Question

hail 0.5 inch deep and weighing 1800 pounds covers a roof. the hails weight varies directly with its depth. write an equation that relates d and w. then predict the weight on the room of hail that is 1.75 inches deep

Answer 1

In a directly proportional relationship, increasing one variable will increase another. The weight of the roof whose depth is 1.75 inches is 6,300 pounds.

What is the directly proportional relationship?

In a directly proportional relationship, increasing one variable will increase another. This directly proportional relationship between p and q is written as p∝q where that middle sign is the sign of proportionality.

Let there are two variables p and q. Then, p and q are said to be directly proportional to each other if p = kq, where k is some constant number called the constant of proportionality.

Given the hail's weight varies directly with its depth. Therefore, the relation can be written as,

Weight ∝ Depth

W∝D

Introducing the constant to remove the proportionality we will get the equation as,

W = kD

1800pounds = k × 0.5 inches

3600ponds/inches = k

Now, the weight of the roof whose depth is 1.75 inches can be written as,

W = kD

W = 3600 × 1.75

W = 6,300 pounds

Hence, the weight of the roof whose depth is 1.75 inches is 6,300 pounds.

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