Answer:
dA/dt = 140 cm²/s
Step-by-step explanation:
The length of a rectangle is increasing at the rate of 9 cm/s . This means rate at which the length is changing with time = 9 cm/s
dL/dt = 9 cm/s
The width is increasing at the rate of 7 cm/s.
dW/dt = 7 cm/s
When the length is 11 cm and the width is 7 cm, How fast is the area of the rectangle increasing?
Area of a rectangle = Length × width
Area of a rectangle = Lw
we need the product rule to find the rate the area of the rectangle is changing.
dA/dt = LdW/dt + W dL/dt
dA/dt = 11 (7) + 7(9)
dA/dt = 77 + 63
dA/dt = 140 cm²/s