Chapter 5, Problem 11TP

Solution

To calculate: The value of $q$ when $r=5,s=-3,\text{ and }t=25$.

The value of $q$ when $r=5,s=-3,\text{ and }t=25$ is $31.5$.

Given information:

The variable $q$ varies jointly with $r$ and the square of $s$ and inversely with the square root of $t$ . $q=-1.75$ , when $r=-2,s=1,\text{ and }t=16$.

Formula used:

Two variables $x\text{ and }y$ show inverse variation if they are related as below:

  $y=\frac{a}{x}$.

  $z$ varies jointly with $x\text{ and }y$ is shown as:

  $z=axy$.

Where, $a$ is a constant.

Calculation:

It is given that the variable $q$ varies jointly with $r$ and the square of $s$ inversely with the square root of $t$ , so

  $q=\frac{ar{s}^2}{\sqrt{t}}$ ……. (1)

Substitute $q=-1.75$ , $r=-2,s=1,\text{ and }t=16$ in equation (1) and solve for $a$.

  $\begin{array}{c}-1.75=\frac{a\left(-2\right){\left(1\right)}^2}{\sqrt{16}}\\ -1.75=\frac{-2a}{4}\\ a=\frac{-1.75\times 4}{-2}\\ a=3.5\end{array}$

The value of $q$ when $r=5,s=-3,\text{ and }t=25$ will be

  $\begin{array}{c}q=\frac{3.5\left(5\right){\left(-3\right)}^2}{\sqrt{25}}\\ =\frac{157.5}{5}\\ =31.5\end{array}$

Therefore, value of $q$ when $r=5,s=-3,\text{ and }t=25$ is $31.5$.