Question

Consider the relationship 5r+8t=10 A. write the relationship as a function r=f(t) B. Evaluate f(-5) C. solve f(t)= 26

Answer 1

A)
`f(t) = 2 - (8)/(5)\cdot t`, B)
`f(-5) = 10`, C)
`t = -15` for
`f(t) = 26`

Explanation:

A) Let be
`f(t) = r` and
`5\cdot r + 8\cdot t = 10`, the latter expression is a function in implicit form and we need to turn it into its explicit form, where
`t` is the independent variable.

`5\cdot r = 10 - 8\cdot t`

`r = 2 -(8)/(5)\cdot t`

`f(t) = 2 - (8)/(5)\cdot t`

B) If we know that
`t = -5`. then
`f(-5)` is:

`f(-5) = 2 - (8)/(5)\cdot (-5)`

`f(-5) = 10`

C) If we know that
`f(t) = 26`, then we solve for
`t`:

`2 - (8)/(5)\cdot t = 26`

`(8)/(5)\cdot t = -24`

`t = -15`