# calculus

The sides and diagonal of the rectangle above are strictly increasing with time. At the instant when x=4 and y=3, dx/dt=dz/dt and dy/dt=k(dz/dt). What is the value of k at that instant.

solved for z with pythagorean theorem and stuck at that step. z=5

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1. Well I assume that z is the diagonal.

x^2+y^2 = z^2
2 x dx/dt + 2 y dy/dt =2 z dz/dt

4 dz/dt + 3 k dz/dt = dz/dt

4 + 3 k = 1

k = -1

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2. He had it right up until he plugged in x, y, and z. He forgot to multiply each by 2. Answer is 1/3.

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3. It's the same whether he multiply each by 2 or not. Cuz 2 can be cancelled.[Ex:2(x dx/dt+ y dy/dt)= 2 z dz/dt]

He forgot to plug in Z.

Using pythagorean theorem
z=(x^2+y^2)^(1/2)
z=(16+9)^(1/2)
z=5

Thus
4 + 3 k = 5
3k=1
k=1/3

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