Stage: 2 Challenge Level:
Dicey Operations for an adult and child. Can you get close to 1000 than your partner?
### Down to Nothing
##### Stage: 2 Challenge Level:
A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.
### Domino Magic Rectangle
##### Stage: 2, 3 and 4 Challenge Level:
An ordinary set of dominoes can be laid out as a 7 by 4 magic rectangle in which all the spots in all the columns add to 24, while those in the rows add to 42. Try it! Now try the magic square...
### Calculator Bingo
##### Stage: 2 Challenge Level:
A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.
### Chocoholics
##### Stage: 2 Challenge Level:
George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?
### Wild Jack
##### Stage: 2 Challenge Level:
A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.
### Criss Cross Quiz
##### Stage: 2 Challenge Level:
A game for 2 players. Practises subtraction or other maths operations knowledge.
### Intersection Sums Sudoku
##### Stage: 2, 3 and 4 Challenge Level:
A Sudoku with clues given as sums of entries.
### Being Curious - Primary Number
##### Stage: 1 and 2 Challenge Level:
Number problems for inquiring primary learners.
### Transformations Tables
##### Stage: 2 Challenge Level:
These grids are filled according to some rules - can you complete them?
### Integrated Sums Sudoku
##### Stage: 3 and 4 Challenge Level:
The puzzle can be solved with the help of small clue-numbers which are either placed on the border lines between selected pairs of neighbouring squares of the grid or placed after slash marks on. . . .
### Prime Magic
##### Stage: 2, 3 and 4 Challenge Level:
Place the numbers 1, 2, 3,..., 9 one on each square of a 3 by 3 grid so that all the rows and columns add up to a prime number. How many different solutions can you find?
### Difference Sudoku
##### Stage: 3 and 4 Challenge Level:
Use the differences to find the solution to this Sudoku.
### Dicey Operations
##### Stage: 2 and 3 Challenge Level:
Who said that adding, subtracting, multiplying and dividing couldn't be fun?
### Current Playing with Number Upper Primary Teacher
##### Stage: 2 Challenge Level:
Resources to support understanding of multiplication and division through playing with number.
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# What Comes Next in the Sequence: 2, 6, 12, 20, 30, ??, ??
Can you see a pattern in the series below?
What comes next in the sequence?
2, 6, 12, 20, 30, ??, ??
Challenge your friends with this number series riddle and find the smartest ones in your WhatsApp group.
1 x 2 = 2
2 x 3 = 6
3 x 4 = 12
4 x 5 = 20
5 x 6 = 30
So next numbers will be as follows;
6 x 7 = 42 &
7 x 8 = 56
or the second logic is;
1^2 + 1 = 1 + 1 = 2
2^2 + 2 = 4 + 2 = 6
3^2 + 3 = 9 + 3 = 12
4^2 + 4 = 16 + 4 = 20
5^2 + 5 = 25 + 5 = 30
So the next numbers will be as follows;
6^2 + 6 = 36 + 6 = 42
7^2 + 7 = 49 + 7 = 56
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### Home > GB8I > Chapter 5 Unit 6 > Lesson INT1: 5.1.2 > Problem5-22
5-22.
Solve each equation.
1. $2(x-2)=-6$
Option 1: Distribute the $2$ into the $(x-2)$ term.
Option 2: Divide both sides of the equation by $2$.
1. $2(x+1)+3=3(x-1)$
$x=8$
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# Activities to Teach Students About Nth Roots
Nth roots refer to those numbers which, when multiplied by themselves n number of times, become a given value. The concept of nth root plays an important role in various mathematical problems, including algebra and geometry. While it can be a bit difficult for some students to understand the concept of nth roots, teachers can help their students by utilizing activities to make the learning process more exciting and engaging. Below are some of the activities you can use to teach your students about nth roots.
Before introducing your students to the concept of nth roots, it is essential to familiarize them with the radical notation. The radical notation is used to indicate that a number is an nth root of a given value. You can illustrate to your students the underlying structure of the radical notation by showing them examples of square roots and cube roots. With this solid foundation, you can then progress to the actual concept of nth roots.
2. Hands-on Experimental Activity
One of the most effective ways to teach your students about nth roots is through a hands-on experimental activity. Divide your students into groups and ask them to extract the nth root of different numbers using a calculator or manually. Let them explore the concept of how to calculate nth roots through trial and error. Encourage them to share their findings and discuss their approaches to calculating nth roots.
3. Interactive Game
Boost your students’ learning by creating a higher-order thinking game about nth roots. Design a fun and interactive game that involves identifying the nth root of an answer. You can create a game in which the students have to guess the square root or cube root of randomly generated numbers on the board. The game could be played in groups or individually. The game will not only help them learn about the nth roots, but it will also help strengthen their cognitive abilities.
4. Real World Examples
Another effective way to teach your students about nth roots is to relate it to real-world examples. For instance, you can ask your students to calculate the nth root of the side of a cube or a rectangular prism. You can also link the concept of nth roots to different areas of study, such as biology, physics, and geography. By doing so, you can help them understand the practical application of nth roots in different fields.
5. Graphical Representation
Introduce your students to graphical representation because it can be particularly beneficial when trying to teach them about nth roots. You can demonstrate this by plotting the nth roots of various numbers on a coordinate plane, making it easier for them to grasp the concept of nth roots. You can also use the graphical representation of nth roots to show them how the value of an nth root changes when the base number is varied.
In conclusion, teaching students about the concept of nth roots can be exciting and engaging when presented in an interactive and creative way. By utilizing the five activities above, you can help your students understand the concept of nth roots in a way that is both exciting and memorable. These activities will not only enhance their understanding of the subject, but they will also make math more fun and interesting for them.
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# 2Tvwo Ch9 SUMMARY p.110-113 (long version)
Practice Test from Workbook 2B
= Homework for next lesson.
Ch 9 Linear equations is an important chapter.
This LessonUp is meant to:
+ pimp your knowledge and to
+ increase your skill in applying it
You'll get some information several times, followed by a task.
1 / 36
Slide 1: Slide
WiskundeMiddelbare schoolhavoLeerjaar 2
This lesson contains 36 slides, with interactive quizzes and text slides.
Lesson duration is: 50 min
## Items in this lesson
Practice Test from Workbook 2B
= Homework for next lesson.
Ch 9 Linear equations is an important chapter.
This LessonUp is meant to:
+ pimp your knowledge and to
+ increase your skill in applying it
You'll get some information several times, followed by a task.
#### Slide 3 -Slide
Now some practice!
+ open your Notebook
+ Copy and make the following task and
+ key in your answer in the slide after the next one
+ maybe using the 'Skill' on p.1112 (the same content as just shown)
#### Slide 4 -Slide
Solve linear equations
Work out on paper in your Notebook:
TASK 1:
Solve y + 137 = 3(6y-113) - 3y
timer
2:00
#### Slide 5 -Slide
TASK 1
y + 137 = 3(6y-113) - 3y
The solution is:
A
y = -34
B
y = 36
C
y = 34
D
y = -36
#### Slide 6 -Quiz
Solve linear equations
SOLUTION TASK 1:
Solve y + 137 = 3(6y-113) - 3y
y + 137 = 18y -339 - 3y work out brackets
y + 137 = 15y - 339 adding like terms
137 = 14y - 339 variables on one side
476 = 14y adding 339 on both sides
34 = y divide by 14
y = 34
#### Slide 7 -Slide
'New old stuff' now:
+ reading off the p.o.i. of two graphs
+ how to calculate the p.o.i. of the graphs of two lines
+ see next slides!
#### Slide 8 -Slide
In this example the graphs were given.
If this isn't the case, we have to
calculate the p.o.i.
How? See next slides!
#### Slide 10 -Slide
Calculate point of intersection
TASK 2:
Calculate the coordinates of the point of intersection between
y = 8x + 5 and y = 11 - 2x
Again:
+ copy and work it out in your Notebook, maybe using Method p.97
(the same as just shown)
+ fill in your answer in the next slide
+ the answer -the coordinates- are not whole numbers!
timer
2:30
TASK 2:
The p.o.i. is:
A
(9.8 , 0.6)
B
(9.6 , 0.9)
C
(6.9 , 0.8)
D
(0.6 , 9.8)
#### Slide 12 -Quiz
Calculate point of intersection
SOLUTION TASK 2:
Calculate the coordinates of the point of intersection between
y = 8x + 5 and y = 11 - 2x
8x + 5 = 11 - 2x
10x + 5 = 11
10x = 6
x = 0.6 Point of intersection is (0.6, 9.8)
y=80.6+5=9.8
y=1120.6=9.8
#### Slide 14 -Slide
You are doing great,
+ going through the whole Chapter in one LessonUp!
+ refreshing your memory and
+ practising are more important than
+ learning new things now!
#### Slide 15 -Slide
High time for everybody's favorite (?):
solving inequalities !
#### Slide 16 -Slide
TASK 3:
For which values of x is are the
results for formula A greater than the results for
formula B?
Key in your answer in the next slide!
#### Slide 17 -Slide
timer
0:20
TASK 3:
For which values of x are the results for graph A greater than the results for graph B?
#### Slide 18 -Mind map
SOLUTION:
For x is greater than 30 the results for graph
A are greater than the results for graph B.
Because then the graph for A lies higher
than the graph for B!
#### Slide 19 -Slide
SOLVING INEQUALITIES goes on:
Below you see the steps to take.
Next slide shows an example
(which explains much more!).
#### Slide 21 -Slide
Solve inequalities
TASK 4:
Solve 5x - 6 > 10 - 3x
Time for action from your side!
+ copy the inequality and
+ solve it, using the 4 steps you find in the SKILL on p.112
+ key in your answer in the next slide
timer
3:00
#### Slide 22 -Slide
TASK 4:
A
x is smaller than 4
B
x is smaller than 2
C
x is greater than 2
D
x is greater than 4
#### Slide 23 -Quiz
SOLUTION TASK 4:
Solve inequalities
Solve 5x - 6 > 10 - 3x
5x - 6 = 10 - 3x
8x - 6 = 10
8x = 16
x = 2
Solution: x > 2
#### Slide 24 -Slide
Next slide is about:
rearranging (herschrijven) a formula, so that
+ you can express one variable p in variable q so that
+ you can calculate p, when you know q
+ confused? you won't be, after the following explanation!
#### Slide 26 -Slide
Rearrange formulas
TASK 5:
Express h in terms of t and write as short as possible:
2(h - 5) = t + 5
+ copy this task in your Notebook and
+ work it out, maybe using the first SKILL on p.113 (the same as just shown!)
+ key in your answer in the next slide
timer
2:00
#### Slide 27 -Slide
TASK 5:
Rearranging 2(h-t) = t + 5
gives: ...................
21
21
21
A
h = 7.5 + 0.5t
B
h = t + 7 1/2
C
h = -0.5t + 7.5
D
h = 0.5t + 7.5
#### Slide 28 -Quiz
SOLUTION TASK 5:
Rearrange formulas
Express h in terms of t and write as short as possible:
2(h - 5) = t + 5
2h - 10 = t + 5
2h = t + 15
h = 0.5t + 7.5
#### Slide 30 -Slide
Finally ....
Substitution!
In football this is something similar:
someone is taken out and
somebody else takes his place.
#### Slide 32 -Slide
Substitute formulas
TASK 6:
Substitute and simplify:
A: a = 7 - 5t B: t = -2h + 3.
Once more:
+ copy this exercise and
+ work it out in your Notebook; then
+ key in your answer n the next slide
timer
2:00
TASK 6:
A
a = 10h - 8
B
a = 8 - 10h
C
a = -8 -10h
D
a = -8 + 10h
#### Slide 34 -Quiz
Substitute formulas
SOLUTION TASK 6:
Substitute and simplify:
A: a = 7 - 5t B: t = -2h + 3
a = 7 - 5(-2h + 3)
a = 7 + 10h - 15
a = 10h - 8 or a = -8 + 10h
#### Slide 35 -Slide
Homework time
p.110-113 SUMMARY
Make (at least) four of the 8 Tasks.
Of course it makes sense trying those Tasks you find difficult!
First Study the Skill prior to (=voorafgaand aan) the Task
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# Solving for a variable. Hard to do in this simple equation.
• Jon9992
In summary, the problem at hand is to solve for "a" in the equation a(a+b+c)=d. The solution involves using the distributive property to get a^2+ab+ac=d, and then dividing both sides by "a" to get a+b+c=d. From there, subtracting "a" and "d" yields b+c-d=-a. However, it is important to note that you cannot divide only one side of an equation, so the solution also involves using the Quadratic Formula to solve for "a".
#### Jon9992
Hi. This isn't for any sort of homework. I've run into a deadend where I have a situation like this where I need to solve for "a":
a(a+b+c) =d
You'd think it would be easy but I can't seem to get "a" by itself. It always end up on both sides of the equation at best which is starting to make me think it's somehow recursive. I know how to solve it if it didn't have the "c" by using the quadratic equation but not sure in this situation.
Thanks so much!
Last edited:
First you would do distributive property, multiply everything inside the parentheses by "a". Then you would get a^2+ab+ac=d. Then even though we just multiplied it, (it's kind of a trick question, you didn't need to multiply since a is already in the problem) you divide. That leaves you with a+b+c=d. Then subtract a to get b+c=d-a. Now you subtract d to get b+c-d=-a.
Gbl911 said:
First you would do distributive property, multiply everything inside the parentheses by "a". Then you would get a^2+ab+ac=d. Then even though we just multiplied it, (it's kind of a trick question, you didn't need to multiply since a is already in the problem) you divide. That leaves you with a+b+c=d.
Absolutely not! You can't divide just one side of an equation. If you divide the left side by a, you have to also divide the right side by a.
Gb said:
Then subtract a to get b+c=d-a. Now you subtract d to get b+c-d=-a.
After carrying out the multiplication on the left side, you get a2 + ab + ac = d. Add -d to both sides to get a2 + ab + ac - d = 0. One more step gets us to a2 + (b + c)a - d = 0. This is a quadratic in a, and can be solved for a by using the Quadratic Formula.
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### CA I.2 Snowflake Exploration Part II
Purpose: To introduce the Koch Snowflake and investigate the area and perimeter (in synthesis) of this snowflake. To achieve this, sigma notation, finite sums, limits of finite sums (series), approximating exact limit with finite sums and error considerations are all introduced.
Classroom Procedure: It is very helpful if you can get through the first page of this activity on the same day that you finish the Part I activity and let students go home to work on and practice sigma notation. This gives them time to become familiar with it before having to use it in a more sophisticated way to represent the area of the snowflake. Students will need time to work on 1 and then discuss it as a class to make sure everyone is understanding the sigma notation and what it means in this case. Then students are given time to work on 2 and 3 followed by a class discussion of these questions and 4. Then students can take time to work on 5 and think about 6 followed by class discussion of both. Finally if there is time to at least start 7 in class that is good although students can be sent home with that along with the synthesis questions for this activity if there is no time. There should be class discussion of 7 after students have had time to work on it as some confusion is highlighted hear about how the area of the finite snowflakes are related to the area of the Koch Snowflake.
Ideas this Activity Builds On: Again as this is a continuation of the first activity there is not a lot that it is building on - however it does build on students having a good understanding of the finite snowflakes developed in the first activity.
Introduction/Motivation of the Activity: As this is a continuation activity there is not much motivation given here other than continuing our work from Part I.
Need to Establish by the End of Activity/Wrap-Up:
• Sigma notation and how to use it
• Finite sums and how to calculate them in Mathematica
• Series and how they relate to finite sums
• That a series (an infinite process) can yield a finite number.
Additional Notes: There are synthesis questions for this activity that deal with the perimeter of the Koch snowflake and two other geometric series (one finite, one infinite). It is important for students to work on synthesis questions outside of class for time reasons and to give them experience with working independently on deep problems without an instructor being at hand.
#### Teacher Journal: CA I.2
• Snowflake Exploration, Part II Students struggle with writing a sum in sigma notation once the sum has gotten slightly more complicated than the original examples that they have worked with. In addition for the area formula the first term of the sum does not follow the pattern so it must be kept outside the sigma form. Once they have figured this out though the main confusion comes from the very unnatural conclusion in their mind that an infinite process can yield a finite number. Although when they consider the size of the snowflake physically they can see that the area is not going to be infinite, they still have a hard time connecting that conclusion to the series form of the area. Then they are even more confused by the notion that the perimeter could indeed be infinite despite the fact that it is contained inside a finite space. I think these are great ideas for students to have to confront immediately in this class as there are a lot of concepts both in series and improper integrals that deal with the notion of infinity and it is an area that students have many misconceptions. I like to have a quick discussion after students have turned in the synthesis questions to highlight some of these findings to the whole class as sometimes it seems that the students can have a reasonably good understanding of the concepts worked on but still might not have put them together to think about these bigger ideas.
Posted Jun 15, 2012, 8:53 AM by Mairead Greene
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## What is The System Function?
The system function which is also called as the transfer functionand the network functions is the mathematical representation of the system which shows the relation between the input and the output of the linear time-invariant systems. This is the frequency domain system representation of the Signal & system’s system function by H(jw)
The system functions are normally used to the analysis of the systems which has a single-input and also a single output filters. This term is widely used in the signal system engineering. The term is refers to as the linear, time-invariant systems (LTI). In the most simple form for the continuous-time the input signal x(t) and the output y(t), the system function is the linear mapping of theLaplace transform of the input, X(s), to the output Y(s):
Y (s) = H ( s ) X ( s )
Or
H ( s) =
The system function is defined as the ratio of the output of the system to the input of the system. In the Laplace transform domain while considering the initial conditions to be zero. If the input function of X(s), and the output function Y(s), So the system function H(s) can be defined as:
In the time domain the variables are generally written with lower-case letters. So in the time domain, the input to a system is denoted as x(t), and the output of the system as the y(t). The relationship between the input and the output is denoted as the impulse response, h(t).We define the impulse response as being the relationship between the system output to its input. We can use the following equation to define the impulse response:
h ( t ) =
## Interconnection of Systems
SERIES INTERCONNECTION OF SYSTEMS
Fig:Systems connected in series
The systems of the system connected in the series format. If all the systems are single input
and single output. So that the total system transfer function can be expressed as
T (s ) =
Here, T(s) is define the total transfer function of the system, and are define the individual system transfer function of the system.The SISO system functions. However, if two MIMO systems are interconnected as shown in the multiplication of the system functions is not anymore applicable.
Fig: Systems Connected into parallel
When the two systems are interconnected into parallel manner so that the system function is defined as the
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## Related Topics
All Engineering Topics
More Q&A
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Discussion Question Essay
868 words - 4 pages
DQ 1
Take any number (except for 1). Square that number and then subtract one. Divide by one less than your original number. Now subtract your original number. Did you reach 1 for an answer? You should have. How does this number game work? Hint. Redo the number game using a variable instead of an actual number and rewrite the problem as one rational expression. How did the number game use the skill of simplifying rational expressions?
Create your own number game using the rules of algebra and post it for your classmates to solve. Think about values that may not work. State whether your number game uses the skill of simplifying rational expressions.
Consider responding to your ...view middle of the document...
_ An example could also possibly be the LCD, which we use in the simplification of a division problem, and the simplification of rational expressions. The use of factoring enables the usage of (one); which is equal to the base (LCD), that reduces the expression by a factor of one lowest common multiple and simplifying the expression.
Create your own number game using the rules of algebra and post it for your classmates to solve. Think about values that may not work. State whether your number game uses the skill of simplifying rational expressions.
Ex: Original # = (variable).
a = “a^2, square root of 2^2, (a)(a), a/a” = a
a^1 = a, (1/2a)(2) = a, the square root(a^2) = a, and ((a)(a)(a/a)) = a/1 = a.
Ex: (x^2-4)/(x+2) = ((x+2)(x-2))/(x+2) = ((x+2)/(x+2))(x-2) = x-2,
X+2 was the LCM, a fraction equivalence of one in the expression.
Note: x = all real numbers, variables or terms.
_ The simplification of rational expressions requires the gathering of like terms. If you can’t gather the terms, then you can’t add them, or anything else to them “plural”; they are independent terms at that point. If you put them to a common base (LCD), you’re able to add them, or anything else.
Consider responding to your classmates by solving their number games or...
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## What shapes have no lines of symmetry?
Two shapes that have no lines of symmetry are the scalene triangle and an irregular quadrilateral.
## What is not a line of symmetry in a triangle?
A scalene triangle is a triangle with no lines of symmetry while an isosceles triangle has at least one line of symmetry and an equilateral triangle has three lines of symmetry.
## Which polygon does not have a line of symmetry?
Parallelogram. A parallelogram is a quadrilateral with no axis of line symmetry. The opposite sides of a parallelogram are equal and parallel.
## Does a right angle have a line of symmetry?
A right angled triangle, if it is isosceles right angled triangle then it will have one line of symmetry. if it is equilateral right angled triangle then it will have three lines of symmetry. if it is scalene right angled triangle then it will have no line of symmetry.
two lines
## What do you call a rectangle that has 4 lines of symmetry?
If a rectangle has four line of symmetry this means that’s the square.
## How many horizontal lines does a rhombus have?
A rhombus has two lines of symmetry i.e horizontal line of symmetry and vertical line of symmetry. In a rhombus, the line of symmetry divides it into two equal halves and each half of the rhombus is considered as the mirror image of the other. The lines of symmetry of rhombus are drawn from its diagonals.
## Does a rhombus have reflection symmetry?
A rhombus has reflectional symmetry over either of its diagonals. Like the parallelogram, it also has rotational symmetry of 180º about its center.
## What is the smallest rotational symmetry of a rhombus?
A rhombus has rotational symmetry of 180º (Order 2). sides and 4 right angles. A square has two pairs of parallel sides.
## Does a rectangle have reflection symmetry?
A rectangle is an example of a shape with reflection symmetry. A line of reflection through the midpoints of opposite sides will always be a line of symmetry. A rectangle has two lines of symmetry. You can imagine folding the rectangle along each line of symmetry and each half of the rectangle would match up perfectly.
## Do parallelograms have reflection symmetry?
And though a parallelogram has a rotational symmetry when rotated at an angle of 1800 about its center, but has no reflection symmetry. Thus, no line can divide the parallelogram in two symmetric shapes.
## Why does a rectangle not have 4 lines of symmetry?
A line of symmetry divides a figure in half. A rectangle cannot have a diagonal line of symmetry like a square because the sides are not the same length. If you fold this rectangle diagonally so that Corner A meets Corner D, the sides would not match.
parallelogram
four right
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Answer : 416 days Explanation:Answer: D) 16 days Explanation: The analogy here is like this: Veeru has 20 lt of petrol and he uses 1 lt per each day and consumes it in 20 days. If he uses 1.25 lt every day, in how many days it will be consumed?We considered 1.25 lt here because it’s 25% more than 1 lt.The answer would be 20/1.25=16 days.
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# NIELIT 2019 Feb Scientist C - Section D: 2
715 views
Determine $a+b$ such that the following system of equations:
$2x-(a-4)y=2b+1 \text{ and }4x-(a-1)y=5b-1$ infinite solutions.
1. $11$
2. $9$
3. $10$
4. $8$
infinitely many solns, so $\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$
$\frac{2}{4}=\frac{-(a-4)}{-(a-1)}=\frac{2b+1}{5b-1}$
On solving, we get a = 7 and b = 3
So, (a+b) = 7 + 3 = 10
## Related questions
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EnchantedLearning.com is a user-supported site.
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Addition is an operation in which one number is added to another number. For example, 1 + 2 = 3 (one plus two equals three).
The additive identity is the number zero because zero plus any number is equal to the original number. For example, 2 + 0 = 0 + 2 = 2.
COMMUTATIVE PROPERTY:
Addition is commutative, that is, a + b is equal to b + a. You can change the order of the terms and not change the outcome of the operation. For example, 3 + 4 = 4 + 3 = 7.
TIPS:
When adding a series of numbers, there are some strategies that help simplify the addition process. One thing to remember is to group numbers to make tens. For example, when adding 2 + 7 + 8, you can add the 2 and the eight first to get ten, and then add the seven to get 17. Some teachers call these groups of numbers that add to ten, "friendly tens," since they make adding easier for the student.
Another tip is to look for doubles, like 4 + 4 or 6 + 6, and add them first in a long addition problem. This is done because most children learn their doubles before they learn random pairs of addends. For example, when adding 6 + 7 + 6, you can first add the two sixes to get 12, and then add the seven to get 19.
The inverse property of addition states that for every number a, a + (-a) = 0 (zero). For example, 6 + (-6) = 0.
In addition, you start on the right (the ones column). Then add each column in turn until you are done (add the ones column, the tens column, the hundreds column, etc.).
Carrying:
In a column, if the number you get after adding the column is greater than ten, you have to carry that ten's digit to the next column on the left. When you add that next column, you add in that carried digit.
Adding DecimalsEach worksheet has decimal numbers to add. Adding Decimals Path-o-Math Puzzles: 2 by 3Make a path through each number matrix so that the sum of the decimals is equal to the given answer. Use only horizontal and vertical trails. You may not have to use all the numbers, and don't use a number more than once. Puzzle #1, or the answers Puzzle #2, or the answers Puzzle #3, or the answers Puzzle #4, or the answers Puzzle #5, or the answers
File Folder Games on Adding Numbers:
Add the Numbers #1: File Folder GameThis is a simple game that can be made from a manila file folder. In this game, the student adds two one-digit numbers, and then checks the answer by opening a paper window under the math problem. This is an activity that stores easily! Add the Numbers #2: File Folder GameThis is a simple game that can be made from a manila file folder. In this game, the student adds two one-digit numbers, and then checks the answer by opening a paper window under the math problem. This is an activity that stores easily!
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# Special Relativity Spaceship Question
Lucille
## Homework Statement
bob and anna are in two space ships of proper length 100m; anna's ship passes bob's and is moving in the -x dir at v=0.75c. the front of anna's ship and the tail of bob's ship coincide at x=x'=t=t'=0. bob sits at the window in his ship and sees a clock inside anna's ship
a) what position is the window in bob's space ship
b) what time does this clock in anna's ship read
## Homework Equations
x'=gamma(x-vt)
x=gamma(x'+vt')
t'=gamma(-v/c^2*x+t)
t=gamma(v?c^2*x+t')
delta t = gamma delta to
L = Lo/gamma
## The Attempt at a Solution
a)
so if bob sees the clock at the end of anna's ship, then:
L=Lo/gamma = sqrt(1-v^2/c^2)*Lo = sqrt(1-0.75^2)*(100)=66.1m <-- position of bob's window in his space ship (distance from the end of his spaceship to the window)
b)
i tried :
x=100m
v=0.75c
t'=x'/v = 4.45 * 10^-7 s
But I'm not sure if this is correct...
## Answers and Replies
Mentor
One thing that isn't clear: Bob is situated at the front of his space ship?
Chet
Lucille
The question doesn't state that. It's asking where the window is - I'm guessing that's the point at which he can see Anna's clock, and her window is at the end of her spaceship.
Mentor
The question doesn't state that. It's asking where the window is - I'm guessing that's the point at which he can see Anna's clock, and her window is at the end of her spaceship.
So, under this interpretation, you are looking at the event at which x' = L0 and t = 0. In part a, you showed that ##x=L_0/\gamma##. Now all you need to do is substitute this into the equation for t'.
Chet
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https://www.physicsforums.com/threads/work-done-by-kinetic-friction-force-without-coefficient.775097/
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# Work done by kinetic friction force without coefficient?
Tags:
1. Oct 8, 2014
### Jessica Sweet
1. The problem statement, all variables and given/known data
A person pulls a box (m=10 kg) horizontally with +2m/s2 acceleration by applying 45 N force. The displacement of the box is 8 meters from initial position.
a) How much work is done by applied force?
b) How much work is done by kinetic frictional force?
2. Relevant equations
Wf = Fcosθs
F=ma
Wfk = -Fks ???
Fk = μN ???
3. The attempt at a solution
I solved for part a, which was 360J.
I don't know how to solve for part b, which it seems like I would need the friction coefficient?
I tried Wfk = -(10)(2)(8) = -160 J, but that is incorrect.
How do I find Fk to solve for the work done by friction?
Last edited: Oct 8, 2014
2. Oct 8, 2014
### jack action
Answer this question: How much of the applied force is used to accelerate the box?
3. Oct 8, 2014
### Jessica Sweet
Um, 45 N of force was applied to it. Would force of kinetic friction be -45 N then? Or am I just getting myself confused?
4. Oct 8, 2014
### Entanglement
Jack has a point.
Yes, you applied 45 N,
but apparently that's not the force used to accelerate the box since its mass is 10 Kg and its accelerations is 2 m / s / s. The net force is what you should be looking at. Rethink. :):)
Last edited: Oct 8, 2014
5. Oct 8, 2014
### jack action
$$\sum F = ma$$
$$F_{total} - F_{friction} = ma$$
6. Oct 8, 2014
### nasu
Write Newton's second law for the box.
7. Oct 8, 2014
### Jessica Sweet
Alright, so Ftotal = 45 N, I am looking for frictional force, and ma = 20.
45-Ffk = 20
Ffk=25
Then I have Wfk = -(25)(8) = -200 J?
8. Oct 8, 2014
### jack action
Look again at your OP and you already found 360 J and 160 J. How does your 200 J fits in there?
Just for the fun of it, can you find the coefficient of friction?
9. Oct 8, 2014
### Jessica Sweet
Are you saying I could have subtracted the 160 from 360? What value does the 160 J represent that I solved for? Gosh, I feel stupid.
10. Oct 8, 2014
### Jessica Sweet
Never mind, I got it all covered. My brain is working again. It's amazing what stress can do to the brain. Thanks for the help everybody.
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Project Euler: Coding to Solve Maths Problems
Project Euler, named after one of the greatest mathematicians of all time, has been designed to bring together the twin disciplines of mathematics and coding. Computers are now become ever more integral in the field of mathematics – and now creative coding can be a method of solving mathematics problems just as much as creative mathematics has always been.
The first problem on the Project Euler Page is as follows:
If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.
Find the sum of all the multiples of 3 or 5 below 1000.
This is a reasonably straight forward maths problem which we can solve using the summation of arithmetic sequences (I’ll solve it below!) but more interestingly is how a computer code can be written to solve this same problem. Given that I am something of a coding novice, I went to the Project Nayuki website which has an archive of solutions. Here is a slightly modified version of the solution given on Project Nayki, designed to run in JAVA:
The original file can be copied from here, I then pasted this into an online JAVA site jdoodle. The only modification necessary was to replace:
public final class p001 implements EulerSolution with public class p001
Then after hitting execute you get the following result:
i.e the solution is returned as 233,168. Amazing!
But before we get carried away, let’s check the answer using some more old fashioned maths. We can break down the question into simply trying to find the sum of multiples of 3 under 1000, the sum of the multiples of 5 under 1000 and then subtracting the multiples of 15 under 1000 (as these will have been double counted). i.e:
(3 + 6 + 9 + … 999) + (5 + 10 + 15 + … 995) – (15 + 30 + 45 + …990)
This gives:
S_333 = 333/2 (2(3)+ 332(3)) = 166,833
+
S_199 = 199/2 (2(5) + 198(5)) = 99, 500
S_66 = 66/2 (2(15) +65(15) = 33, 165.
166,833 + 99, 500 – 33, 165 = 233, 168 as required.
Now that we have seen that this works we can modify the original code. For example if we replace:
if (i % 3 == 0 || i % 3 == 0)
with
if (i % 5 == 0 || i % 7 == 0)
This will find the sum of all the multiples of 5 or 7 below 1000. Which returns the answer 156,361.
Replacing the same line with:
if (i % 5 == 0 || i % 7 == 0 || i % 3 == 0)
will find the sum of all the multiples of 3 or 5 or 7 below 1000, which returns the answer 271,066. To find this using the previous method we would have to do:
Sum of 3s + Sum of 5s – Sum of 15s + Sum of 7s – Sum of 21s – Sum 35s – Sum of 105s. Which starts to show why using a computer makes life easier.
This would be a nice addition to any investigation on Number Theory – or indeed a good project for anyone interested in Computer Science as a possible future career.
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https://astronomy.stackexchange.com/questions/12477/are-objects-in-the-universe-moving-away-from-each-other-at-the-same-acceleration/12564#12564
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# Are objects in the universe moving away from each other at the same acceleration?
This is a follow up question to Does the universe expand at the same rate everywhere in the universe?.
If the universe is expanding, then it would seem necessary for each object (ie galaxy) to be accelerating away from every other object at the same rate of acceleration which is constant (or not?). If that is true, what is the acceleration?
In other words, relative to the Milky Way, does it seem that all the other galaxies are moving directly away from us at the same rate of acceleration? If so, is it possible for us to prove that for any other galaxy that we know, the same observation would be true, were we able to view the universe from that galaxy?
• Note that this acceleration applies to objects that are not gravitationally bound: superclusters of galaxies. Two neighbor galaxies don't yield to space expansion because they are gravitationally bound to each other; they may move in relation to each other, including moving apart, even accelerating due to some other galaxies, but they are not accelerating due to space expansion. Two superclusters of galaxies do though.
– SF.
Nov 20 '15 at 10:08
• I highly recommend you look at hubble's law, Edwin Hubble was the scientist who first discovered that the universe was expanding, he also defined a constant and equation to prove it. en.wikipedia.org/wiki/Hubble%27s_law Nov 26 '15 at 19:09
I assume you mean is $\frac{dv}{dt}$ the same for all objects and/or is it constant for all objects, where $v$ is recessional velocity (and $t$ is cosmic time)? The answer is no it is not the same for all objects and it is not constant for all objects.
$$v=\frac{dD}{dt}=H(t)D$$
Where $D$ is proper distance and $H(t)$ is the Hubble parameter. If we take the Hubble parameter as a constant, then:
$$D = D_0e^{Ht}$$
Where $D_0$ is the proper distance at the present time. So,
$$D''(t) = \frac{dv}{dt} = D_0H^2e^{Ht}$$
So the "recessional acceleration" of an object depends on its present proper distance and is exponentially increasing with time.
Now the Hubble parameter isn't a constant and in LCDM cosmology is currently asymptotically decreasing to a constant. In the current epoch though it is fair to say that the "recessional acceleration" of an object depends on its proper distance and is increasing with time.
• So the farther from the Milky Way the object is, the faster its acceleration away from us is increasing? Is there a term for acceleration of accleration? Nov 11 '15 at 6:59
• Yes, "recessional acceleration" increases with distance. Do you mean is there a name for the first time derivative of acceleration? If so that is sometimes called "jerk", the first time derivative of jerk is sometimes called "jounce". Nov 11 '15 at 19:06
• jerk and jounce. got it. Nov 11 '15 at 19:15
Here's a non-mathematical answer. Something you can think about in your head. The further away a galaxy is from us the faster it will move away from us. There is no exact way to measure the exact speed because the distance is phenomenal, however, we can use red-shift to work out that this is actually happening. A way to prove that this happens is to get a balloon and draw dots on it. Blow it up a little bit, maybe half way. Focus on one dot and blow it up even more. You will notice that the other dots move away from the one you focus on faster than the dot you are looking at. This is a good way of explaining what is actually happening in the universe - and why things further away from us move away faster.
This applies to whatever galaxy we are in. If we were in the andromeda galaxy, we would still experience every other galaxy moving away from us faster.
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# Is there any difference between radial distribution function and pair correlation function?
I have understood the part that for solids pair correlation function is the measure of the probability of finding the center of another particle in the neighborhood of a given particle. On the other hand radial distribution function also determines the periodicity in a system. If we plot g(r) for pair correlation function we eventually get the same pattern for the radial distribution in solids.
I want to know if my understanding for these two are correct and if there is some fundamental difference.
The function $g(\mathbf{r})$, or more properly $h(\mathbf{r})=g(\mathbf{r})-1$ which tends to zero at large separation, is usually termed the pair correlation function. Only when the system is isotropic, such as a liquid, do we usually refer to $g(r)$ as the radial distribution function, since it depends only on the magnitude, not the direction, of the separation vector: $r=|\mathbf{r}|$.
You can find the full definitions in books such as Chaikin and Lubensky, Principles of condensed matter physics. I'll just give a short summary here. The general definition of $g$ takes into account its dependence on both of the positions under consideration. If the instantaneous number density of $N$ atoms is written as a sum of 3D Dirac delta functions of the atomic positions $$n(\mathbf{r}) = \sum_{i=1}^N \delta(\mathbf{r}-\mathbf{r}_i)$$ then the pair correlation function $g(\mathbf{r}_1,\mathbf{r}_2)$ is defined such that $$\langle n(\mathbf{r}_1) \rangle \langle n(\mathbf{r}_2) \rangle \, g(\mathbf{r}_1,\mathbf{r}_2) = \langle n(\mathbf{r}_1) n(\mathbf{r}_2) \rangle - \langle n(\mathbf{r}_1)\rangle \delta(\mathbf{r}_1-\mathbf{r}_2)$$ This has the interpretation that $g(\mathbf{r}_1,\mathbf{r}_2)$ is the probability density (per unit volume), given an atom at $\mathbf{r}_1$ of finding a different atom at $\mathbf{r}_2$, normalized by the number density in both places. Going from this to the radial distribution function involves two stages. Firstly, when the system is homogeneous and translationally invariant, one can express $g$ as a function of the difference in position vectors, $g(\mathbf{r}_1-\mathbf{r}_2)\equiv g(\mathbf{r})$. In this case, $\langle n(\mathbf{r})\rangle=\langle n\rangle$, independent of $\mathbf{r}$. We may integrate over one of the coordinates, and the result may be expressed $$\langle n \rangle \, g(\mathbf{r}) = \left\langle \sum_{i\neq 1}^N \delta(\mathbf{r}-\mathbf{r}_i+\mathbf{r}_1) \right\rangle$$ The probabilistic interpretation is even clearer here: both sides represent the density of (other) atoms per unit volume, at a position $\mathbf{r}$ relative to atom $1$, given that the latter is at $\mathbf{r}_1$.
Secondly, when the system is, additionally, isotropic, one can express $g$ as a function of the separation distance $g(r)$, where $r=|\mathbf{r}|$, and this is what we call the radial distribution function.
| 794 | 2,971 |
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http://nrich.maths.org/5815
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### Plum Tree
Label this plum tree graph to make it totally magic!
### Magic W
Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.
### 2-digit Square
A 2-Digit number is squared. When this 2-digit number is reversed and squared, the difference between the squares is also a square. What is the 2-digit number?
# Interactive Number Patterns
##### Stage: 4 Challenge Level:
This problem involves making a connection between the pattern in a sequence of numbers and the algebra that expresses the general term.
There are two parts to the problem and each has an Excel-based interactivity.
You can right-click and save to get your own copy of each resource: Interactive Number Patterns 1 and Interactive Number Patterns 2
Open the spreadsheet called Interactive Number Patterns 1 and experiment with the control buttons. You should discover that the red and blue numbers in the boxes, and also the algebra, can be made to show or not show. You should also discover that the numbers and the algebra can be changed.
Adjust the view size if necessary using Zoom on the View drop-down menu.
Challenge One has three stages :
• Hide the blue numbers in the boxes, change the algebra and the red numbers and check you can successfully predict the hidden blue values.
• Next hide the red numbers instead and repeat the challenge. Explain to a friend how you manage this. You could even work in pairs to set challenges for each other.
• Finally hide the algebra. Change it without showing it, then predict the formula. You have succeeded with this task when you can explain your method to someone else.
Challenge Two is similar but harder. Open the spreadsheet called Interactive Number Patterns 2. This interactivity works in the same way but now the algebra is quadratic :
• Predict the hidden blue
• Predict the hidden red, explaining your method
• Predict the hidden algebra, again explaining your method and especially why it works
The overall aim of this activity is to understand why our methods work - never be content to just remember a method.
And the "solutions" we would love to receive from you are your best ways of justifying this important method.
Even when we cannot immediately explain why a method is valid it is good to keep it in mind as something we very much want to know.
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| 3.9375 | 4 |
CC-MAIN-2017-22
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longest
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| 0.890323 |
http://www.chegg.com/homework-help/questions-and-answers/chem-problem-chegg-would-let-pot-without-tagging-class-phy-317k-wouldn-t-show-part-1-017-p-q2392721
| 1,464,370,313,000,000,000 |
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| 420,981,599 | 13,827 |
THIS IS NOT A CHEM PROBLEM BUT CHEGG WOULD NOT LET ME POT WITHOUT TAGGING A CLASS AND PHY 317K WOULDN'T SHOW UP
PART 1
017 (part 1 of 3) 5.0 points
A siren at rest has a frequency f0. Standing
at a crosswalk, a student hears a frequency f' from the siren in an approaching police car.
After the car passes, the observed frequency is f ''. Let the speed of the siren (or the car)
be vc, and the speed of sound be vs.What is the wavelength of the sound when
the siren is at rest?
1.
vc/f''
2.
vs/f''
3.
vs/f'
4.
vc/f'
5.
vc/(f' + f'')
6.
vs/(f' + f'')
7.
vs/f0
8.
vc/f0
(part 2 of 3)
If x =vc/vs, what is the frequency f''
heard by the student when the car is moving away?
1.
f0 *(1 + x)
2.
f0 *(1 - x)/(1 + x)
3.
f0
4.
f0/(1 - x)
5.
f0 *(1 - x)
6.
f0/(1 + x)
7.
f0(1 + x)/(1 - x)
8.
f0*x
(part 3 of 3)
If f'and f''are 600 Hz and 400 Hz, respectively, and the speed of sound in air is 340 m/s,
| 332 | 892 |
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| 3.546875 | 4 |
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latest
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| 0.820621 |
http://mathhelpforum.com/differential-equations/189610-verify-solution-print.html
| 1,524,174,129,000,000,000 |
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| 217,653,456 | 2,829 |
# Verify Solution
• Oct 5th 2011, 05:57 AM
moonnightingale
Verify Solution
the book says
Determine for which values of m the function
y=exp(mx) is solution of differential equation
y'' + 6y' + 5y=0
Plz help me
• Oct 5th 2011, 06:31 AM
Soroban
Re: Can u helpmefor this question of differential equations
Hello, moonnightingale!
Quote:
$\displaystyle \text{Determine for which values of }m\text{ the function }y\,=\,e^{mx}$
. . $\displaystyle \text{is solution of differential equation: }\;y'' + 6y' + 5y\:=\:0$
In effect, you are given a differential equation and an answer.
You don't know how to do that?
Differentiate: .$\displaystyle \begin{Bmatrix} y &=& e^{mx} \\ y' &=& me^{mx} \\ y'' &=& m^2e^{mx} \end{Bmatrix}$
Substitute into the differential equation:
. . $\displaystyle m^2e^{mx} + 6me^{mx} + 5e^{mx} \:=\:0$
Divide by $\displaystyle e^{mx}\!:$
. . $\displaystyle m^2 + 6m + 5 \:=\:0$
Can you finish it now?
• Oct 5th 2011, 07:43 AM
HallsofIvy
Re: Can u helpmefor this question of differential equations
It is important to note that $\displaystyle e^{mx}$ is never 0 so you can divide by it.
| 383 | 1,114 |
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| 3.859375 | 4 |
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https://metanumbers.com/13230780
| 1,600,788,176,000,000,000 |
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| 527,438,498 | 7,648 |
## 13230780
13,230,780 (thirteen million two hundred thirty thousand seven hundred eighty) is an even eight-digits composite number following 13230779 and preceding 13230781. In scientific notation, it is written as 1.323078 × 107. The sum of its digits is 24. It has a total of 5 prime factors and 24 positive divisors. There are 3,528,192 positive integers (up to 13230780) that are relatively prime to 13230780.
## Basic properties
• Is Prime? No
• Number parity Even
• Number length 8
• Sum of Digits 24
• Digital Root 6
## Name
Short name 13 million 230 thousand 780 thirteen million two hundred thirty thousand seven hundred eighty
## Notation
Scientific notation 1.323078 × 107 13.23078 × 106
## Prime Factorization of 13230780
Prime Factorization 22 × 3 × 5 × 220513
Composite number
Distinct Factors Total Factors Radical ω(n) 4 Total number of distinct prime factors Ω(n) 5 Total number of prime factors rad(n) 6615390 Product of the distinct prime numbers λ(n) -1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) 0 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 0 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0
The prime factorization of 13,230,780 is 22 × 3 × 5 × 220513. Since it has a total of 5 prime factors, 13,230,780 is a composite number.
## Divisors of 13230780
24 divisors
Even divisors 16 8 4 4
Total Divisors Sum of Divisors Aliquot Sum τ(n) 24 Total number of the positive divisors of n σ(n) 3.70464e+07 Sum of all the positive divisors of n s(n) 2.38156e+07 Sum of the proper positive divisors of n A(n) 1.5436e+06 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 3637.41 Returns the nth root of the product of n divisors H(n) 8.57139 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors
The number 13,230,780 can be divided by 24 positive divisors (out of which 16 are even, and 8 are odd). The sum of these divisors (counting 13,230,780) is 37,046,352, the average is 1,543,598.
## Other Arithmetic Functions (n = 13230780)
1 φ(n) n
Euler Totient Carmichael Lambda Prime Pi φ(n) 3528192 Total number of positive integers not greater than n that are coprime to n λ(n) 220512 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 861814 Total number of primes less than or equal to n r2(n) 0 The number of ways n can be represented as the sum of 2 squares
There are 3,528,192 positive integers (less than 13,230,780) that are coprime with 13,230,780. And there are approximately 861,814 prime numbers less than or equal to 13,230,780.
## Divisibility of 13230780
m n mod m 2 3 4 5 6 7 8 9 0 0 0 0 0 3 4 6
The number 13,230,780 is divisible by 2, 3, 4, 5 and 6.
• Arithmetic
• Abundant
• Polite
## Base conversion (13230780)
Base System Value
2 Binary 110010011110001010111100
3 Ternary 220220012012220
4 Quaternary 302132022330
5 Quinary 11341341110
6 Senary 1151325340
8 Octal 62361274
10 Decimal 13230780
12 Duodecimal 4520850
20 Vigesimal 42dgj0
36 Base36 7vkxo
## Basic calculations (n = 13230780)
### Multiplication
n×i
n×2 26461560 39692340 52923120 66153900
### Division
ni
n⁄2 6.61539e+06 4.41026e+06 3.3077e+06 2.64616e+06
### Exponentiation
ni
n2 175053539408400 2316094868133870552000 30643741659408251821990560000 405440604272465510041356261436800000
### Nth Root
i√n
2√n 3637.41 236.517 60.311 26.5654
## 13230780 as geometric shapes
### Circle
Diameter 2.64616e+07 8.31314e+07 5.49947e+14
### Sphere
Volume 9.70164e+21 2.19979e+15 8.31314e+07
### Square
Length = n
Perimeter 5.29231e+07 1.75054e+14 1.87111e+07
### Cube
Length = n
Surface area 1.05032e+15 2.31609e+21 2.29164e+07
### Equilateral Triangle
Length = n
Perimeter 3.96923e+07 7.58004e+13 1.14582e+07
### Triangular Pyramid
Length = n
Surface area 3.03202e+14 2.72954e+20 1.08029e+07
| 1,391 | 4,032 |
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| 3.515625 | 4 |
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https://metanumbers.com/159477
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| 395,236,838 | 7,454 |
# 159477 (number)
159,477 (one hundred fifty-nine thousand four hundred seventy-seven) is an odd six-digits composite number following 159476 and preceding 159478. In scientific notation, it is written as 1.59477 × 105. The sum of its digits is 33. It has a total of 4 prime factors and 16 positive divisors. There are 96,512 positive integers (up to 159477) that are relatively prime to 159477.
## Basic properties
• Is Prime? No
• Number parity Odd
• Number length 6
• Sum of Digits 33
• Digital Root 6
## Name
Short name 159 thousand 477 one hundred fifty-nine thousand four hundred seventy-seven
## Notation
Scientific notation 1.59477 × 105 159.477 × 103
## Prime Factorization of 159477
Prime Factorization 3 × 17 × 53 × 59
Composite number
Distinct Factors Total Factors Radical ω(n) 4 Total number of distinct prime factors Ω(n) 4 Total number of prime factors rad(n) 159477 Product of the distinct prime numbers λ(n) 1 Returns the parity of Ω(n), such that λ(n) = (-1)Ω(n) μ(n) 1 Returns: 1, if n has an even number of prime factors (and is square free) −1, if n has an odd number of prime factors (and is square free) 0, if n has a squared prime factor Λ(n) 0 Returns log(p) if n is a power pk of any prime p (for any k >= 1), else returns 0
The prime factorization of 159,477 is 3 × 17 × 53 × 59. Since it has a total of 4 prime factors, 159,477 is a composite number.
## Divisors of 159477
16 divisors
Even divisors 0 16 8 8
Total Divisors Sum of Divisors Aliquot Sum τ(n) 16 Total number of the positive divisors of n σ(n) 233280 Sum of all the positive divisors of n s(n) 73803 Sum of the proper positive divisors of n A(n) 14580 Returns the sum of divisors (σ(n)) divided by the total number of divisors (τ(n)) G(n) 399.346 Returns the nth root of the product of n divisors H(n) 10.9381 Returns the total number of divisors (τ(n)) divided by the sum of the reciprocal of each divisors
The number 159,477 can be divided by 16 positive divisors (out of which 0 are even, and 16 are odd). The sum of these divisors (counting 159,477) is 233,280, the average is 14,580.
## Other Arithmetic Functions (n = 159477)
1 φ(n) n
Euler Totient Carmichael Lambda Prime Pi φ(n) 96512 Total number of positive integers not greater than n that are coprime to n λ(n) 6032 Smallest positive number such that aλ(n) ≡ 1 (mod n) for all a coprime to n π(n) ≈ 14599 Total number of primes less than or equal to n r2(n) 0 The number of ways n can be represented as the sum of 2 squares
There are 96,512 positive integers (less than 159,477) that are coprime with 159,477. And there are approximately 14,599 prime numbers less than or equal to 159,477.
## Divisibility of 159477
m n mod m 2 3 4 5 6 7 8 9 1 0 1 2 3 3 5 6
The number 159,477 is divisible by 3.
## Classification of 159477
• Arithmetic
• Deficient
• Polite
• Square Free
### Other numbers
• LucasCarmichael
## Base conversion (159477)
Base System Value
2 Binary 100110111011110101
3 Ternary 22002202120
4 Quaternary 212323311
5 Quinary 20100402
6 Senary 3230153
8 Octal 467365
10 Decimal 159477
12 Duodecimal 78359
20 Vigesimal jidh
36 Base36 3f1x
## Basic calculations (n = 159477)
### Multiplication
n×y
n×2 318954 478431 637908 797385
### Division
n÷y
n÷2 79738.5 53159 39869.2 31895.4
### Exponentiation
ny
n2 25432913529 4055964750864333 646833090573591233841 103155000785404609199261157
### Nth Root
y√n
2√n 399.346 54.2291 19.9836 10.9784
## 159477 as geometric shapes
### Circle
Diameter 318954 1.00202e+06 7.98999e+10
### Sphere
Volume 1.69896e+16 3.19599e+11 1.00202e+06
### Square
Length = n
Perimeter 637908 2.54329e+10 225535
### Cube
Length = n
Surface area 1.52597e+11 4.05596e+15 276222
### Equilateral Triangle
Length = n
Perimeter 478431 1.10128e+10 138111
### Triangular Pyramid
Length = n
Surface area 4.40511e+10 4.78e+14 130212
## Cryptographic Hash Functions
md5 ca6bff62f4e46cbb192152ec843ebdbf 3d76d1908fbe1e0b904fc6069de58a7f29b3fe1d e224f62654fd13b9f67d6a91fa8386789e81ab51c08e6a3cecf2d75cae29a9f7 b0475ba1015ec63ef0c60cbc73b2a5011681e4670ff49485faeddc96e3caf78aac1143e492d7d3bc29ae51e3a38908cb2c31b81544aaa63cd8752cc2e7f0f0d9 8891b7811700ea342dcea64992c43710704d8fed
| 1,454 | 4,214 |
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| 3.71875 | 4 |
CC-MAIN-2022-05
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| 0.803487 |
https://www.jiskha.com/questions/109382/do-you-know-how-to-pronounce-the-f-sound-the-f-sound-is-a-a-labiodental-you-should-put
| 1,643,368,468,000,000,000 |
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| 860,324,804 | 5,350 |
# English
Do you know how to pronounce the f sound. The f sound is a a labiodental. You should put your lower lip and upper teeth together. Then make air pass between them, saying f.
The p sound is a labiodental. You should put your lips together and make the air pass through your lips, saying p. In Korea, people have difficulty in pronouncing the f sound, for we do not have such a sound. So you have to practice how to say the f sound. Look at the picture cards. Let's practice together. Repeat after me.
-------------------
I have made directions for students about how to make the f and p sounds. Would you chek them, plese. If you have better expressions, add them, please.
1. 👍
2. 👎
3. 👁
1. It all sounds fine.
=)
1. 👍
2. 👎
👤
Writeacher
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3. ### Physics
Organ pipes, open at one end, resonate best at their first resonant length. Two pipes have length 23.0 cm and 30.0 cm respectively. What is the wavelength of the sound emitted by each pipe? What are the respective frequencies if
4. ### physics
determine the following distances based on the sonar data given. a ship sends a sound pulse downward and receives the reflected sound 2.50 s later. use the formula d=vt. assume the speed of sound in sea water is 1540 m/s
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Displacement During Uniform Acceleration
Evaluate velocity vs time graphs and calculate displacement over time for objects under uniform acceleration
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Falling From Space
Falling From Space
Credit: U.S. Air Force
Source: commons.wikimedia.org/wiki/File:Kittinger-jump.jpg
In 1960, Capt. Joseph Kittinger stepped off the Excelsior platform, 31 kilometers above the surface of the Earth. He fell for approximately 4 minutes and 36 seconds and reached a maximum speed of 614 miles per hour!
Why It Matters
• Any object that is dropped near the surface of the earth will accelerate towards the earth. If you were to ignore the effects due to air resistance, every dropped object would fall and accelerate at the same rate. This is known as the acceleration due to gravity and any object falling at such a rate is said to be in free fall. By looking at Newton?s 2nd law, the weight of an object is defined by the following equation:
W=mg\begin{align*}\overrightarrow{W}=m \overrightarrow{g}\end{align*}
• The acceleration due to gravity, a fundamental concept of classical physics, only acts along the axis which is perpendicular to the surface of the earth. When looking at real-world applications of two-dimensional motion, torque, and even work, the concept of free fall and the acceleration due to gravity must be taken into consideration.
Credit: Carla MacNeil
Source: http://www.flickr.com/photos/9363874@N07/1039697905
A bungee jumper accelerates towards earth [Figure2]
Can You Apply It?
Using the information provided above, answer the following questions.
1. Why is it okay to ignore air resistance for objects under the influence of gravity for small distance but not large distances?
2. Explain why it is important to consider the acceleration due to gravity of an object that is thrown across a room when you are trying to determine the distance the object will travel.
3. If one were to consider air resistance on an object that is falling, would the velocity of the object be faster or slower when compared to an object that is falling without air resistance?
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# Real analysis question
1. May 22, 2013
### woundedtiger4
Hi all,
I am trying to understand this basic proof but I don't understand that where the equations (3) & (4) have come from?
[img=http://s9.postimg.org/8nwoy04vj/image.jpg]
p.s. sorry if I have posted this thread on wrong website.
2. May 22, 2013
### Fredrik
Staff Emeritus
Here's a link that works. http://s9.postimg.org/8nwoy04vj/image.jpg
(3) is a definition, and (4) is a simple consequence of (3). The reason why the definition (3) and the rewrite (4) are made is that they give us an easy way to prove the theorem. You probably understand all this, so I assume that what you're wondering about is how a person can come up with the idea to define q that way?
I don't know the answer to that. Maybe there's a simple motivation for it, but it's also possible that the person who came up with this just spent a week trying out different ideas and finally found one that works.
3. May 22, 2013
### Hypersphere
When it comes to the form of (3), I suppose it's just a clever choice, such that q gets the properties we want. However, we know that p^2<2 and p^2>2 give distinct cases, so a factor of p^2-2 somewhere in the expression is to be expected. Similarly, the term linear in p is suggested by the different p<q and p>q behaviours (it can be rewritten as q-p, after all). I don't have any argument for the scaling by 1/(p+2) though.
4. May 22, 2013
### micromass
Staff Emeritus
Here is some kind of way to find such things for yourself. Maybe it is what you want.
Basically, given a number x, you want to find a number f(x) (here, this will turn out to be $-\frac{x^2 - 2}{x+2}$ such that the following hold:
1) $x + f(x) < \sqrt{2}$ if $x< \sqrt{2}$.
2) If $x$ is rational, then $f(x)$ is rational.
3) $f(x)\geq 0$
Of course, there are many such functions, so let's try to identify such function. First, let's try to work with rational functions of the form
$$\frac{x + a}{ex + d}$$
If $(2)$ must be satisfied, then we will want $a$ and $b$ to be rational. If they are rational, then we have $(2)$ (this is the reason we pick a rational function).
The function is continuous and satisfies $x+ f(x)<\sqrt{2}$ for all $x<\sqrt{2}$. Thus we will have that $\sqrt{2} + f(\sqrt{2}) \leq \sqrt{2}$. Thus we must have that $f(\sqrt{2}) \leq 0$. It seems like a reasonable demand to ask for equality here. So we demand
4) $f(\sqrt{2}) = 0$
Now, if we pick a function of the form $\frac{x + a}{x + c}$ then this would satisfy $(4)$ only for $a=\sqrt{2}$. This is not a rational value, so we have a problem. So a function of this form will not work. Let's try to work with the next thing and work with functions
$$\frac{ax^2 + bx + c}{ex + d}$$
We want $\sqrt{2}$ to be a root, so it seems rather reasonable to ask that $x^2 - 2$ is the polynomial in the numerator. So we have the following function
$$\frac{x^2 - 2}{ex+d}$$
Now we must find $e$ and $d$ such that the other two conditions are satisfied. We want $x + f(x) - \sqrt{2} < 0$ if $x<\sqrt{2}$ and we have that $x + f(x) - \sqrt{2} = 0$ if $x = \sqrt{2}$. Now, if we could show that the function $g(x) = x + f(x) - \sqrt{2}$ is increasing, then the condition $(2)$ will be satisfied.
So we ask when $g$ would be increasing. We take the derivative and we get that $g^\prime(x)>0$ if and only if $f^\prime(x) > -1$
Now, if we could also get $f$ itself to be decreasing, then $f(\sqrt{2}) = 0$ would imply that $f(x)>0$ for $x<\sqrt{2}$. So condition $(3)$ would be satisfied. So we demand that $f^\prime(x) < 0$
If we work with the previous form we determined then we get that
$$0 > f^\prime(x) > -1$$
if and only if
$$0 > \frac{2x(ex + d) - e(x^2 - 2) }{(ex + d)^2}> -1$$
or
$$- (ex + d)^2 < x^2 e + 2xd + 2e < 0$$
We see from the above form that the problem will simplify if we take $e = -1$. So we get that
$$- (d - x)^2 < -x^2 + 2xd -2 < 0$$
and thus
$$- d^2 < -2 ~\text{and} ~x^2 + 2 > 2xd$$
The first condition will be true if $d^2$ is large enough. For example, for $d^2 = 4$. The last condition is true if $d$ is negative. So choosing $d= -2$ will satisfy all requirements.
5. May 22, 2013
### woundedtiger4
Many Thanks.
exactly, it is my question.
ok, is it possible for you to share something similar to (3)? if not then it's completely OK.
in the picture after equation (4) it says that "if p is in A then p^2 - 2 < 0 "WHY? ". how does (3) shows that q > p and (4) shows that q^2<2, finally q is in A.
for example, lets say that A={5} then here I can only see "p" where is q? I mean in the definition it says that for every p in A we can find rational q in A such that p<q OR should I consider a set with more than one p for example A={1,2,3,4,5} ?
Sorry if you find my question silly.
6. May 22, 2013
### Hypersphere
Well, the text says that "A is the set of ALL positive rationals p such that p^2<2". So a) p in A implies p^2-2<0 by definition and b) you can't say A={5} or something similar.
7. May 22, 2013
### woundedtiger4
Sir, thank you very much. I am relieved :)
In pic it says that "the purpose of the above discussion has been to show that rational numbers has certain gaps.........." what gaps?
8. May 22, 2013
### Useful nucleus
The gaps are the irrationals. Rudin showed that set A, for example, although bounded above, it does not have a least uper bound (which we know intuitively is √2). Reals will fill these gaps.
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## Algebra 2 (1st Edition)
$y=-\frac{2}{3}x-1$
Equation for a line defined by a point and slope is $y-y_{1}=m(x-x_{1})$ in which $m$ is the slope, and $x_{1}$ and $y_{1}$ are the coordinates of a given point, so therefore... $y-(-1)=-\frac{2}{3}(x-0)$ $y=-\frac{2}{3}x-1$
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If a triangle has a height of 12 inches and a base of 5 inches, what's its area? A. 60 sq. in. B. 45 sq. in. C. 90 sq. in. D. 30 sq. in.
Question
Updated 3/23/2020 3:34:38 AM
s
Original conversation
User: If a triangle has a height of 12 inches and a base of 5 inches, what's its area? A. 60 sq. in. B. 45 sq. in. C. 90 sq. in. D. 30 sq. in.
Weegy: If a triangle has a height of 12 inches and a base of 5 inches, its area is 30 square inches. Solution: Triangle Area = 1/2 x b x h = 1/2 x 5 x 12 = 30 square inches.
User: What is the radius of a circle with an area of 32.1 square feet? A. 5.23 ft. B. 10.22 ft. C. 3.20 ft. D. 4.75 ft.
Question
Updated 3/23/2020 3:34:38 AM
Rating
8
The radius of a circle with an area of 32.1 square feet is: 3.20 ft.
Solution:
A = pi * r^2
r = sqr(A/pi)
r = sqr(32.1/3.14)
r = 3.20 (rounded)
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# Factor Theroem
• Feb 13th 2007, 03:54 PM
ty2391
Factor Theroem
Just a quick question about a questoin relating to factor theorem:
Find the value of k so that when http://img250.imageshack.us/img250/6594/untitledfb5.jpg is divided by x + k, the remainder is 3.
Thanks! :)
• Feb 13th 2007, 04:10 PM
ThePerfectHacker
Quote:
Originally Posted by ty2391
Just a quick question about a questoin relating to factor theorem:
Find the value of k so that when http://img250.imageshack.us/img250/6594/untitledfb5.jpg is divided by x + k, the remainder is 3.
Thanks! :)
The division algorithm says we can find the quotient and remainder:
x^3+5x^2+6x+11 = q(x)(x+k)+3
Since these are equal, their evaluations are equal as well.
Let us evaluate this at x=-k.
Thus,
(-k)^3+5(-k)^2+6(-k)+11=q(-k)(0)+3
-k^3+5k-6k+11=3
k^3-5k+6k-8=0
Use the rational root theorem and see that k=4 is a solution. (In fact the only one).
Thus, k=4.
• Feb 13th 2007, 07:37 PM
Soroban
Hello, ty2391!
Quote:
Find the value of k so that when x³ + 5x² + 6x + 11 is divided by x + k, the remainder is 3.
I used the Remainder Theorem:
. . If f(a) = r, then f(x) ÷ (x - a) has a remainder of r.
We want to find a so that f(a) = 3.
If a is nonpositive, we can see that f(a) > 11.
. . Hence, a must be negative.
We find that: . f(-1) .= .9
. . . . . . . . . . .f(-2) .= .11
. . . . . . . . . . .f(-3) .= .13
. . . . . . . . . . .f(-4) .= . 3 . ← There!
Therefore: .k = 4
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Check
(x³ + 5x² + 6x + 11) ÷ (x + 4) . = . x² + x + 2, .remainder 3
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# 7+ Exams & Entry
## What is the 7+?
The 7+ entrance & exam procedure is for entry into independent prep schools into Year 3. This means the child will sit the exam in Year 2 typically in January although schools vary in their timings. So, at this young age it does matter in which month your child was born, which is generally taken into consideration by most schools.
## How is Maths tested in the 7+
Maths for the 7+ is typically assessed with a beyond-year-2 paper targeting mental maths skills which can involve decoding – i.e. where the child is required to decode numbers and the required operation from plain English text.
## Which other subjects are tested in the 7+?
English and Reasoning are important factors in the 7+ and will be assessed. Success here will require a good vocabulary, spelling and ability to write coherent sentences with an overarching meaning.
## How can I best prepare my child for the 7+?
Try using a number of sources including repetitive problem solving in Maths and English. It is more effective for a child to practice for 20 mins a day than for an hour at the weekend.
## 7+ Example Maths questions
19 – 6 = ___
16 + 21 = ___
20 ÷ 5 = ___
___ x 3 = 12
___ + 7 = 23
A packet of sweets cost 20p. How much would it cost to buy seven packs of sweets? ___
John has £24 and spends £11. How much money does he have left? ___
Write “six hundred and thirty one” in numbers ___
500 + ___ + 4 = 504
What is the next number in the sequence 14, 18, 22, 26, ___
How many faces does a cube have? ___
How many corners does a cube have? ___
The time now is 7:55. What will the time be twenty minutes from now? ___
## Key Stage Maths 7+ Practice
We shall soon be publishing a Maths 7+ practice book. Please subscribe to be notified and to receive a discount.
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# Seasonal Systems Of Equations Answer Key With Work
• December 20, 2021
You may solve using graphing substitution or elimination. ANSWER KEY Unit Essential Questions.
Students Graph And Write Systems Of Equations In This Collaborative Activity That Doubles As Math Pennant Algebra Activities Math Interactive Notebook Algebra
### Solve the system of equations by graphing.
Seasonal systems of equations answer key with work. There are four equations to represent a line and each are useful when depending on a set of questions or given data. Plug 3 -16 in for x y in the equation 3x 6y 8. Writing Systems Of Equations Worksheet Answer Key Jan.
To make sure that you solved the system of equations correctly you can just plug in your two answers to both equations to make sure that they work both times. On the return trip the plane only. Displaystyle 6x – y 11 6xy 11.
A Set up the systems of equations you will use l. These worksheets will help develop skills like finding the solving equations and factoring polynomials. B Check whether 6 9 is a solution of the systems of linear equations.
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Then color the corresponding area on the coloring page. 33 6-16 8. Find the key information in the word problem that can help you define the variables.
Students will solve systems of equations. Students will learn how to find the value of both variable in the equation with these system of equations math worksheets. Shadow Creek High School.
6 x y 1 1. 9 bunch of ornamental grass. For each of the following.
Systems of Equations and Inequalities REVIEW Short Answer Solve each system by graphing. Solve equations with radicalsWork with negative and fr actional exponentsand raise exponents to exponents. Solve each system by elimination.
X x and y y. Systems of Equations Word Problems Date_____ Period____ 1 Find the value of two numbers if their sum is 12 and their difference is 4. Systems of equation Date per.
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15 8x 6y 20 16 x 7y 30 16 6x 12 y 24 x 6y 4 17 8x 10 y 24 6x 5y 2 18 24 8x 12 y 1 5 9 y 7 18 x 19 4y 11 x 36 20 10 x 10 y 20 9 5y 4x 11 x 20 9y 21 0 2y 10 6x 14 22 y 18 x 22 16 y 22 6x 11 y 4x 15. B Solve showing all steps c Write the answer in a complete sentence The owner of Natural Delights wants to. Each sheet starts out relatively easy and end with some real challenges.
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# math
Four runners ran the relay, Bill ran his lap in 22.738 seconds, Troy ran in 21.874 seconds, Grace ran in 20.32 second, and Jessica ran 19.047 seconds. Estimate the team's total time to the nearest tenth of a second
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3. 👁 193
1. Estimate: 84.6
Actual: 83.979 = 84.0
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2. thank you :)
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posted by Jess
3. You're welcome.
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Calculation of power factor
## Calculation of power factor
The calculation of power factor is done according to the laws of physics. You have to know the active power value and apparent power value.
#### Apparent power
The product of root mean square (RMS) value of voltage and current is known as Apparent Power. This power is measured in volt-ampere (VA), kilo volt-ampere (kVA) or mega volt-ampere( MVA).
Apparent power is taken into account when designing and operating power systems, because although the current associated with reactive power does no work at the load, it still must be supplied by the power source. Conductors, transformers and generators must be sized to carry the total current, not just the current that does useful work.
Failure to provide for the supply of sufficient reactive power in electrical grids can lead to lowered voltage levels and, under certain operating conditions, to the complete collapse of the network or blackout.
Another consequence is that adding the apparent power for two loads will not accurately give the total power unless they have the same phase difference between current and voltage (the same power factor).
#### Active power
The power which is actually consumed or utilized in an AC Circuit is called True power or Active power or Real power. It is measured in watt (W), kilowatt (kW) or megawatt (MW). It is the actual outcomes of the electrical system which runs the electric circuits or load.
#### Power factor
The power factor of an AC electrical power system is defined as the ratio of the real power absorbed by the load to the apparent power flowing in the circuit
The power factor is defined as the ratio of real power to apparent power. As power is transferred along a transmission line, it does not consist purely of real power that can do work once transferred to the load, but rather consists of a combination of real and reactive power, called apparent power. The power factor describes the amount of real power transmitted along a transmission line relative to the total apparent power flowing in the line.
The calculation of power factor value is very important when you have to calculate the wire size.
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# Computer Networks
397 views
Assume a 10Mbps Ethernet has two nodes, A and B, connected by a 360m cable with three repeaters in between, and they each have one frame of 1,024 bits to send to each other. Further assume that the signal propagation speed across the cable is 2*10^8 m/sec, CSMA/CD uses back-off intervals of multiples of 512 bits, and each repeater will insert a store-and-forward delay equivalent to 20-bit transmission time. At time t=0, both A and B attempt to transmit. After the first collision, A draws K = 0 and B draws K = 1 in the exponential back-off protocol after sending the 48 bits jam signal.
What is the one-way propagation delay (including all repeater delays) between A and B in seconds? At what time is A's packet completely delivered at B?
Now suppose that only A has a packet to send and that the repeaters are replaced with switches. Suppose that each switch has an 8-bit processing delay in addition to a store-and-forward delay. At what time, in seconds, is A's packet delivered at B
Propagation delay $T_p = \frac{360}{2 * 10^8} = 1.8 \mu s$
Store and Forward Delay $S_d = \frac{20}{10*10^6}=2\mu s$
Transmission time for a frame $T_t=102.4\mu s$
$(i)$ Total one way propagation delay $= T_p +3*S_d=7.8\mu s$
$(ii)$ both A and B transmit at $t = 0$ and at $t = 7.8\mu s$ both will know about the collision and after 48-bit jamming signal $i.e. 4.8\mu s$ both nodes will participate in back off algorithm.
A transmits immediately as $K=0$
B waits for $51.2 \mu s$ as $K=1$
Time taken for A's frame to get delivered at B $= T_t + 7.8\mu s + 4.8\mu s = 115\mu s$
$(iii)$ Processing delay $P_d = 0.8\mu s$
Total delay at switches $=3(P_d+S_d)=8.4\mu s$
Time taken for A's frame to get delivered at B $=T_t + T_p+8.4\mu s=112.6\mu s$
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https://kr.mathworks.com/matlabcentral/cody/problems/2579-sum-of-series-v/solutions/1528726
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Cody
# Problem 2579. Sum of series V
Solution 1528726
Submitted on 14 May 2018
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.
### Test Suite
Test Status Code Input and Output
1 Pass
n = 1; s_correct = 2; assert(isequal(sumOfSeriesV(n),s_correct))
2 Fail
n = 3; s_correct = 20; assert(isequal(sumOfSeriesV(n),s_correct))
Error using * Incorrect dimensions for matrix multiplication. Check that the number of columns in the first matrix matches the number of rows in the second matrix. To perform elementwise multiplication, use '.*'. Error in sumOfSeriesV (line 3) s=sum(k*(k+1)); Error in Test2 (line 3) assert(isequal(sumOfSeriesV(n),s_correct))
3 Fail
n = 4; s_correct = 40; assert(isequal(sumOfSeriesV(n),s_correct))
Error using * Incorrect dimensions for matrix multiplication. Check that the number of columns in the first matrix matches the number of rows in the second matrix. To perform elementwise multiplication, use '.*'. Error in sumOfSeriesV (line 3) s=sum(k*(k+1)); Error in Test3 (line 3) assert(isequal(sumOfSeriesV(n),s_correct))
4 Fail
n = 10; s_correct = 440; assert(isequal(sumOfSeriesV(n),s_correct))
Error using * Incorrect dimensions for matrix multiplication. Check that the number of columns in the first matrix matches the number of rows in the second matrix. To perform elementwise multiplication, use '.*'. Error in sumOfSeriesV (line 3) s=sum(k*(k+1)); Error in Test4 (line 3) assert(isequal(sumOfSeriesV(n),s_correct))
5 Fail
n = 21; s_correct = 3542; assert(isequal(sumOfSeriesV(n),s_correct))
Error using * Incorrect dimensions for matrix multiplication. Check that the number of columns in the first matrix matches the number of rows in the second matrix. To perform elementwise multiplication, use '.*'. Error in sumOfSeriesV (line 3) s=sum(k*(k+1)); Error in Test5 (line 3) assert(isequal(sumOfSeriesV(n),s_correct))
6 Fail
n = 42; s_correct = 26488; assert(isequal(sumOfSeriesV(n),s_correct))
Error using * Incorrect dimensions for matrix multiplication. Check that the number of columns in the first matrix matches the number of rows in the second matrix. To perform elementwise multiplication, use '.*'. Error in sumOfSeriesV (line 3) s=sum(k*(k+1)); Error in Test6 (line 3) assert(isequal(sumOfSeriesV(n),s_correct))
7 Fail
n = 88; s_correct = 234960; assert(isequal(sumOfSeriesV(n),s_correct))
Error using * Incorrect dimensions for matrix multiplication. Check that the number of columns in the first matrix matches the number of rows in the second matrix. To perform elementwise multiplication, use '.*'. Error in sumOfSeriesV (line 3) s=sum(k*(k+1)); Error in Test7 (line 3) assert(isequal(sumOfSeriesV(n),s_correct))
8 Fail
n = 99; s_correct = 333300; assert(isequal(sumOfSeriesV(n),s_correct))
Error using * Incorrect dimensions for matrix multiplication. Check that the number of columns in the first matrix matches the number of rows in the second matrix. To perform elementwise multiplication, use '.*'. Error in sumOfSeriesV (line 3) s=sum(k*(k+1)); Error in Test8 (line 3) assert(isequal(sumOfSeriesV(n),s_correct))
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# Which is the most restrictive closed-form expression that still generates all primes?
"The set $\{f(n)\}, n=1,2,\ldots$ includes all primes except a finite number of exceptions."
This statement is true for $$f(n)=\sqrt{1+24n},$$ for which the exceptions are 2 and 3. It also generates non-integers and non-prime integers, however. (spoiler alert) The proof uses the fact that the two neighbours of all primes (except 2 and 3) contain the factors 2, 3 and 4 between them (2*3*4=24).
Since no more factors than 2^3 and 3 can be found generally in the two neighbours of primes, the expression $f(n)=\sqrt{1+24n}$ is the most restrictive expression of that particular functional form that still generates all primes. That is, it generates all primes and the smallest number of non-primes.
Other expressions that fit the statement above are $f(n)=\sqrt{1+4n}$, $f(n)=2n-1$ and of course $f(n)=n$, but they produce more non-primes.
My question: Is it known which closed-form expression $f(n)$ generates all primes and the smallest number (in some sense) of non-primes? Is it perhaps $f(n)=\sqrt{1+24n}$?
• The question isn't well-defined, since as you rightly point out $\sqrt{1+24n}$ doesn't generate all primes, so you'd have to say something about how many exceptions are allowed or how to combine the numbers of false positives and false negatives, e.g. look for the lowest sum of the two. Also, $\sqrt{1+24n}$ generates infinitely many non-primes, so it can't generate the smallest number of non-primes in the sense of cardinality -- are you thinking in terms of asymptotic densities? Oct 7, 2011 at 9:16
• The number of primes in $\{1,2,\ldots,N\}$ is $\pi(N)$ (where $\pi$ is the prime counting function). Since $f(n)=O(\sqrt{n})$, the number of primes in $\{f(n):1 \leq n \leq N\}$ is at most $\pi(f(N))<\pi(N)$ for sufficiently large $N$. So, $f(n)=n$ produces fewer non-primes than $f(n)=\sqrt{1+24n}$. Oct 7, 2011 at 9:21
• Also note that there are expressions which generate exactly the primes. These would be the optimal solutions unless you exclude things like sums or the floor function from your notion of "closed-form expression". Oct 7, 2011 at 9:25
• @Douglas: That depends on whether you compute the density with respect to the arguments or the function values. This underscores my point that the question isn't well-defined. Oct 7, 2011 at 9:26
• For the same reasons that all primes $>3$ occur as values of this formula, all primes greater than $5$ occur as values of $\sqrt[4]{120n+1}$ and all primes greater than $7$ as values of $\sqrt[12]{10920n+1}$. The nonprime integer values of these formulas are a bit sparser than for $\sqrt{24n+1}$. Dec 6, 2011 at 15:41
A number is relatively prime to $24$ if and only if it is a square root of unity mod $24$. So $f(n)$ generates all integers that are not divisible by $2$ or $3$, including all primes greater than $3$. It is possible to do better: $g(x) = \sqrt{\frac{5 + 33 \cdot (-1)^n + 15 n}{2}}$ generates all primes greater than $5$ without including any integers divisible by $2$, $3$, or $5$.
• ,What do you think about my closed form expression which links primes and Lambert W function ? Jan 27, 2012 at 7:52
• I didn't take the time to understand it yet but it looks interesting. Jan 27, 2012 at 8:05
I wrote these two small source codes in Maple:
$1)$
"for n from 1 to 100 by 1 do
if isprime(2n-3) then
print(n);
end if;
end do;"
$2)$
"for n from 1 to 100 by 1 do
if type(sqrt(24n+1),prime) then
print(n);
end if;
end do;"
The first code is giving $44$ values for n when result of expression is prime number,and second code is giving only $13$ values for n.
So we may conclude that closed form $f(n)=2n-3$ is "richer" than closed form $f(n)=\sqrt{24n+1}$
EDIT :
In one of my previous posts I have shown that :
$M_p \equiv 1 \pmod {6\cdot p}$ , where $M_p$ is Mersenne number .
So :
$2^{p}-1=6np+1 \Rightarrow 2^p=6np+2 \Rightarrow 2^{p-1}=3np+1$
If we solve this equality for $p$ we will get the next formula :
$$p=-\left(\frac{3n\cdot W\left(-\frac{2^{-1-\frac{1}{3n}}\cdot \ln 2}{3n}\right)+\ln 2}{n\cdot \ln 8}\right)$$
where $W$ is Lambert W function
This closed-form expression generates all primes greater than $3$ and the small number (in sense of asymptotic density ) of the non-prime integers .
Correction :
Actually this closed expression produces integer values for lower branch of Lambert W function which is denoted as $W_{-1}(x)$ so formula is :
$$p=-\left(\frac{3n\cdot W_{-1}\left(-\frac{2^{-1-\frac{1}{3n}}\cdot \ln 2}{3n}\right)+\ln 2}{n\cdot \ln 8}\right)$$
• See my comments under the question. Oct 7, 2011 at 10:31
• Well, I'm looking for expressions "poorer" than $f(n)=\sqrt{1+24n}$ :). Oct 7, 2011 at 10:57
• @pedja, your code is mistaken because it tests $1 < n < m$ but it needs to test $1 < f(n) < m$ to give a fair comparison. $2n-3$ is a strict superset of the other excepting the element $2$. Jan 27, 2012 at 7:42
It was shown in the answer at: Does the formula $\sqrt{ 1 + 24n }$ always yield prime?
that the expression doesn't generate all primes. There isn't any known algebraic expression that generates an infinite number of consecutive primes. So there can't be a "simplest" such expression. There are of course expressions that generate long strings of primes then fail.
• I think you are misinterpreting the question. It is not the same as the one you linked, but some of the answers there apply here as well. Jan 27, 2012 at 7:45
• Dan you're right. But the question "Is it known which closed-form expression f(n) generates all primes and the smallest number (in some sense) of non-primes?" doesn't make sense now that I read it carefully. F(n) doesn't generate "all primes." The word "and" is a conjunction not a qualifier. So is andreasdr looking for some measure on how much an equation deviates from the ideal of generating all the primes in sequence, then ranking equations against that measure?
– MaxW
Jan 27, 2012 at 21:35
• I think we're looking for functions such that all primes occur as values for some input while minimizing the asymptotic density of composite integers that also occur. Jan 28, 2012 at 1:48
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https://www.esaral.com/q/rekha-deposited-rs-16000-in-a-foreign-bank-which-pays-interest-at-the-rate-of-20-per-annum-compounded-quarterly-49149
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# Rekha deposited Rs 16000 in a foreign bank which pays interest at the rate of 20% per annum compounded quarterly,
Question:
Rekha deposited Rs 16000 in a foreign bank which pays interest at the rate of 20% per annum compounded quarterly, find the interest received by Rekha after one year.
Solution:
Given:
$\mathrm{P}=\mathrm{Rs} 16,000$
$\mathrm{R}=20 \%$ p. a.
$\mathrm{n}=1$ year
We know that:
$\mathrm{A}=\mathrm{P}\left(1+\frac{\mathrm{R}}{100}\right)^{\mathrm{n}}$
When compounded quarterly, we have :
$\mathrm{A}=\mathrm{P}\left(1+\frac{\mathrm{R}}{400}\right)^{4 \mathrm{n}}$
$=\operatorname{Rs} 16,000\left(1+\frac{20}{400}\right)^{4}$
$=\operatorname{Rs} 16,000(1.05)^{4}$
$=\operatorname{Rs} 19,448.10$
Also,
$\mathrm{CI}=\mathrm{A}-\mathrm{P}$
$=\mathrm{Rs} 19,448.1-\mathrm{Rs} 16,000$
$=\mathrm{Rs} 19,448.1-\mathrm{Rs} 16,000$
$=\mathrm{Rs} 3,448.10$
Thus, the interest received by Rekha after one year is Rs $3,448.10$.
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# Inequality problem with negative values
I'm trying to solve the following expression for variable $S$ and having some difficulty manipulating the expression because of some negative terms. I have that
$$QS(1+\frac{x_2}{S})+\frac{2y_2}{S}<QS(1+\frac{x_1}{S})+\frac{2y_1}{S}$$
where $Q<0$ and all other variables are positive. $x_2>x_1$ and $y_2>y_1$
My attempt is as follows:
$$QS+Qx_2+\frac{2y_2}{S}<QS+Qx_1+\frac{2y_1}{S}$$
$$\iff Q(x_2-x_1)<\frac{2}{S}(y_1-y_2)$$
multiplying this by $-1$ gives:
$$Q(x_1-x_2)>\frac{2}{S}(y_2-y_1) \iff \frac{Q(x_1-x_2)}{2(y_2-y_1)}>\frac{1}{S} \iff \frac{(y_2-y_1)}{Q(x_1-x_2)}<S$$
Is this correct?
Your work is correct, if it is clear to you that the manipulations at the end work because $Q(x_1-x_2)>0$.
it is correct because division by $y_2-y_1$ does not change the sign since $y_2>y_1$ by assumption.
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hw2solutions
# hw2solutions - IEOR 162 HW#2 Chapter 3 Section Review 4 OIL...
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IEOR 162 HW#2 Chapter 3 – Section Review 4. OIL = thousands of barrels of purchased oil HOS= thousands of barrels of non-cracked heating oil sold HOP= thousands of barrels of heating oil processed further AFS = thousands of barrels of non-cracked aviation fuel sold AFP = thousands of barrels of aviation fuel processed further Then we should solve: max z = 40HOS + 90HOP - 40(OIL) + 130AFP + 60AFS st OIL 20 .5(OIL) = AFS + AFP .5(OIL) = HOS + HOP AFP + .75HOP 8 All variables 0 11. All variables are in millions of barrels of oil. x 11 = Oil sent each year from LA to Houston. x 12 = Oil sent each year from LA to NY. x 21 = Oil sent each year from Chicago to Houston. x 22 = Oil sent each year from Chicago to NY. y 1 = Capacity added to LA. y 2 = Capacity added to Chicago. Then a correct formulation (objective function is in thousands of dollars) is max z = 10{20x 11 +15x 12 +18x 21 +17x 22 }-120y 1 -150y 2 s.t. x 11 + x 21
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Unformatted text preview: ≤ 5 (Amount shipped to Hous. ≤ Hous. Demand) x 12 + x 22 ≤ 5 (Amount shipped to NY ≤ NY Demand) x 11 + x 12 ≤ 2+y 1 (Don't ship more from LA than is available) x 21 + x 22 ≤ 3+y 2 (Don't ship more from Chicago than is available) All variables ≥ 24. Let Xi = Number of type i DRG cases handled weekly. Then the correct formulation follows. Max z= 2000*X1 + 1500*X2 + 500*X3 + 300*X4 st 2) 7*X1 + 4*X2 + 2*X3 + X4 <= 570 3) 5*X1 + 2*X2 + X3 <= 1000 4) 30*X1 + 10*X2 + 5*X3 + X4 <= 50000 5) 800*X1 + 500*X2 + 150*X3 + 50*X4 <= 50000 6) X1 >= 10 7) X2 >= 15 8) X3 >= 40 9) X4 >= 160 All variables ≥ Chapter 4-Section1 1. max z = 3x 1 + 2x 2 s.t. 2x 1 + x 2 + s 1 = 100 x 1 + x 2 + s 2 = 80 x 1 + s 3 = 40 All variables ≥ 2. min z = 50x 1 + 100x 2 s.t. 7x 1 + 2x 2- e 1 = 28 2x 1 + 12x 2- e 2 = 24 All variables ≥...
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### Browsed byCategory: Money and Kids
Cookie Fun Way to Teach Money, Arithmetic, and Geometry
## Cookie Fun Way to Teach Money, Arithmetic, and Geometry
Cookies in math class? Absolutely! This fun and engaging hands-on activity will get your students excited about doing math.
Students will be designing their perfect cookie within the limits of a budget. They will be filling out order forms for cookies, candy and frosting then designing and drawing their final product. This fun activity seamlessly ties in important concepts in math, specifically, addition, subtraction, multiplication and division with money, and attributes of geometric shapes.
This lesson is divided into grades 2-3 and grades 4-5. In grades 2-3 students get lots of practice adding and subtracting with coins. There are coin counting mats and coin sheets to help students as they fill out their order forms. In grades 4-5, in addition to filling out their order forms, students will get practice using a compass and centimeter ruler.
There’s nothing like cookies and M&Ms to get students motivated about doing math. But the best part is, they get to eat their math work when they’re done!
Along with the pdf, you’ll recieve a private link to the video version of the lesson where I share samples and offer tips.
Check out this video to see a preview of this lesson: Cookie Fun Preview
Supported standards:
CCSS: 2.OA.1,2.OA.2, 2.NBT.5, 2.NBT.6, 2.NBT.7, 2.MD.8, 2.G.1, 3.OA.1, 3.OA.3, 3.OA.4, 3.OA.7, 3.NBT.2, 3.G.1, 4.OA.2, 4.NBT.4, 4.NBT.5, 4.MD.1, 4.MD2, 4.MD5, 4G.1, 4G.2, 5.NBT.5, 5.G.3, 5.G.4
TEKS: Second Grade: 4A, 4B, 4C, 4D, 5A, 6A, 8A, 8C; Third grade: 4A, 4C, 4E, 4G, 4K, 5A, 5B, 5D, 6A, 6B; Fourth Grade: 2E, 4A, 4C, 4D, 4H, 6A, 6C, 6D, 8A, 8C; Fifth Grade: 3A, 3D, 3E, 5, 7
Adding Coins: How Much is Today Worth?
## Adding Coins: How Much is Today Worth?
Here’s a great way to give students practice adding coins. Use the date as their target number and then have them come up with all the different combinations using pennies, nickels, dimes, and quarters. To turn this into a problem-solving activity, ask them to prove that they found all the combinations.
A good way for students to learn how to organize their work is to have them use a table. At first, most kids fill in the table haphzardly which can make it difficult for them to know if they got all the combinations. That’s okay; it’s a learning process. Then ask them if there’s a way to fill in the table in a more organized way that would make it easier to prove that all the combinations are there. The photo above is one example of starting with pennies and working our way down through each coin.
The discussion about filling in the table is super important. This gives them a strategy to use in the future if confronted with a similar activity.
Click here to get a copy of the How Much is Today Worth? table.
CCSS: 2.MD.8
Of Slugs and Budgets – Teaching Money Management to Kids
## Of Slugs and Budgets – Teaching Money Management to Kids
When my oldest son, Nathan, was four years old, I caught him crying silently in bed one night. I had gone back into his room to tuck him in as he liked to spend a few minutes “reading” to himself before saying goodnight. Seeing him crying concerned me.
“Nathan, what’s the matter?” I asked.
He lifted the book he had been reading and turned to the page where a cartoon representation of a slug was sitting behind a ticket booth. The sign read: Hugs and Kisses \$1.00 50¢ 25¢ 05¢. The book he was sharing with me was called The Unhuggables: the truth about snakes, skunks, spiders, and other animals that are hard to love.
“He looks so sad,” Nathan sniffed, pointing to the slug, who did, indeed, look pretty sad. “No-one wants to give him a hug.”
Not being a huge fan of slugs, myself, but relieved that this was what made him upset, I had to quickly figure out what purpose slugs served.
“Oh, honey,” I stalled, “Slugs are misunderstood. They’re actually quite useful. They decompose a lot of dead leaves and that’s a very good thing because it puts nutrients back into the soil which helps flowers grow. But not many people know this otherwise I’m sure they would be giving him hugs and kisses.”
I actually impressed myself that this little bit of information about slugs surfaced in my brain. I guess I really was listening in biology class. And the good news is that hearing this seemed to satisfy Nathan.
“We should tell people that slugs are good,” he said.
“Yes, we should,” I agreed. Five minutes later, he was asleep.
Budgets are like slugs. They’re often misunderstood. And because of that, people find them unhuggable.
But budgets actually serve a very important function. Budgets help us get the things we want in life: a new car, a house, college education for our kids, more time with our family, the ability to travel to exotic places… Money is the tool that can help us achieve those desires. A budget helps us use that tool effectively.
So teaching our kids how to budget is important if we want them to achieve their goals in life. Kids budgeting? Of course! The good news is, teaching them is pretty simple. Here are three ways to give your kids hands-on experiences with budgeting (excerpted from the book Raised for Richness):
The Birthday Party – ages 7+
Decide how much you are willing to spend on your child’s birthday party. Get CASH in that amount (that’s your budget) and put it in an envelope labeled ‘(Sara’s) Birthday Party’. You’ll use the envelope to help you keep track of your running expenses.
Then have your child help you make a list of all the expenses related to the party. Making a list will help you stay focused when you’re shopping. And thinking of these in advance will teach your child to be organized. She’ll need to consider number of guests, party games, food, party favors, paper plates, etc.
Now the fun part…you get to go shopping. As you buy items, write the total on the envelope and keep a running balance. Using cash will underscore the value of a dollar (it makes a difference if you can SEE the money) and help you stick to the budget.
Tweens and teens can go a step further and come up with the “flow” of the party…when to play games, when to eat, etc.
Clothing Allowance: Tweens and Teenagers
This is a great back-to-school-shopping activity, but can still be used any time of the year. Tweens and teens are quite capable of shopping for themselves. They may make mistakes along the way, but those are great learning opportunities. So giving them a lump sum of money and putting them in charge of spending within the limits of a budget is good practice.
Just like the birthday party activity, begin by deciding how much you’re willing to spend on clothing. Consider how long you expect those clothes to last. In other words, are they shopping for all their fall/winter clothes? Then have your child make a list of needed items: 2 pair of jeans, three t-shirts, socks, warm jacket, etc.
Again, get CASH in the needed amount. Tell him that he needs to buy all the items on the list and any money left over is his to keep! This usually gets kids to think carefully about their purchases and look for good deals. Instant savvy shoppers!
The Cell Phone: Teenagers
Parents have been handed an unbelievable tool to help teach teens how to budget. It’s the cell phone. Yup, that object of love and hate. Done correctly, it becomes an object of learning. Here’s how.
Teens need to stay connected to their friends. This is normal as they figure out their place in the world. Cell phones keep them connected. Using their “need” for a cell phone as the motivator, we can teach them basic money management skills such as budgeting and paying bills.
First, teens need to know that along with a cell phone comes responsibility. Keeping track of your cell phone, resisting the urge to text during dinner, and paying your phone bill. Kids paying bills? You bet! And the best time to teach them is while they are still hanging out with you.
Next, it’s important to establish what part of the phone bill your child will be responsible for. For example, you may pay the family plan fee but maybe your teen pays the additional phone line fee, texting, and upgrades…
Now comes the fun part. Kids learn to budget their money in the context of something the love…their cell phone! Upgrades? They pay. Overages? They pay. Lost phone? They pay. Unpaid bill? No phone. See how simple it is? Okay, so it’s going to take a few months before everyone understands how the whole thing works, but when that happens, it’s a thing of beauty. Kids are happy; as long as they budget their money correctly, they stay connected to their friends. Parents are happy, their kids are learning real life skills. It’s a win/win.
Although a lot of parents are willing to pay for their kids’ cell phones because it offers peace of mind, how about the peace of mind that comes with knowing your child is ready to take on the financial challenges that await her out there? Don’t miss this silver platter opportunity. With teens, when you get the chance, take it!
Adopt a Class or School – Change a Life Campaign
## Adopt a Class or School – Change a Life Campaign
We’re working with Sammy Rabbit on his “Adopt a Class or School – Change a Life” campaign. If you’d like to participate, email me. Details are below.
“Adopt a Class Change a Life” Campaign Special
Teach Children SMART Money Habits!
Book + Music + Activity
Strategic Multi media, Multi intelligence approach teaches smart money habits; builds reading and listening skills!
Special (limited time only)
3 Items for price of 1
Get a FREE Story Book: It’s a Habit, Sammy Rabbit!
and a FREE Coloring Book with Stickers Inside
with Purchase of “Dream Big – Set Goals” Audio Song and Story CD (8 Tracks):
Minimum Qty – 50 Units
CDs: 50 x \$4.99 = \$249.50
Storybooks: 50 FREE
Coloring Books with Stickers Inside: 50 FREE
Add shipping, handling, and tax (if applicable)
Offer valid while supplies last
Order or Questions? Email me at:
[email protected]
Teaching Kids Persistence
## Teaching Kids Persistence
What is one of the most common traits of successful people? According to a 2007 study in the Journal of Personality and Social Psychology, it’s the ability to persist at challenging tasks. And it makes sense. Those who don’t allow obstacles to get in their way have a better chance of accomplishing what they set out to do. But being persistent is not always easy. Here are 7 tips to help develop persistence in our kids:
1. Break the task into smaller, manageable pieces. It’s easier to learn an entire piano piece one measure at a time. 2-3 measures practiced each day means that by the end of the week, the whole piece is mastered. This is true for any assignment we take on.
2. Offer encouraging words. When tasks become hard kids often become afraid of failing. Your positive words of encouragement is often all they need to keep going. Let them know how proud you are of their effort and that you believe they can complete the task.
3. Create an environment conducive to new learning. We learn best when our surroundings are calm, our bellies full, and we’ve had plenty of rest. These give us the energy we need to work on tasks that require a little extra hard work.
4. Don’t bail out your kids. It’s hard for a parent not to want to step in when the I-can’t-do-it’s begin. Take a moment to evaluate the situation. Is the immediate task manageable? Is the environment conducive to learning? If so, then it’s time to offer those encouraging words and let your child struggle a little. There is simply nothing like the sense of satisfaction for having made it successfully through to the other side. That said…
5. Stop when your child becomes too frustrated. There’s no sense in pushing through a task when you can see real frustration take hold. No learning happens this way. Close shop and re-visit it on another day.
6. Look for opportunities to have your child practice persistence. Pull out that 200-piece jigsaw puzzle, grab a bowl of pretzels, and spend the afternoon working on mastering those pieces with your child. Along the way, talk about how overwhelming the project seemed at first, but by taking it one step at a time and being persistent, your efforts are paying off.
7. You. You are your childs biggest role model. Talk about the things you are doing that are difficult and require hard work and persistence. Give examples of how you succeeded in the past. Let them know that you understand how difficult it can be but not giving up is something to be admired.
The Money Connection: A great way to help develop persistence in our kids is to have them create and work towards a personal financial goal. Help them figure out the steps needed to accomplish the goal and offer words of encouragement as they make progress. Let them know you admire their stick-to-it-ness. And when they finally arrive at success, let them know that their persistence and determination got them there. Remind them that persistence is what helps people get what they want out of life.
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# Subset Selection ProblemΒΆ
A genetic algorithm can be used to approach subset selection problems by defining custom operators. In general a metaheuristic algorithm might not be the ultimate goal to implement in a real-world scenario, however, it might be useful to investigate patterns or characteristics of possible good subsets. Let us consider a simple toy problem where we have to select numbers from a list. For every solution exactly 10 numbers have to be selected that their sum is minimized. For subset selection problem a binary encoding can be used where 1 indicates a number is picked. In our problem formulation the list of numbers is represented by $$L$$ and the binary encoded variable by $$x$$.
\begin{align} \begin{split} \min f(x) & = & \sum_{k=1}^{n} L_k \cdot x_k\\[2mm] \text{s.t.} \quad g(x) & = & (\sum_{k=1}^{n} x_k - 10)^2\\[2mm] \end{split} \end{align}
As shown above, the equality constraint is handled by making sure $$g(x)$$ can only be zero if exactly 10 numbers are chosen. The problem can be implemented as follows:
[1]:
import numpy as np
from pymoo.model.problem import Problem
class SubsetProblem(Problem):
def __init__(self,
L,
n_max
):
super().__init__(n_var=len(L), n_obj=1, n_constr=1, elementwise_evaluation=True)
self.L = L
self.n_max = n_max
def _evaluate(self, x, out, *args, **kwargs):
out["F"] = np.sum(self.L[x])
out["G"] = (self.n_max - np.sum(x)) ** 2
# create the actual problem to be solved
np.random.seed(1)
L = np.array([np.random.randint(100) for _ in range(100)])
n_max = 10
problem = SubsetProblem(L, n_max)
The customization requires to write custom operators in order to solve this problem efficiently. We recommend to consider the feasibility directly in the evolutionary operators, because otherwise most of the time infeasible solutions will be processed. The sampling creates randomly solution where the subset constraint will always be satisfied. The mutation randomly removes a number and chooses another one. The crossover, first takes the common numbers of both parents and then randomly picks either from the first or from the second parent until enough numbers are picked.
[2]:
from pymoo.model.crossover import Crossover
from pymoo.model.mutation import Mutation
from pymoo.model.sampling import Sampling
class MySampling(Sampling):
def _do(self, problem, n_samples, **kwargs):
X = np.full((n_samples, problem.n_var), False, dtype=np.bool)
for k in range(n_samples):
I = np.random.permutation(problem.n_var)[:problem.n_max]
X[k, I] = True
return X
class BinaryCrossover(Crossover):
def __init__(self):
super().__init__(2, 1)
def _do(self, problem, X, **kwargs):
n_parents, n_matings, n_var = X.shape
_X = np.full((self.n_offsprings, n_matings, problem.n_var), False)
for k in range(n_matings):
p1, p2 = X[0, k], X[1, k]
both_are_true = np.logical_and(p1, p2)
_X[0, k, both_are_true] = True
n_remaining = problem.n_max - np.sum(both_are_true)
I = np.where(np.logical_xor(p1, p2))[0]
S = I[np.random.permutation(len(I))][:n_remaining]
_X[0, k, S] = True
return _X
class MyMutation(Mutation):
def _do(self, problem, X, **kwargs):
for i in range(X.shape[0]):
X[i, :] = X[i, :]
is_false = np.where(np.logical_not(X[i, :]))[0]
is_true = np.where(X[i, :])[0]
X[i, np.random.choice(is_false)] = True
X[i, np.random.choice(is_true)] = False
return X
After having defined the operators a genetic algorithm can be initialized.
[3]:
from pymoo.algorithms.so_genetic_algorithm import GA
from pymoo.optimize import minimize
algorithm = GA(
pop_size=100,
sampling=MySampling(),
crossover=BinaryCrossover(),
mutation=MyMutation(),
eliminate_duplicates=True)
res = minimize(problem,
algorithm,
('n_gen', 60),
seed=1,
verbose=True)
print("Function value: %s" % res.F[0])
print("Subset:", np.where(res.X)[0])
===========================================================================
n_gen | n_eval | cv (min) | cv (avg) | fopt | favg
===========================================================================
1 | 100 | 0.00000E+00 | 0.00000E+00 | 258 | 4.43940E+02
2 | 200 | 0.00000E+00 | 0.00000E+00 | 205 | 3.54340E+02
3 | 300 | 0.00000E+00 | 0.00000E+00 | 175 | 3.00390E+02
4 | 400 | 0.00000E+00 | 0.00000E+00 | 161 | 2.52240E+02
5 | 500 | 0.00000E+00 | 0.00000E+00 | 124 | 2.18240E+02
6 | 600 | 0.00000E+00 | 0.00000E+00 | 118 | 1.91860E+02
7 | 700 | 0.00000E+00 | 0.00000E+00 | 118 | 1.70050E+02
8 | 800 | 0.00000E+00 | 0.00000E+00 | 85 | 1.49630E+02
9 | 900 | 0.00000E+00 | 0.00000E+00 | 85 | 1.39550E+02
10 | 1000 | 0.00000E+00 | 0.00000E+00 | 85 | 1.30580E+02
11 | 1100 | 0.00000E+00 | 0.00000E+00 | 74 | 1.19930E+02
12 | 1200 | 0.00000E+00 | 0.00000E+00 | 74 | 1.11800E+02
13 | 1300 | 0.00000E+00 | 0.00000E+00 | 74 | 1.06050E+02
14 | 1400 | 0.00000E+00 | 0.00000E+00 | 68 | 1.00100E+02
15 | 1500 | 0.00000E+00 | 0.00000E+00 | 68 | 9.46300E+01
16 | 1600 | 0.00000E+00 | 0.00000E+00 | 52 | 8.97600E+01
17 | 1700 | 0.00000E+00 | 0.00000E+00 | 50 | 8.45100E+01
18 | 1800 | 0.00000E+00 | 0.00000E+00 | 50 | 8.09000E+01
19 | 1900 | 0.00000E+00 | 0.00000E+00 | 50 | 7.66900E+01
20 | 2000 | 0.00000E+00 | 0.00000E+00 | 50 | 7.33700E+01
21 | 2100 | 0.00000E+00 | 0.00000E+00 | 45 | 7.00100E+01
22 | 2200 | 0.00000E+00 | 0.00000E+00 | 45 | 6.78900E+01
23 | 2300 | 0.00000E+00 | 0.00000E+00 | 45 | 6.60300E+01
24 | 2400 | 0.00000E+00 | 0.00000E+00 | 45 | 6.43500E+01
25 | 2500 | 0.00000E+00 | 0.00000E+00 | 45 | 6.36500E+01
26 | 2600 | 0.00000E+00 | 0.00000E+00 | 45 | 6.16100E+01
27 | 2700 | 0.00000E+00 | 0.00000E+00 | 45 | 6.03300E+01
28 | 2800 | 0.00000E+00 | 0.00000E+00 | 43 | 5.94900E+01
29 | 2900 | 0.00000E+00 | 0.00000E+00 | 43 | 5.76600E+01
30 | 3000 | 0.00000E+00 | 0.00000E+00 | 43 | 5.65100E+01
31 | 3100 | 0.00000E+00 | 0.00000E+00 | 42 | 5.54700E+01
32 | 3200 | 0.00000E+00 | 0.00000E+00 | 42 | 5.42800E+01
33 | 3300 | 0.00000E+00 | 0.00000E+00 | 42 | 5.36700E+01
34 | 3400 | 0.00000E+00 | 0.00000E+00 | 42 | 5.27000E+01
35 | 3500 | 0.00000E+00 | 0.00000E+00 | 42 | 5.21800E+01
36 | 3600 | 0.00000E+00 | 0.00000E+00 | 42 | 5.19700E+01
37 | 3700 | 0.00000E+00 | 0.00000E+00 | 39 | 5.14400E+01
38 | 3800 | 0.00000E+00 | 0.00000E+00 | 39 | 5.10500E+01
39 | 3900 | 0.00000E+00 | 0.00000E+00 | 39 | 5.08500E+01
40 | 4000 | 0.00000E+00 | 0.00000E+00 | 39 | 5.05500E+01
41 | 4100 | 0.00000E+00 | 0.00000E+00 | 39 | 5.01200E+01
42 | 4200 | 0.00000E+00 | 0.00000E+00 | 39 | 4.93800E+01
43 | 4300 | 0.00000E+00 | 0.00000E+00 | 39 | 4.88000E+01
44 | 4400 | 0.00000E+00 | 0.00000E+00 | 39 | 4.85700E+01
45 | 4500 | 0.00000E+00 | 0.00000E+00 | 39 | 4.81400E+01
46 | 4600 | 0.00000E+00 | 0.00000E+00 | 38 | 4.76700E+01
47 | 4700 | 0.00000E+00 | 0.00000E+00 | 38 | 4.71800E+01
48 | 4800 | 0.00000E+00 | 0.00000E+00 | 37 | 4.66100E+01
49 | 4900 | 0.00000E+00 | 0.00000E+00 | 37 | 4.62700E+01
50 | 5000 | 0.00000E+00 | 0.00000E+00 | 37 | 4.62000E+01
51 | 5100 | 0.00000E+00 | 0.00000E+00 | 37 | 4.57600E+01
52 | 5200 | 0.00000E+00 | 0.00000E+00 | 37 | 4.56000E+01
53 | 5300 | 0.00000E+00 | 0.00000E+00 | 37 | 4.53400E+01
54 | 5400 | 0.00000E+00 | 0.00000E+00 | 36 | 4.49200E+01
55 | 5500 | 0.00000E+00 | 0.00000E+00 | 36 | 4.46700E+01
56 | 5600 | 0.00000E+00 | 0.00000E+00 | 36 | 4.45100E+01
57 | 5700 | 0.00000E+00 | 0.00000E+00 | 36 | 4.43800E+01
58 | 5800 | 0.00000E+00 | 0.00000E+00 | 36 | 4.42300E+01
59 | 5900 | 0.00000E+00 | 0.00000E+00 | 36 | 4.41400E+01
60 | 6000 | 0.00000E+00 | 0.00000E+00 | 36 | 4.38100E+01
Function value: 36
Subset: [ 5 9 12 31 36 37 47 52 68 99]
Finally, we can compare the found subset with the optimum known simply through sorting:
[4]:
opt = np.sort(np.argsort(L)[:n_max])
print("Optimal Subset:", opt)
print("Optimal Function Value: %s" % L[opt].sum())
Optimal Subset: [ 5 9 12 31 36 37 47 52 68 99]
Optimal Function Value: 36
| 3,603 | 8,740 |
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0}
| 3.625 | 4 |
CC-MAIN-2020-24
|
latest
|
en
| 0.781493 |
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