Question

X^2+5y^2+2y=75; dx/dt =14 when x= 6 and y=-3; find dy/dt

Answer 1

7

Explanation:

x² + 5y² + 2y = 75

2x + 10y * dy/dx + 2 dy/dx = 0

2x + (10y + 2) dy/dx = 0

x + (5y + 1) dy/dx = 0

when x = 6, y = -3

6 + (-15 + 1) dy/dx = 0

6 - 12 dy/dx = 0

dy/dx = 1/2

dy/dt = dy/dx * dx/dt = 1/2 * 14 = 7