a, b, c, and d are all positive real numbers.
Given that
a + b + c + d = 12
abcd = 27 + ab +ac +ad + bc + bd + cd
Determine a, b, c, and d.
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The solution says that using AM - GM on the second equation gives
abcd (is greater than or equal to) 27 + 6*sqrt of (abcd)
From...
Thanks sniffer
The answer to the first question was 6400 N, but I'm getting something different. Since Volume is 0.039, I should take the cube root of that number to figure out the length of one side of the cube, right? Then to find the area of one of the faces of the cube, I square the...
These problems are from Giancoli 5th edition (principles with applications)
A cubic box of volume 0.039 m^3 is filled with air at atmospheric pressure at 20 celsius. The box is closed and heated to 180 celsius. What is the net force on each side of the box?
I first used the ideal gas law...
These are the answers that I got
1) Converges (to 0.5*sqrt (Pi))
2) Diverges
3) Converges to sqrt (Pi)
4) Converges to 0.25 * sqrt (Pi)
Do these look right?
Thanks
I am given that e^(-x^2) = 0.5*sqrt(pi), but I couldn't get the integrals into that form through integration by parts - am I doing something wrong?
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All of these integrals have lower bounds of 0 and upper bounds of infinity:
Problems 1 and 2 just require me to determine whether it converges or diverges. 3 and 4 actually require a value.
1) e^(-x) * sqrt(x)
2) \frac{x*arctan(x)}{(1+x^4)^(1/3)}
3) e^(-x) / sqrt(x)
4) x^2 * e^[-(x^2)]...
Thanks OlderDan, I solved the first two problems, but I'm still having trouble with the third. If I seperate the numbers into a series of fractions, like
1^k over n^k+1 plus 2^k over n^(k+1) plus 3^k over n^(k+1) and end with n^k over n^(k+1), would that give me the answer (which would...
Thanks Cyclovenom, I took \frac{sin(1/x)}{1/x} and did the limit as x approaches infinity with L Hopital's rule, but I got 0, so doesn't that make it inconclusive?
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I need to determine whether Sigma [sin(1/x)] for x=1 to x=infinity converges or diverges. I have a feeling that it diverges, but I don't know how to prove it.
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Sorry I'm not very good at using latex, but here's my shot.
1. Let f(x) = sqrt (1+2x) - 1 - sqrt (x). Find some a where a is positive, such that lim of \frac{f(x)}{x^a} as x approaches 0 from the right is finite and non zero.
I know the problem requires the use of L'Hopital's rule, but I...