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f(x+y) = f(x) + f(y) + 2xy |
2007-11-01 |
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From Marcia: For all real numbers x and y, let f be a function such that f(x+y) = f(x) + f(y) + 2xy and such that the limit as h -> 0 of f(h) / h = 7, find: f(0), use the definition of the derivative to find f'(x), and find f(x). Answered by Penny Nom. |
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A decimal to a fraction |
2007-11-01 |
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From Lisa: i am trying to turn a decimal into a fraction. my example is to turn 10.5 into a fraction at its lowest form Answered by Penny Nom. |
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The volume of a pyramid |
2007-10-31 |
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From San: the volume V of a square-based pyramid with base sides s and height h is V=1/3s2h if the height is half of the length of a base side, express the volume V as a function of s Answered by Penny Nom. |
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A number puzzle |
2007-10-31 |
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From matthew: please help.make 200.take 4 numbers from the numbers 1-9,place the numbers
into a square containing 4 equal squares 1 number to each square.example
13
57 you now have 4 sets of numbers 13 ,57 ,reading across and 15 , 37. reading down
i have to find 2 or more ways of making i have to find the numbers that when added together
using this method make 200.you can only use each number once. Answered by Penny Nom. |
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I am a prime number |
2007-10-31 |
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From sherry: I am a prime number. I can not be shared fairly except by one group. My array can only be one row.
array can only be one row. Can you please explain this out to me so I can help my child with it.
Thanks Answered by Penny Nom. |
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A faulty induction argument |
2007-10-31 |
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From snehal: Find the problem in the following argument. Try to give another example
that illustrates the same problem.
Claim: All Fibonacci numbers are even.
Proof: We will use strong induction. Let P(n) be the proposition that Fn is
even.
Base case: F0 = 0 is even, so P(0) is true.
Inductive step: Assume P(0); : : : ; P(n - 1) to prove P(n): Now
Fn = Fn-1 + Fn-2
and Fn-1 and Fn-2 are both even by assumptions P(n - 1) and P(n - 2); so
Fn is also even. By induction, all Fibonacci numbers are even. Answered by Stephen La Rocque and Claude Tardif. |
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A t-shirt is on sell at 33 1/3% off |
2007-10-31 |
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From kbennett: A t-shirt is on sell at 33 1/3% off. Joey paid $12 for his shirt. What was the original price? Answered by Penny Nom. |
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A wiffleball field |
2007-10-31 |
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From Svitlana: The Adam's family has set up a wiffleball field in their backyard. The bases are arranged like a typical baseball diamond, where the distance between consecutive bases is the same. First base is opposite of third base, and second base is opposite of home plate. The distance between consecutive bases is 50 feet. Now, the pitcher stands 25 feet from home plate and lies on the line between home plate and second base. How far is the pitcher from first base? Round your answer down to the nearest inch. Answered by Penny Nom. |
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The base and height of a triangle triangle |
2007-10-31 |
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From mike: How do you find the length of the base or the height of a triangle if the area is 30 square feet? Answered by Penny Nom. |
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Write each frequency as a decimal |
2007-10-31 |
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From Jazzy: Twins are born once in every 89 births.
Identical twins are born 4 times in every 1000.
Triples are born once in every 6900 births.
write esch frequency as a decimal and order the
decimals from least to greatest frequency. Answered by Penny Nom. |
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A circular table is pushed into the corner |
2007-10-31 |
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From Will: A circular table is pushed into the corner of a square room so that one point is 8 inches from one wall and 9 inches from the other. What is the radius of the table? Answered by Penny Nom. |
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An array for 31 |
2007-10-31 |
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From sherry: How do you make an array with the number 31 Answered by Penny Nom. |
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Density |
2007-10-30 |
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From Ali: Would an object sink or float in pure water if it has a mass of 10g and a volume of 5 cubic centimeters?
314 Answered by Stephen La Rocque. |
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Subsets of a set |
2007-10-30 |
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From Snehal: 1. Let an denote the number of subsets of f{1,2, 3.... n}including the
empty set and the set itself.)
a) Show an = 2an-1
b) Guess a formula for the value of an and use induction to prove you are
right Answered by Stephen La Rocque. |
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Measurements on a test tube |
2007-10-30 |
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From Bruce: I figure that the surface area (SA) of a round bottom test tube
can be determined by the equation SA = 2pi*h*r
where r is the radius of the hemispheric bottom & column part, and
h is the height (h) at any point upwards from the bottommost portion
in the center of the tube.
I haven't been able to come up with an equation yet for the circumference
of such a test tube at any point upwards along the tube based
on the height in its center or on the distance along the outside
of the tube. Answered by Harley Weston. |
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