Question

Express the statement as an equation. Use the given information to find the constant of proportionality.

R is inversely proportional to the square root of x. If$x=121$, then$R=2.5$.

Short answer

The equation is expressed as$R=\frac{k}{\sqrt{x}}$ and constant of proportionality is $k=27.5$.

Step-by-step solution

Step 1. Apply the concept of Inverse variation.

Two quantities are inversely proportional if on increasing one quantity the other quantity also decreases. And on decreasing one quantity the other quantity increases.

Mathematically it is expressed as$y=\frac{k}{x}$ where y and x are quantities and k is the constant of proportionality along with the condition $k\ne 0$.

It is read as y varies inversely with x or y is inversely proportional to x.

Step 2. Example of Inverse variation.

To denote the statement that a number is inversely proportional to the square of other number, denote first number by pand second number by q. Therefore, it is expressed as $p=\frac{k}{q^2}$ where k is the constant of proportionality along with the condition $k\ne 0$.

Step 3. Evaluate the expression.

Consider the provided statement R is inversely proportional to the square root of x.

Compare it with the expression $y=\frac{k}{x}$.

This means y is inversely proportional to x.

When expressions are compared $y=R\text{and}x=\sqrt{x}$.

Therefore, the equation is $R=\frac{k}{\sqrt{x}}$.

According to the question$R=2.5\text{and}x=121$

Replace R by 2.5 and x by 121 to find the value of k.

$\begin{array}{c}2.5=\frac{k}{\sqrt{121}}\\ k=27.5\end{array}$

Therefore, constant of proportionality is 27.5.

Thus, the equation is expressed as$R=\frac{k}{\sqrt{x}}$ and constant of proportionality is $k=27.5$.