Question

It is known that the depth of a lake at a point with coordinates (x, y) is z = 200 + 0.02x2 − 0.001y3, where x, y, and z are measured in meters. a woman in a kayak starts at the point (80, 60) and moves toward another point located at (0, 0). (a) find du f(80, 60). (give your answer correct to at least two decimal places.)

Answer 1

Given that the depth of a lake at a point with coordinates (x, y) is

$z = 200 + 0.02x^2-0.001y^3$

$0.04x-0.003y^2 \frac{dy}{dx} =0 \\ \\ \frac{dy}{dx} = \frac{0.04x}{0.003y^2} \\ \\ \left.\frac{dy}{dx} \right |_{(80, 60)}= \frac{0.04(80)}{0.003(60)^2} = \frac{3.2}{10.8} =0.2963$