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The Shaw family wants a new swimming pool |
2008-01-26 |
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From Mable:
The Shaw family wants a new swimming pool in their backyard. The pool company stated that the first job is to remove dirt from an area 30ft x 60ft. Next, a hole must be dug 25ft x 55ft x an average of 6ft deep. The finished pool would measure 20ft x 50ft x 5ft deep (average). How many square yards of dirt must be removed from the lawn?How much would it cost the Shaw family for dirt removal at $46 a cubic yard (nearest cubic yard)?
Answered by Stephen La Rocque. |
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Cantor's diagonal argument |
2008-01-26 |
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From David:
Cantor's theory using a diagonal across a list of real numbers to proven uncoutability has always puzzled me.First in base ten, it feels like hocus pocus so I began thinking of the Boolean numbers as truer representations of place value (on,off). Secondly his list was always arbitrary or so I recollect. Therefore, I suggested using a seriesA=.10000....,B=.01000. C=.11000, etc.
Any diagonal is already located among the numbers listed. My only alteration is that since the final digit is always unrepresentably either one or zero, but it must be one or the other, I make an assumption that if x= .abc...1 and y= .abc...2 the only two possibilities and I choose to count F=x+y then then the numbers are countable= Z=sumFi,where I=2+2^2+2^3...
I hope this sketch is enough description, I asked Rudy Rucker more formally but got no mathematical response, someone else gave me some tale about slippery epsilon. What do tyou think of recasting his proofs in more rigorous form?
David French
Answered by Claude Tardif and Walter Whiteley. |
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Sum of factorials |
2008-01-26 |
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From Emily:
What is the tens digit in the sum 7! + 8! + 9! ... + 2006!
Answered by Stephen La Rocque. |
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A car goes 15 miles on a gallon of gas |
2008-01-26 |
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From Raven:
A car goes 15 miles on a gallon of gas when it goes 50mph. When the car is driven 60mph it only goes 80% as far.
How far will it travel on a gallon of gas at 60mph?
I solved this two ways:
15 * .80 = 12 It goes only 12 miles or x/60 = 15/50 which is x = 12
This answer in the book is 4/5 * 15 = x. Then x = 12
How did they come up with 4/5?
Answered by Penny Nom. |
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Inflection points |
2008-01-25 |
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From Armando:
Hi, Im trying to write a program that takes an equation ( f(x) = 0 ) and returns a list of the inflexion points in a given interval.
there must be (I think) a mathematical method or algorithm to do this, probably involving the (second) derivate of the function.
However I have not found such a method yet. Any help on this will be much appreciated.
Answered by Stephen La Rocque and Harley Weston. |
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O.T.T.F.F.S.S |
2008-01-25 |
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From Omar:
What is the next letter in the following sequence:
O.T.T.F.F.S.S
Answered by Penny Nom. |
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Linear feet to metres |
2008-01-25 |
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From Jillian:
i have a measurement of something in linear feet. i dont know what a linear foot is so i want to convert it to meters to have an idea.
how do i convert.
Answered by Penny Nom. |
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A developer subdivides a plot |
2008-01-25 |
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From Katherine:
A developer buys a plot of land that is 48,000 sq.feet. She sets aside 1/2 of it to bulid a house for herself, then divides the remaining half into 3 equal plots. Find the area of each lot.
Answered by Penny Nom. |
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Tossing a coin |
2008-01-25 |
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From Christopher:
Jack tosses a coin 30 times. How many times would you expect the coin to land tails side up?
Answered by Harley Weston. |
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The integral of Sqrt(sin x) |
2008-01-24 |
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From tariq:
find integration
Sqrt(sinx) dx , from x=bi/4 to 3bi/4
Answered by Harley Weston. |
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The standard form of a line |
2008-01-24 |
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From James:
I need to put it in Standard from ax+by=c the problem is
(-4,0); parallel to y=-2+1 how can I put this in Standard from
Answered by Stephen La Rocque. |
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Finding the area of an isosceles triangle given one angle and the inradius |
2008-01-24 |
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From Saurabh:
Given an isosceles Triangle, whose one angle is 120 and inradius is √3. So area of triangle is?
Answered by Stephen La Rocque. |
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A relationship between numbers |
2008-01-24 |
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From Robyn:
Study these problems: ? 2=4 ? 5=25 ? 9=81
1. Explain what ? means (hint there are two answers).
2. What number is equal to ? 6
3. What number does ? 12 represent?
Answered by Stephen La Rocque and Penny Nom. |
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An integral |
2008-01-24 |
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From Meghan:
Evaluate the indefinite integral of (x^3 +1)^(1/3) * x^5 * dx.
Answered by Brennan Yaremko. |
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Three consecutive odd integers |
2008-01-24 |
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From daniel:
find three consecutive odd integers such that three times the second minus the third is 11 more than the first.
help! i have x+1, x+3, x+5 as my 3 odd integers is this correct its been a while.
Answered by Penny Nom. |
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