Answer: 5 milimeters.
Step-by-step explanation:
The formula for calculate the volume of a rectangular prism is:
Where "V" is the volume, "l" is the lenght, "w" is the width and "h" is the height.
You know that the volume, the lenght, and the width of this rectangular prism are:
Substitutute these values into the formula and solve for the the height "h":
Height of the woman = 5 ft
Rate at which the woman is walking = 7.5 ft/sec
Let us assume the length of the shadow = s
Le us assume the <span>distance of the woman's feet from the base of the streetlight = x
</span>Then
s/5 = (s + x)/12
12s = 5s + 5x
7s = 5x
s = (5/7)x
Now let us differentiate with respect to t
ds/dt = (5/7)(dx/dt)
We already know that dx/dt = 7/2 ft/sec
Then
ds/dt = (5/7) * (7/2)
= (5/2)
= 2.5 ft/sec
From the above deduction, it can be easily concluded that the rate at which the tip of her shadow is moving is 2.5 ft/sec.
