Question #17235

If z^2=x^2+y^2 with z>0, dx/dt=2, and dy/dt=5, find dz/dt when x=5 and y=12.
Answer: dz/dt=

Expert's answer

x=5, y=12 then z^2=5^2+12^2 so z=+-13 z>0 so z=13

we can

write

2*z*dz=2*x*dx+2*y*dy ( divide by

dt)

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

dz/dt=( 2*x*dx/dt+2*y*dy/dt

)/2z=(2*5*2+2*12*5)/(2*13)=70/13

we can

write

2*z*dz=2*x*dx+2*y*dy ( divide by

dt)

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

dz/dt=( 2*x*dx/dt+2*y*dy/dt

)/2z=(2*5*2+2*12*5)/(2*13)=70/13

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