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Sagot :
We are given the relationship:
[tex]7r+4t=14[/tex]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:
[tex]7r=14-4t[/tex]Divide by 7:
[tex]r=\frac{14-4t}{7}[/tex]b. We use the function found in part a and evaluate it for t=-7:
[tex]\begin{gathered} r=\frac{14-4\cdot(-7)}{7} \\ \text{Operating:} \\ r=\frac{14+28}{7}=\frac{42}{7}=6 \end{gathered}[/tex]Thus, f(-7) = 6
c. Solve f(t) = 18
Again, we use the function from part a and solve the equation:
[tex]\frac{14-4t}{7}=18[/tex]Multiplying by 7:
[tex]\begin{gathered} 14-4t=7\cdot18 \\ 14-4t=126 \end{gathered}[/tex]Subtract 14 and then divide by -4:
[tex]\begin{gathered} -4t=126-14 \\ -4t=112 \\ t=\frac{112}{-4}=-28 \end{gathered}[/tex]t = -28
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