Question

Assume that r varies directly as p. What is the constant of proportionality if r = 3 when p = 15.

a. k = 3
b. k = 45
c. k = 1/5
d. k = 5​

Answer 1

c

Step-by-step explanation:

given that r varies directly as p, then the equation relating them is

r = kp ← k is the constant of variation

to find k use the condition r = 3 when p = 15

3 = 15k ( divide both sides by 15 )

`(3)/(15)` = k , then

k =
`(1)/(5)`

Answer 2

To determine the constant of proportionality k when r varies directly with p, and given that r = 3 when p = 15, we divide r by p, which results in k = 1/5.

Step-by-step explanation:

When a student asks to assume that r varies directly as p, and wants to know the constant of proportionality when r = 3 when p = 15, we can use the formula r = kp where k is the constant of proportionality.

To find k, we simply divide r by p using the given values:

1. Substitute the given values into the equation: 3 = k * 15.
2. Divide both sides by 15 to solve for k: k = 3 / 15.
3. Simplify the fraction to get the constant of proportionality: k = 1/5.

Therefore, the constant of proportionality is k = 1/5, which corresponds to option (c).