The side of a square is increasing with a rate of 10 inches/minute. The length of the side is given as 25 inches. The rate of change of area of the square is 500 inches/minute.
The side of the square s is given as 25 inches. We know that, area A = s².
Applying differentiation for the above equation, we get
dA/dt² = d(s²)/dt
dA/dt² = 2s* ds/dt
Given that, the side of a square is increasing with a rate of 10 inches/minute and s = 25 inches.
ds/dt = 10 inches/minute
dA/dt² = 2s* ds/dt = 2*25*10 = 500 inches per minute
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