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https://www.physicsforums.com/threads/final-repulsed-velocity-of-two-different-charged-masses.646614/
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math
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1. Two small metal spheres with masses 2.0g and 4.0g are tied together by a 5cm long massless string and are at rest on a frictionless table. Each sphere has a (mue)c charge. The string is cut, what are the velocities of the sphere when they are far apart I know two conservative qualities are at play, electric energy, and I'm not sure of the other I tried using change under the curve with r being the variable (kQq/r) being equal to work and then said mv^2/2. However I can't articulate how I am sure this is the wrong approach. What is the right way/approach?
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CC-MAIN-2018-34
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https://www.slideserve.com/amanda/12-7-surface-area-of-spheres
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math
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12.7 Surface Area of Spheres. Angela Isac Abby Kern 1st hour. Objectives. Recognize and define basic properties of spheres. Find surface areas of spheres. . What is a Sphere?. A sphere is the locus of all points that are a given distance from a given point called the center .
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
In the figure, O is the center of the sphere, and plane R intersects the sphere in circle A. If AO = 3cm and OB=10cm, find AB.
Use the Pythagorean Theorem to solve for AB.
OB2 = AB2 + AO2Pythagorean Theorem
102 = AB2 + 32OB = 10, AO = 3
100 = AB2 + 9 Simplify.
91 = AB2 Subtract 9 from each side.
9.5 = AB Use a calculator.
Answer: AB is approximately 9.5cm.
If a sphere has a surface area of T square units and a radius of r units, then
T= 4 r2
This is simply saying that the surface area (T) of the sphere is 4 times the area of the great circle ( r2).
Find the surface area of the sphere given the area of the great circle.
Use the formula for surface area to solve.
T = 4 r2Surface are of the sphere.
T = 4(201.1) r2 = 201.1
T = 804.4 Multiply.
Answer: 804.4 in2
Since a hemisphere is half a sphere, to find its surface area, find half of the surface area of the sphere and add the area of the great circle.
T = ½(4 r2) + r2
Find the area of the hemisphere.
Use the formula for the surface area of a
hemisphere to solve.
T = ½(4 r2) + r2 Surface are of a hemisphere
T = ½[4 (4.2)2] + (4.2)2 Substitution
T = 166.3 Use a calculator.
Pre-AP Geometry: Page 674 #10 - 29
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CC-MAIN-2018-34
| 1,793 | 28 |
https://canadiantattoogirls.com/the-maturation-of-purely-mathematical-mind/
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math
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The maturation of purely mathematical mind
That period before Euclid Greek and Roman mathematicians
The Greeks divided mathematics into two areas, both of which had their origins in practical applications: arithmetic (the study of “multitude,” or discrete quantity) and geometry (the study of “magnitude,” or continuous number). According to Proclus’s Commentary on Euclid, ancient Egyptian surveying procedures gave rise to geometry (which literally translates to “measure of land”) because yearly flooding along the Nile prompted the Egyptians to redraw property borders. In a similar vein, it was Phoenician merchants that advanced the field of mathematics. Even though Proclus wrote his novel in the fifth century CE, his concepts may be traced back to the likes of Herodotus (mid-fifth century BCE) and Eudemus (a student of Aristotle) from even earlier periods (late 4th century BCE). If you are struggling with percentages or any other mathematical process, Visit their website to solve percentage queries.
Since there is so little evidence of applied mathematics from the early Greek era, the idea is plausible but difficult to test (roughly, the 8th through the 4th century BCE). Stone tablets, for example, attest to the widespread adoption of a numerical system conceptually comparable to the widely used Roman numerals. There are perhaps a dozen abacuses made of stone that date back to the fifth and fourth centuries BCE, indicating that Herodotus was likely aware of the abacus’s use as a calculation instrument in both Greece and Egypt. When surveying new cities in Greek colonies in the sixth and fifth centuries BC, standard lengths of 70 plethra (one plethron equals 100 feet) were frequently used as the diagonal of a square of side 50 plethra; in reality, the diagonal of the square is 50Square root of2 plethra, so using 7/5 (or 1.4) as an estimate for Square root of2 is equivalent to using 7/5 (or 1.4) as an estimate for Square root of Eupalinus of Megara, an engineer from the sixth century BCE, is credited for channelling an aqueduct through a mountain on the island of Samos, although the method he used is controversial among historians. In his Laws, Plato seems to argue that the Egyptians’ method of teaching math to youngsters via practical issues from everyday life was an example the Greeks should follow.
These hypotheses on the character of early Greek practical mathematics are supported by later sources, such as the arithmetic problems in papyrus writings from Ptolemaic Egypt (starting in the third century BCE) and the geometric manuals by Heron of Alexandria (1st century CE). Essentially, this Greek habit was quite close to that of ancient Egypt and Mesopotamia. There is little doubt that the Greeks borrowed ideas and concepts from much earlier civilizations.
The Greeks are commonly credited as the “creators of mathematics,” yet it was the theoretical foundations of their discipline that truly set them apart. This means that mathematical statements hold true everywhere and can be proven correct. For instance, the Mesopotamians created techniques for testing whether or not the equation a2 + b2 = c2 holds for a given set of whole integers a, b, and c. (e.g., 3, 4, 5; 5, 12, 13; or 119, 120, 169). The Greeks demonstrated a general way for producing such sequences, commonly known as Pythagorean triples: for every pair of whole integers p and q, even or odd, a = (p2 + q2)/2, b = pq, and c = (p2 + q2)/2. Such numbers satisfy the relation for Pythagorean triples, as established by Euclid in Book X of the Elements. This conclusion was proved by the Greeks as part of a more comprehensive explanation of the characteristics of flat geometric forms (Euclid proves it twice, once in Book I, Proposition 47, and once in Book VI, Proposition 31). It appears that the Mesopotamians knew that right triangles contain sides that consist of sets of the numbers a, b, and c.
While Euclid’s The Elements (about 300 BCE) is often seen as a seminal work in theoretical geometry, the transition from practical to theoretical mathematics may be traced back to the fifth century BCE at the earliest. Others, including Pythagoreans Archytas of Tarentum, Theaetetus of Athens, and Eudoxus of Cnidus, expanded the theoretical form of geometry by building on the foundations laid by Pythagoras of Samos (late 6th century) and Hippocrates of Chios (late 5th century) (4th century). There are no surviving copies of any of these men’s writings, therefore what we know about them comes from the opinions of other authors. While this sliver of evidence does demonstrate the extent to which Euclid relied on them, it does nothing to explain what motivated their research.
Discussion centres on the how and why of this theoretical change. Commonly cited is the finding of irrational numbers. The early Pythagoreans held the concept that “all things are number” as a fundamental principle. Even though the Greek word for number, arithmos, can only be used to describe whole numbers and, in some cases, ordinary fractions, it is possible to assign a number to any geometric measure (that is, some whole number or fraction; in modern terminology, rational number). In common speech, this is commonly taken for granted, as when the length of a line is expressed as a full number of feet plus a fraction of a foot. The lines that form the square’s sides and diagonal are an exception to this rule. (For instance, assuming that the ratio of two whole integers can be stated for the side and diagonal ratios, it can be demonstrated that they must be even. Since any fraction may be expressed as the ratio of two whole numbers with no common denominator, it is obvious that this cannot occur. This has the geometric implication that no length may be used as a unit of measure for both the side and the diagonal; that is, the side and the diagonal cannot both equal the same length multiplied by (different) whole integers. This is why the Greeks used the term “incommensurable” to characterise such comparisons of lengths. (Modern mathematicians use the word “number” to refer to irrational numbers like Square root of 2, which the Greeks did not.)
Although this was already widespread knowledge by the time of Plato, some late writers, such as Pappus of Alexandria (4th century CE), claim that it was discovered inside the school of Pythagoras in the 5th century BCE. By 400 BCE, it was generally accepted that lines corresponding to the square root of 3, the square root of 5, and other square roots are not directly equivalent to a standard unit of length. An much more complete discovery, that square root of p is irrational whenever p is not a rational square integer, is attributed to Plato’s companion Theaetetus. Book X, Section II, Proposition 115 of the Elements demonstrates that the effort of their pupils finally consolidated into a cohesive system, building on the foundation laid by Theaetetus and Eudoxus.
The discovery of irrationals unquestionably changed the trajectory of early mathematical investigation, regardless of any assumptions made in practical practise. As the irrationals demonstrated, mathematics on its own couldn’t accomplish what geometry needed to do. All mathematical assumptions were theoretically rendered suspect once seemingly obvious ones, such as the commensurability of all lines, were revealed to be incorrect. A minimum level of justification was required for all mathematical claims. The need to identify what makes a certain chain of reasoning worthy of the label “evidence” arose as a more basic issue. Evidently before his death in the fifth century BCE, Hippocrates of Chios and his contemporaries began gathering geometric findings into textbooks dubbed “elements” (meaning “fundamental outcomes” of geometry). A century later, when Euclid was writing his comprehensive textbook, they would be among his key sources.
There was fierce rivalry among the early mathematicians, who were part of a larger intellectual community that included pre-Socratic philosophers in Ionia and Italy and Sophists in Athens. Parmenides, a Greek philosopher from the fifth century BCE, challenged the basic basis of knowing when he claimed that only unchangeable objects could have actual existence. Heracleitus (c. 500 BCE) claimed, on the other hand, that the stability of our senses is an illusion created by a balance of opposing forces. Knowledge and proof both have their respective meanings questioned as a consequence.
In several of the disagreements, mathematical issues served as a focal point. The Pythagoreans (and Plato, who came after them) used the certainty of mathematics as a model for deducing truths in areas such as politics and ethics. Yet others thought that mathematics was riddled with contradictions. Paradoxes about motion and quantity have been attributed to Zeno of Elea, who lived in the fifth century BCE. The premise that a line may be bisected an endless number of times gives rise to a paradox since the outcome can be either a set of points of zero length (in which case the total of an infinite number of such points is zero) or a collection of minuscule line segments (in which case the sum is infinite). In actuality, the length of the provided line must be both and. In the fifth century BCE, Democritus and other atomist philosophers attempted to answer this question by positing that everything in the cosmos is made up of infinitesimally small particles called “atoms” (from the Greek atomon, meaning “indivisible”). However, the idea of incommensurable lines in geometry ran counter to this view since atoms would then be employed to quantify all lines. Tangents to circles can be confusing; not even Sophist Protagoras and Democritus could agree on whether they meet the circle at a point or a line. During the fifth century BCE, Socratic philosophers Antiphon and Bryson grappled with the issue of equating the circle and the polygons that may be made within it.
The pre-Socratics were the first to point out the problems with fundamental ideas like “existence” and “proof,” as well as more specific ones like “infinitely many” and “infinitely tiny.” These philosophical considerations may or may not have impacted mathematicians’ technical research, but they definitely made them more careful of making overly broad claims about their field’s breadth.
Any examination of the possible ramifications of such circumstances is, at best, hypothetical due to the incoherence of the sources and the lack of clarity with which the mathematicians responded to the issues posed. Greek mathematics is distinctive due to its meticulous examination of fundamental assumptions and emphasis on strong proofs. While it would be impossible to offer a comprehensive analysis of the causes of these changes, we may look to the technical advances and cultural climate of the early Greek tradition as two possible explanations.
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CC-MAIN-2023-14
| 10,988 | 14 |
https://avesis.yyu.edu.tr/yayin/1fdca3ab-8103-4bb2-847c-e017bf6301f0/approximation-properties-of-univariate-and-bivariate-new-class-bernsteinkantorovich-operators-and-its-associated-gbs-operators
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math
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The main objective of this work is to derive some approximation properties of univariate and bivariate Kantorovich type new class Bernstein operators by means of shape parameter λ∈ [- 1 , 1]. We obtained some basic results such as moments estimates and Korovkin type approximation theorem. Next, we estimated the degree of convergence in terms of the usual modulus of continuity, for an element of Lipschitz type continuous functions and Peetre’s K-functional, respectively. Moreover, we constructed the bivariate of newly introduced operators and computed the rate of approximation in connection with the partial and complete modulus of continuity, also for the elements of the Lipschitz type class. In addition, we proposed the associated Generalized Boolean Sum (GBS) type of bivariate operators and calculated the order of approximation with the help of mixed modulus of continuity and a class of the Lipschitz of Bögel type continuous functions. Finally, we presented some graphics and an error of estimation table to compare the convergence behavior of univariate, bivariate forms and its associated GBS type operators to certain functions.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100599.20/warc/CC-MAIN-20231206130723-20231206160723-00125.warc.gz
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CC-MAIN-2023-50
| 1,152 | 1 |
https://thenewstandardgallery.com/high-school-physics-epi-report/
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math
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REPORT AIM The aim of this experiment is to: ? Explore the equations of uniform accelerated motion and investigate the relationship between displacement and time ? Determine the magnitude of deceleration due to friction. ? Assess the effect of mass on the car’s accelerated motion. DESIGN Hypothesis – A car moving in a straight line with a non-zero initial velocity will finally come to a rest as a result of friction, given that the car has no engine or external tractions. This motion can be considered as a uniform accelerated motion because: 1.
The car is moving in a horizontal straight line so weight is cancelled by the normal reaction force from the ground. The only other force existed is the friction between the car and the surface therefore it will be equal to the net force 2. According to the formula Fr = ? N, the amount of the friction depends on two factors: the friction coefficient and the normal reaction force, both of which are fixed. Therefore the amount of friction is constant throughout the motion 3. According to Newton’s Second Law F = ma, a constant net force will result in a uniform acceleration (deceleration).
The acceleration is negative in this case as cars are slowing down to a rest. For convenience, this decelerated motion can be inverted into an equivalent motion in which the car is acceleration from rest. It should follow the equation of x = ut + 1/2 at2, where x = distance traveled, u = 0 (seen as the initial velocity but actually is the final velocity which is zero at rest), a = acceleration (actually deceleration) and t = time taken during that motion. This formula can be simplified as x = 1/2 at2.
We will measure the variables of x and t to verify this relationship and determine the magnitude of this deceleration, which can be derived from the gradient of the regression line of x against t2. Theoretically the mass of the car should not influence its deceleration because: Friction is the net force, Fr =? N = ? mg (as N=Weight) = Fnet = ma => ? mg = ma => a = ? g, which implies deceleration depends only on the friction coefficient. The car’s initial velocity at the beginning of the horizontal tract is provided by releasing the car from a ramp connected to the tract.
This design will reduce human interventions to the car’s horizontal part of motion. Three cars of different masses will be tested to see if mass have any effect on the magnitude of deceleration. METHODS A plastic track is connected to a ramp which has a height of 9cm and contact surface of 10cm. A car is hold still on the ramp surface at a position of 3cm from the top (i. e. it will travel 7 cm to reach the bottom of the ramp). Three different cars are used in this experiment and have masses of 0. 231kg, 0. 358kg and 0. 535kg respectively. All of the three cars are released from the same position.
Due to gravity, the car will gain a velocity when entering the horizontal tract. By using a stopwatch, we take measurement of the time from the moment when the car’s rear wheels first reach the horizontal tract and stop the measurement as soon as it comes to rest. The distance traveled by the car along the plastic tract is measured by a hard ruler and distance is taken from the back of the car’s rear wheels (once stopped) to the junction between the ramp and the plastic tract. [pic] This experiment is repeated three times and all data are entered into excel.
A graph of distance against time squared is plotted and a regression analysis is performed to determine the relationship between the two variables and the gradient of the line. RESULTS The results of the experiment are summarized in the following table: | |Distance x (m) |Time (s) |t^2 | |Exp1 Car1 |0. 235 |0. 78 |0. 6084 | |Exp1 Car2 |0. 285 |1. 73 |2. 9929 | |Exp1 Car3 |0. 403 |2. |5. 29 | |Exp2 Car1 |0. 287 |1. 3 |1. 69 | |Exp2 Car2 |0. 308 |1. 82 |3. 3124 | |Exp2 Car3 |0. 335 |2. 03 |4. 1209 | |Exp3 Car1 |0. 104 |0. 63 |0. 3969 | |Exp3 Car2 |0. 255 |1. 54 |2. 3716 | |Exp3 Car3 |0. 374 |1. 98 |3. 9204 |
Car 1 – 0. 231kg Car 2 – 0. 358kg Car 3 – 0. 535kg The Graph of distance against time squared: [pic] The gradient of the regression line is equal to 1/2 a, so a = 2 x 0. 0479 = 0. 0958 ms-2. The uncertainty for time measurement is estimated to be 10% and 1% for distance measurement (±2mm). As a = 2x/(t2), the uncertainty percentage for a is approximately = 1 % + 10% + 10% = 21%. Therefore a = 0. 0958±0. 0201 ms-2. DISCUSSION From the above graph, it is evident that there is a strong linear positive relationship between distance and time squared (R2 = 0. 8067).
The distance traveled by the car during deceleration is proportional to the square of time. This is consistent with our hypothesis that x = 1/2 at2. The gradient of the regression line is equal to 1/2 a. Thus, deceleration = 2 x gradient = 2 x 0. 0479 = 0. 0958 ms-2. A R2 value of 0. 8067 means nearly 81% of the variation in distance can be explained by variation in time, according to the linear model of x against t2. This suggests that mass of the car is not a factor determining the magnitude of acceleration and does not influence the pattern of this decelerated motion.
There are a few factors in this experiment which may cause variations to the result. For example, we assume the friction coefficient of the plastic tract is the same for the three cars thus they will have the same deceleration, as discussed in Experimental Design. However, the tyres of the three cars might be made from different materials so the friction coefficients might be slightly different. As a result, the deceleration is not actually constant and this creates error for our linear regression. Another compounding a factor is the joint between the ramp and the horizontal tract.
As the car passes through this point, the direction of the movement may be slightly diverted due to this sharp turn. Other issues affecting experimental results include not-leveled tract, air resistance, and human errors in measurements such as delayed timing. This experiment can be improved by eliminating these compounding factors. For example, we could use a spirit level to check the plastic tract and ensure that cars are moving in a horizontal plane. The cars’ tyres should be made of the same material. The bottom of the ramp should be connected to the plastic track smoothly without any sharp corners.
More measurements are to be taken to increase the accuracy of data. CONCLUSION From this experiment, we successfully verified the equation for a uniform decelerated motion x = 1/2 at2. Our results showed that distance was proportional to the square of time. The deceleration was determined from the gradient of the regression line of x against t2, which was found to be 0. 0958±0. 0201 ms-2. The mass of the car has no effect on the value of deceleration and the pattern of motion. The accuracy of the results can be improved by eliminating compounding factors such as different tyre material and tract surface layout.
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| 7,001 | 12 |
https://allhiphop.com/news/hacker-takes-over-jessica-alba-s-twitter-account-to-support-ynw-melly-ZBwFbRUjkU2Nqjly9UH9bA/
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math
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(AllHipHop News) A mean spirited hacker took over Jessica Alba's Twitter account to spew hatred while supporting rapper YNW Melly.
The unknown person took aim at Jews, handicapped people and homosexuals.
“Nazi Germany Did Nothing Wrong And That’s On God n##ga," said one tweet.
Another read "God I hate handicapped f##gots," while another shouted out YNW Melly, who is facing a double murder charge in Florida.
"Free My Ni##a YNW Melly That Ni##a Way Too Talented For Jail," read another tweet.
Thankfulky, Jessica and her team were able to wrestle the account away from the hacker with the help of Twitter, but by then, the Tweets had already gone viral.
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CC-MAIN-2019-43
| 659 | 6 |
http://www.mat.dtu.dk/English/Erhvervssamarbejde.aspx
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math
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DTU Mathematics cooperates with industry on mathematical problems within applied functional analysis, discreet mathematics, geometry and dynamical systems.
DTU Mathematics offers BSc/MSc projects and PhD projects in cooperation with industry.
Toyota in Japan has financed a PhD project at DTU Mathematics on the optimation of car components.
If you consider or would like to enter into cooperation with DTU Mathematics, you are welcome to contact Professor Mads Peter Sørensen.
DTU Mathematics and the University of Southern Denmark host an annual European Study Group with Industry, ESGI, by turns.
A group of European mathematicians work on various problems for five days. Subsequently, the results are published on the Internet.
If your company has a proposal for a mathematical modelling project of relevance to the study group, you are welcome to contact Associate Professor Poul G. Hjorth or Associate Professor Jens Gravensen.
Several ESGI events have led to further cooperation between a company and DTU Mathematics.
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http://www.chegg.com/homework-help/questions-and-answers/364-f-638-f-capacitor-connected-series-across-300-v-battery-895-f-capacitor-connected-para-q1959259
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math
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A 3.64-F and a 6.38-F capacitor are connected in series across a 30.0-V battery. A 8.95-F capacitor is then connected in parallel across the 3.64-F capacitor. Determine the voltage across the 8.95-F capacitor.
Three identical resistors are connected in parallel. The equivalent
resistance increases by 800 when one resistor is removed and
connected in series with the remaining two, which are still in
parallel. Find the resistance of each resistor.
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s3://commoncrawl/crawl-data/CC-MAIN-2016-36/segments/1471982296931.2/warc/CC-MAIN-20160823195816-00206-ip-10-153-172-175.ec2.internal.warc.gz
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| 449 | 5 |
https://thewanderlustpilgrim.com/excursionist/why-gravitational-force-is-always-attractive-not-repulsive.html
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math
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In the case of gravity, mediated by spin 2 particles, charge is mass, which is always positive. Thus, q1q2 is always greater than zero, and gravity is always attractive. For spin 0 force mediators, however, there is no restriction on the charges and you can very well have repulsive forces.
Why is gravity attractive force and not repulsive?
The “gravitational force” is part of a theory of gravity that explains the phenomenon in terms of forces (so you can use Newton’s Laws of motion to make predictions). The force is attractive because the phenomenon is one of “accelerating together”. There is no way a repulsive force describes that.
Is gravitational force always attractive or repulsive?
Now, we know that the mass of the objects that is taken into consideration cannot be negative in nature. Hence, the nature of the gravitational force will always be attractive and not repulsive. Thus, we can conclude that gravitational force cannot be repulsive.
Why gravitational force is always attractive?
Gravitational force is always attractive based on the traditional understanding of matter, which has a positive mass.
Can the gravitational force be either attractive or repulsive?
Yes, both the force between charges and the gravitational force between matter can be either attractive or repulsive.
Why does gravity only ever act to attract other objects never repel them?
Gravity never acts to repel two objects. … The formula for gravitational attraction depends on the mass of each object ( m and M ), the distance between them ( r ), and the gravitational constant ( G ).
Is gravitational force attractive or repulsive class 9?
We all know that all the forces in nature exist in opposites, but gravitational force is the only force that always attracts every object and never reples any.
How is gravitational force repulsive?
It is shown that reduction of the gravitational mass of the system due to emitting gravitational waves leads to a repulsive gravitational force that diminishes with time but never disappears. This repulsive force may be related to the observed expansion of the Universe.
Why can the electric force be attractive or repulsive where the gravitational force is always attractive?
What is the main difference between electrical and gravitational forces? Explanation: Electric forces can be attractive or repulsive because charges may be positive or negative. In the case for gravitational forces, there are only attractive forces because mass is always positive.
Are gravitational interactions always attractive?
Gravitational interactions are always attractive and depend on the masses of interacting objects. There is a gravitational force between any two masses, but it is very small except when one or both of the objects have large mass.
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CC-MAIN-2022-05
| 2,785 | 19 |
https://www.photrio.com/forum/index.php?threads/kallitype.368/
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math
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Carl mentioned Kallitype was also a very nice process so it got me curious. Today I picked up 100 gr of silver nitrate at e bay, so I figure why not try? My question, has anybody tried this without sizing the paper? I hate sizing and if there is a paper where this can be done I would love to know which one. Or how about the addition of PVA to prevent the emulsion from sinking too much instead of sizing, has naybody tried this? Thanks.
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| 438 | 1 |
https://uwestroinski.wordpress.com/tag/proof/
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math
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When I asked my guest about his opinion on this little booklet edited by John Brockman, he actually started to smile and answered something like: ‘These smart scientists have a lot of dangerous ideas and have you recognized, all of their ideas are dangerous for other people? Scientists surely must be very caring.’ By then I was already used to his interesting approach to the concept of humor and decided to ignore the last remark. Instead I wanted to know, whether he had his own dangerous idea, preferably an idea dangerous for science.
He told me, that the single most dangerous idea for science is:
There is no proof.
The danger of this idea, according to him, does not stem from the fact that it might be true. The problem is, that you, as a scientist, cannot argue scientifically against it.
I was not able to follow. The Pytagorean theorem is proved! There are dozens of proofs, some of them hundred and thousands of years old. I have checked a few myself and all experts agree on the truth of this theorem. After all, this is not the classification of all finite simple groups and even this is settled. At least I hope so. How can one seriously think that there is no proof?
In a deliberately patient sounding voice he explained again, that the possible truth of the idea is not the problem, but our wrong understanding of what science actually is. Even in this moment when I writing down this post, I have no idea of what he was talking about. My face must have expressed my ignorance and he began a monologue on proofs. In essence he claims, that to deserve its name
a proof has to prove that it is a proof.
Otherwise, it is obviously not a proof, but only some consensus among the participating players. You can call it peer review if you like, but don’t call it a proof.
I am completely lost. No mathematician has ever proved that his proof is indeed a proof. That makes no sense! Or, does it? And if yes, then it is surely impossible! What do you think?
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CC-MAIN-2019-35
| 1,974 | 9 |
https://www.physicsforums.com/threads/non-standard-beam-bending-question-parallel-to-neutral-axis.613389/
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math
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Hi there, first post on these forums. I have a seemingly simply question about beam bending. We (mechanical engineers) are all very familiar with the standard beam bending scenario. The beams are always shown being loaded perpendicular to the neutral axis, regardless of the type of support. My question is, what is the method of solving a beam loaded parallel to the neutral axis? (See attachment) The image depicts a beam being pulled by a rope, lets say. The interesting part of it is that as the beam deflects, the moment arm of the load begins to grow with respect to the support. Any suggestions as to how to solve such a thing without resorting to computer modeling? I'm really just looking for the beginnings of an approach so that I can work it out for myself, but I'm on the fence as to where to begin. Any thoughts appreciated!
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https://steemit.com/mathematics/@drifter1/mathematical-analysis-integration-techniques-for-rational-functions
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math
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Mathematics - Mathematical Analysis Integration Techniques for Rational Functions
Hello its me again drifter1! Today we continue with Mathematical Analysis getting into another Integration Technique! The Integration of Rational Functions is not so difficult, but needs caution cause we can make mistakes in simple algebra calculations. You can check out my previous post about the Integration by Parts Technique here. So, without further do let's get started!
Rational Cases we already know:
Let's first get into Integrals that you already know how to solve, but are Rational.
- Integral of f'(x)/f(x) gives us ln|f(x)|+ c and doesn't need anything more
- Integral of 1/x^2+1 that gives us arctan(x) and other simple integrals like that
- Integrals of 1 / x^2 +- a^2 can be found using Substitution
- Integral of 1 / root(something) can be found using Substitution
Using Substitution to get a "solvable" rational integral:
1. If the rational function contains e^x then we set t = e^x => x = lnt and so dx = dt/t
We set t = e^x and end up with:
This is a rational integral that can be solved with the techniques that we will cover in a bit.
Also, don't forget that sinh(x) and cosh(x) can be represented with e^x like that:
to help us solve rational integrals that contain them or even tanh(x) = sinh(x)/cosh(x).
2. If the integral contains a n-root(ax+b/cx+d), where n a natural number then we set:
and end up with a rational function that contains t and can be solved with the techniques we will cover in a sec.
If the integral contains n-roots of ax+b/cx+d with n = n1, n2, ..., nn then we find the least common multiple (LCM) of n1, n2, ..., nn and t will equal this LCM-root of ax+b/cx+d.
Rational Function Integration Techniques:
A Rational Function is a quotient of the form P(x)/Q(x) .
As you already saw previously we can use substitution to get a rational integral from difficult integrals that else would be unsolvable. But, we didn't cover how to solve this rational integral that comes out.
To solve such integral we use the so called Partial fraction decomposition or expansion method. Where we write the given quotient/fraction as a sum of other fractions with simpler denominators and numerators of a smaller degree in each fraction.
Those fractions can be:
A/(x-r)^m, where m a natural number
(Ax + B) / (x^2 + px + q)^n, where n a natural number and the equation at the denominator has no (real) solutions [p^2 - 4q <0]
Doing this we create factions that are a simple f'(x)/f(x) integrals. But, this can only be done when the degree of P(x) is smaller then the degree of Q(x). So we will try to convert quotients with degree of P(x) >= degree of Q(x) to the other form.
So, we end up with 2 cases depending on the degree.
Case 1: (degP(x) >= degQ(x))
To convert into a Case 2 quotient we have to use the polynomial division of P(x)/Q(x).
To do this we have to find a remainder r(x) and quotient q(x), with 0 <= deg r(x) <= deg Q(x) .
And then the polynomials will be connected using the equation:
P(x) = Q(x) * q(x) + r(x) => P(x)/Q(x) = q(x) + [r(x) / Q(x)]
This second one will be a integral of the second Case.
The integral of q(x) will be a pretty simple linear polynomial case.
Case 2: (degP(x) < degQ(x))
We have to follow the following steps:
1. Write Q(x) as a product of fractions of the type:
(x - r)^m, where r is the solution of Q(x)
(x^2 + px + q)^n, where the equation has no real solutions
2. For each fraction of the type (x-r)^m we write a sum in the form:
A1/x-r + A2/(x-r)^2 + ... + Am/(x-r)^m, where A1, A2, ..., Am are real numbers.
In the same way for each fraction of the type (x^2 + px + q)^n we write a sum in the form:
(B1x + C1) / (x^2+px+q) + (B2x + C2) / (x^2+px+q)^2 + ... + (Bnx + Cn) / (x^2+px+q)^n ,
where Bi, Ci are real numbers and i = 1, 2, ..., n
3. Every rational function can be written as a sum of fractions as we already know from simple Algebra in school and so this sum of fractions or Partial fraction expansion will be equal to the given P(x)/Q(x). So, we have to add those unlike-quantitie fractions and the denominator will be equal either way and so we will check for which Ai, Bj, Cj etc. the numerators are equal to each other. This will give us a linear system of Ai, Bj, Cj etc. that we have to solve to calculate those values.
4. The integral of P(x)/Q(x) can then be written as a sum of those fractions having Ai, Bj, Cj calculated.
Integrals of the type A / (x-r)^m are pretty simple and are a basic f'(x)/f(x) case that gives us ln|f(x)| + c.
Integrals of Ax+B / (x^2 + px + q)^n are more difficult and we have to use substitution.
Setting u = x + c such a integral will become simpler and can then be solved using the same basic f'(x)/f(x) case, other basic integrals (mostly arctanx) or even another substitution!
Examples of Rational Integrals:
1. (x-r)^m example
Because degP(x) < deg Q(x) we are in Case2 directly and can start following the steps.
x^3 - 3x + 2 = (x - 1)^2*(x + 2)
So, (x - 1) ^2 will become two factions A/x-1 + B/(x-1)^2
(x + 2) will get only one faction C/x+2
This means that P(x)/Q(x) = A/x-1 + B/(x-1)^2 + C/x+2 that becomes:
P(x) / Q(x) = A(x-1)(x+2) + B(x+2) + C(x-1)^2 / (x+2)(x-1)^2
Where the numerator is equal to: (A+C)x^2 + (A+B-2C)x + (-2A+2B+C)
We want P(x) to be equal to the numerator and so we have to solve the linear system:
4x^2= (A+C)x^2 => 4 = A + C
-3x = (A+B-2C)x => -3 = A + B - 2C
5 = -2A + 2B + C
Solving this system with any method you like you will end up with:
A = 1, B = 2 and C = 3
And so P(x)/Q(x) = 1/x-1 + 2/(x-1)^2 + 3/x+2.
Integral(P(x)/Q(x))dx = integral(1/x-1)dx + 2*integral(1/(x-1)^2)dx + 3*integral(1/x+2)dx
= ln|x-1| + 2*(-1)*1/(x-1) + 3*ln|x+2| +c = ln|x-1| -2/x-1 + 3*ln|x+2| + c
2. (x^2 + px + q)^n example
Because degP(x) < deg Q(x) we are again in Case2.
x^2 + 2 = 0 has no solutions and so we have to write P(x)/Q(x) as a sum of fractions like that:
(Ax + B) / (x^2+2) + (Cx + D) / (x^2+2)^2
If we add those fractions we end up with:
P(x)/Q(x) = Ax^3 + Bx^2 + (2A+C)x + (2B+D) / (x^2+2)^2
We want P(x) = x^3 = Ax^3 + Bx^2 + (2A+C)x + (2B+D) and so:
x^3 = Ax^3 => A = 1
0x^2 = Bx^2 => B = 0
0x = (2A+C)x => -2A = C => C = -2
0 = 2B + D => D = -2B => D = 0
So, A = 1, B = D = 0 and C = -2.
Setting those values on our fraction sum we end up with:
P(x)/Q(x) = x/(x^2+2) + -2x/(x^2+2)^2.
Integral(P(x)/Q(x))dx = integral(x/(x^2+2))dx + integral(-2x/(x^2+2)^2)dx
The first one is again a ln|f(x)| case and the second again a power case and so the result is:
1/2*ln(x^2+2) + 1/(x^2+2) + c
3. combined types of fractions
You can directly see that P(x) < Q(x).
x^4 - 1 = (x-1)(x+1)(x^2 + 1)
So, we have two types of fractions and 1/x^4-1 now looks like this:
A/x-1 + B/x+1 + Cx+D/(x^2+1) = (A+B+C)x^3 + (A-B+D)x^2 + (A+B-C)x + (A-B-D) / x^4-1
If we set 1 equal to the numerator we end up with the following system:
A+B+C = 0
A-B+D = 0
A+B-C = 0
A-B-D = 1
If you solve this system using any method you like you will end up with:
A = 1/4, B = -1/4, C = 0, D = -1/2
And so our integral now looks like this:
integral(P(x)/Q(x))dx = 1/4*integral(1/x-1)dx -1/4*integral(1/x+1)dx -1/2*integral(1/x^2+1).
The first two are simple ln|f(x)| cases, but the last one is interesting cause its actually arctan(x)!
So, our final result is: 1/4*ln|x-1| -1/4*ln|x+1| - 1/2*arctan(x) + c
4. In Case1
degP(x)>degQ(x) and so we are in Case1
Knowing how to divide polynomials you do the following:
This explains them pretty good if you don't know them already.
This means that we know have to solve the integral:
x^2+3x -1 + (-2x+1)/x^2+1
We know that x^2+1 has no solution and so we can't tranform it into a Case 2. This means that we will try to create simple integrals in another way. We will simply rewrite the numerator as -2x +1 = -(x^2+1)' + 1 and solve the simple ln|f(x)| case and create a simple arctan(x) case.
So, our final integral is:
Integral(P(x)/Q(x)) = integral(x^2+3x-1)dx - integral(x^2+1)'/(x^2+1))dx + integral(1/x^2+1)dx
= x^3/3 + 3x^2/2 - x - ln(x^2+1) + arctan(x) + c .
Try solving the e^x integral example that we didn't finished with the function that contains t.
You must get ln|t^2 - 25| + c = ln|e^(2x) - 25| + c
And this is actually today's post and I hope you enjoyed it!
The next and final techniques that I will cover in our series will be about solving integrals of trigonometric functions. After that we will get into how we solve Limits that contain Roots, something that I completely forgot to talk about my Limit posts.
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http://nxassignmenthdsa.designheroes.us/the-law-of-gravity-by-newton-changed-the-course-of-history.html
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math
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The newton's law of gravity is also termed as newton's law of universal gravitation the physics law is given by the scientist sir isaac newton. Bibliography primary sources newton, isaac, philosophiae naturalis principia mathematica (“mathematical principles of natural philosophy”), london, 1687. I frequently get emails wanting to know whether gravity is a law or a theory is gravity a theory or a law newton's law of universal gravitation tells us. Timeline: the history of gravity newtonian gravity isaac newton publishes could an artificial intelligence be considered a person under the law. A falling apple supposedly made newton think about the 'gravity' of the a paradigm shift brought about by newton's law of gravitation was the history of the.
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https://www.hackmath.net/en/example/711
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Determine the discriminant of the equation:
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https://tvg.packprint.it/in-the-visible-spectrum-which-color-has-the-shortest-wavelength.html
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math
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In the visible spectrum which color has the shortest wavelength
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Violet. Violet waves have the most energy of the visible spectrum. Remember: " "c=flambda Therefore: " "f=c/lambda Here c is the speed of light in a vacuum. So: As wavelength decreases, frequency increases and, as E=hf, where h is constant (Planck's constant), so does the energy that the waves carry. Waves with a short wavelength have the most energy. Red waves have a relatively long ...|Light velocity v = 3×108m/sec. According to the light wavelength formula λ= ν*f. λ = (3×10^8 / 1)* 06.24×1014. λ = 4.80 x 10−7. Thus, this is all about the wavelength of visible light. From the above information, finally, we can conclude that these light waves are electromagnetic waves that are visible.| which part color of visible light has the longest wavelength || Shortest wavelength: Violet In the visible spectrum the shortest wavelength is of violet. Violet is right before ultraviolet in the spectrum. And according to the wave equation (i.e. speed= frequency * wavelength), frequency is inversely proportional to wavelength so shortest …|As the full spectrum of visible light travels through a prism, the wavelengths separate into the colors of the rainbow because each color is a different wavelength. Violet has the shortest wavelength , at around 380 nanometers, and red has the longest wavelength , at around 700 nanometers.|True or false: as you move along the spectrum, left to right, the wavelengths decrease in size (get smaller) Electromagnetic Spectrum Test Review DRAFT. 6th grade. 112 times. Other Sciences. ... Q. Put the visible light colors in order from longest wavelength to shortest wavelength. answer choices . Violet, Indigo, Blue, Green, Orange, Yellow ...| Visible light. Visible light is the small part within the electromagnetic spectrum that human eyes are sensitive to and can detect. Visible light waves consist of different wavelengths. The colour of visible light depends on its wavelength. These wavelengths range from 700 nm at the red end of the spectrum to 400 nm at the violet end.| Also, what color has the shortest wavelength? As the full spectrum of visible light travels through a prism, the wavelengths separate into the colors of the rainbow because each color is a different wavelength. Violet has the shortest wavelength, at around 380 nanometers, and red has the longest wavelength, at around 700 nanometers.| Visible light has a wavelength range from ~400 nm to ~700 nm. Violet light has a wavelength of ~400 nm, and a frequency of ~7.5*10 14 Hz. Red light has a wavelength of ~700 nm, and a frequency of ~4.3*10 14 Hz. Visible light makes up just a small part of the full electromagnetic spectrum.|Violet is the most energetic color and red is the least. According to the figure, if someone shined light with a wavelength of 550 nm at us it would look green. If someone shined white light at us, what wavelength does it have? White is not in our visible spectrum because it is composed of all the wavelengths of light. A light bulb is a good ...| The shortest wavelength of visible light produces the color. The shortest wavelength of visible light quizlet. The shortest ... , the concept of the visible spectrum has become more defined, as the light out of the visible range has been discovered and characterized by William Herschel (infrared) and Johann Wilhelm Ritter (Ultravioletto ...| The first factor, hue is what we are usually talking about when we refer to color (a red shirt has a red hue). The hue is basically the specific name for the specific wavelength that is reflected by the object. Violet has the shortest visible wavelength in the visible spectrum (~ 400 nm), and red has the longest (700 nm).User: The shortest wavelength within the visible spectrum is _____ light. A. red B. blue C. violet D. orange Weegy: The shortest wavelength within the visible spectrum is violet. Score 1 User: If a person looking at a poster sees green instead of yellow and doesn't see red at all, this person most likely has color blindness where _____ nerves fail to respond to light properly.|Which color of visible light has the shortest wavelength? the longest wavelength? the lowest frequency? the highest frequency? What color of light in the visible spectrum appears brightest Asked by wiki @ 12/06/2021 in Physics viewed by 31 persons|Gamma rays, a form of nuclear and cosmic EM radiation, can have the highest frequencies and, hence, the highest photon energies in the EM spectrum.For example, a γ-ray photon with f = 10 21 Hz has an energy E = hf = 6.63 × 10 −13 J = 4.14 MeV. This is sufficient energy to ionize thousands of atoms and molecules, since only 10 to 1000 eV are needed per ionization.|lengths of visible light as red and the shortest as violet. This narrow band is very small compared with the rest of the spectrum. In fact, visible light is only about 1/100,000 of the complete EM spectrum. The area below visible light and above microwaves is the infrared part of the EM spectrum. Above visible light is the ultraviolet part of ... |The visible light spectrum (380−750 nm) is the light we are able to see. This spectrum is often referred to as "ROY G BIV" as a mnemonic device for the order of colors it produces. Violet has the shortest wavelength (about 400 nm) and red has the longest wavelength (about 650-700 nm).|The electromagnetic spectrum is a range of frequencies of different energy waves such as gamma rays, X rays, ultraviolet rays, visible light, infrared waves, microwaves and radio waves. The visible light frequencies lie between the frequencies of the ultraviolet rays and infrared waves. Color. Frequency (THz) Wavelength (nm) Red. 400-484. 620-750.|The color with the shortest wavelength among all colors in light spectrum is violet, in electromagnetic spectrum it is the gamma ray with the shortest wavelength among other waves . THE LIGHT AND ELECTROMAGNETIC SPECTRUM. Light spectrum refers to the range of colors, ...|WAVELENGTHS OF VISIBLE LIGHT. As the full spectrum of visible light travels through a prism, the wavelengths separate into the colors of the rainbow because each color is a different wavelength. Violet has the shortest wavelength, at around 380 nanometers, and red has the longest wavelength, at around 700 nanometers.
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https://cetyhemonihu.dirkbraeckmanvenice2017.com/applied-derivatives-book-36357jn.php
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math
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3 edition of Applied Derivatives found in the catalog.
January 15, 2002
by Blackwell Publishers
Written in English
|The Physical Object|
|Number of Pages||384|
Applied Calculus Math Karl Heinz Dovermann Professor of Mathematics University of Hawaii derivative is at least as clear in our approach as it is in the one using limits. and a high school level book by M¨uller which use this approach. Calculus was File Size: 1MB. The Definition of the Derivative – In this section we will be looking at the definition of the derivative. Interpretation of the Derivative – Here we will take a quick look at some interpretations of the derivative. Differentiation Formulas – Here we will start introducing some of the differentiation formulas used in File Size: 2MB.
The book is in use at Whitman College and is occasionally updated to correct errors and add new material. The latest versions may be found by going to this work or a derivative, include the history of the document. This text was initially written by David Guichard. The . Partial Derivatives, pp. Surface and Level Curves, pp. Partial Derivatives, pp. Tangent Planes and Linear Approximations, pp. Directional Derivatives and Gradients, pp. The Chain Rule, pp. Maxima, Minima, and Saddle Points, pp.
Finding increasing interval given the derivative (Opens a modal) Increasing & decreasing intervals review (Opens a modal) Rates of change in other applied contexts (non-motion problems) 4 questions. Practice. Mean value theorem. Learn. Derivative applications challenge. 4 questions. Practice. Derivatives describe the rate of change of quantities. This becomes very useful when solving various problems that are related to rates of change in applied, real-world, situations. Also learn how to apply derivatives to approximate function values and find limits using L’Hôpital’s rule.
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Local wage rates for selected occupations in public and private construction, 1936.
Inaugural address of Robert Maynard Hutchins
Technical report on the potential growth of obnoxious aquatic plants and practical systems of control in the Republic of India
Report of all contracts for carrying the mail made within the fiscal year ended June 30, 1890.
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Suggested Books for MBA Financial Derivatives. Gupta S.L., FINANCIAL DERIVATIVES THEORY, CONCEPTS AND PROBLEMS PHI, Delhi, Kumar S.S.S. FINANCIAL DERIVATIVES, PHI, New Delhi, Achievements and Prospects,’’ Journal of Applied Corporate Finance, 4 (Winter ): 4– MBA 4th Sem Notes, Study Materials & : Daily Exams.
In Commodity Derivatives: Markets and Applications, Neil Schofield provides a complete and accessible reference for anyone working in, or studying commodity markets and their associated derivatives. Dealing primarily with over the counter structures, the book provides extensive coverage of both hard and soft commodities, including gold, crude oil, electricity, plastics, emissions and.
Get this from a library. Applied derivatives: options, futures, and swaps. [Richard J Rendleman, Jr.] -- Based on some of the ground-breaking work Richard Rendleman did helping to develop the Binomial Option Pricing Model inthis book is the culmination of 18 years of research in option pricing.
Prelude to Applications of Derivatives A rocket launch involves two related quantities that change over time. Being able to solve this type of problem is just one application of derivatives introduced in this chapter.
We also look at how derivatives are used to find maximum and minimum values of functions. However, the book will also be useful for applied scientists from engineering and physics.” (Jan Lovíšek, zbMATH, Vol.) “The book under review concerns new methods of solving a class of shape optimization problems appearing in continuum mechanics, mainly in solid mechanics, composites and plate-like bodies.
The resulting derivative values are useful for all scientific computations that are based on linear, quadratic, or higher order approximations to nonlinear scalar or vector functions.
AD has been applied in particular to optimization, parameter identification, nonlinear equation solving, the numerical integration of differential equations, and.
BASICS OF EQUITY DERIVATIVES CONTENTS 1. Introduction to Derivatives 1 - 9 2. Market Index 10 - 17 3. Futures and Options 18 - 33 4. Trading, Clearing and Settlement 34 - Historical notes. In applied mathematics and mathematical analysis, a fractional derivative is a derivative of any arbitrary order, real or complex.
Its first appearance is in a letter written to Guillaume de l'Hôpital by Gottfried Wilhelm Leibniz in Fractional calculus was introduced in one of Niels Henrik Abel’s early papers where all the elements can be found: the idea of.
Following the table of contents in Applied Calculus 7e by Stefan Waner and Steven R. Costenoble You can get back here from anywhere by using the Everything for Applied Calc link. Note: To change the edition of the book, use the navigation on the top left.Applications of the Derivative tion Optimiza Many important applied problems involve finding the best way to accomplish some task.
Often this involves finding the maximum or minimum value of some function: the minimum time to make a certain journey, the minimum cost for doing a task, the maximum power that can be generated by a device.
Derivatives Demystified follows a sequence that is designed to show that, although there are many applications of derivatives, there are only a small number of basic building blocks, namely forwards and futures, swaps and options.
The book shows how each building block is applied to different markets and to the solution of various risk.
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http://proxy.osapublishing.org/josa/abstract.cfm?uri=josa-29-2-101
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math
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When the temperature of a black body is such that the maximum spectral efficiency of production of radiant energy occurs a t a given wave-length there also occurs at that wave-length, both the maximum spectral rate of production and the maximum spectral efficiency of production of photons. The particular wave-length involved is the effective wave-length for the total radiation, which is defined as the wave-length at which, for a given temperature, the percentage rate of increase in spectral radiancy with temperature is the same as for the total radiation from the black body source.
© 1939 Optical Society of AmericaFull Article | PDF Article
OSA Recommended Articles
A. G. Worthing
J. Opt. Soc. Am. 29(2) 97-100 (1939)
J. Opt. Soc. Am. 29(2) 92-96 (1939)
J. Opt. Soc. Am. 29(12) 520-530 (1939)
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| 801 | 7 |
https://www.mcknights.com/news/study-coordinated-care-doesnt-lead-to-medicare-savings/article/101832/
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math
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Study: Coordinated care doesn't lead to Medicare savings
Programs with low-cost enrollees are not likely to generate savings for Medicare, a study of a coordinated care demonstration indicates.
Coordinated care programs are not likely to realize large enough savings to offset their intervention cost, according to the authors of a study of Medicare Coordinated Care Demonstration (MCCD) sites by Mathematica Policy Research Inc.
"[A] few programs may be unable to generate net savings even if they were to reduce Medicare costs by 20 percent," the study stated.
The study is part of an early examination of 15 sites participating in the MCCD, a demonstration project mandated by Congress and administered through the Centers for Medicare & Medicaid Services. Only four of the 15 sites had met their own enrollment targets for the first year, Mathematica found.
Still, patients in the demonstration were pleased with their care, reporting increased satisfaction with their overall care and appearing to have increased understanding of their diseases, Mathematica researchers said. The report can be found at http://www.mathematica-
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https://www.coursehero.com/tutors-problems/Nursing/11512637-1-A-physician-orders-03-epinephrine-subcutaneous-stat-for-a-cl/
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math
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1.) A physician orders 0.3 epinephrine subcutaneous stat for a client experiencing anaphylaxis. Calculate the amount the nurse should administer if the label indicates that the drug is supplied in a 1:1000 strength solution. Record your answer using one decimal place.
The correct dose amount is 0.3mls... View the full answer
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| 326 | 2 |
https://www.hackmath.net/en/math-problem/35253
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math
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Replace the two cube-shaped containers with 0.8 dm and 0.6 dm edges with a single cube-shaped one so that it has the same volume as the two original ones together. What is the length of the edge of this cube?
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Related math problems and questions:
- Cube containers
Two containers shaped of cube with edges of 0.7 m and 0.9 m replace a single cube so that it has the same volume as the original two together. What is the length of the edges of the new cube?
- Three cubes
Two cube-shaped boxes with edges a = 70 cm; b = 90 cm must be replaced by one cube-shaped box. What will be its edge?
- Two rectangular boxes
Two rectangular boxes with dimensions of 5 cm, 8 cm, 10 cm, and 5 cm, 12 cm, 1 dm are to be replaced by a single cube box of the same cubic volume. Calculate its surface.
- The cube
The cube has a surface area of 216 dm². Calculate: a) the content of one wall, b) edge length, c) cube volume.
- Length of the edge
Find the length of the edge of a cube with a cm² surface and a volume in cm³ expressed by the same number.
- Cube 9
What was the cube's original edge length after cutting 39 small cubes with an edge of 2 dm left 200 dm³?
- Cube into cylinder
If we dip a wooden cube into a barrel with a 40cm radius, the water will rise 10 cm. What is the size of the cube edge?
- Cube basics
How long is the edge length of a cube with volume 15 m³?
- Cube edge
Determine the edges of the cube when the surface is equal to 37.5 cm square.
- Cube 5
The surface of the cube is 15.36 dm². How will change the surface area of this cube if the length of the edges is reduced by 2 cm?
- Cube 8
The surface of the cube is 0.54 m². Calculate the length of the cube edge.
- Cube surface and volume
Find the surface of the cube with a volume of 27 dm³.
- Water level
How many cm will the water level in a cube-shaped tank with an edge of 3 m drop if we discharge 189 hl of water?
- Tetrahedral prism
The height of a regular tetrahedral prism is three times greater than the length of the base edge. Calculate the length of the base edge, if you know that the prism volume is 2187 cm³.
- Two boxes-cubes
Two boxes cube with edges a=38 cm and b = 81 cm is to be replaced by one cube-shaped box (same overall volume). How long will be its edge?
- Cube edges
If the edge length of the cube increases by 50%, how does the volume of this cube increase?
- The height of prism
The base of the perpendicular prism is formed by a right triangle with perpendiculars 30 cm and 40 cm long. This prism has the same volume as a cube with an edge length of 3 dm. Find its height in cm.
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http://fruitcomputing.com/time-warp
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math
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A look at the history and development of computing and why Raspberry has done the 'TIME WARP"
This insight into history of computing hardware covers the developments from simple devices to assist with calculation, to mechanical calculators, punched card data processing systems to modern stored programme computers.
Before the 20th century, most calculations were done by humans. Those mechanical devices to help humans with calculations were called "calculating machines" and the machine operator was called the computer.
The first 'computers' were just mechanical devices that required the user to set up the initial values of an elementary arithmetic operation, then the operator would manipulate the machine to obtain the result. For instance, the slide rule and analogue computers represented numbers in a continuous form, for example the distance along a scale, a voltage or rotation of a spindle.
Things have been used to help computation for thousands of years, usually ways of counting things, using sticks and stones or whatever else was available. The abacus was widely used in ancient times for arithmetic tasks and was used in Babylonia as early as 2400 BC. Since then many other forms of reckoning devices have been invented. Several simple mechanical analog computers were built in ancient and medieval times to perform astronomical calculations.
Scottish mathematician and physicist John Napier found that the multiplication and division of numbers could be done by the addition and subtraction of their logarithms. This led to a device called 'Napier's bones', an abacus-like device that simplified these calculations. This led to the invention in the 1600's of various slide rules and other mathmatical calculating devices.
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https://archive.sap.com/discussions/thread/1313906
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math
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How to change pricing Decimal Places?
Howm can I change decimal places in material pricing?Till now system allow us prices to appear upto two decimal places. How to get it till three decimal places?
I did not find it in condition type control. This price is maual.
Can I chage this decimal places in material master level?
Can I chage it in PO/ SA level?
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https://mathpuzzlewiki.com/index.php?title=Three_princesses&oldid=665
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math
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Found this one on the xkcd logic puzzle forum. I really like it.
You are the most eligible bachelor in the kingdom, and as such the King has invited you to his castle so that you may choose one of his three daughters to marry. The eldest princess is honest and always tells the truth. The youngest princess is dishonest and always lies. The middle princess is mischievous and tells the truth sometimes and lies the rest of the time.
As you will be forever married to one of the princesses, you want to marry the eldest (truth-teller) or the youngest (liar) because at least you know where you stand with them.
The problem is that you cannot tell which sister is which just by their appearance, and the King will only grant you ONE yes or no question which you may only address to ONE of the sisters. What yes or no question can you ask which will ensure you do not marry the middle sister?
Although you might be able to solve this puzzle using a meta-question along the lines of "if I asked them what you would say if...", there is a simpler solution. Also, the question you ask can be something that all three sisters definitely know the true answer to.
Assume the three sisters are standing in a straight line. As the sister in the middle, "Is your sister on your right older than your sister on your left?" Marry the sister she indicates as younger.
There are three four possible cases. The sister standing in the middle could be the eldest, in which case she would answer truthfully. In this case, you should marry whichever sister she claims is younger, as this will be the youngest sister of the three. If the sister standing in the middle is the youngest, then she will lie to you. Thus you want to marry the sister she identifies as the younger, who will actually be the elder of the two, and as such the eldest sister of the three. Cases 3 and 4 are that you are actually asking the middle-aged sister, and she either answers truthfully or falsely. But in either case, you can select the sister she claims is younger, as that sister would either be the youngest or the eldest of the three. So always selecting the sister indicated to be the youngest leaves you with an acceptable outcome.
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https://are5community.ncarb.org/hc/en-us/community/posts/360029549033-What-percentage-of-candidates-pass-all-ARE-tests-without-failing-a-single-one-
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math
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What percentage of candidates pass all ARE tests without failing a single one? This question is directed at NCARB as they would be the only ones that know. It doesn't have to be version specific, but it can if that's easier. I am curious what the answer is, but can't seem to find it anywhere.
Post is closed for comments.
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https://studysoup.com/note/73424/university-of-south-carolina---columbia-stat-517-fall-2015
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math
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COMPUTING IN STATISTICS
COMPUTING IN STATISTICS STAT 517
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This 10 page Class Notes was uploaded by Shane Marks on Monday October 26, 2015. The Class Notes belongs to STAT 517 at University of South Carolina - Columbia taught by D. Hitchcock in Fall. Since its upload, it has received 47 views. For similar materials see /class/229653/stat-517-university-of-south-carolina-columbia in Statistics at University of South Carolina - Columbia.
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STAT 517 DelwicheSlaughter Chapter 2 HitchcockGrego Chapter 2 Getting Data Into SAS 0 Data stored in many different formsformats 0 Four categories of methods to read in data 1 Entering data directly through keyboard small data sets 2 Creating SAS data sets from raw data files 3 Converting other software s data files eg Excel into SAS data sets my favorite 4 Reading other software s data files directly often need additional SASACCESS products University of South Carolina Page 1 STAT 517 DelwicheSlaughter Chapter 2 HitchcockGrego Import Window 0 Allows you to import various types of data files Microsoft Excel formats 0 Default is for first row to be variable names Change this using Options button 0 Options button also selects worksheet from workbook 0 Work library data set deleted after exiting SAS 0 Other libraries data set saved after exiting SAS but not necessarily library location 0 Can save PROC IMPORT statements used to import the data University of South Carolina Page 2 STAT 517 DelwicheSlaughter Chapter 2 HitchcockGrego Reading in Raw Data If you type data directly into a SAS program this is indicated with a statement like cards datalines lines o If your raw data is in an external file use an INFILE statement to tell SAS where it is o Specify full path name 0 If your lines are longer than 256 characters use LRECL University of South Carolina Page 3 STAT 517 DelwicheSlaughter Chapter 2 HitchcockGrego Data Separated by Spaces 0 This style is called free format since the number of spaces in between variables is flexible 0 Use INPUT statement to name variables 0 Include a after names of character variables University of South Carolina Page 4 STAT 517 DelwicheSlaughter Chapter 2 HitchcockGrego Data Arranged in Columns 0 Knowledge of this approach is less important nowadays 0 Important applications still exist 0 Each value of a variable is found at the same spot on the data line 0 Advantages 1 Don t need space between values 2 Missing values don t need special symbol can be blank 3 Character data can have blanks 4 Can skip variables you don t need to read into SAS Example INPUT varl 1 10 var2 11 15 var3 16 30 University of South Carolina Page 5 STAT 517 DelwicheSlaughter Chapter 2 HitchcockGrego Data Not in Standard Format 0 Types of nonstandard data 1 Numbers with commas or dollar signs 2 Dates and times of day 0 We can read nonstandard data using codes known as informats 0 Most informats end in so SAS won t confuse them with a variable 0 Import from Excel often assigns informats automatically 0 p 4445 lists many SAS informats Note that date informats are converted to a numerical value Julian date University of South Carolina Page 6 STAT 517 DelwicheSlaughter Chapter 2 HitchcockGrego Other Inputting Issues 0 You can mix input styles read in some variables liststyle others columnstyle others using informats even the order can be shuffled o Eg you can explicitly move SAS to a specific column number Example 5 0 moves SAS to the 50th column Messy Data 0 colon modifier Tells SAS exactly how many columns long a variable s field is but stops when it reaches a space 0 Example Deptname 15 tells SAS to read Deptname for 15 characters or until it reaches a space 0 This method is not appropriate for character data with embedded spaces University of South Carolina Page 7 STAT 517 DelwicheSlaughter Chapter 2 HitchcockGrego Multiple Lines of Data per Observation 0 Sometimes each observation will be on several lines in the raw data file census data standardized test scores etc 0 Use to tell SAS when to go to the next line 0 Or use 2 for example to tell SAS to go to the 2nd line of the observation Multiple Observations per Line of Raw Data 0 Sometimes several observations will be on one line of data 0 This is common for textbook exercises 0 Use to tell SAS to stay on the raw data line and wait for the next observation Reading Part of a Data File 0 Sometimes we want to modify data input based on values of one variable 0 We can read just the first variables using the sign University of South Carolina Page 8 STAT 517 DelwicheSlaughter Chapter 2 HitchcockGrego Reading Delimited Files 0 These instructions have been completely subsumed by Excel imports o DLM allows you to have something other than spaces separated data values 0 Comma delimiters DLM 0 Tab delimiters DLM O 9 X o delimiters DLM o This assumes two delimiters in a row is the same as a single delimiter o What if two commas in a row indicate a missing value c What if some data values contain commas 0 Can use DSD option 0 Note Data values with commas in them must be in quotes 0 Default with DSD is comma delimiters but can specify other delimiters with DLM option University of South Carolina Page 9 STAT 517 DelwicheSlaughter Chapter 2 HitchcockGrego SAS data sets Temporary and Permanent 0 Data sets stored in Work library are temporary removed upon exiting SAS 0 Data sets stored in other libraries are permanent will be saved upon exiting SAS 0 You can specify the library when creating a data set in the DATA step Example Suppose you have a library called sportlib this is a libref DATA sportlibbaseball creates a data set baseball to be stored in the sport lib library permanent DATA workbaseball would store baseball in the work library temporary DATA baseball by default stores ba s ebal l in the we rk library temporary University of South Carolina Page 10
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http://www.sparkpeople.com/mypage.asp?id=KAYLEEN1989&comment_page=2
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math
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You're doing amazing. Starting out I weighed about 180. At my last weigh in (last weds) I weighed 175. My first MAJOR goal is 165. I want to be able to fit into my size 14 again, then go from there. I would love to talk and we can help each other if that is okay with you? 2455 days ago
Hi! I got your comment about the coke. Funny that you said that you would get an attitude if you didn't have a coke, that is exactly like me! If I start wanting a coke and I can't get one I start getting B**chy! LOL! I think I have tried coke zero only once and I am not sure if I liked it or not but I am going to try it again and see if I can start replacing a can a day. I am hoping to wean myself off of pop in the next 3months and only allow myself to have it on special occasions. I don't necessarily want move over to diet pops or coke zero because I don't want the temptation because I would still be drinking pop. I don't know we will see! Hopefully (fingers crossed) 2455 days ago
¸.•*¨¸.•´¸.•*¨) ¸.•*¨) (¸.•´ (¸.•´ (¸.•´¸¸.•¨¸♥¨`*,¸.•*´¨`*• .¸♥. ¸.•♥´ .•´¨¨ ¸´¸.•´¨Welcome to the EE team!! I’ve belonged to a lot of teams here on spark-- i really do believe that the Emotional Eaters team is one of the very best, it’s a great group of people- very supportive and encouraging-- and it is very refreshing to talk with people who "get" what you're going through!! ¸¸.•¨¸♥¨`*,¸.•*´¨`*• .¸♥.*¸.•´¸.•*¨¸.•*¨¸.•´¸.•*¨) ¸.•*¨) Check out the main page of the EE team- there are “stickied” topics you may be interested in to get involved- a buddy thread, a place to introduce yourself, weigh-in challenge, a birthday post. ¸.•*¨¸.•´¸.•*¨(¸.•´ (¸.•´ (¸.•´¸¸.•¨¸♥¨`*,¸.•*´¨`*• .¸♥. ¸.•♥´ .•´¨¨ ¸´¸.•´¸.•*¨)¸¸.•´ ..•-~'¸.•*¨) Spark has a lot of great tools, and you will learn which ones work best for you. The best tools are the people tho, always willing to lend a hand, an ear, or a shoulder. I’ve been here for over a year now, and I still am overwhelmed, every day, by the kindness and goodness of others on this team!! That has made a world of difference for me. I hope you have the same success! ¸¸.•¨¸♥¨`*,¸.•*´¨`*• .¸♥.*.•*¨¸.•´¸.•* (¸.•´ (¸.•´ ♥¸.•´¸¸.• (¸.•´ (¸.•*¨ (¸.¸.•*´¨`*• .¸♥. You are- WONDERFUL-cuz you’re you!!! BELIEVE IT!!! operationbeautiful-- END THE FAT TALK!!! ¸.•*¨¸.•´¸.•*¨(¸.•´ (¸.•´(¸.•´¸¸.•¨¸♥¨`*,¸.•*´¨`*• .¸♥. (¸.¸.•*´¨`*• .¸♥. ~~best of luck to you on all of your goals!!! (¸.¸.•*´¨`*• .¸♥.
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https://www.quantamagazine.org/authors/leila-sloman/
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math
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“Ribbon concordance” will let mathematicians compare knots by linking them across four-dimensional space.
The famed Navier-Stokes equations can lead to cases where more than one result is possible, but only in an extremely narrow set of situations.
Van der Waerden’s conjecture mystified mathematicians for 85 years. Its solution shows how polynomial roots relate to one another.
A new computer program fashioned after artificial intelligence systems like AlphaGo has solved several open problems in combinatorics and graph theory.
A team of mathematicians has solved an important question about how solutions to polynomial equations relate to sophisticated geometric objects called Shimura varieties.
The n-queens problem is about finding how many different ways queens can be placed on a chessboard so that none attack each other. A mathematician has now all but solved it.
Get highlights of the most important news delivered to your email inbox
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https://chemteam.info/Metric/Metric-Conv-TwoUnit.html
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math
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Return to Metric Table of Contents
Metric conversion where only one unit is converted
Go to 10 two-unit metric problems
Doing this type of problem is simply a succession of conversions from one unit to another. You first convert one side of the fraction, say, the numerator, then you do the denominator.
Often, a teacher will present these solutions as one long string of conversions. You also see this type of presentation in textbooks. It can be quite confusing when you first see it.
This technique is called "dimensional analysis" (the older term), with "factor label method" being the newer term. DA can also called "unitary conversions," or "unitary rates." The word unitary comes from the fact that the numerator and the denominator in a conversion both describe the same quantity.
As an example, take this conversion factor:
1000 mL / 1 L
Both 1000 mL and 1 L describe the same-sized volume, so 1000 mL / 1 L is referred to as a unitary rate. Since 1000 mL and 1 L describe the same volume, we can think of 1000 mL / 1 L as being like multiplying some number by 1. The description of the volume changes units, but it still describes the same sized volume.
The ChemTeam tends to present two-unit conversion problems as a sequence of one-step calculations. However, I will also reference the one-line type presentation that is the hallmark of dimensional analysis. On a professional basis, I do not believe the one-line approach is the proper tool to use when teaching these types of problems. There are those that disagree with me.
Doing DA problems, to me, are like balancing equations or predicting products of a reaction. There are LOTS of little bits that you have to remember and, when that is the case, experience is really, really important. The problem you would face is to be able to read a one-line solution and back-track to the logic the writer used. That can be difficult, especially for a rookie.
Conclusion: lots of examples for you to study!
Example #1: Convert the speed of light (3.00 x 108 m/s) to km/year.
1) We'll start with the numerator, since that can be done in a one step conversion.
3.00 x 108 m 1 km –––––––––– x –––––– = 3.00 x 105 m/s 1 s 1000 m
2) Now, we turn to converting seconds to years. This I will do in a step-by-step manner. I happen to have memorized that there are 3600 seconds in one hour. So, we start with that conversion.
3.00 x 105 km 3600 s ––––––––––– x ––––– = 1.08 x 109 km/hr 1 s 1 hr
3) Continuing the calculations, we move step-by-step from hours to days and then to years (we can skip months, since we know how many days there are in a year.
1.08 x 109 km 24 hr ––––––––––– x ––––– = 2.592 x 1010 km/day 1 hr 1 day
2.592 x 1010 km 365.25 day ––––––––––––– x ––––––––– = 9.47 x 1012 km/yr (to three sig figs) 1 day 1 yr
4) If I were to present it as a one-line type calculation (the usual presentation form in dimensional analysis), it would be this:
3.00 x 108 m 1 km 3600 s 24 hr 365.25 day –––––––––– x ––––––– x ––––––– x ––––––– x ––––––– = 9.47 x 1012 km/yr 1 s 1000 m 1 hr 1 day 1 yr
On the Internet, it may also be seen this way:
3.00 x 108 m/s x (1 km / 1000 m) x (3600 s / hr) x (24 hr / day) x (365.25 day / yr) = 9.47 x 1012 km/yr
5) One advantage to the above presentation is that you simply carry out the steps in sequence (divide by 1000, multiply by 3600, mult by 24 and mult by 365.25) on your calculator and then round off.
6) Doing it step-by-step results in intermediate answers along the way, but I think it's better to teach the steps rather than confront a student with the dimensional analysis method right from the start of instruction.
Notes on variations of the above problem:
1) Notice that I used 365.25 days rather than 365. Using the latter figure results in an answer of 9.4608 x 1012 km/yr, which rounds off to 9.46 x 1012 km/yr.
2) This problem can start with cm/s rather than m/s. The speed of light in cm/s is 3.00 x 1010 cm/s.
3) Often, this problem ends in km/hr. Consequently, the question you could see might ask for the conversion from cm/s to km/hr. As in, right now . . . .
Example #2: Light travels at a speed of 3.00 x 1010 cm/s. What is the speed of light in kilometers/hours?
1) Convert cm/s to km/s:
(3.00 x 1010 cm/s) (1 m / 100 cm) (1 km / 1000 m) = 3.00 x 105 km/s
2) Convert seconds to hours:
(3.00 x 105 km/s) (60 s / 1 min) (60 min / 1 hr) = 1.08 x 109 km/hr
3) A slightly more compact version:
(3.00 x 1010 cm/s) (1 km / 105 cm) = 3.00 x 105 km/s
(3.00 x 105 km/s) (3600 s / 1 hr) = 1.08 x 109 km/hr
4) Done in DA (dimensional analysis) style:
3.00 x 1010 cm 1 m 1 km 60 s 60 min –––––––––– x ––––––– x ––––––– x ––––––– x ––––––– = 1.08 x 109 km/hr 1 s 100 cm 1000 m 1 min 1 hr
The two length conversions could be combined (1 km = 105 cm) and the two time conversions could be combined (1 hr = 3600 s).
Example #3: Convert 6.43 g/mL to its equivalent in kg/L.
1) Convert grams to kilograms:
6.43 g/mL x (1 kg/1000 g) = 0.00643 kg/mL
2) Convert mL to L:
0.0643 kg/mL x (1000 mL/L) = 6.43 kg/L
3) Dimensional analysis:
6.43 g 1 kg 1000 mL –––––– x –––––– x ––––––– = 6.43 kg/L 1 mL 1000 g 1 L
Comment: teachers like to ask this question on the test.
Example #4: A cylindrical piece of metal is 4.50 dm in height with radius of 5.50 x 10¯5 km.
(a) Calculate the volume in milliliters to the correct significant figures given V = π r2 h for a cylinder.
(b) Calculate the volume in mm3
Solution to (a):
1) The key to solving part (a) is to remember that cm3 and mL are the same volume, so 1 cm3 = 1 mL. So, convert both measurements of the cylinder to cm::
4.50 dm 10 cm ––––––– x ––––– = 45.0 cm 1 1 dm
5.50 x 10¯5 km 105 cm ––––––––––– x ––––– = 5.50 cm 1 1 km
2) Plug our numbers into the volume formula provided to get cm3.
V = π r2 h
V = (3.14159) (5.50 cm)2 (45.0 cm)
V = 4276.5 cm3
Rounding to three sig figs and noting that 1 cm3 = 1 mL, we have this for the final answer:
V = 4280 mL = 4.28 x 103 mL
Solution to (b):
1) The unit we need on the height and radius is mm, so convert 45.0 cm to 450 mm and 5.50 cm to 55.0 mm. Then plug back into the volume formula:
V = (3.14159) (55.0 mm)2 (450 mm)
V = 4276489 mm3
To three sig figs, we have 4.28 x 106 mm3
2) Notice that both numbers got increased by a factor of 10 and then within the volume formula, there is a total factor increase of 103 (because one of factor of 10 increase was squared to give a factor of 100 increase). That means the answer to part (b) is the answer to part (a) times 1000, resulting in 4.28 x 106 mm3.
Example #5: Convert 4.09 x 10¯6 kg/L to mg/cm3 using dimensional analysis.
1) When dimensional analysis is specified in a problem, the usual answer desired is in the form of all the conversions gathered together into one line. I will build the final answer up one conversion at a time. Each comment with an arrow is about the last conversion in each line.
4.09 x 10¯6 kg/L x (1000 g / kg) <--- converts kg to g
4.09 x 10¯6 kg/L x (1000 g / kg) x (1000 mg / 1 g) <--- converts g to mg
4.09 x 10¯6 kg/L x (1000 g / kg) x (1000 mg / 1 g) x (1 L / 1000 mL) <--- converts L to mL
4.09 x 10¯6 kg/L x (1000 g / kg) x (1000 mg / 1 g) x (1 L / 1000 mL) x (1 cm3/mL) <--- converts mL to cm3
the answer is 0.00409 mg/cm3
2) Notice that the above conversion converted through the base unit of grams, as in kg to g, then g to mg. You can combine those two conversions if so desired:
4.09 x 10¯6 kg/L x (106 mg / kg) x (1 L / 1000 mL) x (1 cm3/mL) = 0.00409 mg/cm3
3) Here's the most-common way DA solutions are formatted:
4.09 x 10¯6 kg 106 mg 1 L 1 cm3 ––––––––––– x –––––– x ––––––– x ––––– = 0.00409 mg/cm3 1 L 1 kg 1000 mL 1 mL
4) Some teachers prefer the DA method for homework and test answers. Some prefer the steps to be separated (with intermediate answers shown). Others do not care. Be sure to check what your teacher desires.
Example #6a: Convert 303.0 mi/hr to feet/min.
V = (303.0 mi/hr) (1 hr / 60 min) (5280 ft / mile) = 26600 ft/min
303 mi 1 hr 5280 ft –––––– x ––––– x –––––– = 26660 ft/min (to 4 sig figs) 1 hr 60 min 1 mi
The hr/min factor converts 303.0 mi per hr to 5.05 mi per min.
The ft/mi factor converts 5.05 mi per min to 26664 ft per min.
The factors used algebraically cancel units to give the units wanted.
The final answer is 26660 ft/s. It has been rounded off to four significant figures.
Note that this example uses English units. The principles of converting are the same as with metric units.
The hr/min conversion as well as the foot/mile conversion are defined amounts. As such, they play no role in determining significant figures.
Example #6b: Convert 303.0 mi/hr to feet/second.
The dimensional analysis set-up will be presented without comment.
303 mi 1 hr 1 min 5280 ft ––––––– x ––––––– x ––––––– x ––––––– = 444.4 ft/s <--- 4 sig figs 1 hr 60 min 60 sec 1 mi
Example #7: Convert 2113 km/h into cm/s.
1) Do the hour to second conversion:
2113 km 1 hr ––––––– x ––––– = 0.5869444 km/s 1 hr 3600 s
2) Convert km to m, then convert m to cm (as opposed to converting km directly to cm in one step):
0.5869444 km 1000 m ––––––––––– x –––––– = 586.9444 m/s s 1 km
3) Now, the m to cm conversion:
586.9444 m 100 cm –––––––––– x –––––– = 58694.44 cm/s = 5.869 x 104 cm/s (to 4 sig figs) s 1 m
4) Here's the full conversion, with km being directly converted to cm:
2113 km 1 hr 105 cm ––––––– x ––––– x ––––– = 5.869 x 104 cm/s 1 hr 3600 s 1 km
Example #8: How many grams of lead are there in a lead brick 5.00 cm by 13.0 cm by 24.0 cm? The density of lead is 11300 kg/m3.
We could change the cm to m and calculate the volume in m3, then use the density to get the mass of lead. Another path would be to change the density to use cm3 and then calculate the volume in cm3 and thence to the mass.
I think I will do both!!
Solution where cm is changed to m first:
1) Change cm to m:
(5.00 cm) (1 m / 100 cm) = 0.0500 m
(13.0 cm) (1 m / 100 cm) = 0.130 m
(24.0 cm) (1 m / 100 cm) = 0.240 m
2) Calculate the density in m3:
(0.0500 m) (0.130 m) (0.240 m) = 0.00156 m3
3) Determine mass in kg, then g:
(11300 kg/m3) (0.00156 m3) = 17.628 kg
(17.628 kg) (1000 g / kg) = 17628 g
to three sig figs, 17600 g
Solution where m3 is changed to cm3 first:
1) Convert density to g/cm3:
11300 kg 1 m3 1000 g ––––––– x ––––––– x –––––– = 11.3 g/cm3 m3 (100 cm)3 1 kg
Notice that I included both conversions into this step.
2) Determine volume of the lead brick:
(5.00 cm) (13.0 cm) (24.0 cm) = 1560 cm3
3) Determine mass in grams:
(11.3 g/cm3) (1560 cm3) = 17628 g
To three sig figs, 17600 g
Bonus Example: The SI unit for density is kg/m3. Convert the density of platinum (21450 kg/m3) to the more commonly-used unit of g/cm3
1) Convert kg/m3 to g/m3:
(21450 kg/m3) (1000 g / 1 kg) = 21450000 g/m3
2) Convert g/m3 to g/cm3
(21450000 kg/m3) (1 m3 / 1003 cm3) = 21.45 g/cm3
Note the use of 1003. 1 m3 is a cube 100 cm on a side: 100 cm x 100 cm x 100 cm = 1003 cm3.
3) Many teachers that teach dimensional analysis want the solution in one line of calculation steps:
(21450 kg/m3) (1000 g / 1 kg) (1 m3 / 1003 cm3) = 21.45 g/cm3
Note the interim values/units such as 21450000 g/m3 do not appear in a one-line dimensional analysis presentation.
Textbooks will often present a dimensional analysis set-up in this manner:
21450 kg 1000 g 1 m3 ––––––– x ––––––– x ––––––– = 21.45 g/cm3 1 m3 1 kg 1003 cm3
Your teacher may require it in that manner as well. One of the advantages to the above set-up is that it's much more obvious which units cancel. For example, you can clearly see the kg in the numerator of the first factor and in the denominator of the second factor.
Comment: it is easy to imagine a situation (test or homework) where, in the problem, you are given the density of a substance in units of kg/m3 but, in the problem solution, you must use the density in units of g/cm3. Consequently, I recommend that the above conversion be in your "bag of tricks."
By the way, please notice that the net effect of the above conversion is to divide the kg/m3 value by 1000 to get the g/cm3 value. if you are not required to show the conversion as I did above, you can use the 'divide by 1000" step as a convenient shortcut.
Go to 10 two-unit metric problems
Metric conversion where only one unit is converted
Return to Metric Table of Contents
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https://nethercraft.net/how-many-moles-of-o2-are-produced-when-0-425mol-of-ko2-reacts-in-this-fashion/
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math
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Using the chemical equation: 4KO2+2CO2→2K2CO3+3O2 How many moles of O2 are produced when 0.425 mol of KO2 reacts in this fashion? Also, how many grams of KO2 are needed to form 6.5g of O2? And how many grams of CO2 are used when 6.5g of O2 are produced?
So it’s simple math. set up the equation and put the words into math.
1) 0.425 mol x 3mol/ 4mol = .319 mol
2) 6.5g x 188g / 32g = 38.2 grams —-> convert to formula weight
3) 6.5g x 44g / 32g = 8.9 grams
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CC-MAIN-2022-49
| 462 | 5 |
https://essayteachers.com/post-755/
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math
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Homework 81. The actual results and static budget are given below for Clark Company. a) Create a flexible budget for Clark CompanyActualFlexible BudgetStatic BudgetSales Volume (units)8000
1800Total variable overhead
8000Total fixed overhead
b) How much of the difference between actual and the static budget is due to cost control and how much is due to activity? Provide numbers and direction.2. Huron Company produces a commercial cleaning compound called Zoom. The direct material standards for one unit of Zoom are given below: Standard Quantity Standard Price Standard Cost per UnitDirect material 4.6 pounds $2.50 per pound $11.50During the most recent month the following activity was recorded:o Twenty thousand pounds of material were purchased at a cost of $2.35 per pound.o All of the material purchased was used to produce 4000 units of Zoom.a) Compute the material cost variances. Indicate whether they are favorable or unfavorable.3. The following information is provided by the Atlantic Company:Actual direct material cost$24000Standard direct material cost$20000Direct material usage variance$3000 unfavorable a) What is the direct material price variance (indicate whether it is favorable or unfavorable)?
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CC-MAIN-2021-04
| 1,222 | 4 |
https://www.hackmath.net/en/example/4960
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math
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The meter of the textille was reduced by CZK 42, so 4 meters of the new price was 20 CZK cheaper than 3 meters of the original price. What was the original and new price of the textille?
Leave us a comment of example and its solution (i.e. if it is still somewhat unclear...):
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Jozef and Michael saved 46 euros together. Michael saved 22 euros more than Jozef. How much did save each of them?
Peter, Jane and Thomas have together € 550. Tomas has 20 euros more than Jane, Peter € 150 less than Thomas. Determine how much has each of them.
- Three friends
The three friends spent 600 KC in a teahouse. Thomas paid twice as much as Paul. Paul a half less than Zdeněk. How many each paid?
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Dalibor and Adam together scored 97 goals in the season. Adam scored 9 goals more than Dalibor. How many goals scored each?
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The sum of three numbers, if each is 10% larger than the previous one, is 662. Determine the figures.
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Three students participated in the summerjob. Altogether they earn 1780, -. Peter got a third less than John and Paul got 100,- more than Peter. How much got every one of them?
Eva and Jane collected 114 mushrooms together. Eve found twice as much as Jane. How many mushrooms found each of them?
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Belgium played a match with Italy and Belgium win by 2 goals. The match fell a total 6 goals. Determine the number of goals scored by Belgium and by Italy.
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A short and long sightseeing tour is possible at the castle. Ticket for a short sightseeing circuit costs CZK 60, for a long touring circuit costs CZK 100. So far, 13 tickets have been sold for 1140 CZK. How much did you pay for tickets for a short tour?
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5 t-shirts and a hat cost £62.00 2 t-shirts and a hat cost £29.00 How much does a t-shirt cost ? How much does a hat cost ?
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We have two numbers. Their sum is 140. One-fifth of the first number is equal to half the second number. Determine those unknown numbers.
x walnuts were in the mission. Dano took 1/4 of nuts Michael took 1/8 from the rest and John took 34 nuts. It stayed here 29 nuts. Determine the original number of nuts.
3 chocolate and 7 cakes cost 85, - CZK. 2 chocolates and 6 cakes cost 86, - CZK. How much is 5 chocolates and 9 cakes? I wonder how to get the result, but only by logic without the use of a system of equations
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35 people went on a tour and paid 8530, -. Employees pay 165, and family members 310. How many employees and how many family members went to the tour?
solve equations by substitution: x+y= 11 y=5x-25
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CC-MAIN-2018-39
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https://link.springer.com/chapter/10.1007%2FBFb0011179
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math
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Graf W.H. (1991) Flow resistance over a gravel bed: Its consequence on initial sediment movement. In: Armanini A., Di Silvio G. (eds) Fluvial Hydraulics of Mountain Regions. Lecture Notes in Earth Sciences, vol 37. Springer, Berlin, Heidelberg
The first part concerns itself with the friction factor of a gravel bed. Velocity distributions are measured in a gravel-bed flume having large slopes of 0.2<So (%)<2 and total water depths of 7<D(cm)<23. Two uniform gravel sizes of ds=2.35 cm and ds=1.35 cm are investigated. It is shown that : (i) the velocity distribution (see Fig.1) can be described by the logarithmic law, eqn (2) (see Fig.2a) in the inner region and by a parabolic law, eqn (4) (see Fig.2b) in the outer region; (ii) the friction velocities are reasonably equal to the ones computed from the energy slope; (iii) the position of the reference level, yo, can be established. The flow-resistance relations, eqns (6) and (6a), were researched and rendered : (i) the numerical constants, Br (see Fig.3) and \(\bar B\)r, depend upon the relative roughness (see Fig.4); (ii) where 3 zones can be identified; (iii) zone 1 being for small relative roughness with \(\bar B\)r≈6.25, proposed by Keulegan (1938); (iv) zone 3 being for large relative roughness with \(\bar B\)r≈3.25, proposed by Graf (1984). Two independent laboratory experiments and one set of field data (see Fig.6) are used to demonstrate the validity of the proposed flow-resistance relation.
The second part deals with the consequence of the above-developed flow-resistance relation on the initiation of grain movement on the bed. The results for steep-sloped and gravel-bed channels do not seem to agree with the well-accepted Shields diagram (see Fig.8). The understanding of the hydrodynamics of the turbulent flow over rough surfaces, expressed with the flow resistance, eqn (6a), and an appropriate constant, \(\bar B\)r (see Fig.4), help to explain the deviation from the Shields diagram if relative roughness are of importance, i.e. : (ds/D)>0.04. Data, now available in the literature, are used (see Fig.10) to present in a simple way for the determination of initial sediment movement.
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| 2,176 | 3 |
https://repository.rudn.ru/en/records/article/record/6844/
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math
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EPJ Web of Conferences. EDP Sciences. Vol. 173. 2018.
In general, the investigation of the electromagnetic field in an inhomogeneous waveguide doesn't reduce to the study of two independent boundary value problems for the Helmholtz equation. We show how to rewrite the Helmholtz equations in the "Hamiltonian form" to express the connection between these two problems explicitly. The problem of finding monochromatic waves in an arbitrary waveguide is reduced to an infinite system of ordinary differential equations in a properly constructed Hilbert space. The calculations are performed in the computer algebra system Sage. © 2018 The Authors, published by EDP Sciences.
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https://www.engineeringchoice.com/how-to-read-vernier-caliper/
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math
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What is Vernier Caliper?
A vernier scale, named after Pierre Vernier, is a visual aid to take an accurate measurement reading between two graduation markings on a linear scale by using mechanical interpolation, thereby increasing resolution and reducing measurement uncertainty by using vernier acuity to reduce human estimation error.
The vernier is a subsidiary scale replacing a single measured-value pointer, and has for instance ten divisions equal in distance to nine divisions on the main scale. The interpolated reading is obtained by observing which of the vernier scale graduations is coincident with a graduation on the main scale, which is easier to perceive than visual estimation between two points.
Such an arrangement can go to a higher resolution by using a higher scale ratio, known as the vernier constant. A vernier may be used on circular or straight scales where a simple linear mechanism is adequate.
Examples are calipers and micrometers to measure to fine tolerances, on sextants for navigation, on theodolites in surveying, and generally on scientific instruments. The Vernier principle of interpolation is also used for electronic displacement sensors such as absolute encoders to measure linear or rotational movement, as part of an electronic measuring system.
The vernier scales may include metric measurements on the lower part of the scale and inch measurements on the upper, or vice versa, in countries that use inches. Vernier calipers commonly used in industry provide a precision to 0.01 mm (10 micrometers), or one thousandth of an inch. They are available in sizes that can measure up to 1828 mm (72 in).
Measurement Reading Technique for Vernier Caliper
In order to read the measurement readings from vernier caliper properly, you need to remember two things before we start. For example, if a vernier caliper output a measurement reading of 13.42 mm, this means that:
- The main scale contributes the main number(s) and one decimal place to the reading (E.g., 13 mm, whereby 1 is the main number and 0.3 is the one decimal place number)
- The vernier scale contributes the second decimal place to the reading (E.g., 21 divisions)
We will just use a two steps method to get the measurement reading from this:
To obtain the main scale reading: Look at the image above, 13mm is to the immediate left of the zero on the vernier scale. Hence, the main scale reading is 13mm
To obtain the vernier scale reading: Look at the image above and look closely for an alignment of the scale lines of the main scale and vernier scale. In the image above, the aligned line corresponds to 21. Hence, the vernier scale reading is 21*0.02=0.42mm. (least count is 0.02)
In order to obtain the final measurement reading, we will add the main scale reading and vernier scale reading together. This will give 13mm + 0.42mm = 13.42mm.
Use the following formula: Obtained reading = Main scale reading + Vernier scale reading
Least count or vernier constant
The difference between the value of one main scale division and the value of one vernier scale division is known as the least count of the vernier, also known as the vernier constant.
Let the measure of the smallest main-scale reading, that is the distance between two consecutive graduations (also called its pitch) be S, and the distance between two consecutive vernier scale graduations be V, such that the length of (n − 1) main-scale divisions is equal to n vernier-scale divisions.
Then the length of (n − 1) main-scale divisions = the length of n vernier-scale division, or
(n − 1) S = n V, or
nS − S = nV.
Vernier scales work so well because most people are especially good at detecting which of the lines is aligned and misaligned, and that ability gets better with practice, in fact far exceeding the optical capability of the eye.
This ability to detect alignment is called vernier acuity. Historically, none of the alternative technologies exploited this or any other hyperacuity, giving the vernier scale an advantage over its competitors.
Zero error is defined as the condition where a measuring instrument registers a reading when there should not be any reading. In case of vernier calipers it occurs when a zero on main scale does not coincide with a zero on vernier scale.
The zero error may be of two types: when the scale is towards numbers greater than zero, it is positive; otherwise, it is negative. The method to use a vernier scale or caliper with zero error is to use the formula
Actual reading = main scale + vernier scale − (zero error).
Zero error may arise due to knocks or other damage which causes the 0.00 mm marks to be misaligned when the jaws are perfectly closed or just touching each other.
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CC-MAIN-2023-50
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http://springrts.com/phpbb/viewtopic.php?p=387891
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math
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If I get an event say for example that a vehicle factory entered my line of site (or the line of site of a specific unit.....btw, there is no way to determine what unit actually 'spotted' another, is there?), I can get it's position and I can get it's x and z size from the unitdef.... but where is the position with relation to the x and z 'widths'? Is the position the upper left corner...and it extends X units right and z units down? Or is it (god forbid) centered on the position?
As I understand it the position is the center of a unit and the x-size and z-size are the width and height of the building in map coodinates (1/8 of the position coordinates) and that is only given that the facing is 0.
If the facing is different (ranges from 0-3), the x-size and z-size changes its meaning from width to height and from height to width. I think 0 and 2 it is normal and 1 and 3 it has the other meaning.
btw, there is no way to determine what unit actually 'spotted' another, is there?)
possibly not directly but the lua api provides a GetClosestEnemy(unit) function which you could simply pass the factory id to. Of course there's no guarentee that the closest unit is actually the one that spotted it (due to los distance differences) but you'd probably find that's good enough for most practical purposes.
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https://www.physicsforums.com/threads/calculus-by-stewart-3rd-ed.3517/
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math
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Well, I saw that this section of the forum was empty and since I have read through plenty of school texts... Calculus - 3rd Edition James Stewart Brooks/Cole Publishing Company Approximate price: $110 USD (New), $72 USD (used - what I paid many years ago) The most current is 4th Edition but everything is about the same, chapters are rearranged. Contents: Review and preview 1. Limits and rates of change 2. Derivatives 3. The mean value theorem and curve sketching 4. Integrals 5. Applications of integration 6. Inverse funcitons 7. Techniques of integration 8. Further applications of integrations 9. Parametric equations and polar coordinates 10. Infinite sequences and series 11. Three-dimensional analytic geometry and vectors 12. Partial derivatives 13. Multiple integrals 14. Vector calculus 15. Differential Equations Pros: This book covers pretty much every aspect of calculus that an aspiring student, or other, would need to know. It has ample examples with pretty thorough explainations of the rules involved for problem solving. And plenty of problems to solve, too! Cons: The main downside of this book (IMO) is the tendency to not explain what algebraic (or other) function is used to help solve example problems which leave the reader to wonder "how?" certain numbers 'magically' appeared (a little confused). Benefits: The reader will be a much stronger mathematician and problem solver. Not only in math but in regards to other subjects as well; such as physics, statics, dynamics, statistics, etc... Conclusion: My overall rating is an enthusiastic two thumbs up. I have probably been through the book 3 or 4 times over throughout my educational career, and it always presents a challenge. I definitely recommend anyone wanting to learn and possibly master calculus to pick up this book and get to work! Look for more reviews by me to follow!
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https://www.hackmath.net/en/example/857
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math
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Car goes from point A to point B at speed 86 km/h and back 53 km/h. If they goes there and back at speed 67 km/h trip would take 10 minutes shorter. What is distance between points A and B?
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Pedestrian goes for a walk first at plane at 4 km/h, then uphill 3 km/h. Then it is in the middle of the route, turns back and goes downhill at speed 6 km/h. Total walk was 6 hours. How many kilometers went pedestrian?
Cyclist goes uphill 10 km for 50 minutes and downhill minutes for 29 minutes, both applied to the pedals same force. How long he pass 10 km by plane?
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Find the distance and mid-point between A(1,2) and B(5,5).
Find the equation of hyperbola that passes through the point M [30; 24] and has focal points at F1 [0; 4 sqrt 6], F2 [0; -4 sqrt 6].
What is the average speed of the car, where half of the distance covered passed at speed 66 km/h and the other half at 86 km/h.
Two masons with the same performance would have made of plaster for 6 days. One of them, however, has increased its daily performance by 50%. How long would take they now to make plaster together?
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The local Utah Department of Child Service office wants to project staffing needs based on current social worker assignments. They have the number of cases per social worker for the following staff: Mary: 25 John: 35 Ted: 15 Lisa: 45 Anna: 20 Calculat
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Fields go plow two tractors with various performance. The first tractor plow whole field in 20 hours, the second tractor plow whole field 30 hours déle. How long take plow whole field with two tractors?
- Minute average
In a factory, four workers are assigned to complete an order received for dispatching 1400 boxes of a particular commodity. Worker A takes 4 mins per box, Worker B takes 6 minutes per box, C takes 10 mins per box, D takes 15 mins per box. Find the average.
Mix 20 l of water with temperature of 53 °C, 27 l warm of 86 °C and 11 l water of 49 °C. What is the temperature of the mixed water immediately after mixing?
If water flows into the pool by two inlets, fill the whole for 18 hours. First inlet filled pool 10 hour longer than second. How long pool is filled with two inlets separately?
- The pool
The pool has a volume of 40 m3 and the water temperature is 20 °C. How much water at 100 °C should we pour into the pool to increase the water temperature by 5 °C?
- Daily average
Calculate the average temperature during the day, when 13 hours was 22 °C and 11 hours was 17 °C.
- 5 people
5 people have $122000 and 1 person has $539000 How much should each person (equally) pay?
- 75th percentile (quartille Q3)
Find 75th percentile for 30,42,42,46,46,46,50,50,54
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CC-MAIN-2018-26
| 3,195 | 31 |
https://www.osapublishing.org/oe/fulltext.cfm?uri=oe-21-12-14056&id=256457
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math
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Two-photon interference with independent classical sources, in which superposition of two indistinguishable two-photon paths plays a key role, is of limited visibility with a maximum value of 50%. By using a random-phase grating to modulate the wavefront of a coherent light, we introduce superposition of multiple indistinguishable two-photon paths, which enhances the two-photon interference effect with a signature of visibility exceeding 50%. The result shows the importance of phase control in the control of high-order coherence of classical light.
© 2013 OSA
Interference is an essentially important topic in optical physics, resulting in many interesting phenomena and important applications. The key physics lying behind interference is the superposition principle. After the birth of quantum physics, it was realized that superposition of multiple single-photon paths plays a key role in the traditional optical interference phenomenon, which is usually known as Dirac’s famous statement: “Each photon interferes only with itself. Interference between different photons never occurs”.
In 1956, Hanbury Brown and Twiss (HBT) introduced the second-order correlation measurement, and reported a new type of interference effect between independent photons, i.e., the bunching effect of thermal light [2, 3]. Soon after, it was realized that superposition of two indistinguishable two-photon paths plays a key role in the HBT interferometer . To explain it briefly, as shown in Fig. 1, for every pair of independent photons, there are two indistinguishable paths for the pair of photons to trigger a coincidence count. The phase of the complex amplitude of a two-photon path is composed of two components: the initial random phase component ϕs1 + ϕs2 with ϕsi being the initial random phase of the point source emitting photon si (i = 1, 2), and the propagation phase component related to the optical paths for the photons propagating from the sources to the respective detectors . Since the amplitudes of the two paths are always of the same initial random phase ϕs1 +ϕs2, their interference term will survive in the ensemble average, leading to the constructive or destructive two-photon interference.
Later, Mandel gave a detailed theoretical analysis of HBT-type two-photon interference between two independent sources with random phases, and predicted that the visibility of two-photon interference fringes has a maximum value of 50% for classical light . In general, for the case of two-photon interference with independent light sources, the coincidence counts consist of two parts: (i) The self-correlation part with the pair of photons from the same source which contributes a constant to the correlation function. (ii) The cross-correlation part with the pair of photons from different sources, which is dominated by the superposition of the two indistinguishable paths as depicted in Fig. 1, resulting in the two-photon interference fringes. It is the existence of part (i) that will low down the visibility of two-photon interference fringes. For a quantum source such as the single-photon state, the self-correlation contribution could be eliminated, and therefore giving rise to a 100%-visibility two-photon interference . However, for a classical light, the self-correlation always contributes, which makes the visibility of two-photon interference fringes not exceeding 50%. This property of two-photon interference with independent random-phase sources was further discussed by Paul , Ou and Klyshko , and confirmed experimentally for both the quantum light [10–12] and classical light [13–15]. Nevertheless, when one considers the multi-photon interference, the visibility could be higher than 50% for classical lights based on the third- and higher-order coherence [16–19].
In this paper, without the introduction of third- and higher-order correlation measurement, we explore another way to achieve high visibility two-photon interference with classical light. Instead of reducing or even removing the self-correlation contribution as in the case of quantum sources, we increase the cross-correlation contribution by introducing the superposition of multiple indistinguishable two-photon paths (path number >2) to enhance the two-photon interference effect of a classical light. This could be practically realized by introducing a random-phase grating to modulate the wavefront of a coherent light.
The paper is organized as follows. In Sec. 2, we described the structure of the random-phase grating, which was followed by a detailed theoretical study on both the first-order and the second-order spatial correlations of a coherent light transmitting through the random-phase grating. The experimental verification on the theoretical predictions was given in Sec. 3. And finally, we summarized the paper in Sec. 4.
2. Theoretical model and results
2.1. Random-phase grating
The random-phase grating is shown schematically in Fig. 2(a). It is a transmission N-slit mask with specially designed random-phase structure shown in the inset of Fig. 2(a), in which b is the transmission slit width and d is the distance between neighboring slits, respectively. The phase encoded on the nth transmission slit of the grating is designed to be Φ(xs, t) = rect((xs − nd)/b)(n − 1)ϕ(t), where rect(xs) is the one-dimensional rectangular function, xs is the position on the grating plane with xs = nd being the center of the nth slit of the grating, n is a positive integer and the elementary phase ϕ(t) is a temporally random phase (In the following, we will use ϕ to represent ϕ(t) for simplicity but without causing confusion). In this way, a random phase (n − 1)ϕ will be encoded on the light wave transmitting through the nth slit. Such a random-phase grating can be realized through a spatial light modulator (SLM) in practice, as we will demonstrate experimentally in Sec. 3. In the following, we will consider the single-photon and two-photon interference effects when a collimated coherent light transmits through the random-phase grating, as shown in Fig. 2(b).
2.2. Theoretical results
To clearly illustrate the single-photon and two-photon interference effect of the light field transmitting through the random-phase grating, we will calculate the first-order and second-order correlation functions of the transmitting field in the Fraunhofer zone, i.e., in the focal plane of a lens put behind the random-phase grating, as shown in Fig. 2(b). For simplicity, we assume that the coherent light incident normally onto the random-phase grating is a plane wave and a single-mode one, in one-dimensional case, the field operator on the detection plane is expressed as [20–22]Eq. (1) into Eq. (2) and taking the condition 〈eiϕ〉 = 0, one gets Eq. (1) into Eq. (4) and taking the condition 〈eiϕ〉 = 0, the second-order spatial correlation function can be deduced as (see Appendix A) Fig. 1: (1) one photon transmitting through the mth slit goes to the detector D1, while the other transmitting through the nth slit goes to the detector D2; and (2) one photon transmitting through the mth slit goes to the detector D2, while the other transmitting through the nth slit goes to the detector D1. Here we introduce the delta function δ(m − n) to show that there is only one path when the two photons transmit through the same slit to trigger a coincidence count. It can also be found that a random phase (m + n − 2)ϕ will be encoded on the amplitudes of the twin two-photon paths as represented in the first line of Eq. (5). For a N-slit random-phase grating as shown in Fig. 2, there could be many such twin two-photon paths originated from different pairs of slits (m, n), and the amplitudes of those twin paths with equal (m + n) will contain the same random phase (m + n − 2)ϕ. These twin two-photon paths are indistinguishable in principle. In this way, multiple different but indistinguishable two-photon paths are introduced through the N-slit random-phase grating. As shown in the second line of Eq. (5), the amplitudes of all different but indistinguishable two-photon paths with the same random phase lϕ(l = 0, 1,⋯ , 2N − 2) are superposed to calculate their contributions to the coincidence probability, and then the coincidence probability contributions from those with different random phases lϕ are added to get the total coincidence probability. Next, we will show that such a superposition of multiple two-photon amplitudes would enhance the two-photon interference, leading to high-visibility two-photon interference for classical light.
Thus, the normalized second-order spatial correlation function can be calculated as (see Appendix B)22], and therefore can be called as multiple-slit two-photon interference function. It is seen that g(2)(x1, x2) in Eq. (6) is a sum of (2N −1) multiple-slit two-photon interference functions sin2((l′ +1)(β1 −β2)d/2) / sin2((β1 − β2)d/2) introduced by the random-phase grating, each one is associated with a group of different but indistinguishable two-photon paths which are characterized by the same random phase lϕ(l = 0, 1,⋯ , 2N − 2) in Eq. (5). These multiple-slit two-photon interference functions are periodical functions of the position difference (x1 − x2) with the same period Λ = λf/d in the paraxial approximation, which is exactly the same as that of the multiple-slit single-photon interference pattern of a normal grating with respect to the position x on the detection plane . Therefore, two-photon interference fringes can be observed on the detection plane.
The visibility of two-photon interference fringes can be calculated through a formula , where and are the peak and valley, respectively, of the interference fringes described by Eq. (6). It is not hard to find out that these multiple-slit two-photon interference functions are peaked at the same position differences satisfying (β1 − β2)d = ±2nπ (n = 0, 1, 2, ⋯) due to the constructive interference effect, i.e., when the phase difference among different but indistinguishable two-photon paths are an integer multiple of 2π. The constructive interference peak for each multiple-slit two-photon interference function is (l′ + 1)2, and therefore, one can get the interference peak of g(2)(x1, x2) to be (2N2 + 1)/(3N), according to Eq. (6). On the other hand, the minimum of g(2)(x1, x2) is achieved at the condition (β1 − β2)d = ±(2n + 1)π (n = 0, 1, 2, ⋯) due to the destructive interference effect among multiple two-photon paths. However, the minimum of g(2)(x1, x2) is not zero but calculated to be 1/N due to the existence of the cases when the two photons transmit through the same slit of the grating. Therefore, the visibility of the two-photon interference fringes is found to be V = (N2 − 1)/(N2 + 2), which grows quickly with the increase of slit number N and exceeds 50% when N > 2, as shown in Fig. 3.
In the following Sec. 3, we will give an experimental verification on the high-visibility two-photon interference fringes described by Eq. (6) for a coherent light transmitting through the random-phase gratings.
3. Experimental demonstration and discussions
Experimental setup — Figure 4 shows the experimental setup that we used to measure the two-photon interference effect of the light field scattering from the random-phase grating. In our experiments, a single mode, continuous-wave laser with a wavelength of 780 nm was introduced as the light source, which was expanded and collimated through a beam expander to obtain a plane wave. The expanded and collimated light beam was then reflected by a beam splitter BS and incident normally onto a random-phase grating. Here the random-phase grating was composed of a N-slit amplitude mask (b = 72 μm and d = 400 μm) and a reflection-type phase-only SLM (HEO 1080P from HOLOEYE Photonics AG, Germany) put just behind the mask. The light first transmitted through the N-slit amplitude mask, and then was reflected back from the SLM and finally re-transmitted through the N-slit amplitude mask again. Here we put the SLM as close as possible to the mask, ensuring that the light goes in and out of the same slit of the mask. The SLM provided the desired phase structure on the N-slit mask as shown in the inset of Fig. 2(a). At last, the light waves scattered from the random-phase grating were collected by a lens L with a focal length f = 80 cm. Both the intensity and the second-order spatial correlation measurements were performed on the focal plane of the lens L by using a charge coupled device (CCD) camera with a frame acquisition time of 0.79 ms.
Figure 5 shows the measured single-photon and two-photon interference patterns on the detection plane (i.e., the focal plane of the lens L) at different conditions, in which the empty circles are the experimental results while the red curves are the theoretical fits, respectively.
Results for traditional grating — When there is no electric signal loaded on the SLM, our experimental configuration is essentially the same as a typical setup to measure the single-photon interference of a traditional N-slit grating. In the experiment, we measured the stationary single-photon interference patterns of the N-slit gratings (N = 2, 3, 4 and 5, respectively). The results are shown in the first column of Fig. 5. As expected, stationary single-photon interference fringes described by the multiple-slit single-photon interference function sin2(Nβd/2)/sin2(βd/2) were observed. The period between the neighboring principal intensity peaks was measured to be 1.57 mm on the detection plane, and (N − 2) sub-peaks appear between the two neighboring principal peaks of the stationary single-photon interference fringes. Note that the normalized second-order spatial correlation function g(2)(x1, x2) in this case was confirmed to be a unity (not shown in Fig. 5).
Results for random-phase grating — When the SLM was loaded with the random phases, the random-phase grating was constructed. In this case, there should be no stationary single-photon interference fringes since the phase difference between every two slits changes randomly with time. The second column of Fig. 5 shows the experimental results, in which each one is an intensity average over 10000 frames of the intensity distribution measured by the CCD camera, corresponding to 10000 realization of the random elementary phase ϕ which is uniformly distributed within [0, 2π]. Note that the elementary phase ϕ was kept to be a fixed value with a duration time of 500 ms for each intensity measurement, but it changed randomly from one measurement to the other. It is seen that the single-photon interference fringes were almost erased, leaving an intensity distribution enveloped by a diffraction profile (see the respective red curves) described by Eq. (3). One notes that there are still some residual intensity fluctuations which deviate from the intensity envelop predicted by Eq. (3). This is mainly due to the unavoidable phase flicker of the SLM during each intensity measurement.
Although the single-photon interference fringes disappear with the random-phase grating, two-photon interference fringes appear as predicted by Eq. (6). The third column of Fig. 5 shows the measured second-order spatial correlation function g(2)(x1, x2), which is calculated through a formula g(2)(x1, x2) = 〈I(x1)I(x2)〉/(〈I(x1)〉〈I(x2)〉) [18,23] by using the same 10000 frames of the measured intensity distributions as those used in the second column of Fig. 5. Here the red curves are the theoretical fits using Eq. (6). It is seen that the second-order correlation function exhibits itself in the form of high quality interference fringes, in good agreement with the theoretical prediction by Eq. (6).
It is seen from the experimental results shown in the third column of Fig. 5 that, the two-photon interference fringes are peaked at the position differences x1 − x2 = ±2nπf / (kd) and minimized at the position differences x1 − x2 = ±(2n + 1)πf / (kd) (n = 0, 1, 2, ⋯), respectively. The period of the two-photon interference fringes Λ was measured to be 1.57 mm, in good agreement with the prediction of Eq. (6). On the other hand, sub-peaks typical for the single-photon interference fringes shown in the first column of Fig. 5 were not observed in the two-photon interference fringes in the third column of Fig. 5. This is due to the fact that g(2)(x1, x2) is a sum of (2N − 1) different multiple-slit two-photon interference functions (see Eq. (6)), and these different multiple-slit two-photon interference functions are always in phase at their principal peaks but out of phase at the sub-peaks. Moreover, the visibility of the two-photon interference fringes was measured to be 44.9%, 59.1%, 62.3% and 71.9% for the N-slit random-phase gratings with N = 2, 3, 4 and 5, respectively. As predicted by Eq. (6), the visibility of the two-photon interference fringes increases with the increase of the slit number N of the random-phase gratings and surpasses 50% when N > 2.
Further discussions — One may note that, except for the N = 2 case, the random phases encoded on the slits of the random-phase grating are not fully independent but indeed correlated with respect to each other. Therefore, our case is different from the case discussed by Mandel , where classical lights with fully independent random phases are considered, and which in fact corresponds to the N = 2 case in our configuration. For classical lights with fully independent random phases, the visibility of two-photon interference fringes cannot exceed 50%, as also confirmed by the N = 2 case in our configuration (V = 44.9%, see the two-photon interference fringes in the top first one of the third column in Fig. 5). More importantly, our results show that, by appropriately controlling the random phase structure encoded on a coherent light field, one could achieve two-photon interference fringes with the visibility exceeding 50%. It is known that controlling optical phase plays a key role in the single-photon interference effect , our results show that it may also play an important role in controlling the high-order coherence of light.
In summary, we have designed a kind of two-photon grating with a special random-phase structure, through which the single-photon interference is smeared out but the two-photon interference appears. With such a random-phase grating, superposition of multiple indistinguishable two-photon paths is introduced, which leads to high-visibility two-photon interference fringes of classical light. Theoretically, the visibility of the two-photon interference fringes for a coherent light transmitting through a N-slit random-phase grating reaches (N2 −1)/(N2 +2). Experimentally, the visibility of the two-photon interference fringes with a N-slit random-phase grating (N = 2, 3, 4 and 5) was measured to be 44.9%, 59.1%, 62.3% and 71.9%, respectively. The results show the possibility to control the high-order coherence of light through optical phase.
For the case when a coherent light, which is the eigenstate of the annihilation operator â, is incident normally onto the random-phase grating as shown in Fig. 2(b), one arrives atEq. (1) into Eq. (4). After taking the square of mould in Eq. (7), one needs to do the ensemble average for the terms Eq. (7), one arrives at Eq. (5).
This work was supported by the 973 program ( 2013CB328702), the CNKBRSF ( 2011CB922003), the NSFC ( 11174153, 90922030 and 10904077), the 111 project ( B07013), and the Fundamental Research Funds for the Central Universities.
References and links
1. P. Dirac, The Principles of Quantum Mechanics, 2nd edition (Oxford University, 1935).
2. R. Brown and R. Twiss, “Correlation between photons in two coherent beams of light,” Nature 177(4497), 27–29 (1956) [CrossRef] .
3. R. Brown and R. Twiss, “A test of new type of stellar interferometer on sirius,” Nature 178(4541), 1046–1048 (1956) [CrossRef] .
4. U. Fano, “Quantum theory of interference effects in the mixing of light from phase-independent sources,” Am. J. Phys. 29(8), 539–545 (1961) [CrossRef] .
5. J. Liu and G. Zhang, “Unified interpretation for second-order subwavelength interference based on Feynmans path-integral theory,” Phys. Rev. A 82(1), 013822 (2010) [CrossRef] .
6. L. Mandel, “Photon interference and correlation effects produced by independent quantum sources,” Phys. Rev. A 28(2), 929–943 (1983) [CrossRef] .
7. H. Paul, “Interference between independent photons,” Rev. Mod. Phys. 58(1), 209–231 (1986) [CrossRef] .
9. D. Klyshko, “Quantum optics: quantum, classical, and metaphysical aspects,” Phys. Usp. 37(11), 1097–1123 (1994) [CrossRef] .
11. E. J. S. Fonseca, C. H. Monken, and S. Pádua, “Measurement of the de Broglie wavelength of a multiphoton wave packet,” Phys. Rev. Lett. 82(14), 2868–2871 (1999) [CrossRef] .
12. K. Edamatsu, R. Shimizu, and T. Itoh, “Measurement of the photonic de Broglie wavelength of entangled photon pairs generated by spontaneous parametric down-conversion,” Phys. Rev. Lett. 89(21), 213601 (2002) [CrossRef] [PubMed] .
13. G. Scarcelli, A. Valencia, and Y. Shih, “Two-photon interference with thermal light,” Europhys. Lett. 68(5), 618–624 (2004) [CrossRef] .
14. J. Xiong, D. Cao, F. Huang, H. Li, X. Sun, and K. Wang, “Experimental observation of classical subwavelength interference with a pseudothermal light source,” Phys. Rev. Lett. 94(17), 173601 (2005) [CrossRef] [PubMed] .
15. Yan-Hua Zhai, Xi-Hao Chen, Da Zhang, and Ling-An Wu, “Two-photon interference with true thermal light,” Phys. Rev. A 72(4),043805 (2005) [CrossRef] .
16. I. Agafonov, M. Chekhova, T. Iskhakov, and A. Penin, “High-visibility multiphoton interference of Hanbury Brown-Twiss type for classical light,” Phys. Rev. A 77(5), 053801 (2008) [CrossRef] .
17. D. Cao, J. Xiong, S. Zhang, L. Lin, L. Gao, and K. Wang, “Enhancing visibility and resolution in Nth-order intensity correlation of thermal light,” Appl. Phys. Lett. 92(20), 201102 (2008) [CrossRef] .
18. X. Chen, I. Agafonov, K. Luo, Q. Liu, R. Xian, M. Chekhova, and L. Wu, “High-visibility, high-order lensless ghost imaging with thermal light,” Opt. Lett. 35(8), 1166–1168 (2010) [CrossRef] [PubMed] .
19. Y. Zhou, J. Simon, J. Liu, and Y. Shih, “Third-order correlation function and ghost imaging of chaotic thermal light in the photon counting regime,” Phys. Rev. A 81(4), 043831 (2010) [CrossRef] .
20. R. Glauber, “The quantum theory of optical coherence,” Phys. Rev. 130(6), 2529–2539 (1963) [CrossRef] .
21. R. Glauber, “Coherent and incoherent state of radiation field,” Phys. Rev. 131(6), 2766–2788 (1963) [CrossRef] .
22. G. Brooker, Modern Classical Optics (Oxford University, 2003).
23. Y. Bromberg, Y. Lahini, E. Small, and Y. Silberberg, “Hanbury Brown and Twiss interferometry with interacting photons,” Nature Photonics 4, 721–726 (2010) [CrossRef] .
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| 23,078 | 48 |
https://digitalcommons.mtu.edu/math-fp/110/
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math
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On affine designs and Hadamard designs with line spreads☆
Rahilly [On the line structure of designs, Discrete Math. 92 (1991) 291–303] described a construction that relates any Hadamard design H on 4m − 1 points with a line spread to an affine design having the same parameters as the classical design of points and hyperplanes in AG(m, 4). Here it is proved that the affine design is the classical design of points and hyperplanes in AG(m, 4) if, and only if, H is the classical design of points and hyperplanes in PG(2m−1, 2) and the line spread is of a special type. Computational results about line spreads in PG(5, 2) are given. One of the affine designs obtained has the same 2-rank as the design of points and planes in AG(3, 4), and provides a counter-example to a conjecture of Hamada [On the p-rank of the incidence matrix of a balanced or partially balanced incomplete block design and its applications to error-correcting codes, Hiroshima Math. J. 3 (1973) 153–226].
Mavron, V. C.,
McDonough, T. P.,
On affine designs and Hadamard designs with line spreads☆.
Retrieved from: https://digitalcommons.mtu.edu/math-fp/110
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| 1,141 | 6 |
https://getpractice.com/subjects/maths/linear-equations?page=1756
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math
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Linear Equations in One Variable
Solving Linear Equations in One Variable
Linear Equations in Two Variables
Pair of Linear Equations
Consistency of Pair of Equations
Solution of Pair of Equations
The sum of digits of a two digit number is $$15$$. The number obtained by reversing the order of digits of the given number exceeds the given number by $$9$$. Find the given number.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710534.53/warc/CC-MAIN-20221128171516-20221128201516-00054.warc.gz
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CC-MAIN-2022-49
| 377 | 7 |
https://brainmass.com/physics/rotation/understanding-center-mass-571665
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math
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Not what you're looking for?
Explain in detail the concept of center of mass of a system of bodies or a rigid body with solved examples.
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In this six page solution the concept of center of mass has been explained in detail. Three solved examples have been included to explain how the center of mass can be determined for a system of bodies and a rigid body (cone).
** Please refer to the attachment for the complete solution **
Understanding Centre of Mass
Before we proceed to understand the concept of Centre of Mass, let us define a few terms we will use subsequently.
System of bodies (or masses): It is a collection of two or more distinct bodies interacting with each other through some form of force. For example, the solar system is a system of bodies (comprising the sun, planets, moons of the planets etc.) interacting with each other through the gravitational force. The configuration of the bodies comprising the system with respect to each other may or may not be fixed. For example, in the case of the solar system the configuration of the planets, moons etc. is constantly changing. However, in the case of two steel balls connected rigidly at the ends of a thin, massless rod (which constitutes a two body system) the configuration of the balls is fixed.
Rigid body: A rigid body as the term suggests is a body whose shape does not change. Sphere, rod, plate, rock are examples of rigid bodies.
The text book definition of centre of mass is as follows:
Centre of mass (CM) of a system of bodies or a rigid body is that imaginary point whose dynamic behaviour (i.e. motion) will remain unchanged if the entire mass of the bodies comprising the system or the rigid body were to be concentrated at that point and the resultant of the external forces acting on different bodies comprising the system or the rigid body were to act at that point.
This definition of centre of mass is somewhat abstract and needs some elaboration to really grasp the concept. Before we do so, let's recall from Newton's Laws of Motion that the motion of a body can be defined by i) its instantaneous momentum and ii) the rate of change of momentum if the body is in accelerated (or decelerated) motion. In this case the rate of change of momentum equals the net external force acting on the body. We can approach the concept of Centre of Mass either via momentum or via force. We take up both approaches as follows:
Centre of Mass via momentum approach: We can now explain the definition of CM of a system of bodies using the momentum to define motion as follows: At any given instant each body in the system has some momentum. The resultant momentum of the system is the vector sum of the momenta of different bodies in the system. Now imagine that the net mass of the ...
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Some short-answer questions involving the basic vocabulary of string, sound, and water waves.
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https://www.readyratios.com/reference/asset/accounts_payable_turnover_ratio.html?PAGEN_2=3
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math
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Accounts Payable Turnover Ratio
Accounts payable turnover ratio is an accounting liquidity metric that evaluates how fast a company pays off its creditors (suppliers). The ratio shows how many times in a given period (typically 1 year) a company pays its average accounts payable. An accounts payable turnover ratio measures the number of times a company pays its suppliers during a specific accounting period.
Accounts payables turnover trends can help a company assess its cash situation. Just as accounts receivable ratios can be used to judge a company's incoming cash situation, this figure can demonstrate how a business handles its outgoing payments.
Accounts-payable turnover is calculated by dividing the total amount of purchases made on credit by the average accounts-payable balance for any given period.
Accounts payable turnover ratio = Total purchases / Average accounts payable
There is no single line item that tells how much a company purchased in a year. The cost of sales in the income statement (statement of comprehensive income) shows what was sold, but the company may have purchased either more or less than it eventually sold. The result would be either an increase, or a decrease in inventory. To calculate the purchases made, the cost of goods sold is adjusted by the change in inventory as follows:
Purchases = Cost of sales + Ending inventory – Starting inventory
Again, as with the accounts receivable turnover ratios, this can be expressed in terms of a number of days by dividing the result into 365:
Days Payable Outstanding (DPO) = 365 /Accounts payable turnover ratio
Norms and Limits
Payment requirements will usually vary from supplier to supplier, depending on its size and financial capabilities. A high ratio means there is a relatively short time between purchase of goods and services and payment for them. Conversely, a lower accounts payable turnover ratio usually signifies that a company is slow in paying its suppliers.
But a high accounts payable turnover ratio is not always in the best interest of a company. Many companies extend the period of credit turnover (i.e. lower accounts payable turnover ratios) getting extra liquidity.
Exact Formula in the ReadyRatios Analytic Software
Days Payable Outstanding = ((F1[b][TradeAndOtherCurrentPayables] + F1[e][TradeAndOtherCurrentPayables]+F1[b][CurrentProvisionsForEmployeeBenefits] +F1[e][CurrentProvisionsForEmployeeBenefits])/2)/((F2[CostOfSales]+ F1[e][Inventories] - F1[b][Inventories])/NUM_DAYS)
Accounts payable turnover ratio = 365 / Days payable outstanding
F2 – Statement of comprehensive income (IFRS).
F1[b], F1[e] - Statement of financial position (at the [b]egining and at the [e]nd of the analysed period).
NUM_DAYS – Number of days in the the analysed period.
365 – Days in year.
Note: Employee benefits are considered here as a part of purchases because they are also account payables and also form cost of sales.
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| 2,936 | 20 |
https://minerva-access.unimelb.edu.au/collections/0683f0c3-cd5f-58bf-8c53-334699329f2d?spc.page=1&view=listElement&spc.sf=dc.date.available&spc.sd=DESC&f.author=JORET,%20GWENAEL,equals
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School of Mathematics and Statistics - Research Publications
Permanent URI for this collection
Now showing 1 - 3 of 3
ItemA Note on the Cops and Robber Game on Graphs Embedded in Non-Orientable SurfacesClarke, NE ; Fiorini, S ; Joret, G ; Theis, DO (Springer Science and Business Media LLC, 2014-01-01)
ItemBoxicity of graphs on surfacesEsperet, L ; JORET, G (Springer, 2013-05)The boxicity of a graph G = (V, E) is the least integer k for which there exist k interval graphs Gi = (V, Ei), 1 ≤ i ≤ k, such that E = E1∩... ∩Ek. Scheinerman proved in 1984 that outerplanar graphs have boxicity at most two and Thomassen proved in 1986 that planar graphs have boxicity at most three. In this note we prove that the boxicity of toroidal graphs is at most 7, and that the boxicity of graphs embeddable in a surface Σ of genus g is at most 5g + 3. This result yields improved bounds on the dimension of the adjacency poset of graphs on surfaces.
ItemIrreducible triangulations are smallJoret, G ; Wood, DR (ACADEMIC PRESS INC ELSEVIER SCIENCE, 2010-09-01)
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https://www.blogs.unicamp.br/zero/378/
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math
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There is a “famous math joke” known as The Infinite Mathematical Jokes Theorem, which says the following:
List all math jokes in order of lenght.
Assume there is a largest math joke, L.
Create a new math joke J by appending to L that joke about the pirate who has a wheel on his crotch that is “drivin’ me nuts!”
J is now larger than L, which is a contradiction.
Therefore the set of math jokes is infinite.
Now, assume a good math joke, M.
If M is a good joke, then it is funny.
If a joke is funny then everyone will know it.
If everyone knows a joke, the joke will not be funny.
If a joke is not funny, then it is not a good joke.
Therefor, if M is a good joke, M is not a good joke.
By contradiction, there are no good math jokes.
There are infinitely many math jokes and none of them are good.
In fact, this is a famous math joke, but it’s still not very funny. However, the purpose of this text is not to laugh, but to be reasonably happy as we discuss and correct some errors in this theorem.
First let’s look at the idea that if there is a bigger math joke called L, then the total of jokes has to be finite, that is, N jokes formed with up to L characters. But this is false, as we can insert at the end of a joke with L characters, the joke of “Pirate who has the rudder wheel in the groin”, soon there would be a joke with more than L characters, that is, there is no greater math joke. Thus, there must be infinite mathematical jokes. Although this statement is true, we can demonstrate this in a more “simple” way.
Realize that creating endless math jokes is not as complex as it appears in the famous joke, in fact, it doesn’t need a construction as strange as “the biggest math joke”. To demonstrate, I will create endless math jokes from the structure of this joke:
“What did 2 say to the thousand? You may be great, but it’s not 2!
So, keeping the structure of this joke apart from the word in bold, we can create jokes for any Real number greater than 2, for example:
What did 2 say to 1001? You may be great, but it’s not 2!
What did 2 say to 100? You may be great, but it’s not 2!
What did 2 say to 10? You may be great, but it’s not 2!
What did 2 say to √5? You may be great, but it’s not 2!
What did 2 say to π? You may be great, but it’s not 2!
What did 2 say to 2.1? You may be great, but it’s not 2!
Thus, as the set of Real numbers greater than 2 is infinite, there are infinite mathematical jokes of this type.
This construction can be used to show that there is no longer a joke, as we can always increase the length of a joke by increasing the number of characters that make up the number with whom 2 talks.
Another contradiction in the joke theorem is the definition that if M is a good joke, then M is funny, and if M is funny, everyone knows it. But if everyone knows the joke, then it is not funny, and if it is not funny, then the joke is not good. The problem here is that the set of good jokes will always be empty, since any good joke will be a bad joke, so there could be no good jokes.
The joke theorem was intended to be a joke (maybe even funny) and funny proof that there are infinite mathematical jokes, but that none of them are good, yet it does not form a definition of a good joke. One way to correct this definition and not change the purpose of the theorem is to define a joke as not being funny if everyone already knows it. Thus, a condition for a given M joke is not funny, is that everyone knows M.
Thus we arrive at the desired result. Take the joke:
“What did 2 say to x∈ℝ, x> 2?
You may be big, but you’re not 2! ”
For any x> 2, this will be a different joke, thus, there are infinites not countable (because it has the cardinality of ℝ) mathematical jokes of this type, but that by the known and valid property for any Real number greater than 2, we know the infinites variations that this joke can have. So, there are endless math jokes that are not funny! With this, the Theorem that states that there are infinite mathematical jokes that are not funny, is demonstrated.
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| 4,087 | 33 |
https://dspace.sunyconnect.suny.edu/handle/1951/69636/discover?filtertype=subject&filter_relational_operator=equals&filter=Amenable+group
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math
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Now showing items 1-2 of 2
On the spectrum and Martin boundary of homogeneous spaces
(Statistics and Probability Letters, 1995)
Given a conservative, spatially homogeneous Markov process X on an homogeneous spaces χ, we show that if the bottom of the spectrum of the generator of X is zero then the Martin boundary of contains a unique point fixed ...
Amenability and superharmonic functions
(Proceedings of the American Mathematical Society, 1993)
Let G be a countable group and u a symmetric and aperiodic probability measure on G . We show that G is amenable if and only if every positive superharmonic function is nearly constant on certain arbitrarily large subsets ...
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| 675 | 7 |
http://freepages.rootsweb.com/~celia/genealogy/wwii.html
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math
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Jr. & Thelma in uniform. Jr. had only been in the
service for 6 days at this time
Thelma Price in northern Africa
RootsWeb is funded and supported by
Ancestry.com and our loyal RootsWeb community.
About Us | Contact Us | Rootsweb Blog | Copyright | Report Inappropriate Material
Corporate Information | Privacy | Terms and Conditions
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| 345 | 7 |
https://www.teacherspayteachers.com/Product/Bases-Other-Than-e-Inverse-Trig-Derivatives-Integrals-Test-Calculus-AP-1960439
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math
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Calculus / Calc AP Chapter Test Bases Other Than e, Inverse Trig Functions - Derivatives and Integrals
This is an 18-question test on Natural Bases Other Than e, Inverse Trig Functions - Derivatives and Integrals - that can also be used as homework, review, or self-teaching.
Included in this file are:
1. The chapter test with complete, detailed, teaching-oriented solutions. A student could use this to self-teach the concepts.
2. The test with answers only, no solutions.
3. The blank test with room for students' responses.
4. The blank test condensed to two pages, with no room for students' responses. This gives you the choice to significantly reduce the number of photocopied pages.
Questions include: evaluate expressions involving log and inverse trig functions, sketch graph of exponential function, solve log equation, derivatives and integrals involving a^u and log(u), derivatives and integrals involving inverse trig (including completing the square), logarithmic differentiation (x^u), compound interest, area of enclosed region, equation of tangent line.
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| 1,071 | 8 |
http://it-pomoc.pl/sap/definicja/key-figure-bw
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math
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Definicja key figure (BW)
Values or quantities.
In addition to the key figures saved on the database, you have the option of defining derived (calculated) key figures in the query definition in the Business Explorer. Such key figures are calculated using a formula from the key figures of the InfoCube.
Examples of key figures include the following:
Sales revenue, fixed costs, sales quantity, or number of employees.
Examples of derived key figures include the following:
Sales revenue per employee, variance as a percentage, or contribution margin.
Słownik i definicje SAPa na K.
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| 582 | 8 |
https://www.gcestudybuddy.com/additional-math/coordinate-geometry
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math
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If A ( x1, y1) and B( x2, y2,), then distance d, from A to B =
4. Equation of a line
y = mx + c
y - y1 = m(x - x1)
5. Parallel lines
If two lines are parallel, then they have the same gradient.
6. Perpendicular lines
If two lines are perpendicular, then the product of the gradients of the two lines is -1.
or: perpendicular gradient = -1/m where m is the gradient of the line perpendicular to it.
7. Area of triangle
The area of the triangle formed by the three points (x1, y1), (x2, y2), (x3, y3)
8. Shoelace formula
go anti-clockwise direction
must go back to first coordinate
The equation of a circle whose center is (h,k) and radius is a is given by the equation
(x - h)2 + (y - k)2 = 0
The equation of a circle whose centre is the origin and whose radius is a is given by the equation
x2 + y2 = a2
The general equation of a circle is
x2 + y2 + 2gx + 2fy + c = 0
where the centre is (-g,-f) and radius is
The equation of a circle whose one diameter is the line segment joining the points
(x1, y1), (x2, y2) is given by
(x - x1)(x - x2) + (y - y1)(y - y2) = 0
1. Find the equation of the line with gradient 2 passing through (1, 4).
y - 4 = 2(x - 1)
y - 4 = 2x - 2
y = 2x + 2
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https://ir.lib.uwo.ca/iveypub/57/
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math
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URL with Digital Object Identifier
In this paper we analyze policies for optimally disposing inventory using online auctions. We assume a seller has a fixed number of items to sell using a sequence of, possibly overlapping, single-item auctions. The decision the seller must make is when to start each auction. The decision involves a trade-off between a holding cost for each period an item remains unsold, and a higher expected final price the fewer the number of simultaneous auctions underway. Consequently the seller must trade-off the expected marginal gain for the ongoing auctions with the expected marginal cost of the unreleased items by further deferring their release. We formulate the problem as a discrete time Markov Decision Problem and consider two cases. In the first case we assume the auctions are guaranteed to be successful, while in the second case we assume there is a positive probability that an auction receives no bids. The reason for considering these two cases are that they require different analysis. We derive conditions to ensure that the optimal release policy is a control limit policy in the current price of the ongoing auctions, and provide several illustration of results. The paper focuses on the two item case which has sufficient complexity to raise challenging questions.
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| 1,321 | 2 |
http://concreteinstitute.realviewtechnologies.com/?iid=79547&startpage=page0000035
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math
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by clicking the arrows at the side of the page, or by using the toolbar.
by clicking anywhere on the page.
by dragging the page around when zoomed in.
by clicking anywhere on the page when zoomed in.
web sites or send emails by clicking on hyperlinks.
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Archive - view past issues
Concrete In Australia : June 2013
Concrete in Australia Vol 39 No 2 35 Figure A1. Analysing inter plank shear. Figure A2. A typical example of a finite width solution. Figure A3. A loaded plank at the edge. erefore, if we know v1 at either side of the loaded plank and r, we know all the inter plank shears. e finite width solution may then be found by applying a shear correction to make v edge = 0, and reflecting this from edge to edge until no further correction is required. Figure A2 shows a typical example of this process taking v1 = 100, and r = 0.5. Figure A3 shows another example with the same arbitrary values for v1 and r, but with the loaded plank at the edge. To fi nd r, consider the following typical compatibility requirement: [(v n -v n+1)(L/π)4]/EI + [(v n+ v n+1)B2(L/π)2]/GJ =[(v n+1-vn+2)(L/π)4]/EI - [v n+1 + v n+2)B2(L/π)2]/GJ erefore: [(vn --2vn+1+vn+2)(L/π)2]/EI=[(-vn -2vn+1-vn+2)(B2)]/GJ -vn-2vnr--vnr2=(L/π)2GJ=Q vn-2vnr+vnr2B2EI -(r+1)2=Q (r-1)2 r=√Q-1 (1) √Q+1 Equation 1 permits r to be determined where Q = (L/π)2 GJ B2 EI And G = Shear modulus of plank concrete (= E/2(1+v) & v = Poisons ratio = 0.15, say) J = Torsional inertia of plank section E = Modulus of elasticity of plank concrete I = Moment of inertia of plank concrete L=Span B = Half the plank width To fi nd v1 at locations a and b, as shown in Figure A4, with l1 applied at any eccentricity within the plank, consider the symmetrical and anti-symmetrical cases shown in Figure A4. en the general case may be found by combining these symmetrical and anti-symmetrical cases such that: P=l1 , andM=Pe =l1EB(whereE=e/B=0for no eccentricity, & 1 for maximum e =B) en for the symmetrical case, v = va = vb : Forcom patibility (P-2v)(L/π)4 /EI = (v-rv)(L/π)4 /EI + (v+rv) B2 (L/π)2 /GJ Which simplifies to v = QP/(1+r +Q[3-r]) Or v = Q l1 /(1+r+Q[3-r]) for P=l1 (2) And for the anti-symmetrical case, v = vb = -va Forcom patability (M-2vB)B(L/π)2 /GJ = (v-rv)(L/π)4 /EI + (v+rv) B2 (L/π)2 /GJ Which simplifies to v = M / (Q[1-r] +3+r) Or v = EBl1 / (Q[1-r]+3+r) for M=EBl1 (3) en v1 values may be determined from the previously determined values of Q and r. A more realistic example is considered by analysing the 16 m span superstructure with 10 hollow plank units connected via elastomeric shear keys, as shown in Figure A5. manual computations. erefore, the feasibility of manual computations is maintained by adopting a different approach in this Appendix. Consider one line of wheels on one plank (the solution for multiple lines of wheels being available by a simultaneous superimposition process which is demonstrated in this Appendix) within an infinitely wide deck. en by inspection of Figure A1, each successive inter plank shear is a constant proportion r of the previous one. atisvn+1=rvn vn+2=r2vnetc.
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http://nrich.maths.org/public/leg.php?code=-99&cl=1&cldcmpid=938
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Start with three pairs of socks. Now mix them up so that no
mismatched pair is the same as another mismatched pair. Is there
more than one way to do it?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
El Crico the cricket has to cross a square patio to get home. He
can jump the length of one tile, two tiles and three tiles. Can you
find a path that would get El Crico home in three jumps?
Chandra, Jane, Terry and Harry ordered their lunches from the
sandwich shop. Use the information below to find out who ordered
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
My briefcase has a three-number combination lock, but I have
forgotten the combination. I remember that there's a 3, a 5 and an
8. How many possible combinations are there to try?
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Can you find out in which order the children are standing in this
Lorenzie was packing his bag for a school trip. He packed four
shirts and three pairs of pants. "I will be able to have a
different outfit each day", he said. How many days will Lorenzie be
How many different shapes can you make by putting four right-
angled isosceles triangles together?
Use the information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Imagine that the puzzle pieces of a jigsaw are roughly a
rectangular shape and all the same size. How many different puzzle
pieces could there be?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
This challenge is about finding the difference between numbers which have the same tens digit.
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Can you find all the ways to get 15 at the top of this triangle of numbers?
This task follows on from Build it Up and takes the ideas into three dimensions!
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
You have two egg timers. One takes 4 minutes exactly to empty and
the other takes 7 minutes. What times in whole minutes can you
measure and how?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
In this maze of hexagons, you start in the centre at 0. The next
hexagon must be a multiple of 2 and the next a multiple of 5. What
are the possible paths you could take?
There are 78 prisoners in a square cell block of twelve cells. The
clever prison warder arranged them so there were 25 along each wall
of the prison block. How did he do it?
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
My coat has three buttons. How many ways can you find to do up all
Winifred Wytsh bought a box each of jelly babies, milk jelly bears,
yellow jelly bees and jelly belly beans. In how many different ways
could she make a jolly jelly feast with 32 legs?
There are 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.
The Red Express Train usually has five red carriages. How many ways
can you find to add two blue carriages?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
You have 5 darts and your target score is 44. How many different
ways could you score 44?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
The brown frog and green frog want to swap places without getting
wet. They can hop onto a lily pad next to them, or hop over each
other. How could they do it?
Explore the different snakes that can be made using 5 cubes.
In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
How many different shaped boxes can you design for 36 sweets in one
layer? Can you arrange the sweets so that no sweets of the same
colour are next to each other in any direction?
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http://theory.uwinnipeg.ca/physics/curr/node2.html
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math
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Next: Resistance Up: Current and Resistance (Ch. Previous: Current and Resistance (Ch.
|I = .||(1)|
One can relate the current I in a material to properties of
the atomic charges.
Suppose in the material there are n charges per unit volume, each carrying
a charge q . When acted upon by an electric field these charges begin to
move; let us associate an average drift velocity vd with each individual
charge. Consider now a section of the material with cross-sectional area A ,
as in Fig. 17.1.
In a time t a charge Q has moved a distance x . Since Q = (nAx)q , we have for the current
|I = = nAq = nAqvd.||(2)|
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CC-MAIN-2017-39
| 611 | 11 |
https://publications.hse.ru/en/articles/?mg=50029945
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math
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The paper is concerned with the problem of stabilization of an $n$-link inverted pendulum on a movable base (cart). A cart is allowed to move along the horizontal axis. A force applied to the cart is considered as a control. The problem is to minimize the mean square deviation of the pendulum from the vertical line. For the linearized model it is shown that, for small deviations from the upper unstable equilibrium position, the optimal regime contains trajectories with more and more frequent switchings. Namely, the optimal trajectories with infinite number of switchings are shown to attain, in a finite time, the singular surface and then continue these motion with singular control over the singular surface approaching the origin in an infinite time. It is shown that the costructed solutions are globally optimal.
This review focuses on the presentation of results related to the energy function of discrete dynamical systems, as well as with the technique of constructing such functions for certain classes of Ω-stable and structurally stable diffeomorphisms on manifolds of dimension 2 and 3.
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CC-MAIN-2020-05
| 1,105 | 2 |
http://mathematica.stackexchange.com/questions/tagged/scaling+charts
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math
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https://cadmus.eui.eu/handle/1814/16512
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math
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A Small Sample Correction for Tests of Hypotheses on the Cointegrating Vectors
Journal of Econometrics, 2002, 111, 2, 195-221
JOHANSEN, Soren, A Small Sample Correction for Tests of Hypotheses on the Cointegrating Vectors, Journal of Econometrics, 2002, 111, 2, 195-221 - https://hdl.handle.net/1814/16512
Retrieved from Cadmus, EUI Research Repository
The main purpose of the analysis of the cointegrated VAR model is conducting inference on the cointegrating relations. Asymptotic inference is chi(2), but the asymptotic results are not accurate enough for small samples. Therefore, we derive here a correction factor, depending on sample size and parameters, for the likelihood ratio test of some linear hypotheses on the cointegrating space in a vector autoregressive model. We have to assume that the adjustment coefficients are known. The main idea is to condition on the common trends when calculating the correction factor. Some simulation experiments illustrate the findings.
Cadmus permanent link: https://hdl.handle.net/1814/16512
Full-text via DOI: 10.1016/S0304-4076(02)00104-5
Publisher: Elsevier Science Sa
Keyword(s): VAR model cointegration small sample properties Bartlett correction likelihood ratio test test on cointegrating relations
Earlier different version: http://hdl.handle.net/1814/694
Version: The article is a published version of EUI ECO WP; 1999/09
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http://core-cms.prod.aop.cambridge.org/core/search?filters%5BauthorTerms%5D=B.%20N.%20Moyls&eventCode=SE-AU
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math
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denote the algebra of n-square matrices over the complex numbers; and let Un, Hn
, and Rk
denote respectively the unimodular group, the set of Hermitian matrices, and the set of matrices of rank k, in Mn. Let ev(A) be the set of n eigenvalues of A counting multiplicities. We consider the problem of determining the structure of any linear transformation (l.t.) T of Mn
having one or more of the following properties:
T(Rk) ⊆ for k = 1, …, n.
T(Un) ⊆ Un
(c)det T(A) = det A for all A ∈ Hn.
(d)ev(T(A)) = ev(A) for all A ∈ Hn.
We remark that we are not in general assuming that T is a multiplicative homomorphism; more precisely, T is a mapping of Mn into itself, satisfying
T(aA + bB) = aT(A) + bT(B)
for all A, B in Mn and all complex numbers a, b.
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https://www.sportbikeworld.com/forums/31-all-other-topics/65697-tees-knowledge-quiz.html
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math
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Join Date: Jan 2007
Location: Sacramento, CA USA 96814
As a side note, the secondary English unit of mass is the pound-mass (lbm), which, by definition is 1 slug/32.2. This is so one lbm will numerically approximately equal one pound-force (lbf, primary weight unit) when placed on a scale. And in fact, most balance scales that display pounds actually are calibrated in lbm, which is a mass. (Since the actual acceleration due to gravity is 31.some odd and variable number feet/sec/sec, 1 lbm doesn't exactly weigh 1 lbf. The difference is less than the accuracy of a normal balance or scale so we don't worry about it.)
Also, and this really screws with people when doing complex thermodynamic calculations between the units, but in the metric system, mass (grams) is a base unit, and weight (newtons) is a derived unit, calculated from mass. In the English system, it's opposite - weight (lbf) is a base unit, and mass (the slug) is a derived unit. A slug, by definition, is the mass that will incur a force of 1 lbf when subjected to an acceleration of 1 ft/sec/sec. Likewise, a Newton is the force incurred when 1 kg is subjected to an acceleration of 1 m/sec/sec. Note that neither system uses gravity in the definition of either force or mass.
(EDIT: I think I received payback)
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http://www.chegg.com/homework-help/linear-algebra-2nd-edition-chapter-7.4-solutions-9780135367971
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math
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Let be a matrix in , where is set of all matrices whose entries are polynomials over the field .
Use the result, if is a matrix with entries in the polynomial algebra, then the matrix is invertible is equivalent to the condition that the matrix is row-equivalent to identity matrix.
Also recollect the fact, every upper-triangular matrix is row-equivalent to the identity matrix and in the same way identity matrix is row-equivalent to the upper-triangular matrix.
If it is not invertible matrix in , then it does not row-equivalent to the identity matrix, then it gives that is not row-equivalent to the upper-triangular matrix.
Hence, the statement given in the questions is.
Chegg is one of the leading providers of homework help for college and high school students. Get homework help and answers to your toughest questions in math, calculus, algebra, physics, chemistry, science, accounting, English and more. Master your homework assignments with our step-by-step solutions to more than 3000 textbooks. If we don't support your textbook, don't worry! You can ask a homework question and get an answer in as little as two hours. With Chegg, homework help is just a few clicks away.
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https://apps.dtic.mil/sti/citations/ADA556755
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math
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A GPU Parallelization of the Absolute Nodal Coordinate Formulation for Applications in Flexible Multibody Dynamics
Conference paper preprint
ARMY TANK AUTOMOTIVE RESEARCH DEVELOPMENT AND ENGINEERING CENTER WARREN MI
Pagination or Media Count:
The Absolute Nodal Coordinate Formulation ANCF has been widely used to carry out the dynamics analysis of flexible bodies that undergo large rotation and large deformation. This formulation is consistent with the nonlinear theory of continuum mechanics and is computationally more efficient compared to other nonlinear finite element formulations. Kinematic constraints that represent mechanical joints and specified motion trajectories can be introduced to make complex flexible mechanisms. As the complexity of a mechanism increases, the system of differential algebraic equations becomes very large and results in a computational bottleneck. This contribution helps alleviate this bottleneck using three tools 1 an implicit time-stepping algorithm, 2 fine-grained parallel processing on the Graphics Processing Unit GPU, and 3 enabling parallelism through a novel Constraint-Based Mesh CBM approach. The combination of these tools results in a fast solution process that scales linearly for large numbers of elements, allowing meaningful engineering problems to be solved.
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https://communities.sas.com/t5/SAS-Data-Mining-and-Machine/Predictive-Model-Results/td-p/325236?nobounce
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math
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01-17-2017 05:58 AM
I used several predictive models to in order to score the probability of an obsarvation to stop paying his bill.
I use logistic regression and forest and SVM '
The best chosen model for my population was theForest with AUC = 0.81 and misclssification rate = 0.058.
Do these results reflect good predictive ability of the model?
01-23-2017 02:08 PM
Depends on what the prediction would be without a model. If the proportion of observations with the most common target value in the data is near 1 - 0.058, then a misclassification rate of 0.058 is not good. On the other hand, if the proportion is around 1/2, then 0.058 is a great number.
I suspect AUC of 0.81 is good, because it is much larger than 0.5.
01-24-2017 06:16 AM
Adding to Padraic's great comments- rather than focusing on one number, you may also use the cumulative captured response values with different percentile thresholds to decide if the model is good enough.
Let's say you have a budget to take action for the top 5 percent of your population (send reminder sms, call from contact center etc). What would be the response rate of your model at the 5th percentile vs the overall event rate (random selection)? There might be cases where the model that has a lower ROC compared to the champion model will be performing better at the extreme percentiles. You may also compute the total loss (unpaid invoice) in the top buckets to justify the value of your model before deploying in production.
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http://intermath.coe.uga.edu/topics/algebra/graphing/a27.htm
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math
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| Travel of Ant
Travel of Ant Z on a Parabola
Ant Z wants to go from the point (-1,1) to the point (2,4) by staying on the curve y = x
. How long is the distance Ant Z travels on this portion of the curve?
Submit your idea for an investigation to
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| 246 | 5 |
https://socratic.org/questions/the-bill-is-100-82-what-is-the-amount-of-a-15-tip
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math
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The bill is 100.82. What is the amount of a 15% tip?
To find tips, multiply the value by the percent. Don't know how to find the numeric value of a percent? It is the
For this example, it is
If you are told to round to the nearest cent, it would be
To find the value of the whole thing, simply add the tip to the bill. For this example, it would end up being
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http://www.thespectrumofriemannium.com/2013/04/18/log095-group-theoryxv/
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math
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The topic today in this group theory thread is “sixtors and representations of the Lorentz group”.
Consider the group of proper orthochronous Lorentz transformations and the transformation law of the electromagnetic tensor . The components of this antisymmetric tensor can be transformed into a sixtor or and we can easily write how the Lorentz group acts on this 6D vector ignoring the spacetime dependence of the field.
Under spatial rotations, transform separately in a well-known way giving you a reducible representation of the rotation subgroup in the Lorent orthochronous group. Remember that rotations are a subgroup of the Lorentz group, and it contains Lorentz boosts in addition to those rotations. In fact, in the space of sixtors and they are thus a reducible representation, a direct sum group representation. That is, rotations leave invariant subspaces formed by and invariant. However, these two subspaces mix up under Lorentz boosts! We have written before how transform under general boosts but we can simplify it without loss of generality and for some matrices . So it really seems that the representation is “irreducible” under the whole group. But it is NOT true! Irreducibility does not hold if we ALLOW for COMPLEX numbers as coefficients for the sixtors/bivectors (so, it is “tricky” and incredible but true: you change the numbers and the reducibility or irreducibility character does change. That is a beautiful connection betweeen number theory and geometry/group theory). It is easy to observe that using the Riemann-Silberstein vector
and allowing complex coefficients under Lorent transformations, such that
i.e., it transforms totally SEPARATELY from each other () under rotations and the restricted Lorentz group. However, what we do have is that using complex coefficients (complexification) in the representation space, the sixtor decomposes into 2 complex conjugate 3 dimensional representaions. These are irreducible already, so for rotations alone transformations are complex orthogonal since if you write
with and . Be aware: here is an imaginary angle. Moreover, transforms as follows from the following equation:
Remark: Rotations in 4D are given by a unitary 4-vector such as and the rotation matrix is given by the general formula
If you look at this rotation matrix, and you assign with , the above rotations are in fact the same transformations of the electric and magnetic parts of the sixtor! Thus the representation of the general orthochronous Lorentz group is secretly complex-orthogonal for electromagnetic fields (with complex coefficients)! We do know already that
are the electromagnetic main invariants. So, complex geometry is a powerful tool too in group theory! :). The real and the imaginary part of this invariant are also invariant. The matrices of 2 subrespresentations formed here belong to the complex orthogonal group . This group is a 3 dimensional from the complex viewpoint but it is 6 dimensional from the real viewpoint. The orthochronous Lorentz group is mapped homomorphically to this group, and since this map has to be real and analytic over the group such that, as Lie groups, . We can also use the complex rotation group in 3D to see that the 2 subrepresentations must be inequivalent. Namely, pick one of them as the definition of the group representation. Then, it is complex analytic and its complex parameter provide any equivalent representation. Moreover, any other subrepresentation is complex conjugated and thus antiholomorphic (in the complex sense) in the complex parameters.
Generally, having a complex representation, i.e., a representation in a COMPLEX space or representation given by complex valued matrices, implies that we get a complex conjugated reprentation which can be equivalent to the original one OR NOT. BUT, if share with original representation the property of being reducible, irreducible or decomposable. Abstract linear algebra says that to any representation in complex vector spaces there is always a complex conjugate representation in the complex conjugate vector space . Mathematically, one ca consider representations in vector spaces over various NUMBER FIELDS. When the number field is extended or changed, irreducibility MAY change into reducibility and vice versa. We have seen that the real sixtor representation of the restricted Lorentz group is irreducible BUT it becomes reducible IF it is complexified! However, its defining representation by real 4-vectors remains irreducible under complexification. In Physics, reducibility is usually referred to the field of complex numbers , since it is generally more beautiful (it is algebraically closed for instance) and complex numbers ARE the ground field of representation spaces. Why is this so? There are two main reasons:
1st. Mathematical simplicity. is an algebraically closed filed and its representation theory is simpler than the one over the real numbers. Real representations are obtained by going backwards and “inverting” the complexification procedure. This process is sometimes called “getting the real forms” of the group from the complex representations.
2nd. Quantum Mechanics seems to prefer complex numbers (and Hilbert spaces) over real numbers or any other number field.
The importance of is understood from the Maxwell equations as well. In vacuum, without sources or charges, the full Maxwell equations read
These equations are Lorentz covariant and reducibility is essential there. It is important to note that
implies that we can choose ONLY one of the components of the sixtor, or , or one single component of the sixtor is all that we need. If in the induction law there were a plus sign instead of a minus sign, then both representations could be used simultaneously! Furthermore, Lorentz covariance would be lost! Then, the Maxwell equations in vacuum should satisfy a Schrödinger like equation due to complex linear superposition principle. That is, if and are solutions then a complex solution with complex coefficients should also be a solution. This fact would imply invariance under the so-called duality transformation
However, it is not true due to the Nature of Maxwell equations and the (apparent) absence of isolated magnetic charges and currents!
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http://mathnexus.wwu.edu/archive/problem/detail.asp?ID=150
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math
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A Difficult Problem?
In the multiplication problem ABA x CD = CDCD,
The American Mathematics Contest 8 exam is designed for students in grades 6-8. Based on the scores for the 2006 exam, this problem was considered to be the "hardest" problem:
where A, B, C, and D are different digits,
what is A+B?
What is your answer?
Note: Another difficult problem on the exam was: "Circle X has a radius of π. Circle Y has a circumference of 8π. Circle Z has an area of 9π. List the circles in order from smallest to largest radius." Do you see why almost 40% of the students selected the wrong answer of X, Y, Z?
Source: Adapted from MAA FOCUS, February 2007
Hint: The problem actually was a multiple choice problem, where 15.39% of the students chose (A) 1, 16.15% chose (B) 2, 26.01% chose (C) 3, 17.68% chose (D) 4, 12.09% chose (E) 9, and 12.55% of the students did not answer the question.
Does this information help?
Solution Commentary: It is perhaps easier to turn the problem into a division problem: CDCD/CD = ABA. Now CD "gozinta" CD** how many times...etc.
A Sidenote: The perplexity of the problem perhaps is increased by dual roles of letters. For example, B is a digit (actual value is 0)...but also is a choice for an answer (B) 2, etc.
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| 1,245 | 12 |
https://www.forginghistorysaga.com/wikia/post/multiverse-in-string-theory/
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math
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MULTIVERSE - 5
As you can see better in its pages, String Theory tells that matter is composed of tiny vibrating strings in an 11-dimension space. They can aggregate into 3D, or more, membranes inside a larger space, and each membrane could be a distinct universe. The Big Bang, indeed, would have resulted from the collision between two or more membranes.
The infinite parallel universes would then exist in the same dimensional space vibrating at different frequencies. Each of them has an independent number of dimensions, ranging from a minimum of four to a maximum of 11. If the dimensions are four, they correspond to spacetime: then our spacetime would be shared with a practically infinite number of parallel universes and with physical laws similar to ours. The great novelty of this theory is that universes are not placed in parallel dimensions, but in the same physical space.
Universes as brane in the String Theory multiverse
GO BACK TO MULTIVERSE
GO BACK TO SUMMARY
Unknown - Prince
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| 997 | 7 |
https://www.tutoreye.com/answer-the-statistic-questions-asap-qa
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math
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oups were used (lawyer, physical therapist, cabinetmakers, and system analysts). The results obtained for a sample of 5 individuals from each groups. Using the "ANOVA Output" below, please answer the following questions ( Use the significance level 5%).
Q1. The value of the test statistic is ____________
Q2. The p- value of the test is _________________
Q3. At the 5% significance level, the null hypothesis is rejected if the value of the F statistics is >= _________________
Q4. Interpret the ANOVA result at the 5% significance level. Is there any difference in the job satisfaction among the four occupational groups? Answer either yes or no. Explain the reason of your answer statistically.
Data from a Trucking Company is Southern California were utilized to examine the relationship among total daily travel time (y), miles to traveled (X1), and the number of deliveries (x2). Based on the "Regression Output" below, please answer the following questions.
Q5. The number of sample used in this regression analysis is______________
Q6. What is the value of the coefficient of determination?
Q7. What is the F test statistic value for the regression model significane test?
Q8. What is the predicted travel time for X1 =95, and X2= 6?
Q9. Is X2 (number of deliveries) related to Y (travel time)? Answer either yes or no. Explain the reason of your answer statistically.
ATTACHED ARE GRAPHS
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| 1,396 | 12 |
https://loufranco.com/blog/write-while-true-episode-28-complex-sentences
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math
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I like to sketch, mostly with pencil and charcoal on paper. One of the first things I needed to learn was how my drawing tools and the paper interacted. What kind of mark did each level of pencil hardness make, and how was that different from charcoal? What kind of paper worked best?
I did various exercises that helped me understand my own tools.
I’ve been thinking a lot about this and trying to figure out what is the equivalent for this in writing. Here’s what I’ve come up with.
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https://www.varsitytutors.com/tutors/878467093
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math
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Hello, My name is Cody and I am currently a student at Santa Barbara City College. I tend to excel at most science and math-related subjects including calculus-level math and physics. Subjects that I specialize in are math, physics, and chemistry.
Education & Certification
Undergraduate Degree: Santa Barbara City College - Engineer, Mechanical Engineering
SAT Math: 730
Dirt bike riding, playing sports and video games
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| 420 | 5 |
https://scorekhel.com/d/q/physics/class-10th-cbse-electricity
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math
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Class 10 Physics1)
A boy records that 4000 joule of work is required to transfer 10 coulomb of charge between two points of a resistor of 50 Ω. The current passing through it is
Class 10 Physics2)
To get 2 Ω resistance using only 6 Ω resistors, the number of them required is
Three resistors of 2 Ω is required to get 6 Ω because resultant is more than individual so they all must be connected in series.
Class 10 Physics3)
Two devices are connected between two points say A and B in parallel. The physical quantity that will remain the same between the two points is
In parallel combination, voltage remains same across two points.
Class 10 Physics4)
Two resistors are connected in series gives an equivalent resistance of 10 Ω. When connected in parallel, gives 2.4 Ω. Then the individual resistance are
6 Ω and 4 Ω
In series, Rs = R1 + R2 = 10 Ω
Class 10 Physics5)
he resistance of hot filament of the bulb is about 10 times the cold resistance. What will be the resistance of 100 W-220 V lamp, when not in use?
Class 10 Physics6)
A fuse wire repeatedly gets burnt when used with a good heater. It is advised to use a fuse wire of
In order to get the working of heater properly, fused wire of higher rating must be used.
Class 10 Physics7)
A cooler of 1500 W, 200 volt and a fan of 500 W, 200 volt are to be used from a household supply. The rating of fuse to be used is
Total power used, P = P1 + P1 = 1500 + 500 = 2000 W.
Current drawn from the supply,
Class 10 Physics8)
If the current I through a resistor is increased by 100 % (assume that temperature remains unchanged), the increase in power dissipated will be
Class 10 Physics9)
The resistivity does not change if
the shape of the resistor is changed
The resistivity does not change if the shape of resistor is changed because nature of material will remain same.
Class 10 Physics10)
Electric potential is a:
X can complete half of the work in 20 days and Y can do one-fifth of the same work in 10 days. X started the work and left after 8 days. Then Y took over to complete the remaining work. The total number of days taken by them to complete the work is:Watch Solution
A can do a work in 5 days while B can do the same work in 8 days. They worked together to complete the work and earned Rs. 6760. Find A’s share?Watch Solution
18 men can complete a certain work in 15 days working 8 hours a day. How many men can complete the same work in 12 days working 9 hours a day?Watch Solution
5 men, 6 women and 4 children can complete a work in 10 days. 6 women and 6 children can do it in 20 days, while 2 men and 6 women can do it in 18 days. In how many days will 2 men and 1 woman will complete the same work?Watch Solution
40 persons take 6 days to complete a certain task, working 10 hours a day. How many hours a day will be sufficient for 30 persons to complete the same task in 10 days?Watch Solution
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| 2,879 | 34 |
http://www.mathconsult.ch/static/icosahedra/index.html
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math
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There are 59 stellations of the icosahedron.
These pages contain various images of these stellations and some
This information is an excerpt of an article published in Mathematica in Education [Maeder94b].
An expanded version appears in Chapter 10 of
R. Maeder's book The Mathematica Programmer II.
About the Images on These Pages
The metric properties and graphics data were computed with a
developed by R. Maeder.
The ray-traced images on these pages were rendered with
from data computed with the program mentioned above,
using a conversion program
from Mathematica graphics format to
Programs and Images are Available!
The Mathematica programs to compute and render the polyhedra
are included on the CD-ROM that comes with
The Mathematica Programmer II.
The book contains also high-resolution color images of all stellated icosahedra.
Follow the link to the book's home page
for more information and
direct ordering in association with amazon.com.
Guide to the Images
The images on these pages have been ordered by increasing circumradius.
This ordering is different from the ordering used in
[Coxeter82] or the ordering used in our program.
The number used in the program is listed on the pages of the individual solids.
An index sorted by old numbers is available here.
- The guided tour of all 59 stellations starts here.
- A visual index (clickable map) of all 59 stellations
- Floor plans
(clickable map) of all 59 stellations
You may also want to have
a look at the collection of all uniform polyhedra.
Programs and high-resolution images for all stellated icosahedra are available in
the book The Mathematica Programmer II by R. Maeder.
All 59 stellated icosahedra, with background information and a clickable map.
A service provided by MathConsult Dr. R. Mäder, http://www.mathconsult.ch/.
© Copyright 1995, 1998 by Roman E. Maeder. All rights reserved.
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| 1,867 | 37 |
https://numbersciences.org/index.php/astronomy/geometrical
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math
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- Category: Geometry
- Hits: 3435
First Published on MatrixOfCreation.co.uk in Thursday, 24 May 2012 14:22 where it was read 362 times
In working at Lochmariaquer, an early discovery has returned in the form of a near-Pythagorean triangle with sides 18, 19 and 6. But first, how did this work on cosmic N:N+1 triangles get started?
Robin's earliest work couched the Lunation Triangle within three right angled triangles that could easily be constructred yet describe the number of lunar months and orbits in the solar year and the length of the eclipse year, using the number series 11, 12, 13, 14 to form N:N+1 triangles. Each triangle could then have an intermediate hypotenuse set at the 3:2 point of the shortest side, so as to form the eclipse year (11.37 mean solar months) and solar year (12.368 in lunar months), plus the orbits in a solar year (13.368 orbits). The 12 length is the lunar months in a lunar year but also the mean solar months in a solar year and the length 13 is the length of another type of lunar year (in lunar months) and the number of orbits in a 12 month lunar year. A bit of a mouthful so I have made a diagram of them below in figure 1.
Figure 1 Robin Heath's original set of three right angled triangles that exploit the 3:2 points to make intermediate hypotenuses so as to achieve numerically accurate time lengths in units of lunar or solar months and lunar orbits.
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http://www.gallifrance.net/docs/cyborg-soldier-rzhuxis/archive.php?id=oscillatory-motion-and-periodic-motion-db062d
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math
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They are also the simplest oscillatory systems. Periodic motion is defined as the motion that repeats itself after fixed intervals of time. Consequently, there is no mean … The to-and-fro motion of a body is called oscillatory motion. Harmonic motion refers to the motion an oscillating mass experiences when the restoring force is proportional to the displacement, but in opposite directions. The complete oscillation: the complete oscillation is the motion of an oscillating body when it passes by a fixed point on its path two successive times in the same direction. Motion which repeats itself after a fixed interval of time is called periodic motion. Oscillatory motion is defined as the to and fro motion of the … Answer: Any motion that repeats itself at regular interval of time is called periodic motion. Around the sum is 365 h. Oscillatory Motion: When a body moves in to and fro motion over and over again about a fixed point, then its motion is called oscillatory motion. the motion of bob of an oscillating simple pendulum is an oscillatory motion as well as periodic motion, while the motion of the earth around the sun is a periodic motion but not … All the oscillatory motions are not periodic such as the revolution of the earth is periodic but not an oscillatory motion. It is also known as periodic motion. "Oscillatory motion" is motion that repeats over and over again after a time T that is called the "period." In simple harmonic motion, the restoring force is directly proportional to the displacement of the mass and acts in the direction opposite to the displacement direction, pulling the particles towards the mean position. Thus, it is a periodic motion. Oscillatory motion is always periodic motion. Some periodic motion examples are: The earth completes one round around the sun in 356-1/4 days and this motion gets repeated after every 356-1/4 days. Oscillatory motion is a repetitive motion between two or more states. Simple harmonic motion is an important topic in the study of mechanics. Search in book: Search Contents. According to Newton’s law, the force acting on the mass m is given by F =-kxn. Examples: Motion of the pendulum of a clock, motion of planets around the Sun, etc. The periodic motion is the type of motion that gets repeated after a regular interval of time. In some cases of periodic motion, the body moves periodically (back and forth, up and down, to and fro, etc. ) We’ve already encountered two examples of oscillatory motion - the rotational motion of Chapter 5, and the mass-on-a-spring system in Section 2.3 (see Figure 1.1.1).The latter is the quintessential oscillator of physics, known as the harmonic oscillator.Recapping briefly, we get its equation of motion … In oscillatory motion, the fixed point or position about which the body oscillates is called equilibrium position. For e.g. Oscillatory motion is a type of periodic motion. 01. Oscillatory Motion • Periodic motion • Spring-mass system • Differential equation of motion • Simple Harmonic Motion (SHM) • Energy of SHM • Pendulum BRAC University, Summer 2020 Periodic Motion • Periodic motion is a motion that regularly returns to a given position after a fixed time interval. The motion of the pendulum of … The time taken for an oscillation to occur is often referred to as the oscillatory period. Let us consider a string fixed tightly between two walls. The period is the duration of one cycle in a repeating … If an objects motion is periodic, then there is a characteristic time: the time … Oscillatory motions are well defined for damped oscillations, simple harmonic oscillations, and for … Simple Harmonic Motion: A Special Periodic Motion. Simple harmonic motion is the to-and-fro motion of body … f 1 T T 1 f 2 f 2 T Simple harmonic motion: if the restoring force is proportional to the distance fromis proportional to the distance from equilibrium, the motion will be of the SHM type. All oscillatory motions are periodic motions. Ans: All oscillatory motions are said to be periodic motion because each oscillation is completed in a fixed interval of time. Oscillatory motion is a motion in which to and fro movement is done about its mean in fixed interval of time or periodically whereas periodic motion is the motion in which motion is repeated periodically, it is not necessary to have to and fro movement in periodic motion . The angular frequency and period do not depend on the amplitude of oscillation. Period and Frequency. PERIODIC MOTION. But every periodic motion need not be an oscillatory motion. meanwhile, an oscillatory motion is a motion in which particle moves to and fro about a fixed point, for example motion of a pendulum. Periodic motion can be any motion after a certain period that the motion of the previous period repeats. Periodic motion, in physics, motion repeated in equal intervals of time.Periodic motion is performed, for example, by a rocking chair, a bouncing ball, a vibrating tuning fork, a swing in motion, the Earth in its orbit around the Sun, and a water wave.In each case the interval of time for a repetition, or cycle, of the motion is … In mechanics and physics, simple harmonic motion is a special type of periodic motion where the restoring force on the moving object is directly proportional to the object's displacement magnitude and acts towards the object's equilibrium position. Circular motion is a periodic motion; however, it is still not oscillatory as the net force on the particle in a circular motion is never zero and is always directed towards the centre. Periodic motion: motion that repeats itself in a defined cycle. about a fixed point or position, these types of motions are known as Oscillatory motion or Vibratory motion. When the string is plucked and released, it executes to-and … Periodic motion is also exhibited in other cases such as the to-and-fro motion of a sewing machine needle and the movement of the piston of an engine. About OpenStax; About This Book It is essential to keep in mind that every oscillatory motion is periodic; however, every periodic motion may not be oscillatory. a periodic motion is a motion in which a particle repeats its motion after a fixed time period. In addition, oscillatory motion is bounded … A to and fro or back and forth motion of a body along the same path, without any change in shape of the body, is called an oscillatory motion. An example of this is a weight bouncing on a spring. Periodic Motion Periodic motion is motion that repeats itself. Examples of periodic motion are motion of hands of the clock, motion of planets around the sun etc. This fixed interval of time is known as time period of the periodic motion. A periodic motion may or may not be oscillatory. An oscillation can be a periodic motion that repeats itself in a regular cycle, such as a sine wave —a wave with perpetual motion as in the side-to-side swing of a pendulum, or the up-and-down motion of a spring with a weight. for example circular motion, pendulum motion are periodic motions. Examples of oscillatory motion are vibrating strings, swinging of the swing etc. Examples to understand oscillatory motion and periodic motion; Define periodic motion; Understand every oscillatory motion is periodic but every periodic motion need not be oscillatory; Difference between oscillation and vibration, Define time period; Units of time period; Define frequency; Represent displacement as mathematical function of time; Derive T =2π / ω; Knosw that any periodic … Here, k is the constant and x denotes the displace… The systems where the restoring force on a body is directly proportional to its displacement, such as the dynamics of the spring-mass system, are described mathematically by the simple harmonic oscillator and the regular periodic motion … The fixed interval of time after which a periodic motion is repeated is called as the period of that periodic motion. Harmonic Oscillator. Oscillatory motion is defined as the to and fro motion of the body about its fixed position. The oscillations of a system in which the net force can be described by Hooke’s law are of special importance, because they are very common. But every periodic motion need not be an oscillatory motion. Oscillatory motions are motions where an equilibrium point exists. The to-and-fro motion of a body is called oscillatory motion. Periodic motions are motions that repeat itself over time. Examples of periodic motion are motion of hands of the clock, motion of planets around the sun etc. For example, the motion of planets around the Sun is always periodic but not oscillatory. An oscillating movement occurs around an equilibrium point or mean value. Introduction to Oscillatory Motion and Waves; 16.1 Hooke’s Law: Stress and Strain Revisited; 16.2 Period and Frequency in Oscillations; 16.3 Simple Harmonic Motion: A Special Periodic Motion; 16.4 The Simple Pendulum; 16.5 Energy and the Simple Harmonic Oscillator; 16.6 Uniform Circular Motion and Simple Harmonic Motion; … The main difference between simple harmonic motion and periodic motion is that periodic motion refers to any type of repeated motion whereas simple harmonic motion (SHM) refers to a specific type of periodic motion where … are examples where the objects motion "approximately" keeps repeating itself. Harmonic motion is periodic and can be represented by a sine wave with constant frequency and amplitude. Oscillatory and periodic motions are very abundant in nature and are, therefore, very important in many systems. For example, a small object oscil-lating at the end of a spring, a swinging pendulum, the earth orbiting the sun, etc. These are periodic and non-periodic motion. The periodic time: the periodic time is the time taken by an oscillating body to make one complete oscillation, The measuring unit of the … Oscillatory motions are a type of periodic motion. This motion is also called "periodic motion" with a "repeat time" T. Examples of periodic motion include (1) a mass on a spring, (2) the simple pendulum, (3) the motion of a planet like the Earth about the Sun, and (4) the … 8.1.1. Preface to College Physics. It results in an oscillation which, if uninhibited by friction or any other dissipation of … Example period motion: Period of earth around its own axis is 24n. An oscillatory motion is always periodic.
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CC-MAIN-2022-21
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http://slideplayer.com/slide/1671715/
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math
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SyllabusSyllabus Prior Knowledge: Understanding of basic Probability theory
Numbers Up! You win the number that appears on the die in uro 4 for a 4 6 for a 6 etc A funfair game called Numbers Up! involves rolling a single die. Here are the rules:
Activity 1 1.How much did you win? 2. Work out your average(mean) amount you won per game having played the game 20 times. 3. When you have the value for the class mean, fill in the table below:
Activity 1 4. Does your average differ from that of the class? What could explain this? 5. What do you think the class average figure represents in the context of the game? 6. Would you pay 3 to play this game? Give a reason for your answer. 7. If you ran the Numbers Up! game at the funfair, how much would you charge people to play it? Explain your answer. 8. What do you think would be a fair price to pay to play this game? Why?
A Fair Price? If I roll a standard die many times what is the average score I can expect?
Probability Distribution Table Score (X) 123456 Probability P(X) 1/6 Numbers Up!
Probability Distribution Table Score (X) 123456 Probability P(X) Numbers Up!
Expected Value How much money a player can expect to win/lose in the long run on a particular bet The House Edge/ Risk Analysis and Insurance/ Economics (Decision Theory) Mean: average of what HAS happened Expected Value: average of WHAT IS GOING to happen
Fair Games Fair Game A game is said to be fair if the expected value (after considering the cost) is 0. If this value is positive, the game is in your favour; and if this value is negative, the game is not in your favour.
Problem Solving with Expected Value Jyme has three cars with one roll remaining. Assuming the car is worth 15,000, (a)Find the probability that shell win the car on the last roll. (b)Find her expected pay-off based on re-rolling the last two dice. How much money would you need to have showing on those remaining dice after the second roll not to risk it?
Two Way Table Car 50010001500 CarCAR 50010001500 CarCAR 50010001500 CarCAR 50010001500 500 100015002000 1000 150020002500 1500 200025003000
SolutionSolution X5001000150020002500300015,000 P(X)6/367/368/363/362/361/369/36 The expected payoff if you re-roll the two dice is $500(6/36) + $1000(7/36) + … + $15,000(9/36) = $4,750 But if you have exactly three cars showing after two rolls, the largest money amount you could win is $3000. So, based on expected value, you should re-roll the last two dice no matter what.
Making Decisions Should I buy that extended warranty on my new 99.99 printer?
In Summary The Expected Value of a random variable X is the weighted average of the values that X can take on, where each possible value is weighted by its respective probability Informally, an attempt at describing the mean of what is going to happen. Expected Value need not be one of the outcomes.
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| 2,855 | 14 |
https://questioncove.com/updates/5f69650f5e81faddf5ce1800
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math
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Dependent variables can be the result of more than one independent variable. Consider your phone bill as presented in the Opening Activity. Aside from being charged for minutes over 300, you are charged $1.25 for each directory assistance call and $.75 per minute for long distance roaming calls. You also have to contribute at least $1.50 to the federally required Universal Service Fund per month and this value may vary on your phone bill. Month Fixed monthly fee ($35.00 per month) Additional minutes used ($.40 per min.) Directory assistance ($1.25 per call) Long distance roaming minutes ($.75 per minute) USF monthly charge Total Monthly Bill January 55 2 0 1.50 February 14 1 15 1.50 March 0 3 0 2.25 April 86 4 35 1.50 May 75 2 15 2.50 June 0 0 0 1.50 What is the constant? How many independent variables are there in this situation? What are the independent variable(s)? What independent variable(s) do you have control over and what independent variable(s) do you not have control over? What is the dependent variable? Write an equation expressing your monthly cost using the below independent and dependent variables. Let x = additional minutes used Let d = number of directory assistance calls made Let r = number of long distance minutes used Let u = USF monthly charge Let y = total monthly bill Using your equation, fill in the Total Monthly Bill column in the above table. You can upgrade your service to $40 a month for 500 anytime minutes? Which independent variable would you consider to determine if this is in your best interest? Do you think you should upgrade?
Join our real-time social learning platform and learn together with your friends!
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| 1,666 | 2 |
http://awcourseworktwqf.alisher.info/ch6-solutions.html
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math
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Solutions to chapter 6 valuing bonds 1 a coupon rate = 6%, which remains unchanged the coupon payments are fixed at $60 per year b when the market yield increases, the bond price will fall the cash flows are verify the solution as follows: $94998 109119 $1,000 009119(109119) 1. Giancoli 6th edition problem solutions chapter #6 ü problem #3 question: a 1300 nt crate rests on the floor how much work is required to move it at constant speed. Get here ncert solutions for class 10 maths chapter 6 these ncert solutions for class 10 of maths subject includes detailed answers of all the questions in chapter 6 – triangles provided in ncert book which is prescribed for class 10 in schools. Problem set –chapter 6 solutions 1 ch 6, problem 61 a firm uses the inputs of fertilizer, labor, and hothouses to produce roses suppose that when the quantity of labor and hothouses is fixed, the relationship between the quantity of fertilizer and the number of roses. 1 chapter 6 discrete probability distributions ch61 discrete random variables objective a: discrete probability distribution a1 distinguish between discrete and continuous random variables.
Unlike the unicellular organisms, the multi-cellular organisms have complex body structures with specialized cells and tissues to perform various necessary functions of the body since these cells are not in direct contact with surrounding environment so, simple diffusion cannot meet the oxygen. Access systems analysis and design 9th edition chapter 6 solutions now our solutions are written by chegg experts so you can be assured of the highest quality. Ilmkidunyacom has brought to you lecture of sibghat ullah on 9th class chemistry chapter 6 solutions topic 61 introduction about solutions.
All chapters of science for class 10th final's [sa-2] brief summary here get all chapters of science for class 10th final's [sa-2] brief summary here: 1. Learn chapter 6 application of derivatives (aod) of class 12 free with solutions of all ncert questions for maths boards we learned derivatives in the last chapter, in chapter 5 class 12 in this chapter we will learn the applications of those derivatives. To enroll in courses, follow best educators, interact with the community and track your progress. Answer: each speech channel in the 125 ms frame is now divided into two parts: a 5 µs preamble and 8/40 µs of speech bits, giving a total of 5 × 40 + 8 = 208 bits/ speech channel each frame sends 40 mbps × 125 µs = 5000 bits. Ch 6 solutions - ebook download as pdf file (pdf), text file (txt) or read book online scribd is the world's largest social reading and publishing site search search.
Video solutions for introduction to trigonometry for free video solutions for chapter 6 triangles for free ncert solutions for class 10 chapter 6 triangles exercise 61. Programming in haskell, ch6 solutions github gist: instantly share code, notes, and snippets. Pom10_solutions_ch6_finalpdf - google docs. Author(s) cooke, roger date 1976 subject(s) mathematical analysis abstract solutions manual developed by roger cooke of the university of vermont, to accompany principles of mathematical analysis, by walter rudin.
(a) equal, (b) proportional 2 give two different examples of pair of (i) similar figures (ii) non-similar figures answer (i) two twenty-rupee notes, two two rupees coins. Wwwcsunedu. Solutionbank edexcel as and a level modular mathematics integration exercise a, question 1 question: integrate the following with respect to x.
These ncert solutions for class 11 of maths subject includes detailed answers of all the questions in chapter 6 – linear inequalities provided in ncert book which is prescribed for class 11 in schools. Chapter 6, exercise solutions, principles of econometrics, 3e 114 exercise 62 the model from exercise 61 is yiiii=β+β +β +12 3xzethe sse from estimating this model is 979830 the model after augmenting with the squares and the cubes of.
Answer key chapter 6 6th edition 2 a) hamilton circuits must pass through all the vertices once and only once and start and stop at the same vertex. Access cfin4 4th edition chapter 6 problem 4p solution now our solutions are written by chegg experts so you can be assured of the highest quality. This feature is not available right now please try again later. View homework help - ch6 solutions from acct 2302 at university of texas, dallas accounting 2302 chapter 6 answers to assigned exercises and.
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http://branchingnature.org/domain-and-range-worksheet-2-answer-key-algebra-1.html
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math
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Domain And Range Worksheet 2 Answer Key Algebra 1
Cumulative review homework answer key.
Domain and range worksheet 2 answer key algebra 1. Algebra 1 downloadable resources. Understand that a function from one set called the domain to another set called the range assigns to each element of the domain exactly one. Please carefully read and follow your directions each day. A spreadsheet is an interactive computer application for organization analysis and storage of data in tabular form.
The measurement worksheet will produce twenty conversion problems per. Module 1 copy ready materials relationships between quantities and reasoning with equations and their graphs. Spreadsheets developed as computerized analogs of. Please review the faqs and contact us if you find a problem with a link.
Exponential functions 20 problems 4 determine whether it is an exponential function given an equation. Discover what you understand about linear transformations with these study assessments. About this quiz worksheet. Algebra 2 trig skills review packet.
Topics that the quiz will test include what a. Algebra 2 trig. 2 determine whether it is linear or exponential given a. Learn and research science biology chemistry electronics mathematics space terminology and much more.
Division worksheets long division worksheets. This long division worksheet the number of digits for the divisors and quotients may be varied from 1 to 3.
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http://www.abovetopsecret.com/forum/thread879485/pg1
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math
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posted on Sep, 8 2012 @ 12:08 AM
Hey there, I am looking for some mathletes to help me out. I recently asked/responded to a question on
and I would like anyone to check the math and let me know where I went
First the facts:
Now the question I asked:
Can this get through Iran's UHPC
? The article states that it is 150
newton/millimeter². I don't know if I'm doing it right or not, but that would equal 21755 psi. Which would cut in half the penetration depth of 25 ft
that the GBU-57A/B is claimed to get to. Please correct me if I am wrong with the math.
Thanks in advance...surely I can't be right as there is no way I am smarter than the rocket nerds who developed it.
Edit: I see in this article
that they claim they don't know if it
will do anything but collapse some passageways and force rebuilding work.
edit on 8-9-2012 by superman2012 because: (no reason given)
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| 873 | 14 |
http://www.mathisfunforum.com/post.php?tid=19973&qid=283526
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math
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Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °
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Topic review (newest first)
I suspect this work is leading up to quadratics and the quadratic formula **.
OMG ... when i seen the answer I felt stupid... I know that i have to list the numbers of what it could be until i find both numbers that match... i guess i really need to work on my multiplication. Thank you Agnishom
Of course the answer is 14 and 1
The example that i have given is similar to the worksheet.
I was give a worksheet... And I need to find the base numbers from the product of 14 and the sum of 15. the base numbers have to be the same and equal to the product and sum given. I'm trying to find a method the would help me find the base numbers. please help i have eleven questions that need answers.
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s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609530136.5/warc/CC-MAIN-20140416005210-00081-ip-10-147-4-33.ec2.internal.warc.gz
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| 904 | 9 |
https://www.prep4usmle.com/forum/thread/105097/
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math
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|Prep for USMLE|
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A 14 years old young man that was healthy before due to fever, migratory pain and swelling of large joints plus chest pain which became better in sithing and bending forward position was brought to ED, apparently patient 4 weeks ago was affected with pharyngitis and consumed ampicillin for a while. in laboratory exams pharynx culture became negative, ESR=100 mm in first hour and ASO titer was more than 633 Todd, in heart physical exam which of the findings below is more probable?
B. pansystolic 3/6 murmur at mitral locus
C. lng diastolic rumble at apex
D. pericardial friction rub
I'll go with D. pericardial friction rub, which is consistent with an inflammatory condition such as Rheumatic Fever and his symptoms of bending forward.
This thread is closed, so you cannot post a reply.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337731.82/warc/CC-MAIN-20221006061224-20221006091224-00244.warc.gz
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http://www.fivedoves.com/letters/aug2010/james82.htm
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math
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Have been a follower of the " Five Doves" for a number of months. Came across the figure about seven and "11" and not sure if Holy Father
have prompted to mean " Is the World's population" ?
Quote : the United Nations estimated the population to reach 7,000,000,000 in 2011
Is 7, 100, 100 , 000 the figure ?
With GOD's Grace and Mercy
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s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368701614932/warc/CC-MAIN-20130516105334-00031-ip-10-60-113-184.ec2.internal.warc.gz
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| 334 | 5 |
https://findanyanswer.com/what-are-cost-drivers-in-abc-costing
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math
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What are cost drivers in ABC costing?
Similarly, it is asked, what is a cost driver give three examples?
Examples of cost drivers are as follows: Direct labor hours worked. Number of customer contacts. Number of engineering change orders issued. Number of machine hours used.
In respect to this, what are cost drivers in accounting?
cost driver is any factor which causes a change in the cost of an activity. — Chartered Institute of Management Accountants. "Cost drivers are the structural determinants of the cost of an activity, reflecting any linkages or interrelationships that affect it".
Find the total cost for the activity in your given information. For instance, you would use the total cost to produce all of the widgets. Divide the activity cost by the volume to find the cost driver rate. For example, if you made 100 widgets for a cost of $3,000: $3,000/100 = $30 per widget.
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s3://commoncrawl/crawl-data/CC-MAIN-2024-18/segments/1712296816863.40/warc/CC-MAIN-20240414002233-20240414032233-00093.warc.gz
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https://in.mathworks.com/matlabcentral/answers/1663434-ros-simulink-algebraic-loop
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math
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ROS Simulink algebraic loop
32 views (last 30 days)
I am tryining to build up a HIL environment by using ROS in Simulink. If I try to run a simulation, I get the following error:
"Algebraic loops are not supported in generated code. Use the 'ashow' command in the Simulink Debugger to see the algebraic loops. If algebraic loops only exist during code generation, please check if configset parameter 'CombineOutputUpdateFcns' is on, set it off might resolve algebraic loops."
Is there a ways to turn off 'CombineOutputUpdateFcns' in Simulink? Trying to do so in the Configuration Parameters is not possible, since this setting is blocked (see figure).
Thank you very much for your help!
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100677.45/warc/CC-MAIN-20231207153748-20231207183748-00791.warc.gz
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https://bathmash.github.io/HELM/25_2_applications_of_pdes-web/25_2_applications_of_pdes-web.html
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math
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In this Section we discuss briefly some of the most important PDEs that arise in various branches of science and engineering. We shall see that some equations can be used to describe a variety of different situations.
- have a knowledge of partial differentiation
- recognise the heat conduction equation and the wave equation and have some knowledge of their applicability
Key Point 4 by no means exhausts the types of PDE which are important in applications. In this Section we will discuss those three PDEs in Key Point 4 in more detail and briefly discuss other PDEs over a wide range of applications. We will omit detailed derivations.
2 Heat conduction equation
3 Transmission line equations
4 Laplace’s equation
5 Other important PDEs in science and engineering
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https://socratic.org/questions/please-solve-q-99-2#631472
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math
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Please solve q 99?
This is called Viviani's theorem: https://en.wikipedia.org/wiki/Viviani%27s_theorem
ABC is the triangle. It's height
Remember that the area of a triangle is
Now all three triangles APC, BPC and APB have a base = 10 since all sides are equal and 10. Their total area is equal to the area of ABC
Another one from Rahul's Book!
I'd say that given we're given choices, the result doesn't depend on our choice of
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https://math.answers.com/algebra/What_does_three_over_four_divided_by_nine_equal
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math
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6 and three over four
it is nine eighths it is nine eighths
Technically, any number can be divided by any and all non-zero numbers, but I'll assume you mean evenly. There is no number that is evenly divisible by nine but not three because 9 is equal to 3x3. So when you divide by 9 it is the same as dividing by 3 twice.
4,508,020,993 in word form is: four billion five hundred eight million twenty thousand nine hundred ninety-three.
The square root of a number is the inverse of the square. For example, three squared equals nine, so the square root of nine is equal to three.
3/8 divided by 9/10 = 3/8 times 10/9 ie 30/72 = 5/12
8 and 1/3
Fifty-four divided by six is equal to positive nine because fifty-four and six are both positive numbers.
(-9) / 3 = -3 . Minus nine divided by three is equal to minus three
Six plus four divided by eight times nine minus four is equal to 6.5
81 divided by 9 ie 9
Sixty three thousand, two hundred and ninty-nine divided by twelve is equal to five thousand, two hundred and seventy-four point nine one six six. This and other math questions are simple to solve with a calculator.
Nine tenths is 9 divided by 10 which is equal to 0.9. Nine hundredths is 9 divided by 100 which is equal to .09 and it continues. So the numeric value would 4.9.
50000000000 / 309000000 = 161.8123
nine divided by three equels 3
Three fours (12) is not equal to nine twelves (108). However, three over four (3/4) is equal to nine over twelve (9/12) which are known as equivalent fractions to each other.
The number sixty-three thousand two hundred ninety nine divided by the number twelve is 5274.97. The number 12 is not equally divided into the number 63,299.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-23/segments/1685224655244.74/warc/CC-MAIN-20230609000217-20230609030217-00093.warc.gz
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CC-MAIN-2023-23
| 1,682 | 17 |
http://exxamm.com/QuestionSolution16/Chemistry/Calculate+molality+m+of+each+ion+present+in+the+aqueous+solution+of+2+M+NH+4Cl+assuming+100+dissociation+accor/1210656519
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math
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Ask a Question
Question Asked by a Student from EXXAMM.com Team
Q 1210656519. Calculate molality (m) of each ion present in the aqueous solution of `2 M` `NH_4Cl` assuming ` 100%` dissociation according to reaction.
`NH_4Cl (aq) -> NH_4^(+)(aq) + Cl^(-) (aq)`
Given : Density of solution = `3.107`gm / ml
(Provided By a Student and Checked/Corrected by EXXAMM.com Team)
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s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578530040.33/warc/CC-MAIN-20190420200802-20190420222802-00320.warc.gz
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CC-MAIN-2019-18
| 375 | 6 |
http://cffmv.blogspot.com/2013/06/featured-6-6-2013-formulasheet.html
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math
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Store all your formulas in one place with FormulaSheet. All your formulas will be accessible from anywhere you can connect to the Internet.
Using FormulaSheet, formulas can be organized into lists, or combined with text and diagrams to create sheets.
With FormulaSheet, you can:
- Search Wikipedia and/or FormulaSheet for the formulas you need. Instantly get an image or copy the formula to LaTeX or MS Word.
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- Share formula lists and sheets with other users.
- Render your formula, list, or sheet as a pdf document, as a tex file, or as a png image.
The new Calculator feature lets you solve selected formulas right on FormulaSheet. Enter the variables that you know, and the calculator will solve for the one that you are trying to find. Any constants used by the formula are provided.
Watch the Formulasheet intro video
FormulaSheet is a free web app, but voluntary donations are welcomed.
DISCLOSURE OF MATERIAL CONNECTION: http://cmp.ly/0
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s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125946807.67/warc/CC-MAIN-20180424154911-20180424174911-00513.warc.gz
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CC-MAIN-2018-17
| 1,110 | 12 |
http://goodriddlesnow.com/riddles/view/2292
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math
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Question: You are walking down a path until there is a fork in the road. One side is the good path and the on the other side is the bad path. However you don't know which one is which. Both paths have identical twins guarding the paths. One guard tells the truth, the other lies all the time no matter what. But still you don't know which one tells the truth or which one tell lies. If you want to to go to the good path, what question should you ask the guards
Answer: You would ask "which path would your brother go?" Take the opposite path they are pointing
Question: There were 2 doors. Behind the 1 door, is hell and behind the other door, is heaven but you don't know which door will take you to heaven. In front of them, there were 2 brothers, which is guarding the door. One of the brother always lie and the other one always tell the truth. Of course you don't know who is lying and who is not. You only get 1 question to ask one of them to figure out which door leads to heaven. What question you might ask? Remember you only get to ask 1 question. it means that you can't ask one question each of them. that will be 2 questions. You only ask 1 question to any of them and no more. How do you do that?
Answer: Go up to one of the guy and ask this question, " Hello, which door that your brother will point if I ask him which way is the heaven." Then take the other door. Don't enter the door that he was pointing. This question will work for both of them because if you ask this question to the truth guy, he will point the hell because he knows that his brother will point hell and if you asked to the liar, he'll still point hell because he knows that his brother will point to heaven door, so he lied. That's why you take the other door.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463612003.36/warc/CC-MAIN-20170528235437-20170529015437-00476.warc.gz
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CC-MAIN-2017-22
| 1,750 | 4 |
http://www.defendersource.com/forum/f6/equal-balance-how-much-for-35-swamper-10089.html
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math
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Equal balance, how much for 35" Swamper?
Waiting for a set of 35 10.5x16 SSR radials.
I am a fan of equal balance, but have heard how heavy these tires are.
I figure the more equal balance the better, but has anyone found the "correct" amount?
.....I ask this because I remember a post where someone had trouble getting these to balance....
Thanks in advance
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s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948594665.87/warc/CC-MAIN-20171217074303-20171217100303-00016.warc.gz
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CC-MAIN-2017-51
| 358 | 6 |
https://www.construct.net/forum/construct-2/how-do-i-18/how-to-make-a-scrolling-backgr-110922
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math
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maybe a silly question,
I've been using the autorunner events to make my background scroll infinitely, but it's scrolling left instead of right. I tried modifying the bullet speed to a negative number but then my background disappears alltogether. Anyone know how to get this done?
Thanks in advance.
If you're using bullet, you should be able to set the angle of motion to 180. Turn off set angle in the bullet behavior properties.
thanks for your reply, but changing the background angle of motion to 180 doesn't seem to work. If you can get it done, perhaps you could show me how to do it? Or have a capx file?
Develop games in your browser. Powerful, performant & highly capable.
Thanks man, got it to work using your sample.
Thanks for your help!
Regards - R
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s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267864953.36/warc/CC-MAIN-20180623074142-20180623094142-00518.warc.gz
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CC-MAIN-2018-26
| 763 | 9 |
https://www.enotes.com/homework-help/quadratic-equation-help-370195
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math
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Quadratic Equation The flight of an aircraft is represented by the equation h(t) = -10t^2 + 500t +9050 where h is the height in metres and t is the...
The flight of an aircraft is represented by the equation h(t) = -10t^2 + 500t +9050 where h is the height in metres and t is the time in seconds. What is the maximum altitude of the plane.
Please explain thank you!
`h(t) = -10t^2+500t+9050`
`First take -10 out of the expression. h(t) = -10(t^2-50t-905)`
Now we have to complete a square in the left side.
Look at following expression.
`(t-a)^2 = t^2-2at+a^2`
Consider` t^2-50t-905 ` with the right side of the above. Compare the component of t in both equations.
`-2a = -50`
` a = 25`
`(t-25)^2 = t^2-50t+25^2 = t^2-50t+625`
But what we want is t^2-50t-905.
So we write;
`t^2-50t-905 = (t^2-50t+625)-625-905`
`t^2-50t-905 = (t-25)^2-1530`
`h(t) = -10[(t-25)^2-1530]`
`h(t) = -10(t-25)^2+1530`
We know that `(t-25)^2 >=0` always.
So h(t) will have a maximum when -`10(t-25)^2 ` has lesser negative value or the maximum value.
maximum here is 0. all others are negative.
So h(t) will be maximum when `-10(t-25)^2 = 0`
maximum h(t) = 1530
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s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496665726.39/warc/CC-MAIN-20191112175604-20191112203604-00315.warc.gz
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CC-MAIN-2019-47
| 1,137 | 23 |
http://www.kgbanswers.com/if-a-1-gallon-jug-was-filled-with-dimes-what-would-be-your-estimate-of-roughly-how-much-money-would-be-in-it/18406107
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math
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Here's our best estimate: 8904 dimes.
Dime, the smallest, thinnest coin in use today has the following specifications:
Weight: 2.268 g
Diameter: 0.705 in (17.91 mm)
Thickness: 1.35 mm
Get the volume of the dime using the formula: VOLUME = π * (radius)² * height
Plug in the numbers:
V = 3.14159 * (8.955 mm)² * 1.35 mm
V = 3.14159 * 80.192025 mm * 1.35 mm
V = 340.10641343226 mm³
We know that 1 gallon = 3785412 mm³ - Metric-Conversions.org
Now, divide the volume of the jug by the volume of a dime:
3785412 mm³ / 340.10641343226 mm³
But since they don't fit in perfectly, you are really looking at less. Upon estimation, they pack about 80% efficiently.
Now, divide your estimate for the volume of a penny into 80% of the volume of the jug.
80% of 3785412 mm³ = 3028329.6 mm³
3028329.6 mm³ / 340.10641343226 mm³
Tip! Find out Ten Ways to Improve Math Skills, shared by SCCPS.
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s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257823947.97/warc/CC-MAIN-20160723071023-00018-ip-10-185-27-174.ec2.internal.warc.gz
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CC-MAIN-2016-30
| 887 | 18 |
https://www.sae.org/publications/technical-papers/content/380146/
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math
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Airplane Performance Calculations by Means of Logarithmic Graphs 380146
THE ideas presented in this paper are designed to eliminate all the faults of previous formulas or charts for finding airplane performance, and to provide a method which will be satisfactory for all types of propellers, engines, and airplanes. The same equation for the power required is retained as was used previously, but corrections are applied to it to take care of the increase in power as the burble points are reached.
By a simple device employing two parameters determined by the airplane dimensions, the power-required curve is generalized and then plotted logarithmically. The power-available curve is generalized in a similar manner and likewise plotted logarithmically. Then, by a simple calculation, the method of placing properly these two generalized curves one over the other is found. This procedure results in being able to read directly with no plotting the values from which the performance can be obtained.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039746465.88/warc/CC-MAIN-20181120150950-20181120172950-00152.warc.gz
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CC-MAIN-2018-47
| 1,000 | 3 |
https://www.physicsforums.com/threads/choosing-the-right-magnet-stuck.145497/
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math
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Hello, I am an engineering student doing my first real engineering project with a group of other engineering students. To give a background of my issue, I am charged with the task of designing a system which is able to detect when a rotating shaft spins too fast and send an appropriate signal to a device that will disengage this shaft from its driving source. I've decided to use the rotating shaft to generate a small emf using a wire loop in a constant magnetic field, or at least am using this model, as a voltage source to a circuit which will then interpret the signal and detect when the signal gets too large. I've already simulated the circuit, but what's getting me is how to actually build the voltage source when it comes to prototype building time: The area I have to work with isn't all that small - maybe a cubic foot or so around this rotating shaft - so I have some leeway on how big I can make the wire loop or how large the magnets can be, but I can't seem to get good info on how to determine what magnetic field my wire loop will be seeing if I place opposite poles on either side of my wire loop. My electromagnetic fields book says that the field can be treated as constant, but I'm not so sure. With that being said, the only listings on websites regarding magnetic field are measurements taken at the surface of the magnet. If I place a wire loop between two similar magnets spaced say half a foot apart, I infer from my book that on a direct path between the two surfaces of the magnets the field will be the same as on the surface of either, but this seems very wrong to me. I think the book may be assuming the surface area of the magnets is much greater than the length between them, and I will not have that sort of convenience. Am I just going to have to do calculus on each length of wire based on the surface shape of my magnets, or can I do something easier with the information given on websites that I'm looking at to purchase magnets from?
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s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583657557.2/warc/CC-MAIN-20190116175238-20190116201238-00272.warc.gz
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CC-MAIN-2019-04
| 1,977 | 1 |
http://ned.ipac.caltech.edu/level5/March02/Sahni/Sahni3_2.html
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math
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3.2. Spatially open and flat cosmological models
The preceding discussion referred to closed universe models for which = 1 and E < 0. For flat and open models ( = 0, - 1) the total energy is non-negative E 0 and motion in the potential V(a) becomes unbounded, since a particle always has sufficient energy to surmount the potential barrier in figure (2). As a result the expansion factor a(t) shows monotonic behaviour, starting from the singular point at a = 0, t = 0 and increasing without bound as t . For > 0 the universe passes through an inflection point at which the expansion of the universe changes from deceleration ( < 0) to acceleration ( > 0) (from (3) & (4) it can be shown that this usually occurs at a redshift when is still not dominating the expansion dynamics of the universe; see section 4.3).
In the important case when the universe is spatially flat and contains pressureless matter (dust) and a positive cosmological constant, the expansion factor has the exact analytical form:
which interpolates smoothly between the matter dominated epoch in the past (a t2/3) and an inflationary epoch in the future (a e(/3)1/2t). Equation (12) will be used later, when we examine some observational aspects of a universe with a cosmological constant in Section 4.
Finally, oscillating, bouncing and loitering models, as well as the static Einstein universe, are clearly absent in flat and open FRW models.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257648113.87/warc/CC-MAIN-20180323004957-20180323024957-00412.warc.gz
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CC-MAIN-2018-13
| 1,416 | 5 |
http://www.solutioninn.com/south-side-corporation-is-expected-to-pay-the-following-dividends
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math
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Question: South Side Corporation is expected to pay the following dividends
South Side Corporation is expected to pay the following dividends over the next four years: $10, $8, $5, and $3. Afterward, the company pledges to maintain a constant 5 percent growth rate in dividends forever. If the required return on the stock is 13 percent, what is the current share price?
Answer to relevant QuestionsAntiques R Us is a mature manufacturing firm. The company just paid a $12 dividend, but management expects to reduce the payout by 4 percent per year, indefinitely. If you require a 9 percent return on this stock, what will ...Pre Satellite Corporation earned $12 million for the fiscal year ending yesterday. The firm also paid out 40 percent of its earnings as dividends yesterday. The firm will continue to pay out 40 percent of its earnings as ...One potential criticism of the net present value technique is that there is an implicit assumption that this technique assumes the intermediate cash flows of the project are reinvested at the required return. In other words, ...Suppose you are offered a project with the following payments. a. What is the IRR of this offer? b. If the appropriate discount rate is 10 percent, should you accept this offer? c. If the appropriate discount rate is 20 ...Consider two mutually exclusive new product launch projects that Nagano Golf is considering. Assume the discount rate for both projects is 12 percent. Project A: Nagano NP-30 Professional clubs that will take an initial ...
Post your question
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s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886112539.18/warc/CC-MAIN-20170822181825-20170822201825-00206.warc.gz
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CC-MAIN-2017-34
| 1,543 | 4 |
http://ieeexplore.ieee.org/xpl/articleDetails.jsp?reload=true&arnumber=5694436&contentType=Conference+Publications
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math
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Skip to Main Content
ABC cost function model is established to calculate the reasonable and lowest cost of construction engineering, by using the idea of Activity-Based Costing (ABC) method that "resources consumed by activities and the products use up activities”. And then, the actual costs are calculated by combining with the accounting records and the calculation method of traditional cost. Now we get the actual cost and the reasonable and lowest cost of construction engineering respectively. So the implicit cost function model of construction engineering can be established by the idea of actual costs minus reasonable and lowest costs. Above all, the implicit cost and the compressible space of the cost in construction engineering will visualize theoretically by using the implicit cost function model.
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s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1393999664205/warc/CC-MAIN-20140305060744-00015-ip-10-183-142-35.ec2.internal.warc.gz
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CC-MAIN-2014-10
| 816 | 2 |
https://brainmass.com/business/annuity/pg13
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math
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34. Valuing Delayed Annuities. Suppose that you will receive annual payments of $10,000 for a period of 10 years. The first payment will be made 4 years from now. If the interest rate is 5 percent, what is the present value of this stream of payments? 36. Amortizing Loan. You take out a 30-year $100,000 mortgage loan with
Please check my computations to the following questions on the attached spreadsheet. I know that my answers for # 3 are wrong and that the correct answers are $4,167.62, $ 4,313.71, and $ 5,001.15 but I can't figure out what I'm doing wrong. I don't know if my other answers are correct or not. Question 3 - Future Value and Mu
BE2-4 Becky Sherrick's regular hourly wage rate is $14, and she receives an hourly rate of $21 for work in excess of 40 hours. During a January pay period, Becky works 45 hours. Becky's federal income tax withholding is $95, her FICA tax withheld is $53.20, and she has no voluntary deductions. Compute Becky Sherrick's gross e
Question: The $40 million lottery payment that you just won actually pays $2 million per year for 20 years. If the discount rate is 8%, and the first payment comes in 1 year, what is the present value of the winnings? What if the first payment comes immediately?
Cathy is saving for her retirement by putting $325 each month into an ordinary annuity. If the annuity is expected to pay an annual interest rate of 8.5%, how much will she save for her retirement in 30 years?
Please help with the following problem. Andahl Corporation stock, of which you own 500 shares, will pay a $2-per-share dividend one year from today. Two years from now Andahl will close its doors; stockholders will receive liquidating dividends of $17.5375 per share. The required rate on return on Andahl stock is 15 percent.
A couple is planning for the education of their two children. They plan to invest the same amount of money at the end of each of the next 16 years. The first contribution will be made at the end of the year and the final contribution will be made at the time the oldest child enters college. The money will be invested in sec
You deposited $1,000 in a savings account that pays 8 percent interest, compounded quarterly, planning to use it to finish your last year in college. Eighteen months later, you decide to go to the Rocky Mountains to become a ski instructor rather than continue in school, so you close out your account. How much money will you r
Multiple Choice Questions: Stock's beta, R2 for a stock and a portfolio, present value of an ordinary annuity Please see attached.
1) Stock A has a beta = 0.8, while Stock B has a beta = 1.6. Which of the following statements is most correct? a. Stock B's required return is double that of Stock A's. b. An equally weighted portfolio of Stock A and Stock B will have a beta less than 1.2. c. If market participants become more risk averse, the required re
Multiple Choice- Annuities ________________________________________ Solution The future value of a lump sum at the end of five years is $1,000. The nominal interest rate is 10 percent and interest is compounded semiannually. Which of the following statements is most correct? d. Both statements b and c are correct. e.
The future value of a lump sum at the end of five years is $1,000. The nominal interest rate is 10 percent and interest is compounded semiannually. Which of the following statements is most correct? a. The present value of the $1,000 is greater if interest is compounded monthly rather than semiannually. b. The effective a
1. If you borrow $15,618 and are required to pay the loan back in 7 equal annual installments of $300. What is the interest rate assocated with this loan? 2. Your rich uncle has offered you a choice of one of the three following alternatives. Which one would you take? a) $10,000 now b) $2000 a year for 8 years -equal inv
1. The future value of a $500 ordinary annuity received for three years is $________, assuming an investment rate of 10%. a. 1,655.00 b. 665.50 c. 1,820.50 d. 335.65 2. With an interest rate of 9 percent, your investment would double in about a. 4 years. b. 6 years. c. 8 years. d. 10 years. 3. An ordinary annuity
What is the effective return of an investment account that pays a 9.9 APR compounded daily (for 365 days)? Okay let's say the annual interest rate is 10%. a.) What would be the present value of a 5-year ordinary annuity with annual payments of $200? b.)What is the present value if it is a 5-year annuity due (all the rest is
1. Determine the future value of an annuity that pays $5,000 at the end of the next 11 years. Similar securities pay an interest rate of 7%. 2. How much money would you be willing to pay in order to receive $800,000 40 years from today? Assume that your required rate of return on investments is 8% compounded semiannually.
1. Today you borrow $80,000 to finance the purchase of your new sports car. Interest will be 5% compounded monthly. Payments will be made at the beginning of the month. You will repay the loan over 4 years. How much will the payments be? 2 If you borrow $100 and pay back $3600 in 5 years, what annual interest rate are you pay
You plan to retire in twenty years. When you retire, you will need $150,000 per year for thirty years with the first payment needed at t=21. You expect to receive $50,000 from a trust at t=12 which you will deposit in your retirement account. At t=10, you plan to take a world cruise that will cost you $15,000 to be paid out o
You plan to take a long trip through Europe, leaving in 5 years. You're plan is to save money for the next five years, leave at the end of the fifth year, and then survive on your savings for 3 years. You estimate you can survive in Europe on $10,000 a year. You estimate that your investment account will earn 8% forever. You
Your client plans to contribute an equal amount of money each year until her retirement. Her first contribution will come in exactly 1 year; her 10th and final contribution will come in 10 years (on her 85th birthday). How much should she contribute each year to meet her objectives?
Your client just turned 75 years old and plans on retiring in exactly 10 years (on her 85th birthday). She is saving money today for her retirement and is establishing a retirement account with your office. She would like to withdraw money from her retirement account on her birthday each year until her death. She would ideall
1. Which of the following should be used to calculate the amount of the equal periodic payments that could be equivalent to an outlay of $3000 at the time of the last payment? a) Amount of 1 b) Amount of an annuity of 1 c) Present value of an annuity of 1 d) Present value of 1 (Please give reason for answer)
1. Assume the current (4) year cost to attend Park University for tuition and books is $12,500. It is estimated that these costs will grow at a 7% annual rate. 2. The money that you annual set aside to meet this financial obligation is expected to earn an estimated 5% annually for the 7-year period (period from age 10 t
Assume you now have a child and you are planning for her college education. You would like to make monthly deposits over the next 21 years (first payment to be made one month from today) with the final payments to be made at her 21st birthday(a total of 252 deposits) so that you will be able to cover her expected expenses while
12. Your baby girl, Jessica, was born yesterday!! You have made a decision that you need to start a savings program to fund that future college education. After speaking with members of your finance class you decide to save $150 a month for the next 18 years. You feel you can get 8% average return on the savings over the 18 year
Discussion Question 1: Many people, as evidenced by the large payoffs provided for picking 6 out of 53 (or more) numbers, play the lottery. The big choice the winners face: taking a lump sum payment today or an annual payment over 20 years. Is a dollar today worth more than a dollar tomorrow? Why or why not? Which do you prefer
1) Terry Austin is 30 years old and is saving for her retirement. She is planning on making 36 contributions to her retirement account at the beginning of each of the next 36 years. The first contribution will be made today (t = 0) and the final contribution will be made 35 years from today (t = 35). The retirement account will
BE2-27 Kilarny Company is considering investing in an annuity contract that will return $20,000 annually at the end of each year for 15 years. What amount should Kilarny Company pay for this investment if it earns a 6% return?
Unless stated otherwise, interest is compounded annually and payments are at the end of the year. Explanations should be brief (1 or 2 sentences). 1. Jana, who just turned 55, would like to have an annual annuity of $25,000 paid each year for 15 years, the first payment occurring on her 66th birthday. How much must Jana sa
1. Compounding frequency and future value You plan to invest $2,000 in an individual retirement account (IRA) today at a nominal rate of 8 percent, which is expected to apply to all future years. a. How much will you have in the account after 10 years if the interest is compounded: 1. Annually 2. Semi-Annually 3. Daily
What will the monthly payment be if you take out a $100,000 15 year mortgage at an interest rate of 1% per month?
In May 1992, a 60 yr old nurse gambled $12 in a Reno casino and walked away with the biggest jackpot in history - $9.3 million. In reality, the jackpot wasn't really worth $9.3 million. The sum was to be paid in 20 annual installments of $465,000 each. What is the present value of the jackpot?
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s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988720380.80/warc/CC-MAIN-20161020183840-00500-ip-10-171-6-4.ec2.internal.warc.gz
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CC-MAIN-2016-44
| 9,651 | 32 |
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