Let l be the length of a diagonal of a rectangle whosesides have lengths x and y, and

Chapter 3, Problem 8

(choose chapter or problem)

Let \(l\) be the length of a diagonal of a rectangle whose sides have lengths \(x\) and \(y\), and assume that \(x\) and \(y\) vary with time.

(a) How are dl/dt, dx/dt, and dy/dt related?

(b) If \(x\) increases at a constant rate of 1 2 ft/s and \(y\) decreases at a constant rate of 1 4 ft/s, how fast is the size of the diagonal changing when \(x = 3 ft\) and \(y = 4 ft\)? Is the diagonal increasing or decreasing at that instant?

Equation Transcription:

dl/dt

dx/dt

dy/dt

Text Transcription:

l

x

y

dl/dt

dx/dt

dy/dt

x = 3 ft

y = 4 ft