Question

If x2 + y2 = 100 and dy/dt = 3, find dx/dt when y = 8. (enter your answers as a comma-separated list.)

Answer 1

Answer;

dy/dx = - or + 4 and y = 8

Explanation;

x² + y² = 100

when y = 8

Then, x² + 8² = 100

thus; x² = 100 - 64 = 36

x² = 36

therefore; x = + 6 or -6

2x (dx/dt) + 2y (dy/dt) = 0

x(dx/dt) + y (dy/dt) =0

When dy/dt = 3

= (- or + 6) dx/dt + 8 (3) = 0

thus; dx/dt = - 8 (3/6)

= + or - 4.

Answer; y = 8 and dx/dy = - or + 4