The length of the rectangle is changing at a rate of 4 cm/s and the ar...
Let the length be l, width be b and the area be A.
The Area is given by A=lb

Given that, dl/dt =4cm/s and dA/dt =8 cm/s
Substituting in the above equation, we get

Given that, l=4 cm and b=1 cm

The length of the rectangle is changing at a rate of 4 cm/s and the ar...
To find the rate of change of width, we need to use the formula for the area of a rectangle: A = length * width. We are given that the length is changing at a rate of 4 cm/s and the area is changing at a rate of 8 cm/s. We are also given the values of length and width at a particular point in time, which are 4 cm and 1 cm respectively.
Let's denote the rate of change of width as dw/dt (where t represents time). We can express the area as a function of time using the given values:
A = length * width
A = 4 cm * 1 cm
A = 4 cm^2
Now, we can differentiate both sides of the equation with respect to time (t):
dA/dt = (d(length)/dt) * width + length * (d(width)/dt)
Given that dA/dt = 8 cm/s, d(length)/dt = 4 cm/s, length = 4 cm, and width = 1 cm, we can substitute these values into the equation:
8 cm/s = 4 cm/s * 1 cm + 4 cm * (d(width)/dt)
Simplifying the equation, we have:
8 cm/s = 4 cm/s + 4 cm * (d(width)/dt)
Rearranging the terms, we get:
4 cm/s = 4 cm * (d(width)/dt)
Now, we can solve for (d(width)/dt):
(d(width)/dt) = (4 cm/s) / (4 cm)
(d(width)/dt) = 1 cm/s
Therefore, the rate of change of width is 1 cm/s. Option D is the correct answer.