Question

Y varies as t. If y = 6 when t =4, calculate:

a) the value of y, when t = 6
b) the value of t, when y = 4

Answer 1

see explanation

Explanation:

given y varies as t , then the equation relating them is

y = kt ← k is the constant of variation

to find k use the condition y = 6 when t = 4

6 = 4k ( divide both sides by 4 )

`(6)/(4)` = k , that is

k =
`(3)/(2)`

y =
`(3)/(2)` t ← equation of variation

(a)

when t = 6 , then

y =
`(3)/(2)` × 6 = 3 × 3 = 9

(b)

when y = 4 , then

4 =
`(3)/(2)` t ( multiply both sides by 2 to clear the fraction )

8 = 3t ( divide both sides by 3 )

`(8)/(3)` = t