For the average person that is still growing, the rate of change in weight W (in pounds) with respect

to height h (in inches) is approximately dW/dh=0.0015h^2 pounds per inch. Suppose that the average
person that is 60 inches tall weighs 108 pounds. Find the weight of an average person that is 5 feet
10 inches tall.

dW/dh = .0015 h^2

W = constant + .0005 h^3
108 = c + .0005(60)^3
108 = c + 108
c = 0
so
W = .0005 h^3
W(70) = .0005 (70)^3
= 171.5

To find the weight of an average person who is 5 feet 10 inches tall, we need to convert the height to inches first.

1 foot is equal to 12 inches, so 5 feet is equal to 5 * 12 = 60 inches.

Thus, the height of an average person who is 5 feet 10 inches tall is 60 + 10 = 70 inches.

Now, let's use the given information to solve for the weight of a person at that height.

We are given that the rate of change in weight with respect to height is given by dW/dh = 0.0015h^2 pounds per inch.

Substituting the height h = 60 inches into the formula, we can find the weight at that height:

dW/dh = 0.0015(60^2)
dW/dh = 0.0015(3600)
dW/dh = 5.4 pounds per inch

Now, we can use the initial weight given to find the weight at the new height:

Weight at h = 60 inches = 108 pounds

Let's assume the weight at h = 70 inches is W.

We can set up a proportion to solve for W:

(Weight at h = 60 inches) / (height change from 60 to 70 inches) = (Weight at h = 70 inches) / (1 inch)

108 / (70 - 60) = W / 1

108 / 10 = W

W = 10.8 pounds per inch

Therefore, the weight of an average person who is 5 feet 10 inches tall is approximately 10.8 pounds per inch.

To find the weight of an average person who is 5 feet 10 inches tall, we first need to convert their height into inches.

1 foot = 12 inches. Therefore, 5 feet = 5 * 12 = 60 inches.

Adding the additional 10 inches, the total height is 60 + 10 = 70 inches.

Now, we use the given rate of change formula to calculate the weight difference between the average person's height of 60 inches and the new height of 70 inches.

dW/dh = 0.0015h^2

dW/dh = 0.0015 * 60^2

dW/dh = 0.0015 * 3600

dW/dh = 5.4 pounds per inch

Since the initial weight of an average person who is 60 inches tall is 108 pounds, we can find the weight difference by multiplying the rate of change (5.4 pounds per inch) by the height difference (70 - 60 = 10 inches).

Weight difference = 5.4 pounds per inch * 10 inches

Weight difference = 54 pounds

To find the weight of an average person who is 5 feet 10 inches tall, we add the weight difference to the initial weight:

Weight = 108 pounds + 54 pounds

Weight = 162 pounds

Therefore, the weight of an average person who is 5 feet 10 inches tall is 162 pounds.