Question

A rectangle has width w inches and height h inches, where the width is twice the height. Both w and h are functions of time t, measured in seconds. If A represents the area of the rectangle, which of the following gives the rate of change of A with respect to t ?
A. dA/dt=4h in/sec
B. dA/dt=3h dh/dt in^2/sec
C. dA/dt=4h dh/dt in/sec
D. dA/dt=4h dh/dt in^2/sec

Answer 1

Answer:

D.

Step-by-step explanation:

Area=w*h

w*h=(2h)*(h)=2h^2

dA/dt=2(2h)=4h

dA/dt=4h dh/dt in^2/sec

Answer 2

The expression that gives the rate of change of A with respect to t

is dA/dt = 4h * dh/dt in²/s. Option D is correct

The formula for calculating the area of a rectangle is expressed as:

A = wh

h is the height

w is the width

If the width is twice the height, then w = 2h

A = (2h)h

A = 2h²

The rate of change of area will be expressed as dA/dt

dA/dt = dA/dh * dh/dt

dA/dt = 4h * dh/dt in²/s

Hence the expression that gives the rate of change of A with respect to t

is dA/dt = 4h * dh/dt in²/s

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