Given the following function:
[tex]h(r)=\sqrt{4-r}[/tex]
We will find the value of (r) when 3h(r)+2=4
So, we can write the following equation:
[tex]3\sqrt{4-r}+2=4[/tex]
We will solve the equation as follows:
1) subtract 2 from both sides
[tex]\begin{gathered} 3\sqrt{4-r}+2-2=4-2 \\ 3\sqrt{4-r}=2 \end{gathered}[/tex]
2) Divide both sides by 3
[tex]\sqrt{4-r}=\frac{2}{3}[/tex]
3) Square both sides to eliminate the square root.
[tex]\begin{gathered} 4-r=(\frac{2}{3})^2 \\ \\ 4-r=\frac{4}{9} \end{gathered}[/tex]
4) Combine the like terms
[tex]\begin{gathered} r=4-\frac{4}{9} \\ \\ r=\frac{32}{9} \end{gathered}[/tex]
So, the answer will be r = 32/9
