Question

F(t) = 212 - 61


what the value of t when F(t)= 140 ?

Answer 1

`t = -7\ \ \ or\ \ t = 10`

Explanation:

Given

`f(t) = 2t^2 - 6t`

Required

Find t, when
`f(t) = 140`

Substitute 140 for f(t) in
`f(t) = 2t^2 - 6t`

`140 = 2t^2 - 6t`

Divide through by 2

`(140)/(2) = (2t^2 - 6t)/(2)`

`70 = t^2 - 3t`

`t^2 - 3t = 70`

Subtract 70 from both sides

`t^2 - 3t - 70= 70 - 70`

`t^2 - 3t - 70= 0`

Expand

`t^2 -10t + 7t - 70 = 0`

Factorize:

`t(t - 10) + 7(t - 10) = 0`

`(t + 7)(t - 10) = 0`

Split:

`t + 7 = 0\ \ \ or\ \ t - 10 = 0`

`t = -7\ \ \ or\ \ t = 10`

Hence, the values of t are -7 and 10