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Mth 277
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MthhQuestion3
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I am not sure how to answer this question. Could you give me some pointers?
Find three positive numbers such that the sum of the first, double the second and triple the third is 50, and the sum of whose squares is as large as possible.
I believe you start with equations:
x+2y+3z=50; z,y,z >=0
x^2+y^2+z^2= larg # possible
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Good start.
You are therefore trying to maximize the function
f(x, y, z) = x^2 + y^2 + z^2
subject to the constraint
x + 2 y + 3 z = 50.
The methods of the section show you how to maximize a function given a constraint.
I believe this should be enough to move you forward, but let me know if you have additional questions on this problem.
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Mth 277
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MathQuest4
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I am also having trouble with this problem as well. Im not sure what it is really asking for. I've looked through the assignments and havent found anything very similar so I was hoping you could help me out.
The ideal gas law states that P V = n k T, where k is a constant. Suppose V is also held constant, so that V / k can be regarded as constant. Then n becomes a function of P and T, with n ( P, T) = ( V / k) * P / T, with (V / k) being constant. In the P vs. T plane, sketch a representative series of level curves of n ( P , T ).
Thanks
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n ( P, T) = ( V / k) * P / T
is a function of P and T.
A graph of P vs. T would consist of points that satisfy this equation.
A level curve is a curve along which n(P, T) is constant.
If you set
( V / k) * P / T = c
and solve for P in terms of V, you will get the equation of a level curve for value c.
What sort of P vs. V curve do you get?
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