We are supposed to find slope of the parametric equations using implicit differentiation with the given value of T.
We are given: X = sqrt((5-sqrt(T))) , Y(T-1) = sqrt(T) and T=4
Note that the X portion of the equation reads as X equals 5-T all under the square root, and T by itself under an additional square root within the original square root.
So far, what I have for dx/dt is, using the chain rule:
dx/dt = 1/2((5-T^(1/2)))^(-1/2) * ((-1/2T^(-1/2)))
After multiplying I got,
dx/dt = -1/4T((5-T^(1/2)))^(-1)
by multiplying the -1/2T by the 1/2, and adding the exponents of (-1/2) + (-1/2) = -1
Is this the right way to multiply the terms?
After working through the entire problem, evaluating dy/dt divided by dx/dt using the values for X, Y, and T, and assuming that is the correct way to find dx/dt, I got 5/12 as the slope.
2007-03-20
21:06:29
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2 answers
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asked by
Ryan_1770
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in
Mathematics