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http://www.chem.ox.ac.uk/vrchemistry/orbitals/html/page11a.htm
|
math
|
An s and a p orbital as in (c)
cannot be combined, because they have different bond-axis symmetries.
Any positive overlap between the s and the upper lobe of the p would
be canceled exactly by negative overlap between s and the bottom
lobe, and nothing would result. If the p orbital is turned 90 degrees
so one lobe points toward s along the bond axis as in (d), then
both AO's have s symmetry along the bond axis. They can be combined
without canceling, provided the similar-energy requirement is met.
With these three principles, we
are now ready to build MO's from the 2s, 2p,
orbitals of two atoms. The two 2s orbitals are added and subtracted
to produce bonding and antibonding MO's in the way seen previously
|
s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084891539.71/warc/CC-MAIN-20180122193259-20180122213259-00018.warc.gz
|
CC-MAIN-2018-05
| 715 | 12 |
http://www.ask.com/web?qsrc=6&o=102140&oo=102140&l=dir&gc=1&qo=popularsearches&ad=dirN&q=When+Did+Wallace+Introduce+the+Symbol+for+Infinity
|
math
|
Inventing the symbol ∞. John Wallis (23 November 1616 – 28 October 1703)
was an English mathematician who is ... In his Opera Mathematica I (1695) Wallis
introduced the term "contin...
Mathematician who developed calculus and who introduced the symbol for '
infinity', ∞. John Wallis, 'the greatest of Newton's precursors in mathematics', did
Oct 5, 2011 ... He states, but does not prove, the corresponding result for a curve of the form ....
He also introduced the symbol for infinity, ∞, which is still used ...
time, introduces the ideas of the infinitesimal and the infinite process. ... Curiously
, the prospect of time having no beginning did not perplex the. Greeks, nor ...
The order in an encyclopedia is an alphabetical one and does not lead to the ....
Wallace opted to connect the idea of "infinity" with the infinity symbol, the ...
Buy Everything and More: A Compact History of Infinity on Amazon.com ✓ FREE
... David Foster Wallace (Author), Neal Stephenson (Introduction) ..... The
librarian who sent back the book did a disservice to some readers. ... Russell and
Whitehead more wordy and symbolic, and Alain Badiou more leading edge, but
One of the outstanding voices of his generation, David Foster Wallace has ......
and that really does not do justice to the book -it really is more of a biography of ...
Oct 18, 2003 ... Everything and More: A Compact History of Infinity ... Brian Clegg begins at the
beginning, introducing one great name after another until, with ... David Foster
Wallace starts straight in with Cantor but takes a look back at his ... is remote in
sense from the mathematical symbol for infinity, the invention of the ...
Apr 1, 2011 ... Wallace, and he does place his hope in a rethinking of the self in relation to
something ... Wallace introduces the culture of substance abuse at.
Oct 30, 2015 ... Not only does he pose an interesting consideration of the role of ... Wallace was
fastidious about this terminating symbol; he corrects a ...
|
s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257823805.20/warc/CC-MAIN-20160723071023-00134-ip-10-185-27-174.ec2.internal.warc.gz
|
CC-MAIN-2016-30
| 1,996 | 25 |
https://www.enotes.com/homework-help/body-100-n-weight-placed-table-another-smaller-432211
|
math
|
A body A of 100 N weight is placed on a table. Another smaller body B of 50 N is placed on top of A.What is the force on (1) upper body B from the lower body A and (2) the lower body B from the table?
a. 150 N, 150 N
b. 100 N, 150 N
c. 50 N, 50 N
d. 50 N, 150 N
Every action has an equal and opposite reaction. A body A of 100 N weight is placed on a table. Another smaller body B of 50 N is placed on top of A. The force exerted by the the smaller body B on the larger body A is equal to the weight of the body or 50 N. As both the bodies and stationary and do not accelerate, the net force acting on them is zero. On body A, the body B exerts a downward force of 50 N, the body A itself exerts a force of 100 N on the table. To make the net force zero, the tables exerts a force of 150 N on block A.
The force exerted on body B by body A is 50 N and the force exerted on body A by the table is 150 N.
The correct option is d.
|
s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549424610.13/warc/CC-MAIN-20170723202459-20170723222459-00600.warc.gz
|
CC-MAIN-2017-30
| 927 | 8 |
https://profession-wissenschaft.de/news/726/6.html
|
math
|
pavestone 0.5 cu. ft. all purpose play sand-55141,a washed natural brown play sand is soft to the touch. ideal for children's play sand, 50 lb. play sand, 50 lbs. play sand. $550. $550. /bag. (405). (1312). (1) .weight per cubic foot of concrete,so 1 cubic yard of concrete weighs 150 pounds per cubic foot. if you break down the weight of the individual aggregates (cement, stone, and sand) in the concrete, that equals 136 lbs per cubic foot for the dry aggregates..dan's dirt and gravel,dan's dirt and gravel provides dirt, sand, gravel, aggregates, mulch and other kane and kendall counties as well as many cities in dupage and will counties. 1 cubic yard of dry dirt is approximately 2,000 lbs. or one ton (this weight will .weight per cubic foot for 1 yard of concrete,so 1 cubic yard of concrete weighs 150 pounds per cubic foot. if you break down the weight of the individual aggregates (cement, stone, and sand) in the concrete, you get the following that equals 136 lbs per cubic foot for the dry aggregates. concrete yardage calculators - how much do i need for any type of job..Get a Quote Send Message
(lbs). source. books, hardback, loose. 1 cubic yard. 529.29. tellus. books, paperback 1. u.s. epa. computer printout, loose. 1 cubic yard. 655. u.s. epa (lbs). source. sand, dry. 1 cubic foot. 90110. feeco. sand, loose.
a cubic yard of sand equals 1 yard wide by 1 yard long by 1 yard high. the sand's weight and volume varies depending on whether it is wet or dry when measured.
pool filter sand is 50 per bag, each bag 1.2cu' dry. i weighed a cup of how much does 1 gallon of sand weigh in pounds? the pounds there are 27 cubic feet in a yard and 7.48 gallons in a cubic foot. 1600/27=59.26
a cubic foot of dry sand weighs between 100 and 115 pounds, depending on how fine it is, it's measured by the cubic yard and it's referred to simply as 'a yard.' i think your question is ,how many kilograme are in 1 cubic feet of water..
order sand & aggregates online order mulch online order soils calculating how much mulch, topsoil, or gravel you need has never been easier. has a weight of around 1,800 pounds per yard because compost is much lighter than soil. since it is clear to us that 1 cubic yard will cover 100 square feet we can
and here 27 cubic feet (a cubic yard of sand) can weigh between 2,600 to 3,000 lbs. how much is 1 cu ft of sand in kg? so x/5=2800/27 - 5 cubic feet would
a cubic yard is the volume of a cube with the length, width and height of one and a cubic yard measures three-dimensional volume, or how much a space can hold. 1 cubic yard of sand, gravel or stone can weigh more than 3,000 pounds.
a cubic yard is a cube of material that is one yard (3) wide, long, and high. there are 27 sand, gravel, stone: can tip the scales at upwards of 3,000 pounds per cubic yard. check with how many wheelbarrow loads are in a cubic yard?
a cubic yard measures volume where a ton measures weight. a yard of topsoil usually weighs about 1,800 pounds and a yard of gravel usually weighs about
gravels, sand & soils, mulches162 sq. ft. 1 cubic yard equals: note: the true cubic footage weights are 145-160 pounds per cubic foot, for solid unbroken
are you buying crushed stone but don't know how much you need? read this crushed stone is quoted at a weight of 2700 pounds per cubic yard. your stone one 20-ton truckload of crushed stone will yield 14-15 cubic yards of crushed stone. again concrete sand mason sand white sand
one cubic yard of topsoil weighs approximately 1080 pounds. if it is made up of a mixture of sand, stone and gravel, the weight can easily
fill sand calculate cubic yards, cubic feet and tons. convert cubic yards to tons. convert tons the density of fill sand : 2,410 lb/yd or 1.21 t/yd or 0.8 yd/t
consequently, how much is a scoop of sand? typically sand and gravel weigh about 1500 pounds (3/4 of a ton) per scoop (1/2 cubic yard). one
1 cubic yard of topsoil weighs approximately 2000-2800 lbs 1 cubic yard of aggregate (3/4-4 sieve size) also know, how much is loam per yard? 1 cubic yard of sand, gravel or stone can weigh more than 3,000 pounds.
fill your child's sandbox with the pavestone 50 lb. desert sand. this play sand is safe for outdoor living areas and sandboxes. covers up to 1 sq. ft. this stuff is more like kosher salt in consistency, and has much less powder sand, the weight & even the guy working the yard didn't know the conversion, but the customer
in a bag, measure the bag, and calculate the number of cubic ft (hint, it's usually no more than 1/2 cubic foot). since 27 cubic ft is a cubic yard, it would take 54
salt - sand yard to ton conversions conversion of pounds per lane mile to pounds per 1000 square feet 1 cup of salt (nacl) = 0.6 lbs.
one cubic yard of beach sand converted to pound equals to 2,577.55 lb. how many pounds of beach sand are in 1 cubic yard? the answer is: the change of 1 cu
weight units from pounds of water ( lb wt. ) material weight pounds per cubic yard - downeaster.1 cubic yard of sand can weigh between 2,600 to 3,000 lbs.or up
so 1 cubic yard of concrete weighs 4050 pounds. if you break down the weight of the individual aggregates (cement, stone, and sand) in the concrete, you get
density of sand is about 100-110lbs per cubic foot. there are 27 cubic feet in a cubic yard. therefore 1 cubic yard of sand weighs about 2,970 lbs
regular mason sand calculate cubic yards, cubic feet and tons. convert cubic the density of regular mason sand: 2,410 lb/yd or 1.21 t/yd or 0.8 yd/t
3 feet = 1 yard; 9 square feet = 1 square yard; 27 cubic feet = 1 cubic yard 1 inch of asphalt = 110 lbs / sy; 1.5 inches of asphalt = 165 lbs / sy sand how many tons of sand are needed to fill in a 50 ft x 50 ft area 1 ft thick? limerock/granite gabhow many tons of gab is needed to construct a 10ft
it's impossible to tell until you define the size (length and width) of the sandbags and how many you pile onto each other to form your line. sand bags are usually
as a general guide, 1 cubic yard of aggregate, sand, or dirt is equivalent to 1.5 tons. concrete weighs around 3900 pounds per cubic yard but can drop to 3500
in united states, based on imperial measurement system and other standard of measurement, 1 cubic yard is unit of measurement of volume represented by 3 feet
a typical 50 pound bag of sand that you can purchase at a home improvement store is 1/2 cubic foot. there are 27 cubic feet in 1 cubic yard. to figure out how
Copyright © 2021.Henan Mining Machinery Co., ltd. All rights reserved. Sitemap
|
s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358688.35/warc/CC-MAIN-20211129044311-20211129074311-00352.warc.gz
|
CC-MAIN-2021-49
| 6,519 | 30 |
http://www.expertsmind.com/questions/explain-the-cash-flow-of-the-volatility-30191885.aspx
|
math
|
1. Let's look at the cash flow of the volatility (variance) spread swap:
It is noticeable from this expression that investor actually takes a long position on the S&P500 variance and a short position on the NASDAQ variance. This trade is able to be put in place by simultaneously entering into a long S&P500 variance swap and a short NASDAQ variance swap.
Pricing here is to conclude the initial variance swap spread which makes the initial value of the swap between the two indices have a value of zero. This price is specified as 21% in the question.
2. Of course we need the correlation between the two markets. If the correlation is high close to one in absolute value among these markets then this implies that most of the time volatility will move in both markets in the same direction which in return indicates that volatility (variance) spread is relatively tight in the long run this makes the position mentioned in the query reasonable. Consequently the fixed leg of the spread has to be set (relatively) higher.
If the correlation is low near to zero in absolute value which implies that these two markets move more or less independently from every other then there is no reason to believe that the volatility spread between the markets should get narrower.
It is less probable that the investor who holds a long position will end up with a positive payoff. In order to make the initial value of the swap equal to zero the fixed leg of the spread requires to be set at a lower level.
3. The smile effect is significant. Nevertheless in this present case the trade concerns realized volatility and not the Black-Scholes implied volatility.
This signifies that the pricing of the swap will make no use of the smile in any direct way. Indirectly the smile is able to be useful to calibrate a model on the other hand.
4. If the position is taken by utilizing volatility (variance) swaps then this may be less risky compared to the other ways of taking the same position. As well the pricing of the instrument may be easier.
The major risk involved here is related to the assumption that the long run dynamics of the volatility spread is stationary. If this underlying supposition is violated then the position may lose.
|
s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154796.71/warc/CC-MAIN-20210804045226-20210804075226-00423.warc.gz
|
CC-MAIN-2021-31
| 2,226 | 10 |
https://www.italki.com/en/post/discussion-204929
|
math
|
a question about "kunnen"
hallo, hoe gaat het met u?
I am a learner of Dutch, and have got a question about "kunnen".
Here is the sentence.
we kunnen heel Europa door.
i don't see any verb here in this sentence! could you help me understand the meaning?
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s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710926.23/warc/CC-MAIN-20221203075717-20221203105717-00325.warc.gz
|
CC-MAIN-2022-49
| 253 | 6 |
http://mathoverflow.net/revisions/33608/list
|
math
|
Did you first try working out what happens for one-variable discrete harmonic functions? You said that "such functions are clearly more constrained than their one-variable counterparts" but must have meant one-variable functions that are real-differentiable rather than harmonic. For one-variable discrete harmonic functions are very constrained:
If you know $f(x+1)$ and $f(x-1)$ you can first interpolate $f(x)$ and then extrapolate $f(x+2)$ and $f(x-2)$. By induction, every value of $f$ is determined this way. That settles the special case of the standard suite of theorems (minimum-maximum principle, Liouville's theorem, mean-value theorem, etc) for a unit interval.
You can piece together unit intervals to prove the more general case. That piecing-together logic is similar to the proof of Green's theorem that reticulates the domain and passes to the limit, so you could say this extends to the infinitary case(, modulo analytic due diligence)diligence.
As for smoothness (harmonic functions are actually real-analytic), I'm not sure of the proper discrete analogue, so I can't help you there.
|
s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368706472050/warc/CC-MAIN-20130516121432-00011-ip-10-60-113-184.ec2.internal.warc.gz
|
CC-MAIN-2013-20
| 1,103 | 4 |
https://www.hackmath.net/en/examples/multiplication?tag_id=100
|
math
|
Multiplication - 5th grade (10y) - examples
Charlie bought 7 same chocolates for 14 Eur. How many euros he pay for 27 chocolates?
One brick is 2 kg and half a brick heavy. What is the weight of one brick?
5 trees in 3 lines grows in the orchard. How many trees are in the orchard?
A cyclist passes 88 km in 4 hours. How many kilometers he pass in 8 hours?
Calculate how many hours take holidays, if take 1 weeks.
55 weeks is equal to how many days?
4 chickens give 4 eggs in 4 days. How many eggs can give 8 chickens for 8 days?
After check of textbooks found that every 8-th textbook should be withdrawn. Together 74 textbooks were withdrawn. How many textbooks were in stock before withdrawn and how many after withdrawn?
Same type of medicament produces a number of manufacturers in a variety of packages with different content of active substance. Pack 1: includes 60 pills of 1200 mg of active substance per pack cost 18 Eur. Pack 2: includes 30 pills of 1000 mg of active s
- School trip
School trip cost 340.8 USD for one class (24 students). How much would cost a trip for two classes? (both classes together have 44 students)
Result of the product of the numbers 5, 1, 7, 2, 6, 1, 0, 6, 6, 5, 1, 9, 6 is:
A line of print on a computer contains 80 characters (letters, spacers or other chars). Find how many characters there are in 20 lines.
You want to cut long board into smaller pieces. Carpenter said that one cut of the board into two pieces will cost you 90 cents. But you need to cut the board into 7 parts. How much you pay?
How many hours is 5 days?
How many millimeters is 1/100 meters?
- Boys and girls
In the class are 15 boys and 3-times less girls. How many girls are in the classroom? How many all children are in the class?
Two cats caught two mice in two days. How many mouses will catch 6 cats for 6 days?
- School trip
8.D class went on a trip. Train ticket cost 11 euros, cable car ticket 6 euro. How many euros must pay classroom teacher for 23 students?
Cyclist goes on a trip. First, drove 3 hours average speed 42 kilometers per hour, then slowed down and another 2 hours driving a speed 39 kilometers per hour. How many total kilometers cycling?
- Efficiency of rail
With subsidies are business easy. Calculate how much must cost rail ticket (x) in today's ticket price € 13 and if the trains was not subsidized, if it is known that without subsidies would cost three times today's ticket prices. Calculate the value of.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128323604.1/warc/CC-MAIN-20170628101910-20170628121910-00397.warc.gz
|
CC-MAIN-2017-26
| 2,455 | 25 |
http://mathforum.org/library/drmath/sets/mid_word_problems.html?start_at=241&num_to_see=40&s_keyid=37338736&f_keyid=37338737
|
math
|
See also the
Dr. Math FAQ:
3D and higher
Browse Middle School Word Problems
Stars indicate particularly interesting answers or
good places to begin browsing.
Selected answers to common questions:
- How Many Freshmen Originally Tried Out? [01/15/2003]
Some freshmen were trying out for the school track team... The 10 who
remained became the track team.
- How Many Men, Women, and Children at the Circus? [10/18/2000]
A circus performance is witnessed by 120 people who have paid $120. The
men paid $5, the women $2, and the children $.10 each. How many of each
went to the circus? A solution without algebra.
- How Many Mice, Cats, and Dogs? [01/13/2003]
You must spend $100 to buy 100 pets, choosing at least one of each
pet. The pets and their prices are: mice @ $0.25 each, cats @ $1.00
each, and dogs @ $15.00 each. How many mice, cats, and dogs must you
- How Many of Each Ticket Were Sold? [09/06/2001]
Five hundred tickets were sold for a play, for $8 at the lower level and
$6 at the upper level, totaling $3600.
- How Many Oxen Can Be Fed? [6/28/1996]
We have three pastures with grass of identical height, density, and
- How Many Pads of Paper? [10/30/2001]
A merchant marked some pads of paper down from $2.00 and sold the entire
lot. If the gross profit from the sale was $603.77, how many pads did he
- How Many Pages? [10/04/1997]
A printer uses 837 digits to number the pages of a book. How many pages
are there in the book?
- How Many Pencils? [09/05/2001]
How many pencils does Al have if all of them are blue except 2, all of
them are yellow except 2, and all of them are red except 2?
- How Many People Went on the Cruise? [12/03/2001]
At the end of a special cruise, the employees could not remember the
total number of people who were on board. However, they had the following
data from the passenger list: 520 European females...
- How Many Seats? [01/15/2003]
There are 40 rows in an auditorium. Each has two more seats than the
previous row. There are 1960 seats in all. How many seats are in the
first row of the auditorium?
- How Many Steps on the Escalator? [7/1/1996]
A famous mathematician who is always in a hurry walks up an up-going
escalator at the rate of one step per second. Twenty steps bring him to
- How Many Stickers...? [8/25/1996]
James has twice as many stickers as John, who has twice as many stickers
- How Many Trains Meet? [09/17/2001]
Every hour, on the hour, a train leaves Tallahassee for Jacksonville,
while another train leaves Jacksonville for Tallahassee. The trip between
the two cities takes exactly two hours. How many trains going in the
opposite direction will a Tallahassee train to Jacksonville meet?
- How Many Valentines? [02/10/2003]
If everyone in your class gave a Valentine to everyone else in your
class, how many valentines would be exchanged?
- How Much did the Tree Grow? [11/07/2001]
A white pine was 16 m tall in 1962. It was 20 m tall in 1965. It is now
34 m tall. How much has it grown since 1962?
- How Much Does the Youngest Boy Get? [05/25/2000]
Five brothers, each born in a different year, share a gift of $100...
- How Much Money Entering the First Store? [09/26/2002]
Timothy spent all of his money at five stores. At each store, he spent
$1 more than half of the amount he had when entering the store. How
much money did he have when he entered the first store?
- How Much Popcorn did Paul Sell? [01/28/2002]
Paul made $44.14 selling 27 items (beer and popcorn). If he made $1.22
selling popcorn and $2.62 selling beer, how many boxes of popcorn were
- How Much to Add? [01/16/1998]
Tonya must add to a mixture enough of a substance to make the whole weigh
2.5 grams - how much should she add?
- How Much Water Evaporated? [06/19/2003]
A substance is 99% water. Some water evaporates, leaving a substance
that is 98% water. How much of the water evaporated?
- How Old Are John and Julia? [05/17/2001]
Julia is as old as John will be when Julia is twice as old as John was
when Julia's age was half the sum of their present ages. John is as old
as Julia was when John was half the age he will be 10 years from now. How
old are John and Julia?
- How Old at $4,000? [10/15/2002]
Aunt Isabella gives each niece and nephew $10 on his or her first
birthday, and on each birthday thereafter the children get $20.00 more
than on the birthday before. How old will a child be when he or she
receives a total of $4,000.00?
- How Old Did This Man Live to Be? [02/23/1998]
A word problem involving fractions.
- How Old in 1900? [11/09/2002]
In 1930, a correspondent proposed the following question: A man's age
at death was one twenty-ninth of the year of his birth. How old was
the man in 1900?
- How Old is Korinth? [09/09/1997]
Korinth is twice as old as Marin was when Korinth was as old as Marin is
now. Marin is 18.
- How to Interpret "Increase" in Word Problems [10/19/2004]
How do I increase 3.7 by 1/10?
- How Wide is the River? [7/2/1996]
Two ferryboats ply back and forth across a river with constant but
- A Hundred Total of Three Varieties — for a Total Price of Exactly a Hundred [10/21/2015]
What combination of all three types of livestock can you buy for exactly 100 euros
that gives you exactly 100 animals? By bringing integer solutions and relative
primality to bear, Doctor Ali picks up where a student left off.
- The Importance of Defining Variables Clearly in Algebra [11/01/2007]
A sample of dimes and quarters totals $18.00. If there are 111 coins
in all, how many are there of each coin?
- Inconsistent System of Equations? Look Closer! [11/17/2004]
When Alexis, Chelsea, and Kammi had lunch together, Alexis spent $1.60
for two small hamburgers, a drink and one order of fries. Chelsea's
two orders of fries, two drinks and one small burger cost $1.40
altogether. How much does Kammi owe for a small burger, one order
of fries and one drink?
- Increase in Chicken Consumption [8/29/1996]
In 1984 the average American ate 55.7 lbs. of chicken. This was 2.8 lbs.
more than the average in 1982. What was the percent of increase in
- Increasing the Average [02/25/2001]
Five members of a basketball team are weighed and an average weight is
recalculated after each weighing. If the average increases 2 pounds each
time, how much heavier is the last player than the first?
- Inequalities: Add or Subtract? [10/21/2001]
Sometimes, when doing inequalities problems, I have to add or subtract
one from the answer I have calculated. I don't understand when to add,
subtract, or do nothing at all.
- Integer problem [11/30/1994]
Find the largest possible 2 integers such that the larger integer is more
than 3 less than 3 times the smaller one.
- Interpreting "Less" and "Less Than" in Word Problems [10/18/2004]
Find all numbers such that 9 less than the product of the number and
-4 is less than 7.
- Introduction to Linear and Exponential Growth [11/04/2003]
A population of beetles increases from 5 to 15 after one month. How
many beetles will there be after 4 months if the population is
increasing linearly? What if it's increasing exponentially?
- Is Henry Guilty? (Geometry Puzzle) [6/10/1996]
In Hughmoar County, residents shall be allowed to build a straight road
between two homes as long as the new road is not perpendicular to any
existing county road...
- Isolating Groceries from Total Expenses, and Problems from Paragraphs [09/03/2011]
Given functions in a word problem, an adult student doesn't know how to begin
subtracting one from the other. Before clarifying her use of variables, Doctor Peterson
suggests reading through the problem strategically, to distill it down to just algebraic
- Jack Climbing the Beanstalk [6/29/1996]
Jack climbed up the beanstalk at a uniform rate. At 2 P.M. he was one-
sixth the way up and at 4 P.M. he was three fourths the way up...
- Jeep [04/07/1997]
A jeep can carry 200 liters of gasoline and can drive 2.5 km/l. You want
to travel 1000 km...
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s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794864968.11/warc/CC-MAIN-20180522205620-20180522225620-00265.warc.gz
|
CC-MAIN-2018-22
| 7,890 | 142 |
http://nrich.maths.org/public/leg.php?code=-420&cl=3&cldcmpid=1848
|
math
|
Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?
What is the largest number which, when divided into 1905, 2587,
3951, 7020 and 8725 in turn, leaves the same remainder each time?
Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...
How many pairs of numbers can you find that add up to a multiple of
11? Do you notice anything interesting about your results?
Investigate how you can work out what day of the week your birthday will be on next year, and the year after...
Take any four digit number. Move the first digit to the 'back of
the queue' and move the rest along. Now add your two numbers. What
properties do your answers always have?
Can you guarantee that, for any three numbers you choose, the
product of their differences will always be an even number?
Some 4 digit numbers can be written as the product of a 3 digit
number and a 2 digit number using the digits 1 to 9 each once and
only once. The number 4396 can be written as just such a product.
Can. . . .
What is the smallest number with exactly 14 divisors?
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?
Ben passed a third of his counters to Jack, Jack passed a quarter
of his counters to Emma and Emma passed a fifth of her counters to
Ben. After this they all had the same number of counters.
A 2-Digit number is squared. When this 2-digit number is reversed
and squared, the difference between the squares is also a square.
What is the 2-digit number?
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
The clues for this Sudoku are the product of the numbers in adjacent squares.
A car's milometer reads 4631 miles and the trip meter has 173.3 on
it. How many more miles must the car travel before the two numbers
contain the same digits in the same order?
Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Can you find an efficient method to work out how many handshakes
there would be if hundreds of people met?
Can you explain the surprising results Jo found when she calculated
the difference between square numbers?
A game for 2 or more people, based on the traditional card game
Rummy. Players aim to make two `tricks', where each trick has to
consist of a picture of a shape, a name that describes that shape,
and. . . .
Take any prime number greater than 3 , square it and subtract one.
Working on the building blocks will help you to explain what is
special about your results.
Five children went into the sweet shop after school. There were
choco bars, chews, mini eggs and lollypops, all costing under 50p.
Suggest a way in which Nathan could spend all his money.
Find a cuboid (with edges of integer values) that has a surface
area of exactly 100 square units. Is there more than one? Can you
find them all?
Can you arrange these numbers into 7 subsets, each of three
numbers, so that when the numbers in each are added together, they
make seven consecutive numbers?
What does this number mean ? Which order of 1, 2, 3 and 4 makes the
highest value ? Which makes the lowest ?
Sissa cleverly asked the King for a reward that sounded quite modest but turned out to be rather large...
The number 2.525252525252.... can be written as a fraction. What is
the sum of the denominator and numerator?
A country has decided to have just two different coins, 3z and 5z
coins. Which totals can be made? Is there a largest total that
cannot be made? How do you know?
Is it always possible to combine two paints made up in the ratios
1:x and 1:y and turn them into paint made up in the ratio a:b ? Can
you find an efficent way of doing this?
A decorator can buy pink paint from two manufacturers. What is the
least number he would need of each type in order to produce
different shades of pink.
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
Explore the effect of reflecting in two parallel mirror lines.
Triangle ABC is isosceles while triangle DEF is equilateral. Find
one angle in terms of the other two.
Square numbers can be represented as the sum of consecutive odd
numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle
contains 20 squares. What size rectangle(s) contain(s) exactly 100
squares? Can you find them all?
Each of the following shapes is made from arcs of a circle of
radius r. What is the perimeter of a shape with 3, 4, 5 and n
Explore the effect of combining enlargements.
A hexagon, with sides alternately a and b units in length, is
inscribed in a circle. How big is the radius of the circle?
There are four children in a family, two girls, Kate and Sally, and
two boys, Tom and Ben. How old are the children?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Two motorboats travelling up and down a lake at constant speeds
leave opposite ends A and B at the same instant, passing each
other, for the first time 600 metres from A, and on their return,
400. . . .
Start with two numbers. This is the start of a sequence. The next
number is the average of the last two numbers. Continue the
sequence. What will happen if you carry on for ever?
Imagine you have a large supply of 3kg and 8kg weights. How many of each weight would you need for the average (mean) of the weights to be 6kg? What other averages could you have?
A circle is inscribed in a triangle which has side lengths of 8, 15
and 17 cm. What is the radius of the circle?
Here is a chance to create some attractive images by rotating
shapes through multiples of 90 degrees, or 30 degrees, or 72
On the graph there are 28 marked points. These points all mark the
vertices (corners) of eight hidden squares. Can you find the eight
If the hypotenuse (base) length is 100cm and if an extra line
splits the base into 36cm and 64cm parts, what were the side
lengths for the original right-angled triangle?
In a three-dimensional version of noughts and crosses, how many winning lines can you make?
Why does this fold create an angle of sixty degrees?
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s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1408500800168.29/warc/CC-MAIN-20140820021320-00144-ip-10-180-136-8.ec2.internal.warc.gz
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CC-MAIN-2014-35
| 6,631 | 102 |
http://notesfromthegeekshow.blogspot.com/2009/03/arguing-with-geeks-4.html
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math
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... rantings, ravings and ramblings of strange fiction writer, THE.... Sodomite Hal Duncan!!
Thursday, March 05, 2009
Sufficiency Threshold Differential Intolerance — For two individuals of the same reasonableness, in any given argument there may be different thresholds of sufficiency such that where one participant considers an explanation convincing the other does not. Where A and B represent the two participants and N represents the number of points required to convince a participant satisfyingly, the ratio A(N) : B(N) is the Sufficiency Threshold Differential. Where x is directly proportional to the reasonableness of a participant, Sufficiency Threshold Differential Intolerance sets in when this differential is substantial enough that A(N + x) is lower than B(N - x), which is to say where too much explanation for one participant is considered too little explanation by another. For the advocate (A) this intolerance may well become manifest in a refusal to recognise that the burden of proof is on them and that they must adapt accordingly, increasing their reasonableness to accommodate the demands of B. This will most likely be articulated in the “You’re just being obtuse” meta-argument.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917123046.75/warc/CC-MAIN-20170423031203-00262-ip-10-145-167-34.ec2.internal.warc.gz
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CC-MAIN-2017-17
| 1,215 | 3 |
http://www.sawaal.com/profit-and-loss-questions-and-answers/a-shopkeeper-expects-a-gain-of-45-2-on-his-cp-if-his-sale-was-rs-392-then-find-his-profit_6436
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math
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A shopkeeper sells one-third of his goods at a profit of 10%, another one-third at a profit of 20%, and the rest at a loss of 6%.What is his overall profit percentage ?
Answer & Explanation
Let the shopkeeper buy 300g for Rs.300. Now he sells 100g for Rs.110, another 100g for Rs120, and the rest 100g for Rs94.
Therefore, the total amount he receives = Rs.110 + Rs.120 + Rs.94 = 324.
Therefore, the shopkeeper spends Rs.300 and gets back Rs.324.
Therefore, his profit percentage = % = 8%
Profit and Loss
- Quantitative Aptitude - Arithmetic Ability
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s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988718278.43/warc/CC-MAIN-20161020183838-00389-ip-10-171-6-4.ec2.internal.warc.gz
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CC-MAIN-2016-44
| 549 | 8 |
https://fastretrieve.com/kitesurfing/pergunta-frequente-is-a-rhombus-always-a-kite.html
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math
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Every rhombus is a kite, and any quadrilateral that is both a kite and parallelogram is a rhombus. A rhombus is a tangential quadrilateral. That is, it has an inscribed circle that is tangent to all four sides.
Is a kite a rhombus yes or no?
A kite is a quadrilateral (four sided shape) where the four sides can be grouped into two pairs of adjacent (next to/connected) sides that are equal length. So, if all sides are equal, we have a rhombus. … A kite is not always a rhombus. A rhombus is not always a square.
Can a rhombus be a kite?
A kite has two sets of adjacent congruent sides. … This means that all Rhombi are kites, but not all kites are rhombi. A square is a rhombus with all right angles.
Why is a rhombus also a kite?
A rhombus is a quadrilateral with all sides of equal length. So a rhombus does have two pairs of adjacent sides of equal length and is therefore a kite.
Is a quadrilateral always a rhombus?
A rhombus is a quadrilateral (plane figure, closed shape, four sides) with four equal-length sides and opposite sides parallel to each other. All rhombuses are parallelograms, but not all parallelograms are rhombuses. All squares are rhombuses, but not all rhombuses are squares.
Can a kite have all 4 sides equal?
∠K = ∠T ∠ K = ∠ T and ∠I = ∠E ∠ I = ∠ E . It is possible to have all four interior angles equal, making a kite that is also a square.
Can a kite have 4 right angles?
No, because a rhombus does not have to have 4 right angles. Kites have two pairs of adjacent sides that are equal. … From this diagram, you can see that a square is a quadrilateral, a parallelogram, a rectangle, and a rhombus!
What are the 4 properties of a rhombus?
Properties of Rhombus
- All sides of the rhombus are equal.
- The opposite sides of a rhombus are parallel.
- Opposite angles of a rhombus are equal.
- In a rhombus, diagonals bisect each other at right angles.
- Diagonals bisect the angles of a rhombus.
- The sum of two adjacent angles is equal to 180 degrees.
What does a kite equal?
By definition, a kite is a polygon with four total sides (quadrilateral). The sum of the interior angles of any quadrilateral must equal: degrees degrees degrees. Additionally, kites must have two sets of equivalent adjacent sides & one set of congruent opposite angles.
Does a kite have a right angle?
The intersection of the diagonals of a kite form 90 degree (right) angles. This means that they are perpendicular. The longer diagonal of a kite bisects the shorter one.
Is a rhombus the same as a diamond?
The main difference between Diamond and Rhombus is that the Diamond is a allotrope of carbon and Rhombus is a quadrilateral in which all sides have the same length.16 мая 2018 г.
What is the shape of kite called?
In Euclidean geometry, a kite is a quadrilateral whose four sides can be grouped into two pairs of equal-length sides that are adjacent to each other. In contrast, a parallelogram also has two pairs of equal-length sides, but they are opposite to each other instead of being adjacent.
Why is a rhombus not a square?
A rhombus is a quadrilateral with all sides equal in length. A square is a quadrilateral with all sides equal in length and all interior angles right angles. Thus a rhombus is not a square unless the angles are all right angles. … A square however is a rhombus since all four of its sides are of the same length.
What is the difference between a rhombus and a quadrilateral?
Rhombus: A rhombus is a flat-shaped quadrilateral and it has four sides which are of equal measures.
What are the Differences Between Rhombus and Parallelogram?S.NoRhombusParallelogram2All the four sides are equalOpposite sides are of equal measureЕщё 4 строки
What is difference between rhombus and square?
How is square different from rhombus? A square and a rhombus both have sides equal in length. But square has all its angles equal to 90 degrees, but a rhombus only has its opposite angles equal.
What are 4 types of quadrilaterals?
Quadrilaterals – Square, Rectangle, Rhombus, Trapezoid, Parallelogram.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703506832.21/warc/CC-MAIN-20210116165621-20210116195621-00131.warc.gz
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CC-MAIN-2021-04
| 4,069 | 38 |
https://chem.libretexts.org/Core/Physical_and_Theoretical_Chemistry/Kinetics/Rate_Laws/Reaction_Mechanisms/Reaction_Mechanisms/The_Effect_of_Pressure_on_Rate_of_Reaction
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math
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This page describes and explains the way that changing the pressure of a gas changes the rate of a reaction.
Increasing the pressure on a reaction involving reacting gases increases the rate of reaction. Changing the pressure on a reaction which involves only solids or liquids has no effect on the rate.
In the manufacture of ammonia by the Haber Process, the rate of reaction between the hydrogen and the nitrogen is increased by the use of very high pressures.
\[ N_2(g) + 3H_2 (g) \rightleftharpoons 2NH_3 (g)\]
In fact, the main reason for using high pressures is to improve the percentage of ammonia in the equilibrium mixture, but there is a useful effect on rate of reaction as well.
The relationship between pressure and concentration
Increasing the pressure of a gas is exactly the same as increasing its concentration. If you have a given mass of gas, the way you increase its pressure is to squeeze it into a smaller volume. If you have the same mass in a smaller volume, then its concentration is higher. You can also show this relationship mathematically if you have come across the ideal gas equation:
Rearranging this gives:
Because "RT" is constant as long as the temperature is constant, this shows that the pressure is directly proportional to the concentration. If you double one, you will also double the other.
The effect of increasing the pressure on the rate of reaction
Collisions involving two particles
The same argument applies whether the reaction involves collision between two different particles or two of the same particle. In order for any reaction to happen, those particles must first collide. This is true whether both particles are in the gas state, or whether one is a gas and the other a solid. If the pressure is higher, the chances of collision are greater.
Reactions involving only one particle
If a reaction only involves a single particle splitting up in some way, then the number of collisions is irrelevant. What matters now is how many of the particles have enough energy to react at any one time.
Suppose that at any one time 1 in a million particles have enough energy to equal or exceed the activation energy. If you had 100 million particles, 100 of them would react. If you had 200 million particles in the same volume, 200 of them would now react. The rate of reaction has doubled by doubling the pressure.
Jim Clark (Chemguide.co.uk)
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s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218190234.0/warc/CC-MAIN-20170322212950-00038-ip-10-233-31-227.ec2.internal.warc.gz
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CC-MAIN-2017-13
| 2,388 | 16 |
https://www.getjar.com/categories/all-games/board-games/Math-Genius-236230
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math
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Math Genius Math Genius is like a crossword puzzle with numbers. You are given a list of math problems, such as 24-6=18. Your task is to find each problem in the grid and swipe the screen to “circle” it. Be sure to check every direction, as some problems are set vertically or right-to-left. Earn points for each problem you find and have fun racing the clock. Please note that this free app is ad supported. - Find the math problems to earn points - Race the clock - Beat your best score Find the formula with numbers and operator which can be found in the below list.
Downloads: 3,685+ (for Android)Report app for spam or abuse!
The Amazing Spider-Man 2 Android Free
Become the Amazing Spider-Man in this open-world 3D adventure full of crime-fighting
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s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323587655.10/warc/CC-MAIN-20211025061300-20211025091300-00653.warc.gz
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CC-MAIN-2021-43
| 757 | 4 |
https://rbspgway.jhuapl.edu/biblio?keyword=WHISTLER-MODE%20WAVES
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math
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NOTICE: Use the parameters below to customize your search. Regular expressions and bolean "AND" will to match the search. In the case of "Author name", the search is performed using only for the last name.
Found 2 entries in the Bibliography.
Showing entries from 1 through 2
The high variability of relativistic (MeV) electron fluxes in the Earth\textquoterights radiation belts is partly controlled by loss processes involving resonant interactions with electromagnetic ion cyclotron (EMIC) and whistler-mode waves. But as previous statistical models were generated independently for each wave mode, whether simultaneous electron scattering by the two wave types has global importance remains an open question. Using >3 years of simultaneous Van Allen Probes and THEMIS measurements, we explore the conte ...
YEAR: 2017 DOI: 10.1002/2017GL073886
In this paper, we study relativistic electron scattering by fast magnetosonic waves. We compare results of test particle simulations and the quasi-linear theory for different spectra of waves to investigate how a fine structure of the wave emission can influence electron resonant scattering. We show that for a realistically wide distribution of wave normal angles theta (i.e., when the dispersion delta theta >= 0.5 degrees), relativistic electron scattering is similar for a wide wave spectrum and for a spectrum consisting in ...
YEAR: 2015 DOI: 10.1063/1.4922061
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s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178358956.39/warc/CC-MAIN-20210227114444-20210227144444-00195.warc.gz
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CC-MAIN-2021-10
| 1,421 | 7 |
https://www.wyzant.com/resources/answers/508259/a_company_has_4000_staff_members_if_3_50_of_these_staff_members_are_managers_how_many_managers_are_there_in_this_company
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math
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a company has 4000 staff members. if 3/50 of these staff members are managers, how many managers are there in this company?
This is for my 7th grade math i am not in advanced so please dont make it advanced ish. please add work so i can copy and simplify. do NOT make a mixed number. my teacher does not want those. please and thank you
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s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057033.33/warc/CC-MAIN-20210920070754-20210920100754-00582.warc.gz
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CC-MAIN-2021-39
| 336 | 2 |
https://www.opuscula.agh.edu.pl/index.php?mm=386&aa=10
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math
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Opuscula Math. 38, no. 6 (2018), 883-898
Initial value problem for the time-dependent linear Schrödinger equation with a point singular potential by the unified transform method
Abstract. We study an initial value problem for the one-dimensional non-stationary linear Schrödinger equation with a point singular potential. In our approach, the problem is considered as a system of coupled initial-boundary value (IBV) problems on two half-lines, to which we apply the unified approach to IBV problems for linear and integrable nonlinear equations, also known as the Fokas unified transform method. Following the ideas of this method, we obtain the integral representation of the solution of the initial value problem.
Keywords: the Fokas unified transform method, Schrödinger equation, interface problems.
Mathematics Subject Classification: 35Q41, 35E15.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267164469.99/warc/CC-MAIN-20180926081614-20180926102014-00347.warc.gz
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CC-MAIN-2018-39
| 857 | 5 |
https://forum.sierrawireless.com/t/bandwidth-and-increasing-sig-noise-value-via-at-commands/22619
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math
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I have one RV50 in a remote location with limited bandwidth (rsrp108,rsrq-14,rssi-77,sinr1.1) Reading through the AT commands I noticed a command !DALSRXBW, see bellow (from AT Command Reference pdf)
My question is, can I reduce the bandwidth (by using this AT command) and increase the sig/noise value thus increasing my overall RSRQ. Right now I have limited bandwidth in this remote location. RSRP and RSSI are good, but my RSRQ is to low to provide the minimal bandwidth needed.
Set LTE Rx bandwidth (LTE only)
Set the LTE Rx bandwidth.
• !DASBAND must be issued before you can use this command.
• This command must be issued before you can use !DALGAVGAGC.
Password required: Yes
• Execution: AT!DALSRXBW=
Purpose: Set the LTE Rx bandwidth.
• 0=1.4 MHz
• 1=3 MHz
• 2=5 MHz
• 3=10 MHz
• 4=15 MHz
• 5=20 MHz
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CC-MAIN-2021-10
| 828 | 15 |
https://www.coursehero.com/file/6185640/tro-questions-chapter-15/
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math
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Unformatted text preview: 710 Chapter 15 Acids and Bases Finding the [OH’] and pH of a Weak Base Solution (15.7) -Examp1e 15.12 - For Practice 15.12 - Exercises 83, 84 Determining Whether an Anion Is Basic or Neutral (15.8) -Example 15.13 - For Practice 15.13 - Exercises 89, 90 Determining the pH of a Solution Containing an Anion Acting as a Base (15.8) 'Example 15.14 ' For Practice 15.14 - Exercises 91, 92 Determining Whether a Cation Is Acidic or Neutral (15.8) Determining the Overall Acidity or Basicity of Salt Solutions (15.8) -Examp1e 15.15 - For Practice 15.15 - Exercises 93, 94 -Example 15.16 - For Practice 15.16 - Exercises 95, 96 Finding the pH of a Polyprotic Acid Solution (15.9) 'Example 15.17 ' For Practice 15.17 - Exercises 105, 106 Finding the [H30+] in Dilute H2804 Solutions (15.9) -Examp1e 15.18 - For Practice 15.18 - Exercise 109 Finding the Concentration of the Anions for a Weak Diprotic Acid Solution (15.9) 'Example 15.19 ' For Practice 15.19 ' Exercises 107, 108 Exercises Review Questions 1. 10. ll.
l2. l3. 14. 15. 16. 17. What causes heartburn? What are some possible ways to alleviate
heartburn? . What are the general physical and chemical properties of acids? Of bases? . What is a carboxylic acid? Give an example. What is the Arrhenius definition of an acid? Of a base?
What is a hydronium ion? Does H+ exist in solution by itself?
What is the Bronsted—Lowry definition of an acid? Of a base? . Why is there more than one definition of acid—base behavior? Which definition is the right one? . Describe amphoteric behavior and give an example.
. What is a conjugate acid—base pair? Give an example. Explain the difference between a strong acid and weak acid and
give one example of each. What are diprotic and triprotic acids? Give an example of each.
Give the definition of the acid ionization constant and explain its
significance. Write an equation for the autoionization of Water and an expres-
sion for the ion product constant for water (Kw). What is fire
value of Kw at 25 °C? What happens to the [011—] of a solution when the [H3O+] is in-
creased? Decreased? What is the definition of pH? What pH range is considered acidic?
Basic? Neutral? What is the definition of pOH? What pOH range is considered
acidic? Basic? Neutral? In most solutions containing a strong or weak acid, the auto-
ionization of water can be neglected when computing [H30+].
Explain why this is so. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28.
3 1. 32. When computing [H3O+] for weak acid solutions, we can
often use the x is small approximation. Explain the nature of this
approximation and why it is valid. What is the percent ionization of an acid? Explain what happens
to the percent ionization of a weak acid as a function of the con-
centration of the weak acid solution. In computing [H3O+] for a mixture of a strong acid and weak
acid, the weak acid can often be neglected. Explain why this is so.
Write a generic equation showing how a weak base ionizes water.
How can you determine whether an anion will act as a weak base?
Write a generic equation showing the reaction by which an anion,
A_, acts as a weak base. What is the relationship between the acid ionization constant for
a weak acid (Ka) and the base ionization constant for its conjugate
base (Kb?) What kinds of cations act as weak bases? Give some examples.
When calculating the [H30+] for a polyprotic acid, the second
ionization step can often be neglected. Explain why this is so. For a weak diprotic acid HZX, What is the relationship between
[X2_] and K32? Under what conditions does this relationship exist?
For a binary acid, H—Y, what factors affect the relative ease with
which the acid ionizes? What factors affect the relative acidity of an oxyacid? What is the Lewis definition of an acid? of a base? What is a general characteristic of a Lewis acid? of a Lewis base?
What is acid rain? What causes it and where is the problem the
greatest? What are fire main detrimental effects of acid rain? What is being
done to address the problem of acid rain? ...
View Full Document
- Spring '06
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CC-MAIN-2018-22
| 4,114 | 38 |
https://nrich.maths.org/4743/index?nomenu=1
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math
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Copyright © University of Cambridge. All rights reserved.
'Team Bus' printed from http://nrich.maths.org/
The coach of the Irish hockey team has a maximum speed of 60 miles per hour. If it travels this speed for two hours, how many kilometers does it travel to the nearest 10 km?
If you liked this problem, here is an NRICH task
which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.
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s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934806070.53/warc/CC-MAIN-20171120145722-20171120165722-00364.warc.gz
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CC-MAIN-2017-47
| 446 | 6 |
https://www.onlinemathlearning.com/complex-fractions.html
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math
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In this lesson, we will learn what is the Reciprocal of a fraction, what is a Complex Fraction and how to simplify a Complex Fraction.
What is the Reciprocal of a fraction?
The reciprocal of a fraction is the fraction turned upside down. That is the numerator becomes the denominator and the denominator becomes the numerator, for example:
The reciprocal of
The reciprocal of or 8.
To get the reciprocal of a mixed number, first convert to improper fraction and then invert, for example:
The reciprocal of is Any number multiplied by its reciprocal will always be 1, for example:
What is a Complex Fraction? A complex fraction is a fraction within a fraction. If we have a fraction as the numerator, then the denominators are to be multiplied to get the simplified fraction.
If we have a fraction as the denominator, then the top numerator is multiplied with the reciprocal of the denominator to get the simplified fraction.
How to simplify a Complex Fraction?
Method 1 : Fraction Division
Method 2 : LCD Multiplication
Simplifying Complex Fractions - Example 1 (Fraction Division Method)
This video shows how to simplify a complex fraction by getting common denominators, flipping, multiplying, and canceling.
Simplifying Complex Fractions - Example 2 (Fraction Division Method)
Simplifying complex fractions (LCD Multiplication Method)
Two examples of simplifying complex fractions using the LCD Multiplication ie. multiplying every term of the complex fraction by the LCD of all the fractions that appear in the complex fraction.
Simplify Complex Fractions (LCD Multiplication Method)
Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320303779.65/warc/CC-MAIN-20220122073422-20220122103422-00449.warc.gz
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CC-MAIN-2022-05
| 1,925 | 22 |
http://www.mywordsolution.com/question/if-a-competitor-develops-a-substitute-for-the/940848
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math
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Solo Creations holds a monopoly position in the production and sale of mano-nanometers. The Total Cost and Marginal Cost functions facing Solo are estimated to be
TC = 200,000 - 30 Q
MC = 30
a) If the price elasticity of demand, ED, is currently -3.0, what price should Solo charge?
b) What is the marginal revenue (MR) at the price computed in part a?
c) If a competitor develops a substitute for the mano-nanometer and the price elasticity increases (in absolute value) to -4.0, what price should Solo charge?
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s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218189667.42/warc/CC-MAIN-20170322212949-00032-ip-10-233-31-227.ec2.internal.warc.gz
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CC-MAIN-2017-13
| 511 | 6 |
https://aidlo.com/the-demand-schedule-for-pens-is-given-below-25-50-and-20-100/
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math
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The demand schedule for pens is given below
|Price of Pen (Rs. per pen)||Quantity Demanded|
Calculate the price elasticity of demand and determine the type of price elasticity.
Q = 50
Therefore, a change in the price of pens is:
In the above calculation, a change in price shows a negative sign, which is ignored. This is because price and demand are inversely related which can yield a negative value of price (or demand). Similarly, a change in quantity demanded of pens is:
The price elasticity of demand for bread is 5, which is greater than one. Therefore, in such a case, the demand for pens is relatively elastic.
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| 620 | 7 |
https://edurev.in/course/quiz/attempt/-1_Olympiad-Test-Direction-Sense-Test-1/a9a1010e-3da0-4b22-9e9b-29fe3bc383af
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math
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A river flows west to east and on the way turns left and goes in a semi-circle round a hillock, and then turns left at right angles. In which direction is the river finally flowing?
I am facing south. I turn right and walk 20 m . Then I turn right again and walk 10 m. Then I turn left and walk 10 m and then turning right walk 20 m . Then I turn right again and walk 60 m. In which direction am I from the starting point?
Here O is the starting point and E is the finishing point.
Clearly E is in North-East direction from the starting point O.
A rat runs 20 towards East and turns to right, runs 10 and turns to right, runs 9 and again turns to left, runs 5 and then turns to left, runs 12 and finally turns to left and runs 6. Now, which direction is the rat facing?
Starting from a point P, Sachin walked 20 metres towards South. He turned left and walked 30 metres. He then turned left and walked 20 metres . He again turned left and walked 40 metres and reached a point Q . How far and in which direction in the point Q from the point P?
P and Q are the starting and finishing positions of Sachin respectively.
∴ Distance between P and Q
= PQ = QC – PC
= 40 – 30
= 10 m and in West direction.
Rohan walks a distance of 3 km towards North, then turns to his left and walks for 2 km. He again turns left and walks for 3 km. At this point he turns to his left and walks for 3 km. How many kilometers is he from the starting point?
A girl leaves from her home. She first walks 30 metres in North-west directions and then 30 metres in South-west direction. Next, she walks 30 metres in south-east direction. Finally, she turns towards her house. In which direction is she moving?
Radha moves towards South-east, a distance of 7 Km, then she moves towards West and travels a distance of 14 m. From here, she moves towards North-west a distance of 7 m and finally she moves a distance of 4 m towards East and stood at that point. How far is the starting point from where she stood?
A man is facing north-west. He turns 90° in the clockwise direction and then 135° in the anticlockwise direction. Which direction is he facing now?
You go North, turn right, then turn right again and then go the left. In which direction are you now?
My end point is C. I am facing east direction and in east direction.
Namita walks 14 metres towards west, then turns to her right and walks 14 metres and then turns to her left and walks 10 metres. Again turning to her left she walks 14 metres. What is the shortest distance between her starting point and the present position?
A man is facing south. He turns 135° in the anti clockwise direction and then 180° in the clockwise direction. Which direction is he facing now?
Manick walked 40 metres towards North, took a left turn and walked 20 metres. He again took a left turn and walked 40 metres. How far and in which direction is he from the starting point?
Going 50 m to the south of her house, Radhika turns left and goes another 20 m. Then, turning to the North, she goes 30 m and then starts walking to her house. In which direction is she walking now?
Laxman went 15 kms to the west from my house, then turned left and walked 20 kms. He then returned East and walked 25 kms and finally, turning left covered 20 kms. How far was he from his house?
Amit walked 30 metres towards East, took a right turn and walked 40 metres. Then he took a left turn and walked 30 metres. In which direction is he now from the starting point?
A walks 10 metres in front and 10 metres to the right. Then every time turning to his left, he walks 5, 15 and 15 metres respectively. How far is he now from his starting point?
A man walks 30 metres towards South. Then I turn right again and walks 30 metres. Then, turning to his left, he walks 20 metres. Again, he turns to his left and walks 30 metres. How far is he from his initial position?
Ramakant walks northwards. After a while, he turns to his right and a little further to his left. Finally, after walking a distance of one kilometre, he turns to his left again. In which direction is he moving now?
From his house, Lokesh went 15 kms to the North. Then he turned West and covered 10 kms. Then, he turned South and covered 5 kms. Finally turning to East, he covered 10 kms. In which direction is he from his house?
Deepak starts walking straight towards east. After walking 75 metres, he turns to the left and walks 25 metres straight. Again he turns to the left, walks a distance of 40 metres straight, again he turns to the left and walks a distance of 25 metres. How far is he from the starting point?
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CC-MAIN-2021-04
| 4,589 | 28 |
https://www.greaterthanzero.com/documentation?_eventName=compoundingAndRor101&pageNo=4
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math
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One can visualize the annualized return in a chart that shows the account balances over time. The chart below shows the actual account balances for the 5-year and the 6-year investments as solid lines. The account balances of the fixed rate accounts that replicate the respective investments are shown as dotted lines. The latter are straight lines because the scale of the vertical axis is logarithmic. Their slope indicates the annualized return of the respective investement.
Calculating the annualized return is not hard. Equation (5) tells us that the ending value E of an investment of B dollars for n years at an annual rate of a is given by
When calculating the annualized return, we are given the beginning balance B, the ending balance E, and the number of years n (possibly a fractional number). Solving this equation for the unknown annualized return a is simple pre-calculus math: divide both sides of the equation above by B, take both sides to the power 1/n, and subtract 1 on both sides:
It is obvious from Equation (2) that the expression E/B in the above is equal to 1 + r, where r is the return of the investment for the full n years. Plugging that into Equation (7) above gives us a way to calculate the annual rate of return a from the ordinary return r:
Applying this to the five year investment with the 30.696% return and the six year investment with the 35.6007% return, we obtain the annual rates of return 5.5% and 5.2% that we mentioned earlier:
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| 1,473 | 5 |
https://downturk.net/2593471-higher-engineering-mathematics-6th-edition.html
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math
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John Bird, "Higher Engineering Mathematics, 6th edition"
English | ISBN: 185617767X | 2010 | 704 pages | PDF | 6 MB
Now in its sixth edition, Higher Engineering Mathematics is an established textbook that has helped many thousands of students to gain exam success. John Bird's approach is ideal for students from a wide range of academic backgrounds, and can be worked through at the student's own pace. Mathematical theories are examined in the simplest of terms, supported by practical examples and applications from a wide variety of engineering disciplines, to ensure that the reader can apply theory to practice. This extensive and thorough topic coverage makes this an ideal book for a range of university degree modules, foundation degrees, and HNC/D units.
This new edition of Higher Engineering Mathematics has been further extended with topics specifically written to help first year engineering degree students and those following foundation degrees. New material has been added on logarithms and exponential functions, binary, octal and hexadecimal numbers, vectors and methods of adding alternating waveforms.
This book caters specifically for the engineering mathematics units of the Higher National Engineering schemes from Edexcel, including the core unit Analytical methods for Engineers, and two optional units: Further Analytical Methods for Engineers and Engineering Mathematics, common to both the electrical/electronic engineering and mechanical engineering pathways. A mapping grid is included showing precisely which topics are required for the learning outcomes of each unit.
Higher Engineering Mathematics contains examples, supported by 900 worked problems and 1760 further problems contained within exercises throughout the text. In addition, 19 revision tests, which are available to use as tests or as homework are included at regular intervals.
(Buy premium account for maximum speed and resuming ability)
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https://collaborate.princeton.edu/en/publications/reconstruction-of-chaotic-signals-using-symbolic-data
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math
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We discuss the reconstruction of dynamical systems from noisy time-series. In particular, we consider the use of the symbol statistics (coarse-grained signal data) as the target for reconstruction. The statistics of symbol sequences is relatively insensitive to moderate amounts of measurement noise (σ(noise)/σ(signal) ≈ 10-20%), while larger amounts produce a substantial bias. We show that it is possible to produce robust reconstructions even when σ(noise)/σ(signal) ≈ O(1). Our study shows that even at such high noise levels the procedure is convergent: i.e. the accuracy of parameter estimates is limited only by the amount of data and computer time available.
All Science Journal Classification (ASJC) codes
- Physics and Astronomy(all)
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https://community.ptc.com/t5/Mathcad/GETTING-EXCEL-COMPONENT-TO-RECOGNIZE-INPUT-EXPRESSION/m-p/672955
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math
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How can we get the Excel Component to accept a dependent variable as a valid Input Expression?
Please see the attached file.
Go to Solution.
I think this does what you want. Note the vectorization of y, and converting x1 to a vector.
View solution in original post
Thank you very much for your timely, and much-needed, response.
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http://jhpaperejft.agorisme.info/mathematics-t-coursework-2014-introduction.html
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math
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Mathematics t coursework 2014 introduction
Introduction of mathematics t coursework ask an introduction for mathematics t coursework 2012 entry 2012 pdf for hire gb stpm 2014 7-4-2018 introduction. Math t coursework 2015 sem 1 parameter equation methodology math t assignment 2014 math t coursework 2015 sem 2 introduction - maulik. Course overview this page focuses on the course 1805 introduction to probability and statistics as it was taught by dr jeremy orloff and dr jonathan bloom in spring 2014. Version 10 12 september 2014 1 introduction 5 skills and understanding common to all gcse mathematics exams within this specification,. Mathematics t 2012 coursework introduction of mathematics t coursework – medmoldsprogram be an ajkersurjodoy24commathematics t coursework 2014.
Edexcel international gcse mathematics a igcse 4ma0 4hr mathematics a paper 4: 21-may-2014 ib french ab initio sl paper 1 & paper 2 d&t coursework. Stpm mathematics t coursework 2015 introductionstpm 2015 mathematics (t) (new syllabus - starting 2012) mathematics t countdown stpm 2014 countdown. This course provides an elementary introduction to probability and statistics discrete mathematics 1805 introduction to probability and statistics spring 2014. Mathematics with finance and economics combines mathematics with various aspects of finance set exercises or coursework, introduction to the mathematics.
Mathematics iv honours (s) the work comprises coursework, students should check the department of mathematics third/fourth year course page for a list of. Stpm math t coursework 2012, stpm mathematics t coursework 2012 introduction mathematics coursework stpm 2017 sem 3 math t answer to 2014. Study notes, guides and examination papers for all malaysian form 6 mathematics m students.Stpm math t coursework 2014 sem 2, difference mathematics t coursework sem 2 for watching mat t coursework how to. Mathematics coursework 1 – “t-totals” maths coursework number the mathematical tripos is the taught mathematics course the story of angelas ashes in the faculty it is designed mathematics gcse t totals coursework to be worn as a gcse t. Join coursera for free and transform your career with degrees, mathematics for machine learning introduction to programming with matlab. The old further mathematics t paper is replaced by a decided that further mathematics will not be offered as there's no coursework like mathematics t q:. View le nguyen dat’s profile on linkedin, mathematics mathematics 2011 – 2014 introduction to management. Sample question of stpm 2015 mathematics (t) term 2 coursework assignment question click the question button below to download the complete question. Massage therapy mathematics introduction to complementary equivalent coursework math-1470 modern mathematics for.
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Teacher's manual for mathematics (t) coursework 13 manual for from this document introduction mathematics coursework. Introduction the university school students seeking the bachelor of science in mathematics at least six semester hours of upper-division coursework must be. Edexcel gce history a2 unit 4 coursework plan template 5th grade physics 2014 2015 waec obj psychology 8 major perspectives assignment answers introduction to.
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http://www.keysight.com/main/editorial.jspx?cc=US&lc=eng&ckey=1000001962:epsg:faq&nid=-11143.0.00&id=1000001962:epsg:faq
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math
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How do you measure electric field strength with an antenna and spectrum analyzer?
Use E=AF*V where E is the field strength in volts/meter, V is the voltage received by the spectrum analyzer, and AF is the antenna factor. The units of AF are 1/meter. The antenna factor is antenna specific and is supplied by the manufacturer.
E=AF*V in dB's becomes E(dBV/m)= AF(dB)/m + V(dB).
For example, if the voltage received is -30 dBV and the AF is 10 dB/m, then E is -20 dBV/m.
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http://www.grahamhancock.com/forum/CreightonS4.php?p=4
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math
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The Great Pyramid and the Axis of the Earth - Part 2 (cont.)
By Gary Osborn and Scott Creighton
So in effect, these two angles of 11.75º that intersect the centre of the Queen's Chamber, add up to 23.5º - the same value as the angle intersecting the King's Chamber from the south vertice.
2 x 23.5º = 47º is meaningful and within context here, because 47º is the radius of the precessional circle traced in the sky over c. 25,920 years by the Earth's tilted axis.
Staying with the theme of Precession which is also associated with the obliquity of the Earth's axis, the angles of the sloping sides of the GP are 51.84º, and using the Platonic value for precession, the value 51,840 amounts to two precessional cycles of 25,920 years.
If this isn't a coincidence then we would have to ask why two precessional cycles? If intentional then perhaps this detail is part of the code we are unravelling here and something we have yet to decipher.
What if we now add the values of these four angles together?
11.75º + 11.75º + 23.5º + 6.5º = 53.5º
As said, as the Earth turns daily on its axis of 23.5º, the GP comes as close as 6.5º and as distant as 53.5º from the Ecliptic Plane (see Fig.1).
Again, what are the odds against this, if what we see here doesn't reflect any intent on behalf of the pyramid's architects?
But this is not all . . .
The next logical step would be to examine the angle between the two chambers. One would suspect that the angle would also be 23.5º and perpendicular with the 23.5º angle that intersects the King's Chamber.
At first, one is disappointed to find that the chambers are centred on an angle of precisely 26.77º - not 23.5º.
However, it's interesting that a line from the centre of the KC to the floor of the QC, intersecting the point where the floor and the central axis of the GP meet, is indeed 23.5º: and the thing that is so appealing about this alignment, is that the floor of the Queen's Chamber is level with the 23.5th Course Layer of the GP.
As many will know the core masonry of the Great Pyramid is now exposed due to its outer limestone casing having been removed centuries ago. The core masonry now consists of 203 steps or layers from the base to the truncated top of the pyramid.
So in effect, this 23.5º angle from the centre of the King's Chamber intersects a point (the centre of the green cross in Fig. 8) that is already marked-up to the value of 23.5.
Figure 8 - The perpendicular angle of 23.5º that runs through the centre of the KC and the point where the centreline of the GP intersects the floor of the QC - the floor being level with the 23.5th Course Layer
It appears that the same number of Course Layers from the base of the GP to the floor of the Queen's Chamber was used by the architects to verify this angle and its alignment.
One could argue with this and ask why go to all this trouble? Why not centre the two chambers on an angle of 23.5 degrees if this was the original intention?
The simple answer is that for the architects this was impossible given the 51.84º angle of the sides, which appear to have been vital to the overall design.
If the architects had already determined the positions of both chambers via the 23.5º and 6.5º angles to the centre of the KC, and the two 11.75º angles that are half the 23.5º value for the QC, then it would have been impossible aligning the centres of both these chambers on a perpendicular 23.5º angle. The only way this would be possible was if the angles of the sides were 48.42º - a difference of 3.5º. This means that the side angles of 51.84º was of paramount importance.
The geophysical-associated message has already been made clear with the angles we have already discovered, and as we will see later, this perpendicular angle, although important, would have been considered secondary in the overall plan.
So to perhaps show that this alignment would have been ideal in practice and was originally intended for reasons which will soon be made clear, the next best thing was to make sure that the intersection point of both the centreline of the GP and the floor of the QC were connected to the centre of the KC by an angle of 23.5º, and that as an afterthought it was decided that the number of Course Layers from the base to the floor of the QC would both reflect and confirm the value of this intended angle.
This could be argued of course, but this is our explanation as to how the architects may have got around the problem of not being able to centre both chambers on a 23.5-degree angle in addition to the other alignments they had already made and on which the overall geometry of the GP depended.
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https://trimhavsandcad.firebaseapp.com/1444.html
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math
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To download the mcdougal litte ii algebra 2 textbook pdf file you need to do an internet search. Learn vocabulary, terms, and more with flashcards, games, and other study tools. Algebra 2 textbooks free homework help and answers. Mcdougal littell algebra 1 answers equation solver. Algebra textbooks free homework help and answers slader. Mcdougal littell algebra 2 2007 algebra 2 textbook. Start studying algebra 2 chapter 1 mcdougal littell. Algebra 2 mcdougal littell practice workbook answers. Timesaving videos related to mcdougal littell algebra 2 2007 textbook topics. Mcdougal littell algebra 1 answers in the leftmost column below. Algebra offers practical strategies on mcdougal littell algebra 2 answers, mathematics content and real numbers and other algebra topics. Mcdougal littell algebra 2 practice workbook answer key pdf. Gnuplot tutorial linear regression, system of equation math quiz, holt physics mathematica, 9th grade poems, converting decimals fraction and percent problems.
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In the event you will need guidance on complex numbers or perhaps syllabus for college algebra, will be the perfect site to head to. Where to download the mcdougal littell algebra 2 text book. Glencoe algebra 2 pdf blitzer algebra and trig online. Sep 24, 20 glencoe algebra 2 pdf blitzer algebra and trig online.810 1321 1184 730 466 1390 42 1223 1312 870 362 1504 722 1102 59 66 1025 528 1294 1161 626 74 145 896 1380 608 1461 552 1206 1332 1280 428 1323 316 12 214 200
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http://blog2glory.blogspot.com/2009/03/pachaas-rupaiye-do-aur-vote-le-lo.html
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math
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WHY, because they can get one kilo of free rice + 50 rupees + and if you are lucky ( one umbrella as well ) Who gives these "election perks"? The currupt politicians ofcourse. But the next question is " where do they get the money to give such rewards" The answer is " Indian Tax payers and the Indians treasury "
So who has the power to stop them? The Election Commission . But why is nothing happening ? kyuki , Yes hai India meri Jaan !!
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https://eanswers.in/math/question4898150
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math
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you for asking question, look at the attached image to understand question better.
if you look at the yellow square you will see it is a square of 90°.
together with angles 1 and 2, form a straight angle so we have:
subtracting 90° from both sides we have:
if the sum of the measures of 2 angles is 90°, the angles are called complementary.
the sum of the measures of angles 1 and 2 is 90°,
then these 2 angles are complementary.
so, are complementary
if there is any confusion leave a comment below.
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http://1004355.ga/qota/first-order-logic-homework-solution-qix.php
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math
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The Syntax of Predicate Logic - Boston University
Homework 3 Solutions, ECE 252A First Order Predictor: ¢ 8
Math 114L: Mathematical LogicHomework 7 First-Order Logic CompSci 171:. and y are assigned to the first domain. 8.6 Represent the following sentences in first order logic, using a.There is no way two or more people will receive the same paper.
mendelson | Logic Matters
Is l Dillig, CS311H: Discrete Mathematics First Order Logic,.Pure logic: Sentential logic and first-order. specified on the respective homework.
Homework for You: We Can Do You Homework | 5Homework.comBe sure the two translations reflect the difference between the two sentences.First Order Logic Homework Solution first order logic homework solution.Enter your First Order Discount code: HOMEFIRST. There is a solution for perfectly done homework.Syntactical first-order unification is used in logic programming and programming.Before your paper is available for download, we send it to our team of.
CS360 Homework 3 Solution First Order Logic 1) For each of the following sentences in rst-order logic, specify.
CS 4811 Arti cial Intelligence Homework 4 | First-Order Logic
What is first-order logic? - Definition from WhatIs.comFirst order logic homework solution Please read my instructions for homework assignments.This is another assignment that students ask us to help them with.We will cover quasi-linear first order equations,. on the homework assignments.
Homework 16 solutions - Full-Time Faculty
A Concise Introduction to Logic (Book Only) | Jet.comHomework: You should hand in solutions to most of the. though please write up the solutions yourself and indicate the.
Homework 4 Solutions - UCLA Department of MathematicsLogic for Knowledge Representation and Reasoning. First-Order Logic (abbreviated FOL or FOPC) is expressive enough to concisely represent this kind of situation.Solution: Let M (x) denote...
Symbolic and Mathematical Logic • r/logic - reddit
Symbolic Logic Study Guide: Homework Solutions 67 SECTION 2: HOMEWORK SOLUTIONS.Main models: propositional logic, first-order predicate logic, higher-order logic.
What are the three components of an interpretation of a first order.
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https://www.canadianhomeeducation.com/Saxon-Algebra--1-2--Set-3rd-Edition
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math
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Saxon Algebra 1/2 is the transition book from arithmetic to algebra and follows Saxon Math 87. It is designed to automate the use of fractions, mixed numbers, decimals, and procedures for simple word problems. The concepts of area, percent, ratio, and order of operations are introduced. The beginning concepts of algebra are practiced thoroughly. Fundamentals of geometry and real world topics about percent and ratio are included.
Saxon Math textbook packages include the textbook, answer key and test book.
Saxon Math Placement Test
Saxon Math Sample Pages
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Saxon Math Scope & Sequence
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https://www.groundai.com/project/spherical-codes-maximal-local-packing-density-and-the-golden-ratio/
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math
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Spherical codes, maximal local packing density, and the golden ratio
Adam B. Hopkins, Frank H. Stillinger and Salvatore Torquato
Department of Chemistry, Princeton University, Princeton, New Jersey 08544
Program in Applied and Computational Mathematics, Princeton University, Princeton, New Jersey 08544
Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544
Princeton Institute for the Science and Technology of Materials, Princeton University, Princeton, New Jersey 08544
School of Natural Sciences, Institute for Advanced Study, Princeton University, Princeton, New Jersey 08544 The densest local packing (DLP) problem in -dimensional Euclidean space involves the placement of nonoverlapping spheres of unit diameter near an additional fixed unit-diameter sphere such that the greatest distance from the center of the fixed sphere to the centers of any of the surrounding spheres is minimized. Solutions to the DLP problem are relevant to the realizability of pair correlation functions for sphere packings and might prove useful in improving upon the best known upper bounds on the maximum packing fraction of sphere packings in dimensions greater than three. The optimal spherical code problem in involves the placement of the centers of nonoverlapping spheres of unit diameter onto the surface of a sphere of radius such that is minimized. It is proved that in any dimension, all solutions between unity and the golden ratio to the optimal spherical code problem for spheres are also solutions to the corresponding DLP problem. It follows that for any packing of nonoverlapping spheres of unit diameter, a spherical region of radius less than or equal to centered on an arbitrary sphere center cannot enclose a number of sphere centers greater than one more than the number that can be placed on the region’s surface.
The densest local packing (DLP) problem in seeks an arrangement of spheres of unit diameter near (local to) an additional fixed central sphere such that the greatest radius between the centers of the surrounding spheres and the center of the central sphere is minimized. For an optimal configuration of spheres, i.e., a configuration for which is minimized, we call the minimized greatest radius . The ’’ in the notation serves to distinguish from , where in the optimal spherical code (OSC) problem is the radius of the minimal radius sphere onto the surface of which can be placed the centers of nonoverlapping spheres of unit diameter. For , , Fig. 1 depicts a conjectured optimal configuration for the DLP problem with minimal radius alongside an optimal spherical code configuration with minimal distance .
The kissing number problem in seeks the maximum number of nonoverlapping spheres that may simultaneously be in contact with a (additional) sphere;CSSPLG1999 () it is a special case of the DLP problem in that is equal to the greatest for which . The DLP problem can also be said to encompass the sphere packing problem in that in the limit as , optimal sphere packings and optimal DLP packings are equivalent.
The maximum possible with for an optimal DLP configuration of spheres in is the maximum of the function . The function is defined for packings of nonoverlapping spheres of unit diameter as the number of sphere centers that are within distance from a sphere center at position , with an index over all centers and where the value of does not count the sphere center at . For a statistically homogeneous packing, the maximum at fixed of is an upper bound on the maximum of the function , where is the expected number of sphere centers within distance from any given sphere center, or equivalently the average of over all . For a packing that is also statistically isotropic, can be related to the pair correlation function , a function proportional to the probability density of finding a separation between any two points and normalized such that it takes the value of unity when no spatial correlations are present, by
where is the constant number density of points and is the surface area of a sphere of radius in dimensions,
The optimal spherical code (OSC) and DLP problems are similar. A spherical code is defined for parameters as a set of vectors from the origin to points on such that the inner product between any two distinct vectors is less than or equal to . The OSC problem is to minimize given , or to maximize given . There have been a number of investigations into the optimality and uniqueness of specific spherical codes (for example, see Ericson and ZinovievEZCES2001 () and Cohn and KumarCK2007a ()), and into providing bounds on given and .CSSPLG1999 ()
A spherical code may be represented by a packing of nonoverlapping spheres of unit diameter with centers distributed on the surface of a sphere of radius . In this representation, the OSC problem for a given requires finding the minimum , , such that no two spheres overlap, i.e., such that the distance between the centers of any two spheres is greater than or equal to unity.
The OSC problem formulated in terms of nonoverlapping spheres and the DLP problem differ for all where only in that the former restricts the placement of sphere centers to a subset of the space allowed in the latter. From this observation, it is clear that when there exists a configuration of spheres that is a solution to the DLP problem with minimal radius that is also a spherical code, it is additionally a solution to the corresponding OSC problem, with .
Ii The Densest Local Packing Problem and Realizability
Only functions obeying certain necessary conditions known as realizability conditions can be correlation functions of point processes in .Lenard1975a (); TS2002a (); KLS2007a () Two realizability conditions on the pair correlation function are the nonnegativity of and its corresponding structure factor at all points and .TS2002a () These two conditions appear to be strong conditions for the realizability of sphere packings (point processes in which the minimum pair separation distance is unity), especially as the space dimension increases.TS2006a () They have been employed, among other uses, to provide conjectures for a lower bound on the maximum packing fraction of an infinite sphere packing in any dimension,TS2006a () and to demonstrate the feasibility in three dimensions of a sequence of disordered packings whose disorder vanishes as density approaches the maximum possible.HST2009a ()
Cohn and ElkiesCE2003a () employ analogs of these two conditions, in conjunction with a linear programming technique, to find the best known bounds on the packing fraction of infinite sphere packings in (at least) dimensions four through 36. In the conclusions of a previous work,HST2009a () we discuss how a third realizability condition, found by solving the DLP problem for a packing of 13 spheres in three dimensions, can improve upon the three-dimensional bound found in Ref. 9.
The technique employed in Ref. 7 to find conjectured lower bounds has been shown to be the dual of the primal infinite-dimensional linear program employed in Ref. 9, and Cohn and KumarCK2009a () have since shown that there is no duality gap between the two programs. This means that when the best test functions are employed, the upper and conjectured lower bounds will coincide. Cohn and Elkies in Ref. 9 were able to find a test function that yields the best upper bound on the maximal packing fraction in three dimensions, a packing fraction of , which is well above the true maximum. This means that there is a test function for the lower bound formulation that will deliver the same packing fraction of , which is clearly not realizable.
A putative improvement on the upper bound in was obtained by employing an estimate for in the DLP problem in .CKT2009a () Requiring that up to some small positive beyond contact, with the estimate for , reduces the bound in Ref. 9. For example, estimating footnote1 () reduces the bound from to . This result strongly suggests that DLP solutions introduce more information than is contained in the pair correlation function alone, in that there is at least one test that obeys the two nonnegativity conditions but violates the bound .
Further solutions to the DLP problem provide additional realizability conditions that might be employed to improve upon the upper bounds on infinite sphere packings in dimensions greater than three. For a statistically homogeneous and isotropic packing of spheres, these additional conditions may be written as
where the function is defined in as the maximum number of sphere centers that fit within distance from a central sphere center.footnote2 () It is clear that in is completely defined by the solutions to the densest local packing problem at all .
In the following section, we show that any configuration of -dimensional spheres near a (additional) sphere fixed at the origin, with the greatest of the distances from the origin to the sphere centers equal to the golden ratio, may be transformed to a spherical code in the sense of nonoverlapping spheres, also of radius . As this statement is applicable to any configuration of spheres that is a solution to the DLP problem with , it follows that any optimal spherical code with radius is also an optimal configuration for the corresponding DLP problem, with .
Iii Translating Unit-Diameter Spheres to the Surface at Radius
The key idea behind the proof of the above statement involves translating sphere centers radially outward to a spherical surface of radius . The idea of radially translating points to a spherical surface has been employed by MelissenMelissen1994a () to aid a proof of the optimality of certain packings of 11 congruent nonoverlapping circles in a circle and more recently by Cohn and KumarCK2009b () to rescale vectors in to terminate on . However, prior to this work, the maximum radius from the center of a fixed nonoverlapping sphere to which the centers of surrounding spheres can be translated without resulting overlap was not known.
Specifically, for any number of nonoverlapping spheres of unit diameter initially situated such that their centers are contained in a spherical shell of radial span with , all sphere centers at a distance less than from the center of the shell may be translated radially outward to distance without any resulting overlap between spheres. This statement more generally applies (via a simple scaling argument) to congruent nonoverlapping spheres of arbitrary diameter that are contained within a spherical shell of radial span , .
Define in as the set of all packings of any number of nonoverlapping spheres of unit diameter with centers situated in a spherical shell of radial span , with the greatest of the distances from the center of the shell (the origin) to the sphere centers. An element of the set represents any arrangement of spheres with greatest distance situated near an additional nonoverlapping sphere fixed at the origin.
Consider any single element of in . For , all spheres may be translated radially outward such that their centers are at distance from the origin and still remain an element of . For , , there exist elements of such that an outward radial translation of a given sphere center to distance will yield overlap between at least two of the spheres.
The proof proceeds from the law of cosines in the method of the proof of Lemma 4.1 in Ref. 15. For any two of the spheres with centers situated at distances , from the origin and separated by distance , the cosine of the angle formed between the two centers at the origin, taken such that , is
For nonoverlapping spheres of unit diameter, , and
where the equality holds when the two spheres are in contact.
Over the range , , the function in Eq. (5) is convex individually in both and . This implies that must be at a maximum at one of the corners of the square , . If , the point (or equivalently ) yields the maximum, whereas for , the point yields the maximum, with and both yielding the maximum at .
It follows directly that for , the minimum possible angle at the origin between any two of the centers of spheres that are an element of is the angle present when two of the centers are placed at distance from the origin and distance unity from one another. An outward radial translation of one or both of any pair of centers to distance will therefore yield no overlap between the two spheres, as the angle between the centers must be greater than or equal to the angle present when two spheres are in contact with one another with centers at distance from the origin. As this holds for any pair of the sphere centers, all centers at a distance less than , , may be translated radially outward to distance without any resulting overlap.
For , , overlap between two spheres is possible after an outward radial translation. For example, when two spheres are initially in contact with centers at distance unity from each other and at distances and from the origin, the angle formed at the origin between centers is smaller than the angle present when the spheres are in contact with centers both at distance . A radial translation outward of the sphere center at distance to distance would thus yield overlap. This concludes the proof of Theorem 1. ∎
Iv Results and Discussion
Theorem 1 applies to any configuration of nonoverlapping spheres that are an element of . In particular, in an optimal DLP configuration for spheres in with , which is by definition an element of , any of the spheres with centers not at distance from the origin may be translated radially outward to distance without any overlap between spheres. The resulting configuration is both a solution to the DLP problem and, in the sense of nonoverlapping spheres, to the corresponding OSC problem, with . Theorem 1 therefore implies that while for there may be solutions to the densest local packing problem that are not spherical codes, for there are no solutions to the optimal spherical code problem that are not also solutions to the corresponding densest local packing problem.
The kissing numbers in are only known rigorously for , and ;Musin2008a (); CSSPLG1999 () for , , and , they are , , and ,Musin2008a () respectively. For , the solution to the DLP problem is simply by necessity as the nonoverlapping sphere of unit diameter at the origin is fixed. For such that , where we define in as the greatest integer such that , the optimal spherical codes are solutions to the corresponding DLP problems with . The questions concerning the values of in each dimension and how grows with naturally emerge.
In one dimension, the answer to the first question is trivial, with . In two dimensions, optimal spherical codes can be found analytically via simple trigonometry, with for , or . Strong conjectured solutions for that serve (at least) as upper bounds to the OSC problem are well-known in low dimensions greater than two for small .SloaneSCweb () For , these yield the conjecture with . For , a unique optimal spherical code is known such that , giving the result that .footnote3 ()
The question of precisely how grows with is still open, and is more complicated; however, bounds may be established via known bounds on (given and ) for optimal spherical codes, such as with those given in chapter two of Ref. 1. The lower bound (due to WynerWyner1965a ()) on for a spherical code of minimum angle in dimension is
giving, for , . This may be compared to the Kabatiansky-LevenshteinKL1978a () upper bound on the kissing number, . Comparing the upper bound on the kissing number and the lower bound on , it is clear that grows exponentially faster than .
The authors thank Henry Cohn for valuable comments and suggestions concerning the manuscript. S.T. thanks the Institute for Advanced Study for its hospitality during his stay there. This work was supported by the Division of Mathematical Sciences at the National Science Foundation under Award Number DMS-0804431 and by the MRSEC Program of the National Science Foundation under Award Number DMR-0820341.
- Conway, J. H. and Sloane, N. J. A. Sphere Packings, Lattices and Groups. Springer, (1999).
- Ericson, T. and Zinoviev, V. Codes on Euclidean Spheres. North-Holland, (2001).
- Cohn, H. and Kumar, A. New York J. Math. 13, 147–157 (2007).
- Lenard, A. Arch. Ration. Mech. Anal. 59, 219–239, 241–256 (1975).
- Torquato, S. and Stillinger, F. J. Phys. Chem. B 106, 8354–8359 (2002).
- Kuna, T., Lebowitz, J. L., and Speer, E. R. J. Stat. Phys. 129, 417–439 (2007).
- Torquato, S. and Stillinger, F. H. Exp. Math. 15, 307–331 (2006).
- Hopkins, A. B., Stillinger, F. H., and Torquato, S. Phys. Rev. E 79, 031123 (2009).
- Cohn, H. and Elkies, N. Ann. Math. 157, 689–714 (2003).
- Cohn, H. and Kumar, A. Unpublished.
- Cohn, H., Kumar, A., and Torquato, S. Unpublished.
- The actual number is strongly conjectured to be , equal to the current best lower bound for in .
- In the sense of defined in Eq. (1) for a statistically homogeneous packing, is generally not a sharp upper bound for , i.e., there is not always a configuration of spheres for which equality in (3) holds. This is because is defined locally, in terms of one central sphere, whereas in Eq. (1) is defined globally in terms of a probability density, or in the case of a finite packing, in terms of an average over all spheres.
- Melissen, H. Geom. Dedicata 50, 15–25 (1994).
- Cohn, H. and Kumar, A. To appear in Ann. Math. http://arxiv.org/abs/math.MG/0403263
- Musin, O. R. Ann. Math. 168, 1–32 (2008).
- Sloane, N. J. A., Hardin, R. H., and Smith, W. D. www.research.att.com/~njas/packings/
- It has been shown that the vertices of the -cell are the unique spherical code,Boroczky1978a (); BD2001a () which corresponds in to .
- Wyner, A. D. Bell Sys. Tech. J. 44, 1061–1122 (1965).
- Rankin, R. A. Proc. Glasgow Math. Assoc. 2, 139–144 (1955).
- Kabatiansky, G. A. and Levenshtein, V. I. Probs. of Info. Trans. 14, 1–17 (1978).
- Böröczky, K. Acta Math. Acad. Sci. Hung. 32, 243–261 (1978).
- Boyvalenkov, P. and Danev, D. Arch. Math. 77, 360–368 (2001).
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https://victoryawards.us/what/what-is-the-relationship-between-mass-and-momentum-yahoo-answers.php
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math
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what is the relationship between mass and momentum? | Yahoo Answers
E.g. An object has mass 2kg and velocity 4m/s. (The negative sign means the direction of velocity is negative, i.e. opposite to the initial. This is not the case. Both will reach the ground at the same time. v2 = u2 + 2gs. ( independent of mass) s= 1/2 at2 (independent of mass). Short Answer. 7 Center of Mass and Momentum. .. problems an equation, or a number (or set of equations or numbers). It is a.
As a prelude to reading my answer, you should read an earlier answer and the earlier answers referred to in that answer. The graph here shows the results derived or cited in that earlier answer. The three graphs all show what is observed of your motion as seen by the twin on earth.
Now, since I have set this up as seen from earth, let me specify the time you travel as the time of your trip out as observed from earth: Light would take 2.
We can get a rough estimate of your clock reading by approximating your average relative speed as 0. What happend to accelaration due to gravity if the earth stops rotating? Because of the centrifugal force, g appears to be somewhat smaller than it really is, but the amount is very tiny.
This effect depends on your latitude and is zero at the poles and greatest at the equator. Also because of this effect, the acceleration is not directly toward the center of the earth except at the poles and equator. Hello, is the mass of a person on a spaceship to provide a suitable upward force important in designing a spaceship? My teacher says otherwise but upon researching I found out that additional fuel is required for every kg of payload that will be sent out into space.
If the ship and all the fuel are much bigger than the mass of the person, then you could neglect the mass of the person in any calculations you know; in other words, the rocket launch would be, as close as you could hope to be measure, identical whether or not an astronaut was on board.
Questions & Answers
However you are also right that the amount of fuel you need depends on the payload you want to deliver, and that would include everything which is not fuel. You might find the an earlier answer illuminating. How exactly do electrons in electric discharges generate radio waves? Whenever someone uses an AM radio while there are electric sparks like lightning strikes nearby the radio waves they emit can be detected.
Any time an electric charge is accelerated it emits electromagnetic radiation. There are many electrons in the spark which accelerate under the influence of the electric fields they experience. I just read about the kilogram being defined by measuring the current of an elector-magnet to balance a scale. How can various electromagnets have exactly the same force to current ratio?
Would variations in the purity of the conductor, variations in the exact coil shape, etc. What am I missing about this new designation?
You cannot use any old electromagnet. There is an exquisitely accurate balance called the Kibble balance which is used. Is the following statement correct? Net radiated energy is made up of emitted and absorbed energy.
I stated that it was incorrect based on the fact that "made up of" usually means putting two or more things together aka addition. Net radiated energy is the difference between emitted energy and absorbed energy. What is the correct answer in this case and why? I do not believe that there is a hard and fast definition of what "net radiated energy" is. It is a matter of semantics. However, radiated energy usually means energy emitted and absorbed energy means energy absorbed; therefore, I would say that this is an incorrect statement because net radiated energy would mean the sum of all radiated energy, absorbed energy having nothing to do with it.
Your reason is quite shaky because "made up of" is even more semantically ambiguous than "net radiated"; it would simply imply that "net" means total energy flux. How is momentum conserved for single or double slit diffraction? I have a photon gun that I can dial the intensity down to fire one photon at a time.
The photon then passes thru two closely spaced slits double slit experiment instead of appearing on the screen directly behind the slits, the photon ends up to the side after many, many photons the interference pattern appears however, for the single event of a single photon, how is momentum conserved? Since the photon ended up to the side, it was no longer travelling in the purely X direction, therefore shouldn't the photon have exchange d momentum with the slit somehow?
If the interference pattern remains, then how do we account for the photons change in momentum? This is for a single event, one photon, not expectation value of many, many photons. You are forgetting that the photon goes through both slits, is being forced if you like to assume its wave-like identity.
It behaves like a wave until something makes it act like a particle, so it is a wave spreading out in both directions, so its net momentum in the direction parallel to the screen is zero.
When the screen is encountered it is a "measurement" which collapses the wave function at some point.
I can imagine 2 similar objects rotating around a sphere at the same velocity but at different orbits. One object would rotate around the sphere faster than the other, right? What is puzzling to me is that if I think of both objects going now in a straight line one could not say that one object was going faster than the other.
Can someone help me through this? Is there a subtlety here? You want to say same speed, not same velocity, but I get the idea. Say one orbit is twice the radius as the other. Then the smaller orbit has a circumference half that of the larger.
So each time the object in the larger orbit goes around once, the one in the smaller orbit goes around twice. But they still have the same speed. The successful candidates should be extremely dynamical and analytically minded individuals.
H That statement on inviolable patterns was very beautiful, very true. Also probably why it was so difficult to formulate in the language of linear equations and operators. Sure, we may be satisfied that natural law dictates certain phenomenological constructs, but not because what we find is satisfactory! At least with the tools we currently have. This goes back to that spat you guys had with Paul Davies.
what is the relation between momentum and velocity? | Yahoo Answers
This is all assuming there is no real problem with the models as they stand today, and that people are at a stage of fundamental knowledge where they are reduced to existential questions, and everything else is fine. But I feel that we are going to get a much better perspective on things soon, and for that I will be very thankful. Sam Cox Very well done, Sean! Perhaps you could also point to the connection between the conservation of momentum and invariance of the laws of physics under translations of the coordinates.
That connection between a symmetry and a conservation law has always amazed me. Finally I think that you have some enough deep thoughts in order to try to build a philosophy, so good luck if you want to go in this way ; before to build mine I was from the group of the ones who did not want to accept the notion of God, but even with all the bad bias I had, the logic I needed was the strongest.
Ernst Zermelo was one of the major advocates of such a view, and he was also responsible for the development of much of axiomatic set theory. As an alternative to set theory, others have argued for category theory as a foundation for certain aspects of mathematics. The intuitive approach silently assumes that all objects in the universe of discourse satisfying any defining condition form a set.
Axiomatic set theory was originally devised to rid set theory of such antinomies. The most widely studied systems of axiomatic set theory imply that all sets form a cumulative hierarchy. Such systems come in two flavors, those whose ontology consists of: This includes the most common axiomatic set theory, Zermelo—Fraenkel set theory ZFCwhich includes the axiom of choice. Fragments of ZFC include: They state that any effectively generated formal theory in which all arithmetic truths can be proved is inconsistent; hence, any such consistent formal theory that can prove some arithmetic truths cannot prove all arithmetic truths.
The theorems are of considerable importance to the philosophy of mathematics. One of the simplest examples of a category which is a very important concept in topology is that of groupoid, defined as a category whose arrows or morphisms are all invertible.
Categories now appear in most branches of mathematics, some areas of theoretical computer science where they correspond to types, and mathematical physics where they can be used to describe vector spaces.
Category theory provides both with a unifying notion and terminology. Categories were first introduced by Samuel Eilenberg and Saunders Mac Lane in —45, in connection with algebraic topology. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism.
In many situations this is too much to hope for and it is more prudent to aim for a more modest goal, classification up to homotopy equivalence. Although algebraic topology primarily uses algebra to study topological problems, the converse, using topology to solve algebraic problems, is sometimes also possible. Algebraic topology, for example, allows for a convenient proof that any subgroup of a free group is again a free group. They appear in virtually every branch of modern mathematics and are a central unifying notion.
The branch of mathematics that studies topological spaces in their own right is called topology. The elements of X are usually called points, though they can be any mathematical objects. A topological space in which the points are functions is called a function space.
A set may be neither closed nor open, either closed or open, or both. A set that is both closed and open is called a clopen set. In older operating systems with cooperative multitasking, infinite loops normally caused the entire system to become unresponsive.
With the now-prevalent preemptive multitasking model, infinite loops usually cause the program to consume all available processor time, but can usually be terminated by the user. Thus, the angular velocity will be different. It started from rest from the first station and comes to rest at the second. Let total distance be x. Substitute for the values of time from above and the highest velocity attained is v and then take the ratio.
Give examples to demonstrate Newton's Laws of Motion. Place a piece of cardboard on it. On top of the cardboard place a coin. Now flick the cardboard away with your finger. The coin will not follow the cardboard but drop into the tumbler. This is because there is no force acting on the coin and it continues to stay in a state of rest.
A cricketer moves his hands back when taking a catch.
This to increase the time period over which the velocity of the ball reduces from a high value to zero. Or in other words the acceleration is reduced. Thus the force transferred to the cricketer's hand is reduced. When a rocket is launched, the downward action of the exhausted gases results in the upward reaction on the rocket, causing it to rise.
How do you solve two dimensional trajectory problems? Trajectory problems may be put into two categories. Horizontal projection and angular projection. During its motion the object covers horizontal distance due to horizontal velocity and vertical distance due to vertical velocity. So each problem can be simplified into two one dimensional problems by taking the components of position, velocity and acceleration along the horizontal and vertical directions. Let us consider the case of horizontal projection.
The object is projected with initial horizontal velocity u. Since the velocity of the object in the horizontal direction is constant so the acceleration ax along horizontal direction is zero. If the initial position of the object was x0, y0 the position of the object at any time t along the horizontal direction i.
If we put the origin of the co-ordinate system at the initial position then the co-ordinates of the initial position become 0,0. Let us take the downward direction as positive. Thus the acceleration in the vertical direction is g 9. This is the equation of a parabola, which is symmetric about the y-axis. Hence the path of the projectile projected horizontally from a certain height from the ground is a parabolic path. How fast must a roller coaster travel around a vertical circular track with radius 10m if it is not to fall from the track?
How long would it take for a ball to fall from a 70 feet tower? This is a problem of free fall. Here, h is the height by which the body falls, u is the initial velocity, t is the time taken to fall by a distance h and g is the acceleration due to gravity. By substituting we can get the answer. If you fire a bullet from a level gun and drop a bullet at the same time, both the bullets will hit the ground at the same time.
Both the bullets have the same acceleration in the vertical direction which is the acceleration due to gravity. Also both the bullets have zero initial velocity in the vertical direction. The bullet fired from the gun has an initial velocity in the horizontal direction but it will not affect the motion in the vertical direction.
Since, both the bullets have to cover the same vertical distance, they will take the same time to do to it and will hit the ground at the same time. What is the minimum speed the pilot of an aircraft should have so as to successfully loop a vertical loop without falling at the top of the loop? Also what is the thrust acting on the aircraft?
The forces acting on the aircraft are - the weight mg acting downwards and the force F by the air upward.
Momentum and Kinetic Energy? | Yahoo Answers
This is the minimum value of velocity at the highest point. If we substitute the value for v', we get, v? Thus, for looping the loop the minimum speed the aircraft should have at the lowest point should be?
Also the maximum thrust on the aircraft will be at the lowest point. When a ball is moving on a smooth plane, it will have acceleration only when there is an external force. Can it be said that the above statement is wrong because when ball is on a smooth inclined plane, it still has acceleration? To understand this question, let us first understand Newton's first law. It says that if the vector sum of all the forces acting on a body is zero then and only then the body remains unaccelerated i.
Let us consider a body moving on a smooth horizontal surface with a uniform velocity. The forces on the body are the gravitational force exerted by the earth and the contact force or the normal reaction exerted by the plane surface on the body.
These forces are equal and opposite and they cancel out. Thus the net force acting on the body is zero and the body remains unaccelerated. Now, let us consider the body moving on a smooth inclined surface.
Thus the body will have acceleration. The prism should be placed in such a manner that if we view the prism from the top, we see one of the triangular faces of the prism. Then one angle of the prism can be taken as the refracting angle. Thus the refracting edge will become vertical. The incident ray falls on one of the faces which contains one of the sides making the refracting angle.
The refracted ray emerges from the face containing the other edge of the refracting angle. Determine the size and location of the mouse's image. Describe the mouse's image in the mirror. Where is its image? The image of an oncoming car is at 3.
What is the actual position of the car? How large and at what distance from the lens will the ant appear to be? Describe the image of the mouse as seen through the lens.
Relationship between mass and velocity?
The focal length of the lens is At what distance is the screen from the lens? How large will a figure 2. We have to know the lens and the mirror formulae and the sign convention to solve the above problems. Sign convention is that all distances measured in the same direction as the incident light are taken as positive and in the opposite direction are taken as negative.
In case of mirrors, distances are measured from the pole and in case of lenses, the distances are measured from the optical center. Thus, the focal length of a concave mirror will be negative and that of a convex mirror will be positive. Also, the focal length of a convex lens will be positive and that of a concave lens will be negative.
Thus the image is real and inverted and at a distance of 30cm from the mirror and on the same side as the object. Thus, image is on the same side as the object at a distance of 36cm from the mirror. Substitute in the mirror formula to find u. Thus, the size of the image of an object of size 2.
For a real image u is negative and v is positive. A block of glass has a critical angle of 39 deg. What is the index of refraction of the glass? Also, i is the angle of incidence and r is the angle of refraction. In the problem, light is passing from the medium glass to the medium air at the angle of incidence being equal to the critical angle. In such a case, the angle of refraction is equal to 90 deg.
For a convex lens, R1 is positive and R2 is negative. For a concave lens, R1 is negative and R2 is positive. When the transmission axes of two Polaroid films are perpendicular to each other, what is the percentage of incident light which will pass the two films? When incident light falls on the first Polaroid film, it allows only those vibrations to pass through which are parallel to its own transmission axis.
The emerging light has vibrations confined to one plane only which is perpendicular to the transmission axis of the second Polaroid film. Thus no light will pass through the second Polaroid film. Why would it be impossible to obtain interference fringes in a double slit experiment if the separation of the slits is less than the wavelength of light used?
The above diagram shows the double slit experiment. Thus it is impossible to obtain interference fringes in a double slit experiment if the separation of the slits is less than the wavelength of the light used.
Moreover, if d is less than wthen S and S' stop being two coherent sources but rather behave like a single source. A noisy machine in a factory produces a decibel rating of 65dB. How many identical machines could you add to the factory without exceeding the dB limit? Let the intensity of sound produced by one machine be I.
Let I' be the intensity of sound when x number of machines are used to produce decibel rating of 95dB. This means that more machines can be used. Explain the terms the fundamental mode of vibration and resonant air columns. Organ pipes are musical instruments which are used for producing musical sounds by blowing air into the pipe. Longitudinal stationary waves are formed on account of superimposition of incident and deflected longitudinal waves.
The fundamental mode of vibration is a simplest mode of vibration and the frequency produced in this mode is the lowest frequency that can be produced and is called the fundamental frequency that can be produced.
For example in a closed organ pipe closed at one end in its fundamental mode of vibration the open end acts as an antinode.
This is because the air can move freely there. The closed end acts as a node because air cannot move too and fro there. Resonant air column It is an apparatus which consists of a long cylindrical tube filled with water having its lower end joined by a rubber tubing to a moveable reservoir of water. The cylindrical water tube is fixed along a meter rod and the level of water in it can be lowered or raised with the help of a reservoir.
A tuning fork of known frequency is gently struck against a rubber pad and is held horizontally at the mouth of the water tube. At the same time the level of water in the tube is lowered till a loud sound is heard.
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http://www.icoachmath.com/math_dictionary/arithmetic_mean.html
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math
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Definition of Arithmetic Mean
More about Arithmetic Mean
Solved Example on Arithmetic Mean
The prices of cheese pizza in five different pizza delivery shops are $5, $4, $6, $8, and $7. Find the mean of the prices.
Correct Answer: A
Step 1: The mean is the average of the prices.
Step 2: Average =
Step 3: = [Substitute the values.]
Step 4: = [Add.]
Step 5: = 6 [Divide.]
Step 6: The mean price is $6.
Related Terms for Arithmetic Mean
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https://www.acmicpc.net/problem/5945
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math
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|시간 제한||메모리 제한||제출||정답||맞힌 사람||정답 비율|
|1 초||128 MB||143||61||40||40.000%|
Bessie and Bonnie have found a treasure chest full of marvelous gold coins! Being cows, though, they can't just walk into a store and buy stuff, so instead they decide to have some fun with the coins.
The N (1 <= N <= 5,000) coins, each with some value C_i (1 <= C_i <= 5,000) are placed in a straight line. Bessie and Bonnie take turns, and for each cow's turn, she takes exactly one coin off of either the left end or the right end of the line. The game ends when there are no coins left.
Bessie and Bonnie are each trying to get as much wealth as possible for themselves. Bessie goes first. Help her figure out the maximum value she can win, assuming that both cows play optimally.
Consider a game in which four coins are lined up with these values:
30 25 10 35
Consider this game sequence:
Bessie Bonnie New Coin Player Side CoinValue Total Total Line Bessie Right 35 35 0 30 25 10 Bonnie Left 30 35 30 25 10 Bessie Left 25 60 30 10 Bonnie Right 10 60 40 --
This is the best game Bessie can play.
4 30 25 10 35
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http://video.stackexchange.com/users/5120/phil
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math
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|location||London, United Kingdom|
|visits||member for||1 year, 3 months|
|seen||Feb 1 '14 at 10:36|
I'm relatively new to role playing, and am a Savage Worlds nut. I currently GM two games, one using the War of the Dead published campaign, the other set in the Deadlands Reloaded world.
0 Votes Cast
This user has not cast any votes
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https://chinese.stackexchange.com/questions/51810/can-%E7%9C%BC%E9%95%9C-be-translated-with-eye-or-eyes
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math
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On Duolingo, a question shows a green paint can, an ear, and an eye, and it asks:
Which one of these is "eye"?
However, under the eye image is the text "眼镜". The dictionaries I work with tell me that this Chinese word translates into "glasses", but not "eye". Also, an internet image search for "眼镜" shows no eyes, but only glasses (and in another question, Duolingo uses the word "眼睛" for "eyes", which is at least inconsistent).
Could somebody please confirm that this is an error on Duolingo? I'd be happy with a very simple and short answer. Many thanks!
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https://pikstagram.com/tag/trader
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math
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Selling my c10, ls 5.3 swap with 4160e built transmission, brand new ac system, brand new suspension components, disc brakes, new drive shaft, custom wheels 20a up front 22x12 in rear, narrow axles to fit the wide wheels, digital dash, 22 gallon fuel cell,
I purchased this truck last year and immediately started to make it the way I wanted to, it had the original 350 v8 but it was tired so instead of putting money into it I had a performance shop drop in a fresh ls engine with all the goodies listed above to make it a super realiable and comfortable driver. Ice cold ac and hot heat, stops on a dime.
The body appears to of been painted before and looks really good, it's not a 40k show truck but would not take much to get there, it's not rusted out but there's a few imperfections on the bottom of the inside of the door and maybe a little bubbling on one side of the cab corner but nothing serious. Clean clear title in my name , open to trades for a newer truck I can put money on top for the right trade up or down, pleas do not contact me to trade for anything that is considered crap if u do you will be ignored , I got a new z06 and just don't need this truck I have paperwork on all the work done all with warranty and all new parts was used using the best available parts. 30k invested will not go lower than 20k so don't bother asking. (785) 393-5848. #honda#camry#lexus#chevy#datsun#toyota#nissan#gmc#cars#bmw#bens#usacars#ford#carsforsale#motorcycle#cadillac#carsandcoffee#sale#buy#trader#mercedes#losangeles#usa#sport#fast#auto#goldwing#dodge#jeep#supra
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http://www.baptistboard.com/threads/hitlers-pope.36073/
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math
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Last night my Holocaust professor mentioned a book by John Cornwell called "Hitler's Pope". In this book Cornwell asserts that Pope Pius XII was not just silent during the early years of the Nazi Holocaust but that Pius actually did things that aided the Nazis. I looked it up on amazon and thought it looked interesting. I don't know when or if I would actually sit down and read this book, since I don't have a great interest in the holocaust, however since I am interested in Church History this might be a book I should at least look at. Btw, my professor did not endorse the book. While he believes that Pius XII's activities during the Holocaust raise some important questions he did not go so far as to suggest that Pius was "Hitler's Pope".
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https://www.stir.ac.uk/research/hub/publication/658626
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math
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Citation Rowlinson P (2007) The main eigenvalues of a graph: a survey. Applicable Analysis and Discrete Mathematics, 1 (2), pp. 455-471. https://doi.org/10.2298/AADM0702445R
Abstract We survey results relating main eigenvalues and main angles to the structure of a graph. We provide a number of short proofs, and note the connection with star partitions. We discuss graphs with just two main eigenvalues in the context of measures of irregularity, and in the context of harmonic graphs.
Keywords Graph; harmonic graph; main eigenvalue; main angle; star partition
Journal Applicable Analysis and Discrete Mathematics: Volume 1, Issue 2
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https://www.physicsforums.com/threads/problems-with-acceleration-results-established-from-equations-of-linear-motion.618685/
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math
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I have 3 separate cases of an object decelerating at different rates. The aim is to find the acceleration for each case. Case 1 Initial velocity: 1.663m/s Displacement: 0.12m Time: 0.139s Case 2 Initial velocity: 1.663m/s Displacement: 0.12m Time: 0.155s Case 3 Initial Velocity: 1.663m/s Displacement: 0.12m Time: 0.24s The attempt at a solution Simply using the equations of linear motion (s=ut+1/2at^2) I got the following results: Case 1: -11.5063m/s^2 Case 2: -11.4685m/s^2 Case 3: -9.69167m/s^2 Why? I expected the magnitude of deceleration to increase from case 1 to case 3 Also deceleration of 11m/s^2 seems excessively high. I need to understand this for an assignment due in a few days. I've done this many times now and with different methods such as finding the final velocity first and then finding the acceleration but every method gives me the same results or at least the same pattern of the deceleration decreasing.
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| 932 | 1 |
https://www.sawaal.com/clocks-questions-and-answers/what-is-the-angle-made-by-the-hour-hand-and-the-minute-hand-if-the-clock-shows-9-15-pm-_12417
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|A) 165 degrees||B) 172.5 degrees|
|C) 112.5 degrees||D) 125.5 degrees|
The minute hand angle is the easiest since an hour (i.e. 60 minutes) corresponds to the entire 360 degrees, each minute must correspond to 6 degrees. So just multiply the number of minutes in the time by 6 to get the number of degrees for the minute hand.
Here 15 minutes corresponds to 15 x 6 = 90 degrees
Next, you have to figure out the angle of the hour hand. Since there are 12 hours in the entire 360 degrees, each hour corresponds to 30 degrees. But unless the time is EXACTLY something o'clock, you have to write the time as a fractional number of hours rather than as hours and minutes.
Here the time is 9:15 which is (9 + 15/60) = 37/4 hours. Since each hour corresponds to 30 degrees, we multiply 30 to get (37/4)(30) = 277.5 degrees.
Since the hour hand is at 277.5 degrees and the minute hand is at 90 degrees, we can subtract to get the angle of separation. 277.5 - 90 = 187.5 =~ 360 - 187.5 = 172.5 degrees.
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https://cerena.pt/bibcite/reference/1266
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math
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Geostatistical seismic inversion uses stochastic sequential simulation and co-simulation as techniques to generate and perturb subsurface elastic models. These steps are computational demanding and, depending on the size of the inversion grid, time consuming. This paper introduces a technique to achieve considerable reductions in the consumption of computational resources of geostatistical seismic inversion without compromising the quality of the inverse elastic models. We achieve these improvements by reducing one of the dimensions of the data domain to a periodic function approximated by a Fourier series of n terms. Then, instead of simulating over the entire original data volume, in the original data domain, we simulate independently each term of the series over the area of interest. If the number of terms in the series is considerably smaller than the size of the collapsed data domain, then the computational overhead of the inversion procedure decreases. Symbolic regression is used to obtain automatically the approximation to the periodic function that captures the behavior of the property in the reduced dimension. The advantages related to the use of symbolic regression over alternative machine learning algorithms are discussed. We use the method to simulate acoustic impedance in a geostatistical seismic inversion of a synthetic dataset representing a hydrocarbon reservoir, where the true acoustic impedance model is available. Results demonstrate a considerable speedup over traditional methods while achieving similar performance in terms of the misfit between real and synthetic seismic and a good representation of the true impedance model. The frequency content of the resulting inverted data is discussed and compared with the one inferred from traditional methods, demonstrating an expected reduction of the high-frequency component. © 2019, Springer Nature Switzerland AG.
Year of publication: 2019
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http://www.signal.uu.se/Publications/abstracts/c891.html
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math
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Adaptive Input Estimation
IFAC Symposium ACASP 89: Adaptive
Systems in Control and Signal Processing,
Glasgow, UK, pp 631-636, April 1989.
The paper studies the problem of estimating the input signal
to a scalar discrete-time linear system
The system is known, while the noise
and input spectra are unknown. (This problem differs from
that of blind deconvolution, where the system is unknown.)
An adaptive algorithm for estimating the input to a linear system
is presented. This explicit self-tuning filter is based on the
identification of an ARMA innovations model. From that model,
input and measurement noise descriptions
Main tools in the algorithm are the solution of two
linear systems of equations.
The basic algorithm can be used for input signals
described by ARMA models and moving average
An extension of the algorithm involves the use of
on-line model reduction and spectral factorization.
Simulation experiments illustrate the filtering performance.
- Related publications:
in IEEE Trans. ASSP 1989 on the design of linear scalar
Later Conference paper
in SPIE'91 on adaptive deconvolution.
Paper in Automatica 1990,
where the identifiability conditions are derived.
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https://brainly.com/question/206120
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math
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Since you're trying to find flight time, angle doesn't matter as it will only change horizontal movement.
Since there is initial velocity and gravity is the only acceleration, we can conclude that initial velocity = final velocity. Since final velocity = initial velocity, the amount of time it takes for the velocity to reach zero because of gravity is 1/2 of time, and so is the amount of time it takes to fall back to the ground.
Time and height scale with initial velocity, but distance traveled because of gravity scale with time, so this works.
2.6 / 2 = 1.3. This is the time it takes to fall back to earth & the time it takes to make velocity reach a state of motionlessness. From here, you simply use the equation h = 1/2gt^2, which turns into h = 1/2(9.81)(1.3)^2. Height ends up becoming 8.28945m.
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https://mrorr-isageek.com/math-resources-so-far/
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math
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Below is a list of resources I like and use. It is a hodgepodge of good stuff for teaching math in a digital classroom.
Math Teaching Resources Menu
Estimation180 is great for warm ups but even better for getting students to practice predicting their answer which allows them to decide if their answer they calculate makes sense.
Here is an example:
Estimate: Day 53
What is the volume of the vase?
Questions we ask to get students thinking of reasonableness of their answers.
Give an estimate that is too low.
Give an estimate that is too high
Give an estimate that is just right.
ASKING STUDENTS TO CHOOSE THEIR OWN PATH AND JUSTIFY IT!
Great way to start a topic/or lesson. Students are eager to justify their choice. Relevant problems.
Here is another example: Would You Rather
Fawn Nguyen’s site has 140 different growth patterns. Find the correct equation!
Here are a few examples:
Along the same lines as this are ….
Vine Videos created by Nat Banting
He takes a pattern like this one from a textbook:
and turns it into this….
or one like this….
and turns it into this…
Engaging Math Problems vs. Standard Math Problems
3-Act Math Problems
Original concept from Dan Meyer – Read about it – The Three Acts of a Mathematical Story
Here is a standard Math problem from grade 9
A water balloon is filled at a rate of 0.22L/s If a standard balloon will hold about 14L of water, how long will it take until it bursts?
Here is the 3-Act Math Approach
Act 1: The Water Balloon
Whatcha Thinking is a project I worked on with Nathan Jeffrey from SCITS in Sarnia. We created a bank of 3-act math problems to use in your grade 9 applied class. The website is designed for student use.
Direct your students to the Whatcha Thinking site.
- Des-Man Activity – Graphing a face using functions. Great for Domain & Range
- Function Carnival – Graphing position vs. time.
Explain Everything as a delivery tool
We began many classes by grabbing an Explain Everything file from our Google Drive. Here is a picture of that file.
Here are some more examples of using Explain everything as a “digital worksheet”
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https://tsfa.co/questions/Trigonometry/362880
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math
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Solve Graphically fifteen cos(x) to the power of two plus eight cos(x) plus one equals zero
Plot both parts of the equation. The solution is the x-value of the point of intersection.
, for any integer
Do you need help with solving Solve Graphically 15cos(x)^2+8cos(x)+1=0? We can help you. You can write to our math experts in our application. The best solution for you is above on this page.
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http://www.spatialtectonics.com/index.php/lib/a-primer-on-wavelets-and-their-scientific-applications-second-edition
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math
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By James S. Walker
Within the first variation of his seminal advent to wavelets, James S. Walker proficient us that the capability functions for wavelets have been almost limitless. because that point hundreds of thousands of released papers have confirmed him real, whereas additionally necessitating the production of a brand new version of his bestselling primer. up-to-date and completely revised to incorporate the most recent advancements, this moment variation of A Primer on Wavelets and Their medical functions courses readers during the major rules of wavelet research so as to boost an intensive appreciation of wavelet purposes. Ingeniously hoping on basic algebra and only a smidgen of calculus, Professor Walker demonstrates how the underlying rules at the back of wavelet research will be utilized to unravel major difficulties in audio and photograph processing, to boot in biology and drugs. approximately two times so long as the unique, this re-creation offers · 104 labored examples and 222 routines, constituting a veritable publication of evaluate fabric · sections on biorthogonal wavelets · A mini-course on picture compression, together with an instructional on mathematics compression · wide fabric on snapshot denoising, that includes a not often lined strategy for elimination remoted, randomly located litter · Concise but whole insurance of the basics of time-frequency research, showcasing its program to audio denoising, and musical thought and synthesis · An advent to the multiresolution precept, a brand new mathematical notion in musical thought · accelerated feedback for study initiatives · An greater record of references · FAWAV: software program designed by means of the writer, which permits readers to copy defined functions and test with different principles. to maintain the ebook present, Professor Walker has created a supplementary web site. This on-line repository comprises ready-to-download software program, and sound and picture records, in addition to entry to a few of the most vital papers within the box.
Read Online or Download A Primer on Wavelets and Their Scientific Applications, Second Edition PDF
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This monograph is devoted to the derivation and research of fluid types taking place in plasma physics. It makes a speciality of versions concerning quasi-neutrality approximation, difficulties regarding laser propagation in a plasma, and coupling plasma waves and electromagnetic waves. utilized mathematicians will discover a stimulating creation to the area of plasma physics and some open difficulties which are mathematically wealthy.
This self-contained ebook is great for graduate-level classes dedicated to variational research, optimization, and partial differential equations (PDEs). It presents readers with a whole advisor to difficulties in those fields in addition to an in depth presentation of an important instruments and techniques of variational research.
Our function in scripting this monograph is twofold. at the one hand, we wish to acquire in a single position the various fresh effects at the exist ence and asymptotic habit of recommendations of definite periods of singularly perturbed nonlinear boundary price difficulties. at the different, we are hoping to elevate alongside the best way a few questions for additional examine, commonly ques tions we ourselves are not able to respond to.
V. G. Mazya is commonly considered as a very notable mathematician, whose paintings spans 50 years and covers many components of mathematical research. This quantity includes a particular number of papers contributed at the party of Mazya's seventieth birthday by means of a uncommon team of specialists of foreign stature within the fields of Harmonic research, Partial Differential Equations, functionality conception, Spectral research, and heritage of arithmetic, reflecting the cutting-edge in those components, within which Mazya himself has made a few of his most vital contributions.
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Extra resources for A Primer on Wavelets and Their Scientific Applications, Second Edition
F · g = 3(2) + 2(−2) − 1(2) + 4(−2) = −8. B Compute the inverse 1-level Haar transform of (a1 | d1 ) = (0, 1, 0, . . , 0 | 0, 0, . . , 0), and of (a1 | d1 ) = (0, 0, . . , 0 | 0, 1, 0, . . , 0). Solution. For transform of (0, 1, √ the inverse √ √0, . . , 0√| 0, 0, . . , 0), we find that f3 = d2 )/ √ 2 = 1/ 2 and all other values of f are (a2 + d2 )/ 2 = 1/ 2 and f4 = (a2 − √ 0. Thus the inverse transform is (0, 0, 2/2, 2/2, 0, 0, . . , 0). For transform of (0, 0,√. . , 0 | 0, 1,√0, . . , 0) we find that f3 = (a2 + √ the inverse √ )/ 2 = √ −1/ 2 and all other values of f are 0.
5. K. Heer and H-E Reinfelder. (1990). Comparison of reversible methods for data compression. In Medical Imaging IV, 354–365. Proceedings SPIE, No. 1233. 8 Examples and exercises Note: Computer exercises, designed for FAWAV, are indicated by a superscript c. 5 is a computer exercise. A subscript s means that a solution is provided. 1(a). Solutions are in Appendix B. A Find the first level Haar transform of f = (2, 2, 2, 4, 4, 4). Solution. The average of the first pair of values is 2, the average of the second pair of values is 3, these √ and the average of the √ third √ pair √ of values is 4.
1 For the following signals, f and g, compute their sum f + g, their difference f − g, and the combination 3f − 2g. 1, compute the first averaged signal A1 and the first detail signal D1 . 3 Find expressions for the first averaged signal A1 and the first detail signal D1 in terms of the values of f = (f1 , f2 , . . , fN ). 4 For each of the following signals, compute the first averaged signal A1 and the first detail signal D1 . 5 Express the 2nd averaged signal A2 and the 2nd detail signal D2 in terms of the values of f = (f1 , f2 , .
A Primer on Wavelets and Their Scientific Applications, Second Edition by James S. Walker
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https://text.123doc.net/document/4955486-fluid-mechanics-by-potter.htm
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math
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Want to learn more? We hope you enjoy this McGraw-Hill eBook! If you’d like more information about this book, its author, or related books and websites, please click here.
This book is intended to accompany a text used in that first course in fluid mechanics which is required in all mechanical engineering and civil engineering departments, as well as several other departments. It provides a succinct presentation of the material so that the students more easily understand those difficult parts. If an expanded presentation is not a necessity, this book can be used as the primary text. We have included all derivations and numerous applications, so it can be used with no supplemental material. A solutions manual is available from the authors at [email protected]. We have included a derivation of the Navier– Stokes equations with several solved flows. It is not necessary, however, to include them if the elemental approach is selected. Either method can be used to study laminar flow in pipes, channels, between rotating cylinders, and in laminar boundary layer flow. The basic principles upon which a study of fluid mechanics is based are illustrated with numerous examples, solved problems, and supplemental problems which allow students to develop their problem-solving skills. The answers to all supplemental problems are included at the end of each chapter. All examples and problems are presented using SI metric units. English units are indicated throughout and are included in the Appendix. The mathematics required is that of other engineering courses except that required if the study of the Navier– Stokes equations is selected where partial differential equations are encountered. Some vector relations are used, but not at a level beyond most engineering curricula. If you have comments, suggestions, or corrections or simply want to opine, please e-mail me at: [email protected]. It is impossible to write an error-free book, but if we are made aware of any errors, we can have them corrected in future printings. Therefore, send an email when you find one. MERLE C. POTTER DAVID C. WIGGERT
Introduction Pressure Variation Manometers Forces on Plane and Curved Surfaces Accelerating Containers
20 20 22 24 27
Introduction Fluid Motion 3.2.1 Lagrangian and Eulerian Descriptions 3.2.2 Pathlines, Streaklines, and Streamlines 3.2.3 Acceleration 3.2.4 Angular Velocity and Vorticity Classification of Fluid Flows 3.3.1 Uniform, One-, Two-, and Three-Dimensional Flows 3.3.2 Viscous and Inviscid Flows 3.3.3 Laminar and Turbulent Flows 3.3.4 Incompressible and Compressible Flows Bernoulli’s Equation
The Integral Equations 4.1 4.2 4.3 4.4 4.5
1 1 4 5 6 10
Fluids in Motion 3.1 3.2
Introduction Dimensions, Units, and Physical Quantities Gases and Liquids Pressure and Temperature Properties of Fluids Thermodynamic Properties and Relationships
Fluid Statics 2.1 2.2 2.3 2.4 2.5
Introduction System-to-Control-Volume Transformation Conservation of Mass The Energy Equation The Momentum Equation
39 39 39 40 41 42 45 46 46 47 48 49
60 60 60 63 64 67
Differential Equations 5.1 5.2 5.3 5.4
84 85 87 92
Dimensional Analysis and Similitude
6.1 6.2 6.3
97 97 102
Introduction Dimensional Analysis Similitude
Internal Flows 7.1 7.2 7.3
Introduction The Differential Continuity Equation The Differential Momentum Equation The Differential Energy Equation
Introduction Entrance Flow Laminar Flow in a Pipe 7.3.1 The Elemental Approach 7.3.2 Applying the Navier –Stokes Equations 7.3.3 Quantities of Interest Laminar Flow Between Parallel Plates 7.4.1 The Elemental Approach 7.4.2 Applying the Navier –Stokes Equations 7.4.3 Quantities of Interest Laminar Flow between Rotating Cylinders 7.5.1 The Elemental Approach 7.5.2 Applying the Navier –Stokes Equations 7.5.3 Quantities of Interest Turbulent Flow in a Pipe 7.6.1 The Semi-Log Profile 7.6.2 The Power-Law Profile 7.6.3 Losses in Pipe Flow 7.6.4 Losses in Noncircular Conduits 7.6.5 Minor Losses 7.6.6 Hydraulic and Energy Grade Lines Open Channel Flow
External Flows 8.1 8.2
Introduction Flow Around Blunt Bodies 8.2.1 Drag Coefficients 8.2.2 Vortex Shedding 8.2.3 Cavitation 8.2.4 Added Mass Flow Around Airfoils
Properties of Water English Properties of Water Properties of Air at Atmospheric Pressure English Properties of Air at Atmospheric Pressure Properties of the Standard Atmosphere
235 235 236 236 237
C.3E C.4 C.5
English Properties of the Atmosphere Properties of Ideal Gases at 300 K (cv ¼ cp k k ¼ cp =cv ) Properties of Common Liquids at Atmospheric Pressure and Approximately 16 to 21–C (60 to 70–F) Figure C.1 Viscosity as a Function of Temperature Figure C.2 Kinematic Viscosity as a Function of Temperature at Atmospheric Pressure
Compressible Flow Table for Air D.1 D.2 D.3
Isentropic Flow Normal Shock Flow Prandtl– Meyer Function
237 238 239 240 241
242 242 243 244
Basic Information 1.1
Fluid mechanics is encountered in almost every area of our physical lives. Blood flows through our veins and arteries, a ship moves through water and water flows through rivers, airplanes fly in the air and air flows around wind machines, air is compressed in a compressor and steam expands around turbine blades, a dam holds back water, air is heated and cooled in our homes, and computers require air to cool components. All engineering disciplines require some expertise in the area of fluid mechanics. In this book we will present those elements of fluid mechanics that allow us to solve problems involving relatively simple geometries such as flow through a pipe and a channel and flow around spheres and cylinders. But first, we will begin by making calculations in fluids at rest, the subject of fluid statics. The math requirement is primarily calculus but some differential equation theory will be used. The more complicated flows that usually are the result of more complicated geometries will not be presented in this book. In this first chapter, the basic information needed in our study will be presented. Much of it has been included in previous courses so it will be a review. But, some of it should be new to you. So, let us get started. 1.2
DIMENSIONS, UNITS, AND PHYSICAL QUANTITIES
Fluid mechanics, as all other engineering areas, is involved with physical quantities. Such quantities have dimensions and units. The nine basic dimensions are mass, length, time, temperature, amount of a substance, electric current, luminous intensity, plane angle, and solid angle. All other quantities can be expressed in terms of these basic dimensions, e.g., force can be expressed using Newton’s second law as F ¼ ma
In terms of dimensions we can write (note that F is used both as a variable and as a dimension) F¼M
where F, M, L, and T are the dimensions of force, mass, length, and time. We see that force can be written in terms of mass, length, and time. We could, of course, write M¼F
Units are introduced into the above relationships if we observe that it takes 1 N to accelerate 1 kg at 1 m=s2 (using English units it takes 1 lb to accelerate 1 slug at 1 ft=sec2), i.e., N ¼ kg·m=s2
lb ¼ slug-ft=sec2
These relationships will be used often in our study of fluids. Note that we do not use ‘‘lbf’’ since the unit ‘‘lb’’ will always refer to a pound of force; the slug will be the unit of mass in the English system. In the SI system the mass will always be kilograms and force will always be newtons. Since weight is a force, it is measured in newtons, never kilograms. The relationship W ¼ mg
is used to calculate the weight in newtons given the mass in kilograms, where g ¼ 9.81 m=s (using English units g ¼ 32.2 ft=sec2). Gravity is essentially constant on the earth’s surface varying from 9.77 to 9.83 m=s2. Five of the nine basic dimensions and their units are included in Table 1.1 and derived units of interest in our study of fluid mechanics in Table 1.2. Prefixes are common in the SI system so they are presented in Table 1.3. Note that the SI system is a special metric system; we will use the units presented Table 1.1 Quantity
Basic Dimensions and Their Units English
Table 1.2 Quantity
Derived Dimensions and Their Units
m3 or L (liter)
Angular velocity O
kg·m=s2 or N (newton)
slug-ft=sec2 or lb
N=m2 or Pa (pascal)
N=m2 or Pa (pascal)
Surface tension s
Specific weight g
N·m or J (joule)
N·m or J (joule)
Heat rate Q_
Table 1.2 Quantity
J=s or W (watt)
Torque T _ Power W
ML =T ML =T
Mass flux m_
Flow rate Q
Specific heat c
L =T Y
Kinematic viscosity n
Table 1.3 Multiplication factor 1012
SI Prefixes Prefix
10 10 10 10 10
in these tables. We often use scientific notation, such as 3 · 105 N rather than 300 kN; either form is acceptable. We finish this section with comments on significant figures. In every calculation, well, almost every one, a material property is involved. Material properties are seldom known to four significant figures and often only to three. So, it is not appropriate to express answers to five or six significant figures. Our calculations are only as accurate as the least accurate number in our equations. For example, we use gravity as 9.81 m=s2, only three significant figures. It is usually acceptable to express answers using four significant figures, but not five or six. The use of calculators may even provide eight. The engineer does not, in general, work with five or six significant figures. Note that if the leading numeral in an answer is 1, it does not count as a significant figure, e.g., 1248 has three significant figures. EXAMPLE 1.1 Calculate the force needed to provide an initial upward acceleration of 40 m=s2 to a 0.4-kg rocket. Solution: Forces are summed in the vertical y-direction: X Fy ¼ may F 2 mg ¼ ma F 2 0:4 · 9:81 ¼ 0:4 · 40 \ F ¼ 19:92 N Note that a calculator would provide 19.924 N, which contains four significant figures (the leading 1 does not count). Since gravity contained three significant figures, the 4 was dropped.
GASES AND LIQUIDS
The substance of interest in our study of fluid mechanics is a gas or a liquid. We restrict ourselves to those liquids that move under the action of a shear stress, no matter how small that shearing stress may be. All gases move under the action of a shearing stress but there are certain substances, like ketchup, that do not move until the shear becomes sufficiently large; such substances are included in the subject of rheology and are not presented in this book. A force acting on an area is displayed in Fig. 1.1. A stress vector is the force vector divided by the area upon which it acts. The normal stress acts normal to the area and the shear stress acts tangent to the area. It is this shear stress that results in fluid motions. Our experience of a small force parallel to the water on a rather large boat confirms that any small shear causes motion. This shear stress is calculated with DFt DA!0 DA
t ¼ lim
Figure 1.1 Normal and tangential components of a force.
Each fluid considered in our study is continuously distributed throughout a region of interest, that is, each fluid is a continuum. A liquid is obviously a continuum but each gas we consider is also assumed to be a continuum; the molecules are sufficiently close to one another so as to constitute a continuum. To determine whether the molecules are sufficiently close, we use the mean free path, the average distance a molecule travels before it collides with a neighboring molecule. If the mean free path is small compared to a characteristic dimension of a device (e.g., the diameter of a rocket), the continuum assumption is reasonable. In atmospheric air at sea level, the mean free path is approximately 6 · 1026 cm and at an elevation of 100 km, it is about 10 cm. So, at high elevations, the continuum assumption is not reasonable and the theory of rarified gas dynamics is needed. If a fluid is a continuum, the density can be defined as Dm DV!0 DV
r ¼ lim
where Dm is the infinitesimal mass contained in the infinitesimal volume DV. Actually, the infinitesimal volume cannot be allowed to shrink to zero since near zero there would be few molecules in the small volume; a small volume E would be needed as the limit in Eq. (1.7) for the definition to be acceptable. This is not a problem for most engineering applications since there are 2:7 · 1016 molecules in a cubic millimeter of air at standard conditions. So, with the continuum assumption, the quantities of interest are assumed to be defined at all points in a specified region. For example, the density is a continuous function of x, y, z, and t, i.e., r ¼ rðx,y,z,tÞ.
PRESSURE AND TEMPERATURE
In our study of fluid mechanics, we often encounter pressure. It results from compressive forces acting on an area. In Fig. 1.2 the infinitesimal force DFn acting on the infinitesimal area DA gives rise to the pressure, defined by p ¼ lim
The units on pressure result from force divided by area, that is, N=m2, the pascal, Pa. A pressure of 1 Pa is a very small pressure, so pressure is typically expressed as kilopascals or kPa. Using English units, pressure is expressed as lb=ft2 (psf) or lb=in2 (psi). Atmospheric pressure at sea level is 101.3 kPa, or most often simply 100 kPa (14.7 lb=in2). It should be noted that pressure is sometimes expressed as millimeters of mercury, as is common with meteorologists, or meters of water; we can use p ¼ rgh to convert the units, where r is the density of the fluid with height h.
Fn Surface A
The normal force that results in pressure.
Pressure measured relative to atmospheric pressure is called gage pressure; it is what a gage measures if the gage reads zero before being used to measure the pressure. Absolute pressure is zero in a volume that is void of molecules, an ideal vacuum. Absolute pressure is related to gage pressure by the equation pabsolute ¼ pgage þ patmosphere
where patmosphere is the atmospheric pressure at the location where the pressure measurement is made; this atmospheric pressure varies considerably with elevation and is given in Table C.3 in App. C. For example, at the top of Pikes Peak in Colorado, it is about 60 kPa. If neither the atmospheric pressure nor elevation are given, we will assume standard conditions and use patmosphere ¼ 100 kPa. Figure 1.3 presents a graphic description of the relationship between absolute and gage pressure. Several common representations of the standard atmosphere (at 40– latitude at sea level) are included in that figure. We often refer to a negative pressure, as at B in Fig. 1.3, as a vacuum; it is either a negative pressure or a vacuum. A pressure is always assumed to be a gage pressure unless otherwise stated (in thermodynamics the pressure is assumed to be absolute). A pressure of 230 kPa could be stated as 70 kPa absolute or a vacuum of 30 kPa, assuming atmospheric pressure to be 100 kPa (note that the difference between 101.3 and 100 kPa is only 1.3 kPa, a 1.3% error, within engineering acceptability). We do not define temperature (it requires molecular theory for a definition) but simply state that we use two scales: the Celsius scale and the Fahrenheit scale. The absolute scale when using temperature in degrees Celsius is the kelvin (K) scale and the absolute scale when using temperature in degrees Fahrenheit is the Rankine scale. We use the following conversions: K ¼ –C þ 273:15 – R ¼ –F þ 459:67
A ( pA )gage Standard atmosphere Atmospheric pressure
101.3 kPa 14.7 psi 30 in Hg 760 mm Hg 1.013 bar 34 ft water
pgage = 0
( pB )gage
( pA )absolute B
( pB )absolute Zero absolute pressure
pabsolute = 0
Figure 1.3 Absolute and gage pressure.
In engineering problems we use the numbers 273 and 460, which allows for acceptable accuracy. Note that we do not use the degree symbol when expressing the temperature in degrees kelvin nor do we capitalize the word ‘‘kelvin.’’ We read ‘‘100 K’’ as 100 kelvins in the SI system (remember, the SI system is a special metric system). EXAMPLE 1.2 A pressure is measured to be a vacuum of 23 kPa at a location in Wyoming where the elevation is 3000 m. What is the absolute pressure? Solution: Use Appendix C to find the atmospheric pressure at 3000 m. We use a linear interpolation to find patmosphere ¼ 70.6 kPa. Then, pabs ¼ patm þ p ¼ 70:6 2 23 ¼ 47:6 kPa The vacuum of 23 kPa was expressed as 223 kPa in the equation.
PROPERTIES OF FLUIDS
A number of fluid properties must be used in our study of fluid mechanics. Mass per unit volume, density, was introduced in Eq. (1.7). We often use weight per unit volume, the specific weight g, related to density by g ¼ rg ð1:11Þ where g is the local gravity. For water, g is taken as 9810 N=m3 (62.4 lb=ft3) unless otherwise stated. Specific weight for gases is seldom used. Specific gravity S is the ratio of the density of a substance to the density of water and is often specified for a liquid. It may be used to determine either the density or the specific weight: r ¼ Srwater
g ¼ Sgwater
As an example, the specific gravity of mercury is 13.6, which means that it is 13.6 times heavier than water. So, rmercury ¼ 13:6 · 1000 ¼ 13 600 kg=m3 , where we used the density of water to be 1000 kg=m3, the value used for water if not specified. Viscosity can be considered to be the internal stickiness of a fluid. It results in shear stresses in a flow and accounts for losses in a pipe or the drag on a rocket. It can be related in a one-dimensional flow to the velocity through a shear stress t by t¼m
where we call du=dr a velocity gradient, where r is measured normal to a surface and u is tangential to that surface, as in Fig. 1.4. Consider the units on the quantities in Eq. (1.13): the stress (force divided by an area) has units of N=m2 (lb=ft2) so that the viscosity has the units N·s=m2 (lb-sec=ft2). To measure the viscosity, consider a long cylinder rotating inside a second cylinder, as shown in Fig. 1.4. In order to rotate the inner cylinder with the rotational speed O, a torque T must be applied. The velocity of the inner cylinder is RO and the velocity of the outer cylinder is zero. The velocity distribution in the gap h between the cylinders is essentially a linear distribution as shown, so that t¼m
du RO ¼m dr h
u T R
Figure 1.4 Fluid being sheared between two long cylinders.
We can relate the shear to the applied torque as follows: T ¼ stress · area · moment arm ¼ t · 2pRL · R ¼m
RO R3 OLm · 2pRL · R ¼ 2p h h
where the shear acting on the ends of the long cylinder has been neglected. A device used to measure the viscosity is a viscometer. In this introductory book, we focus our attention on Newtonian fluids, those that exhibit a linear relationship between the shear stress and the velocity gradient, as in Eqs. (1.13) and (1.14), as displayed in Fig. 1.5. Many common fluids, such as air, water, and oil are Newtonian fluids. Non-Newtonian fluids are classified as dilatants, pseudoplastics, and ideal plastics and are also displayed. Ideal plastic
Dilatant Newtonian fluid Pseudoplastic
Figure 1.5 Newtonian and Non-Newtonian fluids.
A very important effect of viscosity is to cause the fluid to stick to a surface, the no-slip condition. If a surface is moving extremely fast, as a satellite entering the atmosphere, this no-slip condition results in very large shear stresses on the surface; this results in extreme heat which can burn up entering satellites. The no-slip condition also gives rise to wall shear in pipes resulting in pressure drops that require pumps spaced appropriately over the length of a pipe line transporting oil or gas. Viscosity is very dependent on temperature. Note that in Fig. C.1 in App. C, the viscosity of a liquid decreases with increased temperature but the viscosity of a gas increases with increased temperature. In a liquid the viscosity is due to cohesive forces but in a gas it is due to collisions of molecules; both of these phenomena are insensitive to pressure so we note that viscosity depends on temperature only in both a liquid and a gas, i.e., m ¼ m(T ). The viscosity is often divided by density in equations, so we have defined the kinematic viscosity to be m n¼ ð1:16Þ r It has units of m2=s (ft2=sec). In a gas we note that kinematic viscosity does depend on pressure since density depends on both temperature and pressure. The volume of a gas is known to depend on pressure and temperature. In a liquid, the volume also depends slightly on pressure. If that small volume change (or density change) is important, we use the bulk modulus B: B¼V
Dp Dp ¼r DV T Dr T
The bulk modulus has the same units as pressure. It is included in Table C.1 in App. C. For water at 20– C, it is about 2100 MPa. To cause a 1% change in the volume of water, a pressure of 21 000 kPa is needed. So, it is obvious why we consider water to be incompressible. The bulk modulus is also used to determine the speed of sound in water. It is given by pffiffiffiffiffi c ¼ B=r ð1:18Þ This yields about c ¼ 1450 m=s for water at 20– C. Another property of occasional interest in our study is surface tension s; it results from the attractive forces between molecules, and is included in Table C.1. It allows steel to float, droplets to form, and small droplets and bubbles to be spherical. Consider the free-body diagram of a spherical droplet and a bubble, as shown in Fig. 1.6. The pressure force inside the droplet balances the force due to surface tension around the circumference: ppr2 ¼ 2prs \p¼
Free-body diagrams of (a) a droplet and (b) a bubble.
Note that in a bubble there are two surfaces so that the force balance provides p¼
So, if the internal pressure is desired, it is important to know if it is a droplet or a bubble. A second application where surface tension causes an interesting result is in the rise of a liquid in a capillary tube. The free-body diagram of the water in the tube is shown in Fig. 1.7. Summing forces on the column of liquid gives spD cos b ¼ rg
pD2 h 4
where the right-hand side is the weight W. This provides the height the liquid will climb in the tube: h¼
4s cos b gD
D Air Liquid
The rise of a liquid in a small tube.
The final property to be introduced in this section is vapor pressure. Molecules escape and reenter a liquid that is in contact with a gas, such as water in contact with air. The vapor pressure is that pressure at which there is equilibrium between the escaping and reentering molecules. If the pressure is below the vapor pressure, the molecules will escape the liquid; it is called boiling when water is heated to the temperature at which the vapor pressure equals the atmospheric pressure. If the local pressure is decreased to the vapor pressure, vaporization also occurs. This can happen when liquid flows through valves, elbows, or turbine blades, should the pressure become sufficiently low; it is then called cavitation. The vapor pressure is found in Table C.1 in App. C. EXAMPLE 1.3 A 0:5 m · 2 m flat plate is towed at 5 m=s on a 2-mm-thick layer of SAE-30 oil at 38– C that separates it from a flat surface. The velocity distribution between the plate and the surface is assumed to be linear. What force is required if the plate and surface are horizontal? Solution: The velocity gradient is calculated to be du Du 5 2 0 ¼ ¼ ¼ 2500 m=ðs·mÞ dy Dy 0:002 The force is the stress multiplied by the area: F¼t·A¼m
du · A ¼ 0:1 · 2500 · 0:5 · 2 ¼ 250 N dy
Check the units to make sure the units of the force are newtons. The viscosity of the oil was found in Fig. C.1.
EXAMPLE 1.4 A machine creates small 0.5-mm-diameter bubbles of 20– C water. Estimate the pressure that exists inside the bubbles. Solution: Bubbles have two surfaces leading to the following estimate of the pressure: p¼
4s 4 · 0:0736 ¼ ¼ 589 Pa r 0:0005
where the surface tension was taken from Table C.1.
THERMODYNAMIC PROPERTIES AND RELATIONSHIPS
A course in thermodynamics and=or physics usually precedes a fluid mechanics course. Those properties and relationships that are presented in those courses that are used in our study of fluids are included in this section. They are of particular use when compressible flows are studied, but they also find application to liquid flows. The ideal gas law takes the two forms pV ¼ mRT
p ¼ rRT
where the pressure p and the temperature T must be absolute quantities. The gas constant R is found in Table C.4 in App. C. Enthalpy is defined as H ¼ mu~ þ pV
h ¼ u~ þ pv
where u~ is the specific internal energy. In an ideal gas we can use Z Z Dh ¼ cp dT and Du~ ¼ cv dT
where cp and cv are the specific heats also found in Table C.4. The specific heats are related to the gas constant by cp ¼ cv þ R
The ratio of specific heats is k¼
For liquids and solids, and for most gases over relatively small temperature differences, the specific heats are essentially constant and we can use Dh ¼ cp DT
Du~ ¼ cv DT
For adiabatic (no heat transfer) quasi-equilibrium (properties are constant throughout the volume at an instant) processes, the following relationships can be used for an ideal gas assuming constant specific heats: T2 p ¼ 2 T1 p1
p2 r ¼ 2 p1 r1
The adiabatic, quasi-equilibrium process is also called an isentropic process. A small pressure wave with a relatively low frequency travels through a gas with a wave speed of pffiffiffiffiffiffi c ¼ kRT ð1:30Þ Finally, the first law of thermodynamics will be of use in our study; it states that when a system, a fixed set of fluid particles, undergoes a change of state from state 1 to state 2, its energy changes from
E1 to E2 as it exchanges energy with the surroundings in the form of work W1---2 and heat transfer Q1---2 . This is expressed as Q1---2 2 W1---2 ¼ E2 2 E1
To calculate the heat transfer from given temperatures and areas, a course on heat transfer is required, so it is typically a given quantity in thermodynamics and fluid mechanics. The work, however, is a quantity that can often be calculated; it is a force times a distance and is often due to the pressure resulting in W1---2 ¼ ¼
Zl2 l1 Zl2 l1
F dl pA dl ¼
ð1:32Þ p dV
The energy E considered in a fluids course consists of kinetic energy, potential energy, and internal energy: ! V2 E¼m þ gz þ u~ ð1:33Þ 2 where the quantity in the parentheses is the specific energy e. (We use u~ to represent specific internal energy since u is used for a velocity component.) If the properties are constant at an exit and an entrance to a flow, and there is no heat transferred and no losses, the above equation can be put in the form V22 p2 V2 p þ þ z2 ¼ 1 þ 1 þ z1 2g g2 2g g1
This equation does not follow directly from Eq. (1.31); it takes some effort to derive Eq. (1.34). An appropriate text could be consulted, but we will derive it later in this book. It is presented here as part of our review of thermodynamics.
Solved Problems 1.1
Show that the units on viscosity given in Table 1.1 are correct using (a) SI units and (b) English units. Viscosity is related to stress by m¼t
In terms of units this is ½m ¼
N m N·s ¼ 2 2 m=s m m
lb ft lb-sec ¼ 2 ft=sec ft ft2
If force, length, and time are selected as the three fundamental dimensions, what are the dimensions on mass? We use Newton’s second law, which states that F ¼ ma In terms of dimensions this is written as F¼M
FT 2 L
The mean free path of a gas is l ¼ 0:225m=ðrd 2 Þ, where d is the molecule’s diameter, m is its mass, and r the density of the gas. Calculate the mean free path of air at 10 000 m elevation, the elevation where many commercial airplanes fly. For an air molecule d ¼ 3:7 · 10210 m and m ¼ 4:8 · 10226 kg. Using the formula given, the mean free path at 10 000 m is l ¼ 0:225 ·
4:8 · 10226 ¼ 8:48 · 1027 m or 0:848 mm 0:4136ð3:7 · 10210 Þ2
where the density was found in Table C.3.
A vacuum of 25 kPa is measured at a location where the elevation is 3000 m. What is the absolute pressure in millimeters of mercury? The atmospheric pressure at the given elevation is found in Table C.3. It is interpolated to be 1 patm ¼ 79:84 2 ð79:84 2 61:64Þ ¼ 70:7 kPa 2 The absolute pressure is then p ¼ pgage þ patm ¼ 225 þ 70:7 ¼ 45:7 kPa In millimeters of mercury this is h¼
p 45 700 ¼ ¼ 0:343 m or 343 mm rHg g ð13:6 · 1000Þ9:81
A flat 30-cm-diameter disk is rotated at 800 rpm at a distance of 2 mm from a flat, stationary surface. If SAE-30 oil at 20– C fills the gap between the disk and the surface, estimate the torque needed to rotate the disk. Since the gap is small, a linear velocity distribution will be assumed. The shear stress acting on the disk will be t¼m
Du ro rð800 · 2p=60Þ ¼m ¼ 0:38 · ¼ 15 900r Dy h 0:002
where the viscosity is found from Fig. C.1 in App. C. The shear stress is integrated to provide the torque: Z Z Z0:15 0:154 ¼ 12:7 N·m T¼ r dF ¼ rt2pr dr ¼ 2p 15 900r3 dr ¼ 105 · 4 A A 0 Note: The answer is not given to more significant digits since the viscosity is known to only two significant digits. More digits in the answer would be misleading.
Water is usually assumed to be incompressible. Determine the percentage volume change in 10 m3 of water at 15– C if it is subjected to a pressure of 12 MPa from atmospheric pressure. The volume change of a liquid is found using the bulk modulus of elasticity (see Eq. (1.17)): DV ¼ 2V
Dp 12 000 000 ¼ 20:0561 m3 ¼ 210 · B 214 · 107
The percentage change is % change ¼
V2 2 V1 20:0561 · 100 ¼ · 100 ¼ 20:561% V1 10
This small percentage change can usually be ignored with no significant influence on results, so water is essentially incompressible.
Water at 30– C is able to climb up a clean glass of 0.2-mm-diameter tube due to surface tension. The water-glass angle is 0– with the vertical (b ¼ 0 in Fig. 1.7). How far up the tube does the water climb? The height that the water climbs is given by Eq. (1.22). It provides h¼
4s cos b 4 · 0:0718 · 1:0 ¼ ¼ 0:147 m or 14:7 cm gD ð996 · 9:81Þ0:0002
where the properties of water come from Table C.1 in App. C.
Explain why it takes longer to cook potatoes by boiling them in an open pan on the stove in a cabin in the mountains where the elevation is 3200 m. Water boils when the temperature reaches the vapor pressure of the water; it vaporizes. The temperature remains constant until all the water is boiled away. The pressure at the given elevation is interpolated in Table C.3 to be 69 kPa. Table C.1 provides the temperature of slightly less than 90– C for a vapor pressure of 69 kPa, i.e., the temperature at which the water boils. Since it is less than the 100– C at sea level, the cooking process is slower. A pressure cooker could be used since it allows a higher temperature by providing a higher pressure inside the cooker.
A car tire is pressurized in Ohio to 250 kPa when the temperature is 215– C. The car is driven to Arizona where the temperature of the tire on the asphalt reaches 65– C. Estimate the pressure in the tire in Arizona assuming no air has leaked out and that the volume remains constant. Assuming the volume does not change, the ideal gas law requires p2 mRV1 T2 T2 ¼ ¼ p1 mRV2 T1 T1 \ p2 ¼ p1
since the mass also remains constant. (This corresponds to 37 lb=in2 in Ohio and 70 lb=in2 in Arizona.)
A farmer applies nitrogen to a crop from a tank pressurized to 1000 kPa absolute at a temperature of 25– C. What minimum temperature can be expected in the nitrogen if it is released to the atmosphere? The minimum exiting temperature occurs for an isentropic process (see Eq. (1.29)), which is T2 ¼ T1
¼ 298 ·
¼ 154 K or 2 119– C
Such a low temperature can cause serious injury should a line break and nitrogen impact the farmer.
Supplementary Problems 1.11
There are three basic laws in our study of fluid mechanics: the conservation of mass, Newton’s second law, and the first law of thermodynamics. (a) State an integral quantity for each of the laws and (b) state a quantity defined at a point for each of the laws.
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http://arcaro.org/ffshell/index.htm
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This text presents a mathematical modeling to the shape definition of shell structures through the use of mathematical programming techniques combined with the finite element method. It includes a total Lagrangian description of a flexible membrane element using the Green strain definition and assuming a linear elastic material. The model allows the shape definition of shell structures with any horizontal projection. The shapes are generated by loading an initially plane flexible membrane. The model allows the use of concentrated forces, distributed forces, uniform pressure and also non-zero displacement prescriptions.
Download the complete text as MS-Word and PDF documents and computer source codes written in Ada95. The computer codes generate an ANSYS data file using the SOLID65 element (3D Reinforced concrete solid) and also a script file for AutoCAD.
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https://www.coursehero.com/file/194743/hw2/
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Unformatted text preview: 10708 Graphical Models: Homework 2 Due October 17th, beginning of class October 3, 2005 1 [15 pts] Clique Tree I-maps In order to formalize the relationship between clique trees and Bayesian Networks, in this question you will prove that if P factorizes according to a Bayesian Network, then any clique tree T for this BN is an I-map for P . Specifically; In a clique tree, consider a separator S ij between two cliques C i and C j . Let X be any set of variables in the C i side of the tree, and Y be any set of variables in the C j side of the tree. Prove that P | = ( X ⊥ Y | S ij ). 2 [15 pts] Clique Tree Factorization 2.1 [7 pts] Prove that the clique beliefs π ( C i ) = P ( C i ) and edge beliefs μ ij ( S ij ) = P ( S ij ) form a fixed point for the belief propagation algorithm for a clique tree, i . e . , if we start BP with these beliefs, no messages will change them. 2.2 [8 pts] Using the independencies you showed in Question 1, prove that in a clique tree for a BN we can represent the joint distribution by: P ( X ) = producttext i P ( C i ) producttext ij P ( S ij ) . You should not “prove” by corollary from the correctness of BP in clique trees. (Hint: combine the chain rule of probabilities with the definition of conditional probabilities.) 1 3 [6 pts] Triangulation 3.1 [3 pts] A C F G E B D Figure 1: Moralized Graph for Prob. 2.1 Consider the graph in Figure 1.Consider the graph in Figure 1....
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This note was uploaded on 05/25/2008 for the course MACHINE LE 10708 taught by Professor Carlosgustin during the Fall '07 term at Carnegie Mellon.
- Fall '07
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| 1,735 | 5 |
https://byjus.com/maths/square-root-of-20/
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math
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The value of the square root of 20 is 4.472135955 and is denoted as √20 in radical form. This value we can easily get from the calculator. But, students should know how to simplify the root of any number without using a calculator. This is possible by using two methods: Prime factorisation and long division method. Both methods are very simple and are easy ways to find the square root.
Square root of 20, √20 = 4.4721 (in round figures)
The square root of 20 is represented as √20, where √ is the radical sign and 20 is said to be radicand. In the simplest form, the √20 can be written as 2√5. Therefore, here we cannot say that √20 is a rational number since √5 is an irrational number.
Now, let us learn here to find the value of √20.
Simplification of Square Root of 20
The simple method to find the value of √20 is to factorise the number under the root, i.e. 20.
The prime factorisation of 20 gives:
20 = 2 x 2 x 5 = 22 x 5
Thus, here we can see, 20 is not a perfect square, because we cannot pair digit 5 after factoring 20. Only 22 can be taken out of the root.
Hence, if we take the roots on both sides, we get;
√20 = √(2 x 2 x 5)
Here, we just have only one pair of numbers, which is 2. Therefore, taking it outside the root, we get;
√20 = 2√5
From the square root table, we know the value of √5 = 2.236
√20 = 2 x 2.236
√20 = 4.472
Using Long Division Method
We have learned to calculate the value of the square root of 20 using prime factorisation. But it is not a direct method to find the value because 20 is an imperfect square and we need to remember the √5 value to find the accurate value of √20.
By using long division method, we can use the accurate value of √20. Below is the solved step presented to evaluate √20.
Video Lessons on Square Roots
Visualising square roots
Finding Square roots
Find more square roots here:
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https://ctan.org/pkg/concmath-fonts
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math
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concmath-fonts – Concrete mathematics fonts
The fonts are derived from the computer modern mathematics fonts and from Knuth's Concrete Roman fonts; they are distributed as METAFONT source. LaTeX support is offered by the concmath package.
|Licenses||The LaTeX Project Public License|
|Copyright||1995–1999 Ulrik Vieth|
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Download the contents of this package in one zip archive (80.2k).
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http://cogsci.stackexchange.com/questions/tagged/computational-modeling+neurogenesis
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Cognitive Sciences Meta
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Neural networks with biologically plausible accounts of neurogenesis
One of the reasons artificial neural net algorithms like cascade correlation (pdf) have been generating interest is because they start with a minimal topology (just input and output unit) and recruit ...
Jan 31 '12 at 2:46
newest computational-modeling neurogenesis questions feed
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https://publications.hse.ru/en/articles/420284567
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math
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The multiplicative-additive Lambek calculus with subexponential and bracket modalities
We give a proof-theoretic and algorithmic complexity analysis for systems introduced by Morrill to serve as the core of the CatLog categorial grammar parser. We consider two recent versions of Morrill’s calculi, and focus on their fragments including multiplicative (Lambek) connectives, additive conjunction and disjunction, brackets and bracket modalities, and the ! subexponential modality. For both systems, we resolve issues connected with the cut rule and provide necessary modifications, after which we prove admissibility of cut (cut elimination theorem). We also prove algorithmic undecidability for both calculi, and show that categorial grammars based on them can generate arbitrary recursively enumerable languages.
The Lambek calculus can be considered as a version of non-commutative intuitionistic linear logic. One of the interesting features of the Lambek calculus is the so-called “Lambek’s restriction,” that is, the antecedent of any provable sequent should be non-empty. In this paper we discuss ways of extending the Lambek calculus with the linear logic exponential modality while keeping Lambek’s restriction. We present several versions of the Lambek calculus extended with exponential modalities and prove that those extensions are undecidable, even if we take only one of the two divisions provided by the Lambek calculus.
We consider the quantifier-free languages, Bc and Bc°, obtained by augmenting the signature of Boolean algebras with a unary predicate representing, respectively, the property of being connected, and the property of having a connected interior. These languages are interpreted over the regular closed sets of Rn (n ≥ 2) and, additionally, over the regular closed semilinear sets of Rn. The resulting logics are examples of formalisms that have recently been proposed in the Artificial Intelligence literature under the rubric Qualitative Spatial Reasoning. We prove that the satisfiability problem for Bc is undecidable over the regular closed semilinear sets in all dimensions greater than 1, and that the satisfiability problem for Bc and Bc° is undecidable over both the regular closed sets and the regular closed semilinear sets in the Euclidean plane. However, we also prove that the satisfiability problem for Bc° is NP-complete over the regular closed sets in all dimensions greater than 2, while the corresponding problem for the regular closed semilinear sets is ExpTime-complete. Our results show, in particular, that spatial reasoning is much harder over Euclidean spaces than over arbitrary topological spaces.
Modal logics, both propositional and predicate, have been used in computer science since the late 1970s. One of the most important properties of modal logics of relevance to their applications in computer science is the complexity of their satisfiability problem. The complexity of satisfiability for modal logics is rather high: it ranges from NP-complete to undecidable for propositional logics and is undecidable for predicate logics. This has, for a long time, motivated research in drawing the borderline between tractable and intractable fragments of propositional modal logics as well as between decidable and undecidable fragments of predicate modal logics. In the present thesis, we investigate some very natural restrictions on the languages of propositional and predicate modal logics and show that placing those restrictions does not decrease complexity of satisfiability. For propositional languages, we consider restricting the number of propositional variables allowed in the construction of formulas, while for predicate languages, we consider restricting the number of individual variables as well as the number and arity of predicate letters allowed in the construction of formulas. We develop original techniques, which build on and develop the techniques known from the literature, for proving that satisfiability for a finite-variable fragment of a propositional modal logic is as computationally hard as satisfiability for the logic in the full language and adapt those techniques to predicate modal logics and prove undecidability of fragments of such logics in the language with a finite number of unary predicate letters as well as restrictions on the number of individual variables. The thesis is based on four articles published or accepted for publication. They concern propositional dynamic logics, propositional branchingand alternating-time temporal logics, propositional logics of symmetric rela tions, and first-order predicate modal and intuitionistic logics. In all cases, we identify the “minimal,” with regard to the criteria mentioned above, fragments whose satisfiability is as computationally hard as satisfiability for the entire logic.
We use proof-nets to study the algorithmic complexity of the derivability problem for some fragments of the Lambek calculus. We prove the NP-completeness of this problem for the unidirectional fragment and the product-free fragment, and also for versions of these fragments that admit empty antecedents.
In this paper we prove that the derivability problems for product-free Lambek calculus and product-free Lambek calculus allowing empty premises are NP-complete. Also we introduce a new derivability characterization for these calculi.
A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traffic is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the final node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a finite-dimensional system of differential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of differential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.
Event logs collected by modern information and technical systems usually contain enough data for automated process models discovery. A variety of algorithms was developed for process models discovery, conformance checking, log to model alignment, comparison of process models, etc., nevertheless a quick analysis of ad-hoc selected parts of a journal still have not get a full-fledged implementation. This paper describes an ROLAP-based method of multidimensional event logs storage for process mining. The result of the analysis of the journal is visualized as directed graph representing the union of all possible event sequences, ranked by their occurrence probability. Our implementation allows the analyst to discover process models for sublogs defined by ad-hoc selection of criteria and value of occurrence probability
The geographic information system (GIS) is based on the first and only Russian Imperial Census of 1897 and the First All-Union Census of the Soviet Union of 1926. The GIS features vector data (shapefiles) of allprovinces of the two states. For the 1897 census, there is information about linguistic, religious, and social estate groups. The part based on the 1926 census features nationality. Both shapefiles include information on gender, rural and urban population. The GIS allows for producing any necessary maps for individual studies of the period which require the administrative boundaries and demographic information.
Existing approaches suggest that IT strategy should be a reflection of business strategy. However, actually organisations do not often follow business strategy even if it is formally declared. In these conditions, IT strategy can be viewed not as a plan, but as an organisational shared view on the role of information systems. This approach generally reflects only a top-down perspective of IT strategy. So, it can be supplemented by a strategic behaviour pattern (i.e., more or less standard response to a changes that is formed as result of previous experience) to implement bottom-up approach. Two components that can help to establish effective reaction regarding new initiatives in IT are proposed here: model of IT-related decision making, and efficiency measurement metric to estimate maturity of business processes and appropriate IT. Usage of proposed tools is demonstrated in practical cases.
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https://izofile.com/wolfram-mathematica-11-crack/
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Wolfram mathematica 11 crack Final Release is the world best software used to do complexe calculation. It started 30 years early, students, educators, and also teachers need a complete environment. So wolfram mathematica download was the first to make a complete software to help people doing simple and also higher mathematics calculation.
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Updated On: 20-06-2022
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Hey all, new to the fourm and this particular machine. I noticed underneath the machine where it seems to me that there should be some kind of plate/inspection cover, it is completely exposed. Is this meant to be like this from the factory? Any help would be appreciated. The salesman at the dealer says that they are made like this, but i am a bit skeptical given the dust/debris that would get in there when bushhogging, etc. Sorry for the newbie question. Thank you.
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Can you solve this math problem
Here, we debate how Can you solve this math problem can help students learn Algebra. We can solving math problem.
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Can you solve this math problem can help students to understand the material and improve their grades. Precalculus is a course that students take in high school to prepare for calculus. It builds on concepts from algebra and geometry, and introduces new concepts such as limits, derivatives, and integrals. Because of the broad range of topics covered in precalculus, many students find it to be a challenging course. If you are struggling with precalculus, there are a number of resources that can help you. One option is to use a precalculus problem solver. These online tools can quickly generate solutions to specific problems, and they can also provide step-by-step explanations of how the solutions were derived. This can be a valuable resource for understanding difficult concept. In addition, there are a number of websites and books that offer general guidance on solving precalculus problems. These resources can help you to develop your problem-solving skills and confidence. With some practice, you will be able to tackle even the most challenging precalculus problems.
Math can be a tough subject for a lot of students. Word problems in particular can be tricky, since they often require students to use a variety of Math concepts in order to solve them. Luckily, there are a number of online Math word problem solvers that can help. These websites allow students to enter a word problem and receive step-by-step instructions on how to solve it. In addition, many of these websites also provide helpful Math tools, such as calculators and conversion charts. As a result, Math word problem solver websites can be a valuable resource for students who are struggling with Math word problems.
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Imagine being able to simply take a picture of a math word problem and have the answer pop up on your screen almost instantaneously. That's what one new app promises to do. The app, called PhotoMath, uses the camera on your smartphone or tablet to take a picture of a math problem and then displays the answer. Just point your camera at a problem and PhotoMath will do the rest. The app can solve problems ranging from simple addition and subtraction to more complex equations involving fractions and decimals. It can even handle problems that require multiple steps, such as long division. And if you're not satisfied with the answer it gives you, PhotoMath also provides step-by-step instructions for how to solve the problem. PhotoMath is still in its early stages, so it doesn't always get things right. But it shows promise as a tool that could one day make solving math problems a breeze. So if you're struggling with a math problem, why not give PhotoMath a try? It just might be the answer you're looking for.
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https://www.studypug.com/physics-help/rotational-kinetic-energy-and-angular-momentum
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math
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Objects rotating about an axis possess “Rotational Kinetic Energy”
Objects moving along a straight line possess “Translational Kinetic Energy”.
Translational kinetic energy is calculated using, 21mv2
, we can convert this formula to rotational kinetic energy question using the rotational motion analogues:
If we consider a rotating ball, every point on the ball is rotating with some speed.
The ball is made up many tiny particles, each of mass “m”. let’s take “r” to be the distance of any one particle from the axis of rotation (O);
⇒ rotational KE=21Iω2
The center of mass of a rotating object might undergo translational motion (a sphere rolling down an incline), in this case we have to consider both rotational and translational kinetic energy.
M: total mass of the object
ICM: moment of inertia about the axis through center of mass
v: translational speed
ω: angular speed
In the previous section, we used the rotational analogue to translate the translational kinetic energy to rotational kinetic energy.
In like manner, the linear momentum can be changed to angular momentum, using the rotational analogues;
L: is the angular momentum with a standard unit of kg.m2/s
Newton’s 2nd Law for Rotation
The Newton’s 2nd law also can be written in terms of rotational analogues;
∑F=ma=ΔtmΔv=ΔtΔp, in translational motion “Force” causes linear acceleration
Similarly for rotational motion , ∑=ΔtΔL
∑τ=ΔtΔL=ΔtIΔω=I∝, in rotational motion “Torque” causes rotational acceleration
∑F=ma Newton’s 2nd Law in Translational Motion
∑τ=I∝ Newton’s 2nd Law in Rotational Motion
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Open arms: Li=Iωi=mri2ωi Closed arms: Lf=Iωf=mrf2ωf
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A sphere of radius 24.0 cm and mass of 1.60 kg, starts from the rest and rolls without slipping down a 30.0° incline that is 12.0m long.
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https://open.library.ubc.ca/soa/cIRcle/collections/ubctheses/24/items/1.0380808
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math
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UBC Theses and Dissertations
Interference in complex quantum systems : from localization in high-dimensional lattices to surface spin echo with molecules Cantin, Joshua Tyler
This thesis considers (1) novel manifestations and applications of quantum interference in complex systems and (2) development of new approaches to study complex quantum systems. First, I examine a general model of particles with long-range hopping amplitudes. For at least 30 years, it has been widely accepted that these particles do not undergo Anderson localization in 3D lattices. We show that these particles do undergo Anderson localization in 3D lattices if their hopping amplitudes are isotropic. In contrast, particles with anisotropic long-range hopping appear to follow the widely held expectations. We show these results by demonstrating that cooperative shielding extends to 3D cubic lattices with isotropic long-range hopping, but not with anisotropic long-range hopping and by computing the scaling behaviour of participation ratios and energy level statistics. Secondly, I develop a fully quantum mechanical model of molecular surface spin-echo experiments, which study surface properties and dynamics by scattering molecules off the sample surface. This model, based on the transfer matrix method, incorporates molecular hyperfine degrees of freedom, allows for the efficient calculation of the experimental signal given a molecule-surface scattering matrix, and permits us to begin addressing the inverse scattering problem. This fully quantum model is required to properly describe these experiments as the semi-classical methods used to describe experiments using helium-3 atoms do not take magnetic-field induced momentum changes into account. We apply our method to the case of ortho-hydrogen and then apply Bayesian optimization to determine the molecule-surface scattering matrix elements from a calculated signal, for a scattering matrix defined by three parameters. Our work sets the stage for Bayesian optimization to solve the inverse scattering problem for these experiments. Finally, I propose using Bayesian model calibration to improve the convergence of Monte Carlo calculations in regions where the sign problem or critical slowing down are an issue. Specifically, Bayesian model calibration would correct poorly converged Monte Carlo calculations with the information from a small number of well-converged Monte Carlo calculations. As a simple proof of principle demonstration, we apply Bayesian model calibration to a diagrammatic Monte Carlo calculation of the scattering length of a spherical potential barrier.
Item Citations and Data
Attribution-NonCommercial-NoDerivatives 4.0 International
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CC-MAIN-2023-40
| 2,707 | 5 |
https://sites.wit.edu/lit/whats-average-part-1-how-does-blackboard-calculate-an-average/
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math
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Common problems and questions crop up every term around grading. Often grades don’t seem to be calculated correctly and we are asked if there is a bug. The most common reason grades don’t match expectations is that there is a mis-match between how Blackboard performs calculations and how an instructor/student thinks the calculation should be performed.
Calculated Columns – What’s the math behind the columns?
Blackboard has four types of calculated columns, min/max, total, average, and weighted. Not surprisingly, each of these column types calculates differently. Min/max and total columns are the easiest to understand and cause the least confusion. Min/max columns select the smallest or largest values from selected columns. Total columns add up points from specified columns. The only tricky point about Total columns is the automatically generated Total column that appears by default in the grade center. That column is set to include all columns that have been set to “include in grade center calculations.” In fact, the default for a total column is to “include all grade center columns” unless you select “use selected columns.”
Average and weighted cause the bulk of our calls about miscalculations. Averages can be equal or weighted. And weighted columns can have weights on categories (which can be averaged equally or proportionally). Often, we see calculations that are identified as an average but it’s unclear whether the intent is a weighted average or equal average.
For example, let’s consider a midterm grade calculation for the following grades:
- Homework 1 – 80%
- Homework 2 – 100%
- Homework 3 – 60%
- Homework 4 – 80%
- Project topic – 100%
- Project annotated references – 80%
What would the average of these grades be? Most of us would calculate a simple unweighted average (add the grades up and divide by 6) and arrive at a midterm average of 83.3%.
But what about these grades:
- Homework 1 – 4 out of 5 points
- Homework 2 – 5 out of 5 points
- Homework 3 – 3 out of 5 points
- Homework 4 – 12 out of 15 points
- Project topic – 5 out of 5 points
- Project annotated references – 4 out of 5 points
What would be the average of these scores? Would the average be 85.2 % or 83.3 %?
(4 + 5 +3 +12 +5 + 4) ÷ 40 = 0.825 or 82.5%
[(4/5) + (5/5) + (3/5) + (12/15) + (5/5) + (4/5)] ÷ 6 = 0.833 or 83.3%
Both calculations are mathematically correct calculations, however the first weights homework 4 more heavily because it is worth more points. The second calculation is an unweighted average. Dividing each score by the points possible normalizes the values so they are equal in weight. So, which type of average you want, determines the calculation you choose, and which column type you choose in Blackboard. It’s also important to communicate to students how you calculate the average so that they can better understand how they are doing in your course.
So, in Blackboard, choosing to calculate a midterm grade with an average column means you are selecting an unweighted average (all grades count equally), irrespective of what the point values are for each assignment (the second calculation). If you really want homework 4 to count more than the other grades, you need to use a weighted column.
Weighted columns in Blackboard allow you several options not available with the simple average column. First, you can have columns with different possible points weighted based on the points possible (proportional weighting). Second, if you use categories, you can drop grades or base grades on category weights.
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| 3,595 | 25 |
http://sriramdoor.com/download/differential-geometry-reconstructed
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math
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By Kennington A.
Read Online or Download Differential geometry reconstructed PDF
Similar geometry and topology books
Utilizing an encouraged blend of geometric good judgment and metaphors from primary human event, Bucky invitations readers to hitch him on a visit via a 4-dimensional Universe, the place options as different as entropy, Einstein's relativity equations, and the that means of life develop into transparent, comprehensible, and instantly concerning.
Peg Rawes examines a "minor culture" of aesthetic geometries in ontological philosophy. constructed via Kant’s aesthetic topic she explores a trajectory of geometric considering and geometric figurations--reflective topics, folds, passages, plenums, envelopes and horizons--in old Greek, post-Cartesian and twentieth-century Continental philosophies, wherein efficient understandings of area and embodies subjectivities are developed.
This quantity gathers the contributions from the overseas convention "Intelligence of Low Dimensional Topology 2006," which came about in Hiroshima in 2006. the purpose of this quantity is to advertise study in low dimensional topology with the focal point on knot conception and comparable subject matters. The papers comprise complete studies and a few most up-to-date effects.
- Geometrie generale
- Vorlesungen ueber hoehere Geometrie, 3rd Edition
- Cartan for Beginners: Differential Geometry Via Moving Frames and Exterior Differential Systems
- Problemas de Geometría Diferencial
Extra resources for Differential geometry reconstructed
Or is mathematics merely a local culture which is propagated in our civilisation more or less in the manner of natural languages? Is there any sense in which anything in mathematics can be said to be certainly true in an absolute sense? Or is all mathematics merely a socially defined behaviour? To what extent is our mathematics a consequence of the peculiar capabilities of the human brain? Would a more advanced species use a totally different (and superior) mathematics? Since the real number system seems to be a consequence of our system of physical measurements, what is the significance of the absurdly large infinity of elements of the set of real numbers?
7 Remark: The network of mathematical concepts requires coherence. Although the network of mathematical concepts cannot be defined in the sense of deriving all concepts from other concepts in an acyclic manner, the concept network can at least be coherent. 1. Coherence is not the same as logical self-consistency. The latter means that the concept network is tested with respect to a deductive logic framework which is established external to the network. In the situation considered here, the logical framework is part of the concept network which is being tested.
Philosophical considerations The idea that all imperfect physical-world circles are striving towards a single Ideal circle form in a perfect Form-world is quite seductive. 19. Should combine or at least collocate them. 2 Remark: A plausible argument in favour of a Platonic-style ontology for mathematics. A plausible argument may be made in favour of Platonic ontology for the integers in the following form. (1) Numbers written on paper must refer to something. (2) Numbers do not correspond exactly to anything in the sensible world.
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http://udobuv.ru/kindle/a-bayesian-procedure-for-the-sequential-estimation-of-the-mean-of-a
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math
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By Marcus R.
Read Online or Download A Bayesian procedure for the sequential estimation of the mean of a negative-binomial distribution PDF
Best probability books
The elemental query of characterizing continuity and boundedness of Gaussian strategies is going again to Kolmogorov. After contributions through R. Dudley and X. Fernique, it was once solved by means of the writer. This e-book offers an summary of "generic chaining", a totally typical edition at the rules of Kolmogorov.
Welcome to new territory: A path in chance types and statistical inference. the idea that of chance isn't new to you in fact. you have encountered it considering the fact that adolescence in video games of chance-card video games, for instance, or video games with cube or cash. and also you learn about the "90% likelihood of rain" from climate studies.
Additional info for A Bayesian procedure for the sequential estimation of the mean of a negative-binomial distribution
1 even though there are many reasons for allowing relationships to be nonlinear, there are reasons for not testing the nonlinear components for significance, as this might tempt the analyst to simplify the model. 158 Testing for linearity is usually best done to justify to nonstatisticians the need for complexity to explain or predict outcomes. 2. , X 1 X 2 ) can be added to the model and its coefficient tested. 36) and testing H 0 : (33 = ... = (37 = 0. This formulation allows the shape of the X2 effect to be completely different for each level of X 1 .
Formal tests of no overall association, linearity, and additivity can readily be constructed. Confidence limits for the estimated regression function are derived by standard theory. 3. The fitted spline function directly estimates the transformation that a predictor should receive to yield linearity in C(YIX). , square root) of a predictor that can be used if one is not concerned about the proper number of degrees of freedom for testing association of the predictor with the response. 4. The spline function can be used to represent the predictor in the final model.
Disadvantages: Does not easily apply to censored Y, and does not easily handle multiple predictors. 5. Fit a flexible parametric model that allows for most of the departures from the linear additive model that you wish to entertain. Advantages: One framework is used for examining the model assumptions, fitting the model, and drawing formal inference. " Disadvantages: Complexity, and it is generally difficult to allow for interactions when assessing patterns of effects. The first four methods each have the disadvantage that if confidence limits or formal inferences are desired it is difficult to know how many degrees of freedom were effectively used so that, for example, confidence limits will have the stated coverage probability.
A Bayesian procedure for the sequential estimation of the mean of a negative-binomial distribution by Marcus R.
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https://freegraphpapers.com/isometric-graph-paper/
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math
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The Isometric graph paper is a type of graph paper in which the angles of the grid lines at each point are equal. It is an appropriate choice for those who want to create three-dimensional graphs. It is typically used in mathematics and engineering applications where it allows a three-dimensional representation of a two-dimensional object on paper.
Isometric Graph Paper
It offers more space for comparing two sets of data than just two dimensions would, as well as better explanations for data that would otherwise be difficult to interpret with traditional graph paper and coordinate grids.
What is the importance of Isometric graph paper?
Isometric graph paper is a more convenient way to create graphs than other methods of making them such as coordinate graph paper, and its use has become widespread. It can be used in place of a conventional set of parallel coordinates or hyperbolic coordinates to simplify many common problems in mathematics, engineering and design while also providing new methods of working with such data.
Full Page Isometric Graph Paper
In most applications, the graph paper has 90 or 45 degree intervals to improve readability and give engineers an easier way to compare symmetrical and asymmetrical data. The equal angles at each point help make it much simpler for students and others to understand the relationships between points, which is useful for data that can have very different properties depending on which angle is chosen for each one.
Isometric Grid Paper Printable
Feature of Isometric graph paper :
1. Isometric graph paper is inexpensive and convenient to use :
Isometric graph paper comes in many forms, the most common of which are printed grid sheets that can be purchased inexpensively at most office supply stores. Specialized isometric or other graphing software can also be purchased for use on a computer. Isometric graph paper is also less fragile than conventional graph paper because it does not have lines that intersect as many times, making it ideal for anyone who needs to take data from one place to another.
2. Isometric graph paper is easy to use :
Isometric graph paper is designed in a way that makes it very easy to create graphs. It has the same basic format as other types of graph paper, with grid lines on each side, with the lines being spaced further apart at the two edges and closer together at the centre. Anyone who has spent much time with conventional graph paper or coordinate grids can easily pick up how to use an isometric grid given a little practice and experimentation.
Isometric Graph Paper 8 1/2 x 11
3. Isometric graph paper is easy to read :
Isometric graph paper may look different from conventional graph paper at first glance, but it is small differences that end up making a big difference when it comes to how easy the two types of papers are to read and understand. The main difference involves the angles at which each set of grid lines connects, with conventional graph paper typically having 45-degree angles and isometric graph paper having 90 or 45-degree angles instead.
What is the purpose of Isometric graph paper?
Isometric graph paper is designed to make it easier to understand and compare sets of data in a clear, easy-to-read format. It can be used for many different types of data, including anything from angles to weights and measurements. Its ability to provide three dimensions on a piece of paper is especially helpful when trying to explain complex mathematical formulas or show how an object might look from various angles.
Printable Isometric Graph Paper Landscape
Isometric graph paper is most commonly used in maths, engineering, and science classes. It is used to show calculations that would be difficult on a two-dimensional plane graph. It can be useful for graphing anything from trigonometry functions to the phases of the moon. Isometric graph paper is also used to show how an object might transform into another object depending on which way it is rotated, making it a good choice for artists and others who want a visual representation of the third dimensions of an object.
Isometric graph paper has grown in popularity over the last several decades as people have become more interested in learning about the three dimensions of objects, formulas, and other data. It has been used for many types of data. Since its invention several decades ago, and it is likely that its use will continue to grow for both personal and business uses.
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CC-MAIN-2023-14
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http://www.wyzant.com/Ames_IA_Math_tutors.aspx
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math
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Ames, IA 50014
Anna - Experienced Mathematics Tutor
My name is Anna and I love math
ematics! I have over eleven years of math
ematics tutoring experience at all levels, from elementary school math
to Algebra to Calculus to Linear Algebra. I am a certified teacher and have two years of secondary teaching experience...
algebra 1, algebra 2, calculus
| 8 other subjects
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s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1410657129407.88/warc/CC-MAIN-20140914011209-00162-ip-10-196-40-205.us-west-1.compute.internal.warc.gz
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CC-MAIN-2014-41
| 368 | 8 |
https://allthetrivia.com/how-many-letters-are-in-the-alphabet/
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math
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How many letters are in the alphabet?
There are 26 letters in the English alphabet. The letters are: A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, and Z. These letters are used to create words, which are the building blocks of language. Learning the alphabet and the sounds associated with each letter is an important part of early childhood education and language development.
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| 406 | 2 |
http://www.physicsforums.com/showthread.php?t=252761
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math
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|Aug30-08, 11:01 PM||#1|
ti 89 program for vector calculus?
Hi, im not sure where this thread should belong.
Im wondering, is there any ti89 program that does vector calculus, not only in cartesian but in cylindricla and spherical coordinates too? Like i want to symbolically calculate the curl of a vector function thats in crlindrical or spherical coordinates. This is for my electrodynamics course.
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|Vector Calculus||Calculus & Beyond Homework||1|
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s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368703057881/warc/CC-MAIN-20130516111737-00075-ip-10-60-113-184.ec2.internal.warc.gz
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CC-MAIN-2013-20
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https://link.springer.com/book/10.1007%2F978-94-011-4305-9
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math
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About this book
Nonstandard methods of analysis consist generally in comparative study of two interpretations of a mathematical claim or construction given as a formal symbolic expression by means of two different set-theoretic models: one, a "standard" model and the other, a "nonstandard" model. The second half of the twentieth century is a period of significant progress in these methods and their rapid development in a few directions. The first of the latter appears often under the name coined by its inventor, A. Robinson. This memorable but slightly presumptuous and defiant term, non standard analysis, often swaps places with the term Robinsonian or classical non standard analysis. The characteristic feature of Robinsonian analysis is a frequent usage of many controversial concepts appealing to the actual infinitely small and infinitely large quantities that have resided happily in natural sciences from ancient times but were strictly forbidden in modern mathematics for many decades. The present-day achievements revive the forgotten term infinitesimal analysis which reminds us expressively of the heroic bygones of Calculus. Infinitesimal analysis expands rapidly, bringing about radical reconsideration of the general conceptual system of mathematics. The principal reasons for this progress are twofold. Firstly, infinitesimal analysis provides us with a novel under standing for the method of indivisibles rooted deeply in the mathematical classics.
functional analysis mathematical logic set theory
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http://nodus.ligo.caltech.edu:8080/40m/7946?hide=0,
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math
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Summary: Measurement and plot of shot-noise-intercept-current for PDA255.
Motivation:It is to measure the shot noise intercept current for PDA255 - the MC transmission RF photodiode to get an idea for the noise current for the detector
Result: The final plot is attached here. The plot suggests that the value of shot-noise-intercept current is 3.06mA
The plot is for the measured data of Noise voltage (V/sqrt(Hz)) vs DCcurrent(A). The fitted plot to this measured data follows the noise equation
Vnoise = gdet* sqrt[ 2e (iDC+idet)] , where gdet= transimpedance of the PD in RF region as described in manual of PDA255 (i.e. 5e3 when it is not in High-impedance region).
On the other hand for DCcurrent calculation we must use the high-impedance value for the transimpedance i.e. 1e4 Ohm. idet is the shot noise intercept current.
For the rough calculation of the noise level we may use the following formulae:
Vnoise = gdet*sqrt[2e (iDC+idet)] = gdet*sqrt(2e in), when in=iDC+idet;
For say, in1=1mA; Vnoise1=gdet*sqrt(2e *in1)
and sqrt(2e *in1)~18pA/sqrt(Hz)
In current case dark noise is ~1.5e-7 V/sqrt(Hz)
Therefore dark current(in2) ~dark noise voltage/RF transimpedance = 30pA/sqrt(Hz)
i.e. sqrt(2e *in2)=30pA/sqrt(Hz)
therefore, in2~3mA (since in1=1mA)
For, iDC=0, in=idet.
Therefore the shot-noise-intercept current will be ~3mA
Then Vdc = in2*1e4 = 30V
According to the experiment and also from the PDA255 manual the DC voltage level never goes beyond ~10V. Therefore following the photodiode characteristics(we work in reverse bias) we may infer that it can never become shot noise limited.
Also, from PDA255 manual, at 1650nm the dark noise is 30pW/sqrt(Hz) and the responsivity is 0.9A/W. Therefore the noise current level will be = noise power* responsivity ~27pA/sqrt(Hz). The value matches well with our expectation.
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CC-MAIN-2023-06
| 1,830 | 19 |
https://math-faq.com/how-do-i-find-the-equation-of-a-line-that-passes-through-two-points/
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math
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In many linear application problems, you needed to write the given information as ordered pairs and then find the equation that passes through the ordered pairs. Here is a similar example that use p = mt + b instead of y = mx + b.
Problem The percent of births to teenage mothers that are out of wedlock can be approximated by a linear function. In 1960, the percentage was 15% and in 1996 the percentage was 76%.
Use this information to find a linear model for the percentage of births as a linear function of the number of years since 1950.
Solution Since the problem statement specifies a linear function of the number of years since 1950, the input to this function is years since 1950 and the output is the percentage. The information in the problem can be written as ordered pairs (10, 15) and (46, 76).
Define the variables for these quantities as
t: years since 1950
p: percentage of births to teenage mothers out of wedlock
This means the form of the linear function is p = mt + b. The slope of a line passing through these points is
The slope is written as a fraction so no rounding occurs. Writing this as a decimal and rounding the amount would lead to a line that does not pass through the points. With this slope, we know the equation of the line is . To find the value of b, substitute one of the ordered pairs into the equation and solve for b.
This makes the linear function,
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CC-MAIN-2023-50
| 1,392 | 10 |
https://www.physicsforums.com/threads/determining-fuel-efficiency.427163/
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math
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Greetings everyone! Just a few weeks ago, I got it in my head that I'd like to determine some formulas for the efficiency of an engine - particularly mine, a 1991 Geo Metro. The overall goal is to compare various acceleration rates to show how slower acceleration can produce greater gas mileage(and also to determine the lower bound to this trend - certainly accelerating for an hour to reach 25mph is not going to be very efficient!). Very quickly I learned that there are many, many factors involved with which I was not immediately familiar. Not the first of this being the many-layered approach to acceleration. Just wrapping my brain around concepts like http://en.wikipedia.org/wiki/Jerk_%28physics%29" [Broken], torque, air resistance, and internal friction in enough to make my head spin! Suffice to say, I've uploaded https://spreadsheets.google.com/ccc...hzT284VUxhRmd3YXg0dXc&hl=en&authkey=CPSJv-0J" that's quite a mess right now. I haven't accounted for many, many factors - and some of the initial calculations (although they appear correct) seem to imply that you can get better gas mileage by accelerating faster! Clearly there's quite a bit wrong with this. However, I'll be working on it. I've also opened up permission for anyone to edit the file, if they feel like being generous and helping out. Updates to the file and such will be posted here. Cheers!
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CC-MAIN-2018-09
| 1,374 | 1 |
http://nrich.maths.org/9257
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math
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If the numbers 1 to 10 are all multiplied together, how many zeros are at the end of the answer?
The numbers 72, 8, 24, 10, 5, 45, 36, 15 are grouped in pairs so that each pair has the same product. Which number is paired with 10?
The following sequence continues indefinitely... Which of these integers is a multiple of 81?
If $n$ is a positive integer, how many different values for the remainder are obtained when $n^2$ is divided by $n+4$?
How many pairs of numbers of the form x, 2x+1 are there in which both numbers are prime numbers less than 100?
Our school dinners offer the same choice each day, and each day I try a new option. How long will it be before I eat the same meal again?
How many of the numbers 1 to 20 are not the sum of two primes?
How many zeros does 50! have at the end?
At a cinema a child's ticket costs £$4.20$ and an adult's ticket costs £$7.70$. How much did is cost this group of adults and children to see a film?
Flora has roses in three colours. What is the greatest number of identical bunches she can make, using all the flowers?
Can you find three primes such that their product is exactly five times their sum? Do you think you have found all possibilities?
Using the hcf and lcf of the numerators, can you deduce which of these fractions are square numbers?
Can you form this 2010-digit number...
Find out which two distinct primes less than $7$ will give the largest highest common factor of these two expressions.
Tina has chosen a number and has noticed something about its factors. What number could she have chosen? Are there multiple possibilities?
Two numbers can be placed adjacent if one of them divides the other. Using only $1,...,10$, can you write the longest such list?
Roo wants to puts stickers on the cuboid he has made from little cubes. Will he have any stickers left over?
Will this product give a perfect square?
Each time a class lines up in different sized groups, a different number of people are left over. How large can the class be?
Weekly Problem 5 - 2014
Weekly Problem 15 - 2014
Weekly Problem 26 - 2014
Weekly Problem 28 - 2014
Weekly Problem 39 - 2014
Weekly Problem 1 - 2015
Weekly Problem 4 - 2015
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| 2,173 | 26 |
https://www.daretoaks.com/forums/topic/Eye-contact-with-African-Americans/
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math
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When I pass an African American person on the sidewalk, I get nervous and either avoid eye contact or act more friendly than I would with someone of a different race. Is this my own racism coming out, or ‘white guilt’? Afterward, feel confused. Can someone help me figure out this phenomenon?
Name : Louise G, Gender : F, Race : White/Caucasian, Age : 54, City : Salem, State : OR Country : United States, Occupation : Language Instructor, Education level : 4 Years of College, Social class : Lower middle class,
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CC-MAIN-2021-10
| 524 | 2 |
https://www.teacherspayteachers.com/Product/Tic-Tac-Toe-Quadratics-Practice-422714
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math
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One student is x's and one student is o's. Students play in pairs taking turns picking a problem. Both students must answer the question. Goal is to get three in a row.
Topics: Finding the roots (factorable and not factorable), finding the vertex (in standard and vertex form), and expanding binomials.
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CC-MAIN-2018-47
| 302 | 2 |
https://www.rcsb.org/structure/2j85
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math
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A New DNA Binding Protein Highly Conserved in Diverse Crenarchaeal VirusesLarson, E.T., Eilers, B.J., Reiter, D., Ortmann, A.C., Young, M.J., Lawrence, C.M.
(2007) Virology 363: 387
- PubMed: 17336360
- DOI: https://doi.org/10.1016/j.virol.2007.01.027
- Primary Citation of Related Structures:
- PubMed Abstract:
Sulfolobus turreted icosahedral virus (STIV) infects Sulfolobus species found in the hot springs of Yellowstone National Park. Its 37 open reading frames (ORFs) generally lack sequence similarity to other genes. One exception, however, is ORF B116. While its function is unknown, orthologs are found in three additional crenarchaeal viral families. Due to the central importance of this protein family to crenarchaeal viruses, we have undertaken structural and biochemical studies of B116. The structure reveals a previously unobserved fold consisting of a five-stranded beta-sheet flanked on one side by three alpha helices. Two subunits come together to form a homodimer with a 10-stranded mixed beta-sheet, where the topology of the central strands resembles an unclosed beta-barrel. Highly conserved loops rise above the surface of the saddle-shaped protein and suggest an interaction with the major groove of DNA. The predicted B116-DNA interaction is confirmed by electrophoretic mobility shift assays.
Thermal Biology Institute, Montana State University, Bozeman, MT 59717, USA.
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s3://commoncrawl/crawl-data/CC-MAIN-2023-50/segments/1700679100705.19/warc/CC-MAIN-20231207221604-20231208011604-00407.warc.gz
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CC-MAIN-2023-50
| 1,406 | 8 |
https://www.mycoursehelp.com/QA/please-see-attached-for-the-prompt-quest/2365/1
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math
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Please see attached for the prompt, questions are as fallows
a) Show that B1(carrot)is a normal random variable.
b) Show that B1(carrot) is an unbiased estimator of B1, ie
c) Show that
Consider a combined gas–steam power cycle as shown in the figure. The topping cycle is a simple Brayton Cycle that has a pressure ratio of 7. Air enters the compressor at...May 08 2020
Ocean wide Enterprises, Inc., is involved in building and operating cruise ships. Each ship is identified as a separate discrete job in the accounting records. At the end...Jun 16 2020
Durable Goods Consumption Expenditures$350Nondurable Goods Consumption Expenditures$1,000Services Consumption Expenditures$3,000Business Fixed Investment$1,500Change in I...Dec 07 2019
QUESTION 1:Write short notes on all of the following:1. Personal Insurance2. Real Property3. Lease Contract4. Partnerships5. Employee contractsQUESTIO...Aug 18 2020
I have a question about Assets and the order of Assets in terms of where they are placed on the Balance Sheet. Investment Funds/Investment in Stock. That is an Asset corr...Sep 03 2020
Discuss an example of market failure and whether the government has been effective in implementing policies to correct it.Apr 10 2020
A fatigue model for the growth of a crack in a discrete lattice proposes that the size of the crack evolves as a pure birth process with parametersThe theory behind the m...Aug 04 2020
Gregory is an analyst at a wealth management firm. One of his clients holds a $5,000 portfolio that consists of four stocks. The investment allocation in the portfolio al...Apr 04 2020
Which of the following forms of validation becomes relatively more attractive as the sample available for validation becomes smaller? A.Predictive validationB.Concurr...Jan 10 2020
11) Which letter indicates the palatine bone that forms part of the hard palate?A) AB) BC) CD) DE) E12) Which letter indicates the jugular foramen?A) AB) BC) CD) DE) E13)...Dec 23 2019
Welcome to MyCourseHelp Services, World's leading Academic solutions provider with Millions of Happy Students.
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s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178363809.24/warc/CC-MAIN-20210302095427-20210302125427-00314.warc.gz
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CC-MAIN-2021-10
| 2,072 | 15 |
https://ekomia.com/blogs/inside-ekomia
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math
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Design ⚬ ekomia
The best feedback are the pictures that are sent to us. It's nice to see Luke in our customers' bedrooms and we are thrilled to see how many great furnishing ideas are included.
Design ⚬ ekomia ⚬ Nachhaltigkeit ⚬ Ratgeber ⚬ Reparatur
Here we will write articles about material science, innovation and inspiration from the ecodesign industry, repair instructions for furniture, events from ekomia and much more.
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CC-MAIN-2020-10
| 466 | 4 |
https://databot.online/topic/1-1-use-the-language-of-algebra/
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math
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By the end of this section, you will be able to:
The numbers 2, 4, 6, 8, 10, 12 are called multiples of 2. A multiple of 2 can be written as the product of a counting number and 2.
Similarly, a multiple of 3 would be the product of a counting number and 3.
We could find the multiples of any number by continuing this process.
|Multiples of 2||2||4||6||8||10||12||14||16||18||20||22||24|
|Multiples of 3||3||6||9||12||15||18||21||24||27||30||33||36|
|Multiples of 4||4||8||12||16||20||24||28||32||36||40||44||48|
|Multiples of 5||5||10||15||20||25||30||35||40||45||50||55||60|
|Multiples of 6||6||12||18||24||30||36||42||48||54||60||66||72|
|Multiples of 7||7||14||21||28||35||42||49||56||63||70||77||84|
|Multiples of 8||8||16||24||32||40||48||56||64||72||80||88||96|
|Multiples of 9||9||18||27||36||45||54||63||72||81||90||99||108|
Another way to say that 15 is a multiple of 3 is to say that 15 is divisible by 3. That means that when we divide 3 into 15, we get a counting number. In fact, 15÷3 is 5, so 15 is 5⋅3.
If we were to look for patterns in the multiples of the numbers 2 through 9, we would discover the following divisibility tests:
In mathematics, there are often several ways to talk about the same ideas. So far, we’ve seen that if m is a multiple of n, we can say that m is divisible by n. For example, since 72 is a multiple of 8, we say 72 is divisible by 8. Since 72 is a multiple of 9, we say 72 is divisible by 9. We can express this still another way.
Since 8⋅9=72, we say that 8 and 9 are factors of 72. When we write 72=8⋅9, we say we have factored 72.
Other ways to factor 72 are 1⋅72,2⋅36,3⋅24,4⋅18, and 6⋅12. The number 72 has many factors: 1,2,3,4,6,8,9,12,18,24,36, and 72.
The counting numbers from 2 to 20 are listed in the table with their factors. Make sure to agree with the “prime” or “composite” label for each!
The prime numbers less than 20 are 2, 3, 5, 7, 11, 13, 17, and 19. Notice that the only even prime number is 2.
A composite number can be written as a unique product of primes. This is called the prime factorization of the number. Finding the prime factorization of a composite number will be useful in many topics in this course.
To find the prime factorization of a composite number, find any two factors of the number and use them to create two branches. If a factor is prime, that branch is complete. Circle that prime. Otherwise it is easy to lose track of the prime numbers.
If the factor is not prime, find two factors of the number and continue the process. Once all the branches have circled primes at the end, the factorization is complete. The composite number can now be written as a product of prime numbers.
One of the reasons we look at primes is to use these techniques to find the least common multiple of two numbers. This will be useful when we add and subtract fractions with different denominators.
To find the least common multiple of two numbers we will use the Prime Factors Method. Let’s find the LCM of 12 and 18 using their prime factors.
Notice that the prime factors of 12 (2⋅2⋅3) and the prime factors of 18 (2⋅3⋅3) are included in the LCM (2⋅2⋅3⋅3). So 36 is the least common multiple of 12 and 18.
By matching up the common primes, each common prime factor is used only once. This way you are sure that 36 is the least common multiple.
In algebra, we use a letter of the alphabet to represent a number whose value may change. We call this a variable and letters commonly used for variables are x,y,a,b,c.
A number whose value always remains the same is called a constant.
To write algebraically, we need some operation symbols as well as numbers and variables. There are several types of symbols we will be using. There are four basic arithmetic operations: addition, subtraction, multiplication, and division. We’ll list the symbols used to indicate these operations below.
When two quantities have the same value, we say they are equal and connect them with an equal sign.
On the number line, the numbers get larger as they go from left to right. The number line can be used to explain the symbols “<” and “>”.
Grouping symbols in algebra are much like the commas, colons, and other punctuation marks in English. They help identify an expression, which can be made up of number, a variable, or a combination of numbers and variables using operation symbols. We will introduce three types of grouping symbols now.
Here are some examples of expressions that include grouping symbols. We will simplify expressions like these later in this section.
What is the difference in English between a phrase and a sentence? A phrase expresses a single thought that is incomplete by itself, but a sentence makes a complete statement. A sentence has a subject and a verb. In algebra, we have expressions and equations.
To simplify an expression
to do all the math possible. For example, to simplify 4⋅2+1 we would first multiply 4⋅2 to get 8 and then add the 1 to get 9. A good habit to develop is to work down the page, writing each step of the process below the previous step. The example just described would look like this:
By not using an equal sign when you simplify an expression, you may avoid confusing expressions with equations.
We’ve introduced most of the symbols and notation used in algebra, but now we need to clarify the order of operations. Otherwise, expressions may have different meanings, and they may result in different values.
For example, consider the expression 4+3⋅7. Some students simplify this getting 49, by adding 4+3 and then multiplying that result by 7. Others get 25, by multiplying 3⋅7 first and then adding 4.
The same expression should give the same result. So mathematicians established some guidelines that are called the order of operations.
Students often ask, “How will I remember the order?” Here is a way to help you remember: Take the first letter of each key word and substitute the silly phrase “Please Excuse My Dear Aunt Sally”.
It’s good that “My Dear” goes together, as this reminds us that multiplication and division have equal priority. We do not always do multiplication before division or always do division before multiplication. We do them in order from left to right.
Similarly, “Aunt Sally” goes together and so reminds us that addition and subtraction also have equal priority and we do them in order from left to right.
In the last few examples, we simplified expressions using the order of operations. Now we’ll evaluate some expressions—again following the order of operations. To evaluate an expression means to find the value of the expression when the variable is replaced by a given number.
Algebraic expressions are made up of terms. A term is a constant, or the product of a constant and one or more variables.
Think of the coefficient as the number in front of the variable. The coefficient of the term 3x is 3. When we write x, the coefficient is 1, since x=1⋅x.
Some terms share common traits. When two terms are constants or have the same variable and exponent, we say they are like terms.
Look at the following 6 terms. Which ones seem to have traits in common?
7 and 4 are like terms.
5x and 3x are like terms.
n2 and 9n2 are like terms.
We listed many operation symbols that are used in algebra. Now, we will use them to translate English phrases into algebraic expressions. The symbols and variables we’ve talked about will help us do that. Table 1.2 summarizes them.
|Addition||a plus b|
the sum of a and b
a increased by b
b more than a
the total of a and b
b added to a
|Subtraction||a minus b|
the difference of a and b
a decreased by b
b less than a
b subtracted from a
|Multiplication||a times b|
the product of a and b
|Division||a divided by b|
the quotient of a and b
the ratio of a and b
b divided into a
Look closely at these phrases using the four operations:
Each phrase tells us to operate on two numbers. Look for the words of and and to find the numbers.
We look carefully at the words to help us distinguish between multiplying a sum and adding a product.
Later in this course, we’ll apply our skills in algebra to solving applications. The first step will be to translate an English phrase to an algebraic expression. We’ll see how to do this in the next two examples.
The expressions in the next example will be used in the typical coin mixture problems we will see soon.
Identify Multiples and Factors
In the following exercises, use the divisibility tests to determine whether each number is divisible by 2, by 3, by 5, by 6, and by 10.
In the following exercises, find the prime factorization.
In the following exercises, simplify each expression.
In the following exercises, evaluate the following expressions.
In the following exercises, simplify the following expressions by combining like terms.
In the following exercises, translate the phrases into algebraic expressions.
ⓐ the difference of 5×2 and 6xy
ⓑ the quotient of 6y2 and 5x
ⓒ Twenty-one more than y2
ⓓ 6x less than 81×2
ⓐ the difference of 17×2 and 5xy
ⓑ the quotient of 8y3 and 3x
ⓒ Eighteen more than a2;
ⓓ 11b less than 100b2
ⓐ the sum of 4ab2 and 3a2b
ⓑ the product of 4y2 and 5x
ⓒ Fifteen more than m
ⓓ 9x less than 121×2
ⓐ the sum of 3x2y and 7xy2
ⓑ the product of 6xy2 and 4z
ⓒ Twelve more than 3×2
ⓓ 7×2 less than 63×3
ⓐ eight times the difference of y and nine
ⓑ the difference of eight times y and 9
ⓐ seven times the difference of y and one
ⓑ the difference of seven times y and 1
ⓐ five times the sum of 3x and y
ⓑ the sum of five times 3x and y
ⓐ eleven times the sum of 4×2 and 5x
ⓑ the sum of eleven times 4×2 and 5x
Explain in your own words how to find the prime factorization of a composite number.56.
Why is it important to use the order of operations to simplify an expression?57.
Explain how you identify the like terms in the expression 8a2+4a+9−a2−1.8a2+4a+9−a2−1.58.
Explain the difference between the phrases “4 times the sum of x and y” and “the sum of 4 times x and y”.
ⓐ Use this checklist to evaluate your mastery of the objectives of this section.
ⓑ If most of your checks were:
…confidently. Congratulations! You have achieved the objectives in this section. Reflect on the study skills you used so that you can continue to use them. What did you do to become confident of your ability to do these things? Be specific.
…with some help. This must be addressed quickly because topics you do not master become potholes in your road to success. In math every topic builds upon previous work. It is important to make sure you have a strong foundation before you move on. Whom can you ask for help?Your fellow classmates and instructor are good resources. Is there a place on campus where math tutors are available? Can your study skills be improved?
…no – I don’t get it! This is a warning sign and you must not ignore it. You should get help right away or you will quickly be overwhelmed. See your instructor as soon as you can to discuss your situation. Together you can come up with a plan to get you the help you need.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662545326.51/warc/CC-MAIN-20220522094818-20220522124818-00509.warc.gz
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CC-MAIN-2022-21
| 11,166 | 114 |
http://www.chegg.com/homework-help/questions-and-answers/1-disk-starts-rest-rotates-around-fixed-axis-subject-constant-net-torque-work-done-torque--q1351443
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math
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1-A disk starts from rest and rotates around a fixed axis, subject to a constant net torque. The work done by the torque during the time interval from t = 0 to 2 s is W1 and the work done during the time interval from t = 0 to 6 s is W2. The ratioW2/W1 = ??
2-A 2.2 kg block starts from rest on a rough inclined plane that
makes an angle of 25° with the horizontal. The coefficient of
kinetic friction is 0.25. As the block slides 2.0 m down the plane,
the mechanical energy of the Earth-block system changes by
(I know that we should use W=ΔEmec+ΔEth . But I did not get the correct answer )
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s3://commoncrawl/crawl-data/CC-MAIN-2016-30/segments/1469257830064.24/warc/CC-MAIN-20160723071030-00254-ip-10-185-27-174.ec2.internal.warc.gz
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CC-MAIN-2016-30
| 595 | 6 |
https://www.early-warning-signals.org/?page_id=860
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math
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Critical slowing down can lead to stronger fluctuations around the equilibrium state of the system. This causes spatial variance of the system to increase prior to a transition. Spatial variance is formally defined as the second moment around the spatial mean of the state variable.
Fluctuations around the mean can become increasingly asymmetric as the system approaches a transition. This is because the fluctuations in the direction of the alternative stable state take longer to return back to the equilibrium than those in the opposite direction; this asymmetry can also arise due to local flickering events (i.e. occasional jumps of local units between their current and alternative state). The spatial asymmetry can be measured by spatial skewness, which is the third central moment scaled by the standard deviation.
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CC-MAIN-2023-50
| 823 | 2 |
http://trefoiltutors.co.uk/category/puzzle/page/2/
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math
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People are waiting in line to board a 100-seat airplane. Steve is the first person in the line. He gets on the plane but suddenly can’t remember what his seat number is, so he picks a seat at random. After that, each person who gets on the plane sits in their assigned seat if it’s available, otherwise they will choose an open seat at random to sit in.
The flight is full and you are last in line. What is the probability that you get to sit in your assigned seat?
Check our Facebook page for the answer!
We hope you enjoyed solving the festive puzzles published in our December newsletter!
As promised, here are the answers:
1. 12 Days Of Christmas
According to the traditional song, on the first day of Christmas, my true love sent me a partridge in a pear tree. On the second day of Christmas, my true love sent me three presents: two turtle doves and a partridge in a pear tree. On the third day of Christmas, my true love gave me six presents: three French hens, two turtle doves and a partridge in a pear tree. This carries on until the twelfth day of Christmas. After the twelve days of Christmas are over, how many presents has my true love sent me altogether? Is there a quick way to work out the answer?
Click the post to read the answers!
By using the numbers 8, 5, 3 and 1 exactly once each, and with the help of brackets and basic operations (adding, subtracting, multiplying and dividing), can you form an expression with a value of 20?
he owner of a banana plantation has a camel. He wants to transport his 3000 bananas to the market, which is located after the desert. The distance between his banana plantation and the market is about 1000 km. So he decided to take his camel to carry the bananas. The camel can carry at the maximum of 1000 bananas at a time, and it eats one banana for every kilometer it travels.
What is the largest number of bananas you can bring over to your destination?
You are blindfolded and 10 coins are place in front of you on table.
You are allowed to touch the coins, but can’t tell which way up they are by feel. You are told that there are 5 coins head up, and 5 coins tails up but not which ones are which.
How do you make two piles of coins each with the same number of heads up?
At a party, everyone shook hands with everybody else. There were 66 handshakes.
How many people were at the party?
You have 8 balls all of the same size. 7 of them weigh the same, and one of them weighs slightly more.
How can you find the ball that is heavier by using a balance and only two weighings?
You have two ropes and a lighter. Each rope has the following property: If you light one end of the rope, it will take one hour to burn to the other end. They don’t necessarily burn at a uniform rate. How can you measure a period of 45 minutes?
How many triangles can you see in this picture?
What digits should replace the letters M and A to make the equation MA + A = AM correct?
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s3://commoncrawl/crawl-data/CC-MAIN-2018-22/segments/1526794871918.99/warc/CC-MAIN-20180528044215-20180528064215-00631.warc.gz
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CC-MAIN-2018-22
| 2,924 | 21 |
https://mistywrites.wordpress.com/2007/08/23/something-fun/
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math
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haha. well. had fun with our lesson just this afternoon. hmm. fundamental counting principle. hmm. the problem was like this, if there were 5 lamps in a room how many ways can you light up the room. and well, my answer was 15. haha. i was on the right track but, well, it was still wrong since it was lacking. hahaha. just figure out the answer. haha.
anyway, another thing. my bro downloaded this cool app.it was really interesting.
hehehe. just answer this. ^_^
arrange this according to your preference:
describe the following:
who are the persons you remember with these colors?
okay, so there you go. just answer those questions and i’ll give you the answer next time. hehehe.
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s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195526560.40/warc/CC-MAIN-20190720173623-20190720195623-00179.warc.gz
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CC-MAIN-2019-30
| 683 | 7 |
https://socratic.org/questions/how-do-you-solve-the-triangle-given-a-4-b-8-c-5
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math
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How do you solve the triangle given a=4, b=8, c=5?
Please read the explanation for the steps leading to the measures the angles,
Use the Law of Cosines to find one of the angles (I choose angle B):
Use the Law of Sines to find another angle (I choose angle A):
Angle C is found by subtracting the angles A and B from 180°:
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CC-MAIN-2019-26
| 323 | 5 |
https://www.postgraduatestudy.eu/s/3512/74666-Short-postgraduate-programmes/431-Business-Analysis.htm?pa=100&kier=96668
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math
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[A]t the close of the Middle Ages, when the so-called Arabic figures became established throughout Europe with the symbol 0 and the principle of local value, immediate progress was made in the art of reckoning. The problems... led up to the general solutions of equations of the third and fourth degree by the Italian mathematicians of the sixteenth century. Yet even these discoveries were made in somewhat the same manner as problems in mental arithmetic are now solved in common schools; for the present signs of plus, minus, and equality, the radical and exponential signs, and especially the systematic use of letters for denoting general quantities in algebra, had not yet become universal. The last step was definitively due to... Vieta... and the mighty advancement of analysis resulting therefrom can hardly be measured or imagined.
Thomas J. McCormack, "Joseph Louis Lagrange. Biographical Sketch" (1898) in his translation of Joseph Louis Lagrange, Lectures on Elementary Mathematics (1898); 2nd edition (1901) p. viii.
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s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600401601278.97/warc/CC-MAIN-20200928135709-20200928165709-00041.warc.gz
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CC-MAIN-2020-40
| 1,030 | 2 |
http://swooningblue.blogspot.com/2009/07/species-concept.html
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math
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One of my guide books to clouds lists 53 different cloud classifications. On each page, a careful paragraph describes the subtle distinctions between types, explaining how to identify the exact moment when one cloud evolves into another. At some point the entire body of water droplets crosses an imaginary line to be called something else. To say that clouds are ephemeral is simply a temporally broader observation.
If the whole idea of classifying transient bodies seems nearly pointless to you, you're not the first to think so. The sorites paradox sums it up nicely. Darwin recognized this problem with species concepts, of which there are now at least a couple dozen floating around. Systematics is simply a recognition that there is some salient cluster of characteristics that allows us to make a little more sense of what we see, from clouds to barnacles.
"I look at the term species", Darwin wrote, "as one arbitrarily given for the sake of convenience to a set of individuals closely resembling each other." Which is just about all we can agree upon. But at least we agree on that.
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s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676590051.20/warc/CC-MAIN-20180718041450-20180718061450-00399.warc.gz
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CC-MAIN-2018-30
| 1,092 | 3 |
https://www.wyzant.com/resources/answers/214801/summation_exponential_series
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math
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Summation - Exponential series
S = 1+3/1!+5/2!+7/3!......to infinity
a)e b)2e c)3e d)e-1
1 Expert Answer
In addition to knowing the expansion of e as an infinite series here's another series that will help:
e = Σ [ k/k! ]
Can you figure out the answer?
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s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875144027.33/warc/CC-MAIN-20200219030731-20200219060731-00222.warc.gz
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CC-MAIN-2020-10
| 426 | 11 |
https://iimcat.2iim.com/2011/03/05/solutions-mixed-bag/
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math
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Have given solutions to the questions posted here
1. Average of 6 distinct positive integers is 33. The median of the three largest numbers is 43. What is the difference between the highest and lowest possible median of the 6 numbers?
Let a, b, c, d, e, f be the six numbers in ascending order
e = 43; a + b + c + d + e + f = 198
Median of 6 integers = (c +d)/2
(c +d)/2 is maximum when c and d are maximum since e = 43, dmax = 42 and cmax = 41
(c +d)/2 is minimum when c and d are minimum amin = 1, bmin = 2, cmin = 3 dmin = 4
Therefore, = (c +d)/2 min = 3.5
Max – min = 41.5 – 3.5 = 38
2. In class A, the ratio of boys to girls is 2:3. In class B the ratio of boys to girls is 4 : 5. If the ratio of boys to girls in both classes put together is 3 : 4, what is the ratio of number of girls in class A to number of girls in class B?
Let us assume class A has 2x boys and 3x girls, class B has 4y boys and 5y girls.
(2x + 4y)/(3x + 5y) = ¾
8x + 16y = 9x + 15y
x = y
Reqd ratio = 3x/5y (since x = y) = 3/5
3. N is an 80-digit positive integer (in the decimal scale). All digits except the 44th digit (from the left) are 2. If N is divisible by 13, find the 26th digit.
To begin with, the question should read “find the 44th digit”.
Any number of the form abcabc is a multiple of 1001. 1001 is 7 * 11 * 13. So, any number of the form abcabc is a multiple of 13.
So, a number comprising 42 2’s would be a multiple of 13, so would a number comprising 36 2’s. So, in effect, we are left with a two digit number 2a, where a is the 44th digit. 26 is a multiple of 13, so the 44th digit should be 6.
4. A page is torn from a novel. The sum of the remaining digits is 10000. What is the sum of the two page-numbers on the torn page of this novel?
n(n+1)/2 should be nearby 10,000, so n(n+1) is somewhere near 20,000. So n should be around sqrt(20,000) about 141. Try 142
142*143 = 10153
141 *142 = 10011
So, the missing pages are either 76 and 77 or 5 & 6
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CC-MAIN-2021-17
| 1,959 | 24 |
https://virallistclub.com/18777/
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math
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On the unit circle 3pi2 is the point 0-1 DRAW it do see what i mean. DRAW ANGLE ON A UNIT CIRCLE—116pi is the same as -16pi or -30 degrees—If you draw it on the unit circle.
Trigonometry Find the Exact Value tan11pi6 Apply the reference angleby finding the anglewith equivalenttrig values in the first quadrant.
Sin 11pi 6. Sine is given by the y value on the unit circle so sin3pi2 -1. Rewrite Cos x – 11pi6 In Terms Of Sinx And Cosx This problem has been solved. Get your answers by asking now.
Previous question Next question Transcribed Image Text from this Question. Click hereto get an answer to your question Solve 2 cos-1 x sin-1 x 11pi6. Since our angle is greater than 3π2 and less than or equal to 2π radians it is located in Quadrant IV In the fourth quadrant the values for cos are positive only.
Rewrite sin x 11pi 6 – Answered by a verified Tutor. You can put this solution on YOUR website. Make the expressionnegative because tangentis negative in the fourth quadrant.
Enter PI for π Calculate sin11π6 Determine quadrant. You can sign in to. Sin 11pi6 sin 330 -12 How do you think about the answers.
Please Subscribe here thank you. Rewrite Cos x – 11pi6 In Terms Of Sinx And Cosx Question. Stack Exchange network consists of 176 QA communities including Stack Overflow the largest most trusted online community for developers to learn share their knowledge and build their careers.
Sin 11pi4 Csc 11pi4 Cot 11pi4 This problem has been solved. Basically the sin of 0 is the same as 2pi becasue they are coterminal angles same with 4pi 6 pi another full rotation around a circle so instead of thinking of sin -11pi6 think sinpi6 pi6 is like taking 180 and splitting it into 6 pieces so 30 degrees is pi6. Information in questions answers and other posts on this site Posts comes from individual users not JustAnswer.
Our math solver supports basic math pre-algebra algebra trigonometry calculus and more. Find The Exact Value Of The Trigonometric Function At The Given Real Number Cos 3pi4 Cos 5pi4 Cos 7pi4Find The Exact Value Of The Trigonometric Function At The Given Real Number. Ex 329 Find the value of the trigonometric function sin 11π 3 sin 11 𝜋3 sin 11 𝜋3 sin 3 23 π sin 4π 1.
JustAnswer is not responsible for Posts. Find the exact value of sin-1sin11pi5. Cancel the common factor of.
Convert from Radians to Degrees 11pi6 To convert radians to degrees multiply by since a full circle is or radians. 8pi2 is 2 complete revolutions so 11pi2 is the same as 3pi2 as far as the value of sine is concerned. Sin 11pi6 Sin -pi3 Sin 5pi3.
-pi6 and 11pi6 are coterminal angles so the values of the trig functions there are the same. I can try and explain more maybe with a diagram if you need me too. Solve your math problems using our free math solver with step-by-step solutions.
11pi6 330 degrees. Join Yahoo Answers and get 100 points today. HttpsgooglJQ8NysFind the Trigonometric Function Values for 11pi6.
FIND THE EXACT VALUES WHEN ANGLE 11pi6. Ask Question 100. Sin11pi6 Enter angle in degrees or radians– Enter angle or number for inverse functions.
-11pi6 is the same as pi6 using the coterminal angle theorem. If you are uncomfortable with radians then convert to degrees by multiplying by 180pi.
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CC-MAIN-2021-21
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http://jabsto.com/Tutorial/topic-98/Microsoft-Office-2013-660.html
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math
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Microsoft Office Tutorials and References
In Depth Information
Conditional formatting formula examples
Highlighting a row, based on a matching name
The conditional formatting formula is:
Notice that a mixed reference is used for cell A3. Because the column part of the reference
is absolute, the comparison is always done using the contents of column A.
Displaying alternate-row shading
The conditional formatting formula that follows was applied to the range A1:D18, as shown
in Figure 19.24, to apply shading to alternate rows.
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https://stupefied-davinci-2941e0.netlify.app/write-triangle-congruence-statement.html
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math
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Write Triangle Congruence Statement
Congruence and triangles date_____ period____ complete each congruence statement by naming the corresponding angle or side.
Write triangle congruence statement. Play this game to review mathematics. In similar shapes, the sides are in proportion. Suppose line gh ≅ jk, line hi≅kl and ∠i≅∠l.
This concept teaches students how to write congruence statements and use congruence statements to determine the corresponding parts of triangles. The ‘~’ sign is a congruence sign in geometry. To write a correct congruence statement, the implied order must be the correct one.
1) d abc @ 2) d uvw @ 3) d pqr @ 4) d klm @ 5) d def @ 6) d tuv @ 7) d def d str d xyz d jkl @ d nml For example, a congruence between two triangles, abc and def, means that the three sides and the three angles of both triangles are congruent. Sss and sas write which of the sss or sas postulates if either can be used to prove the triangles congruent.
Describe a transformation that can be performed on abc that will result in a triangle in the third quadrant. If , what else do you know? Write the statement and then under the reason column, simply write given.
Comparing one triangle with another for congruence, they use three postulates. You can start the proof with all of the givens or add them in as they make sense within the proof. Also, learn about congruent figures here.
Although congruence statements are often used to compare triangles, they are also used for lines, circles and other polygons. Which congruence statement can you write about the triangles int eh previous problem? Write down what you are trying to prove as well.
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s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662545875.39/warc/CC-MAIN-20220522160113-20220522190113-00096.warc.gz
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CC-MAIN-2022-21
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https://www.yourelectricalguide.com/2017/08/open-circuit-test-of-single-phase-transformer.html
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math
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Open Circuit Test of Single Phase Transformer
The set up for open circuit test of transformer is shown in the figure. This test is carried on the transformer to determine its iron losses.
In this test generally, AC voltage is applied on low voltage side and the secondary is kept open.
The primary reason of performing open circuit test on the low voltage side is that it draws significantly large no load current for convenient reading. Also, it requires only low voltage supply which is easily available and safe to perform the test.
This test is performed to determine the iron losses, Ro and Xo of transformer.
Procedure for Open Circuit Test of Transformer
- Connect the circuit as shown in the figure.
- Keep the autotransformer at its minimum output voltage position.
- Switch on the power supply and adjust the autotransformer to get the rated supply voltage.
- Now note down the current and power shown by the ammeter and wattmeter respectively. Let these are Io and Wo.
- The wattmeter reads the no load input power to the transformer. The no load current of the transformer is very small as compared to full load current (about 3 to 5% of the full load value) and hence the copper loss in the winding connected to the supply is small. As the high voltage winding is kept open therefore the copper loss in that winding is zero. Therefore the total copper loss is very small and can be neglected. Hence the watt meter reading represents the iron losses.
i.e Wo = Pi = Iron losses
While performing the open circuit test of a single phase transformer, high voltage winding should not be touched because it may cause a serious electric shock.
Calculation of Parameters
The two parameters which can be calculated from the open circuit test of transformer are Ro and Xo. They are calculated as follows.
Step 1: Calculate no load power factor (cos φo)
The wattmeter reads the real power input.
Therefore, Wo = VoIocos φo
or cosφo = Wo/VoIo
We can calculate φo from this.
Step 2: Calculate Im and Iw :
Im = Iosin φo
Iw = Iocos φo
Step 3: Calculate Ro and Xo
Ro = Vo/Iw Ω
Xo = Vo/Im Ω
The value of power factor of a transformer at no load is very small. Therefore the watt meter used while performing the open circuit test of a single phase transformer should be able to show accurate readings on small power factors.
Thanks for reading about “open circuit test of single phase transformer”.
Transformer — 8 | Objective Type Question Answers
#1 In a power transformer the efficiency should be maximum at
#2 For minimum weight of a transformer, the weight of iron should be
equal to the weight of copper
#3 The iron loss of a transformer can be calculated by knowing the weights of
cores and yokes
#4 H.R.C. fuses on a transformer provide protection against
#5 Which of the following insulating materials is used in power transformers ?
All of the above
#6 Simple porcelain bushing, an used for transformers up to
#7 Oil impregnated paper condenser bushing for generally used on transformer operating
#8 The color of fresh dielectric oil for a transformer is
#9 Which of the following test on a transformer provides information about regulation, efficiency and heating under load conditions?
Back to back test
#10 Buchholz relay is used on
oil cooled transformers
#11 The kVA rating ratio of transformers operating in parallel, as a general rule, should be within
#12 Which value of flux is involved in the e.m.f equation of the transformer?
#13 In Scott connections the main transformer has centre tap on
both primary and secondary winding
#14 In a transformer over currents affect
all of the above
#15 For transformers up to a capacity of ……… kVA air blast cooling is provided.
#16 As the supply frequency of a transformer increases its rating
#17 Which of the following methods is used for cooling of transformers up to a capacity of 10 MVA?
oil natural cooling
#18 The nominal short-circuit voltage of the transformer is defined as percentage of ….
the rated primary voltage
#19 A distribution transformer has low flux density because
it is constantly connected to the supply
#20 Spiral core transformer which has core made up of steel strip has the following advantage.
#21 A transformer designed for installation in a tropical country if installed in a cold country
is to be loaded in excess of the name plate kVA rating
Do not forget to click the “finish” button to see the correct answers and result.
- Single Phase Transformer Working Principle
- Ideal Transformer
- Construction of Three Phase Transformer
- Types of Transformers
- Equivalent Resistance and Reactance of Transformer
- Equivalent Circuit of Single Phase Transformer
- Power Loss in a Transformer
- Open Circuit Test of Single Phase Transformer
- Short Circuit Test on Single Phase Transformer
- Transformer Efficiency
- Regulation of Transformer
- Instrument Transformers
- Polarity of Transformer Windings
- Significance of Vector Group of Transformer
- Buchholz Relay Construction | Working
- Why current transformer secondary should not be opened
- Dielectric Strength Test of Transformer Oil
- Transformer Moisture Removal Process
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CC-MAIN-2019-47
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https://riddles.net/math-riddles?page=2
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math
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The best selection of riddles and answers, for all ages and categories
Maria went to the bread store to buy a loaf of bread for dinner. She had 2 quarters, 4 dimes, 3 nickels and 2 pennies. The total cost of the bread $0.82. She promised to make sure she had exactly 1 coin remaining after purchase. Which coins did she have left after buying the loaf of bread?
Jeff has $28.75. He purchased three cookies that cost $1.50 each, five newspapers that each cost $0.50, five flowers for $1.25 each, and used the remainder of the cash on a pair of sunglasses. How much were the sunglasses?
Eggs are $0.12 a dozen. How many eggs can you get for a dollar?
A little boy goes shopping and purchases 12 tomatoes. On the way home, all but 9 get mushed and ruined. How many tomatoes are left in a good condition?
If the zookeeper had 100 pairs of animals in her zoo and if two pairs of babies are born for each and every one of the original animals, and then sadly 23 animal don’t survive, how many animals do you have left in total?
A duck was given $9, a spider was given $36, a bee was given $27. Based off of this information, how much money would be given to a cat?
A cell phone and phone case cost $110 in total. The cell phone costs $100 more than the phone case. How much was the cell phone?
How can you make six into an odd number?
What did number 2 say to number 1?
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s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499816.79/warc/CC-MAIN-20230130101912-20230130131912-00824.warc.gz
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CC-MAIN-2023-06
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