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

Answer:

A) $f(t) = 2 - \frac{8}{5}\cdot t$, B) $f(-5) = 10$, C) $t = -15$ for $f(t) = 26$

Step-by-step 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.

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

$r = 2 -\frac{8}{5}\cdot t$

$f(t) = 2 - \frac{8}{5}\cdot t$

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

$f(-5) = 2 - \frac{8}{5}\cdot (-5)$

$f(-5) = 10$

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

$2 - \frac{8}{5}\cdot t = 26$

$\frac{8}{5}\cdot t = -24$

$t = -15$