Q: Point A moves along the x-axis at the constant rate of 8ft/sec while point B moves along the y-axis at the constant rate of 10ft/sec. Find how fast the distance between them is changing when A is at the point (10,0) and B is at the point (0,8).

z^2 = x^2 + y^2

x = 10

y = 8

z = sqrt(10^2 + 8^2) --> sqrt(164)

x' = 8

y' = 10

want to find z'

2z*dz/dt = 2x*dx/dt + 2y^dy/dt

dz/dt = [2x(dx/dt) + 2y(dy/dt)] / 2z

dz/dt = [2*8*10 + 2*8*10] / 2z

dz/dt = 320 / 2z

dz/dt = 160 / sqrt(164) --> FINAL ANSWER!