Question

Write a function describing the relationship of the given variables.

A
varies directly with the square root of
r
and when
r
=
16
,
A
=
40



A
=

Answer 1

A = 10
`√(r)`

Explanation:

Given A varies directly with the square root of r then the equation relating them is

A = k
`√(r)` ← k is the constant of variation

To find k use the condition r = 16 , A = 40

k =
`(A)/(√(r) )` =
`(40)/(√(16) )` =
`(40)/(4)` = 10

A = 10
`√(r)` ← equation of variation

Answer 2

The function is A = 10√r

Explanation:

* Lets explain the meaning of direct variation

- The direct variation is a mathematical relationship between two

variables that can be expressed by an equation in which one

variable is equal to a constant times the other

- If Y is in direct variation with x (y ∝ x), then y = kx, where k is the

constant of variation

* Now lets solve the problem

# A is varies directly with the square root of r

- Change the statement above to a mathematical relation

∴ A ∝ √r

- Chang the relation to a function by using a constant k

∴ A = k√r

- To find the value of the constant of variation k substitute A and r

by the given values

∵ r = 16 when A = 40

∵ A = k√r

∴ 40 = k√16 ⇒ simplify the square root

∴ 40 = 4k ⇒ divide both sides by 4 to find the value of k

∴ 10 = k

- The value of the constant of variation is 10

∴ The function describing the relationship of A and r is A = 10√r