Question

Given: y varies directly as x squared and inversely as z cubed. If y = 12 when x = 4 and z = 2, find x when y = 1.728 and z = 5.

Select one:
a. x=6
b. x=18
c. x=27
d. x=36

Answer 1

a

Explanation:

given y varies directly as x² and inversely as z³ then the equation relating them is

y =
`(kx^2)/(z^3)` ← k is the constant of variation

to find k use the condition y = 12 when x = 4 and z = 2 , then

12 =
`(k(4)^2)/(2^3)` =
`(16k)/(8)` ( multiply both sides by 8 )

96 = 16k ( divide both sides by 16 )

6 = k

y =
`(6x^2)/(z^3)` ← equation of variation

when y = 1.728 and z = 5 , then

1.728 =
`(6x^2)/(5^3)` =
`(6x^2)/(125)` ( multiply both sides by 125 )

216 = 6x² ( divide both sides by 6 )

36 = x² ( take square root of both sides )

`√(36)` = x , that is

x = 6