42. ap calc is hard bros?

Question

the hypotenuse AB of a right triangle ABC is 5ft and one leg AC is decreasing at the rate of 2ft/sec the rate in sq feet per second at which area is chanigng when AC = 3 is

Answer 1

So a^2 +b^2 = c^2 and the area is a*b/2.
da/dt=-2 and let b=sqrt(25-a^2)
Therefore, dArea/dt=d/dt (a*sqrt(25-a^2)/2) =sqrt(25-a^2)+
+ a/2sqrt(25-a^2) *-a
So when a=3, dA/dt= 4 - (81/8) = 32/8-81/8 = -49/8