when the sides of the square are 10 m long, the area of square is changing at a rate of 40 m^2/s.
Let's denote the length of the sides of the square as "s" and the area as "A". The formula for the area of a square is A = s^2.
To find the rate at which the area is changing, we need to find dA/dt, the when the sides of the square are 10 m long, the area of the square is changing at a rate of 40 m^2/s. when the sides of the square are 10 m long, the area of the square is changing at a rate of 40 m^2/s.with respect to time.
Since the side bbs of the square are increasing at a rate of 2 m/s, we have ds/dt = 2 m/s.
Now, let's differentiate the area formula with respect to time:
dA/dt = d/dt (s^2)
Using the power rule for differentiation, we get:
dA/dt = 2s * ds/dt
Substituting the given values, we have:
dA/dt = 2 * 10 * 2
dA/dt = 40 m^2/s
Therefore, when the sides of the square are 10 m long, the area of the square is changing at a rate of 40 m^2/s.