Answer:
Step-by-step explanation:
GIVEN:   dx / dt=5 in./min.  and  dy/ dt=−6 in./min.
FIND: Â Â dz/ dt when x=12 in. and y=9 in.
Use the Pythagorean Theorem to get the equation
x2+y2=z2
Now differentiate this equation with repect to time t getting
D{x2+y2}=D{z2}  ⟶
2xdxdt+2ydydt=2zdzdt  ⟶ Â
(Multiply both sides of the equation by 1/2.)
x dx/ dt+y dy/ dt= z dz/ dt        (DE)
Now let x=12 and y=9 and solve for z using the Pythagorean Theorem.
tex2html_wrap_inline125
122+92=z2  ⟶  z2=225  ⟶  z=15
Plug in all given rates and values to the equation (DE) getting
(12)(5)+(9)(−6)=(15)dz/ dt  ⟶
6=15dzdt  ⟶
dz/ dt=615=25 in/min.
Hope this answer helps you :)
Have a great day
Mark brainliest