# calculus

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A recatangle has constant area of 200 square meters and its lenght L is increasing at the rate of 4 meters per second
a) find the width W at the instant that the width is decreasing at the rate of .5 meters per second
b) at what rate is the diagonal d of the rectangle changing at the instant when the width is 10 meters?

• calculus -

A = 200 = W * L
dL/dt = 4

W = 200/L
dW/dL = -200/L^2
dW/dt = -(200/L^2)dL/dt

if dW/dt = -.5
then
-.5 = -(200/L^2) * 4
L^2 = 1600
L = 40
W = 200/40 = 5

go through that again for W = 10 to get L, dW/dt
then
D^2 = L^2 + W^2
2 D dD/dt = 2 L dL/dt + 2 W dW/dt

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