Question

Consider the relationship 7r+4t=14.a. Write the relationship as a function r=f(t).b. Evaluate f(−7).c. Solve f(t)=18.

Answer 1

We are given the relationship:

`7r+4t=14`

a. It's required to find a relationship where r is a function of t. To do that, we need to solve the equation for r.

Subtract 4t:

`7r=14-4t`

Divide by 7:

`r=(14-4t)/(7)`

b. We use the function found in part a and evaluate it for t=-7:

`\begin{gathered} r=(14-4\cdot(-7))/(7) \\ \text{Operating:} \\ r=(14+28)/(7)=(42)/(7)=6 \end{gathered}`

Thus, f(-7) = 6

c. Solve f(t) = 18

Again, we use the function from part a and solve the equation:

`(14-4t)/(7)=18`

Multiplying by 7:

`\begin{gathered} 14-4t=7\cdot18 \\ 14-4t=126 \end{gathered}`

Subtract 14 and then divide by -4:

`\begin{gathered} -4t=126-14 \\ -4t=112 \\ t=(112)/(-4)=-28 \end{gathered}`

t = -28