Respuesta :
When two quantities (x , y) varies directly, means they increase together or decrease together, we use one of these rules
[tex]\begin{gathered} y=kx \\ OR \\ \frac{y_1}{y_2}=\frac{x_1}{x_2} \end{gathered}[/tex]In the question, y varies directly with square root x, so the rule will be
[tex]\frac{y_1}{y_2}=\frac{\sqrt{x_1}}{\sqrt{x_2}}[/tex]Since y is 48 when x = 144, then
[tex]\begin{gathered} y_1=48 \\ x_1=144 \end{gathered}[/tex]We need to find y when x = 79
[tex]\begin{gathered} y_2=? \\ x_2=79 \end{gathered}[/tex]Let us substitute them in the rule
[tex]\frac{48}{y_2}=\frac{\sqrt{144}}{\sqrt{79}}[/tex]By using cross multiplication
[tex]\begin{gathered} \sqrt{144}\times y_2=48\times\sqrt{79} \\ \sqrt{144}y_2=426.633332 \end{gathered}[/tex]Divide both sides by square root 144
[tex]\begin{gathered} \frac{\sqrt{144}y_2}{\sqrt{144}}=\frac{426.633332}{\sqrt{144}} \\ y_2=35.552777 \end{gathered}[/tex]Round it to 2 decimal places
[tex]y_2=35.55[/tex]To check your answer look at the values of x and y
Since x decreased from 144 to 79, y also decreased from 48 to 35.55
So your answer is right
The value of y is 35.55
