Related rates: calculus
A rectangle is inscribed in a circle of radius 5 inches. If the length of the rectangle is decreasing at the rate of 2 inches per second, how fast is the area changing when the length is 6 inches?
I am stuck at finding w and w'
A = lw
A'= l'w + w'l
Here is what I did.., which is probably wrong.
Since the radius is 5 inches, then the diagonal must be 10 inches.
so l^2 + w^2 = 100
w = 10/l
2ll' + 2ww" = 0
2(6)(-2) 10/3*w' = 0
w' = 24 *3 / 10 = 7.2
A' = -2(5/3) + 7.2(6)
A' = 42.27
The answer was supposed to be decreasing 7 in/s.
I am stuck at finding w and w'
A = lw
A'= l'w + w'l
Here is what I did.., which is probably wrong.
Since the radius is 5 inches, then the diagonal must be 10 inches.
so l^2 + w^2 = 100
w = 10/l
2ll' + 2ww" = 0
2(6)(-2) 10/3*w' = 0
w' = 24 *3 / 10 = 7.2
A' = -2(5/3) + 7.2(6)
A' = 42.27
The answer was supposed to be decreasing 7 in/s.