# Given that P varies jointly as u and B^2 and that when u= 4 and B= 5, P= 300, find P when u= 1...

## Question:

Given that P varies jointly as u and B^2 and that when u= 4 and B= 5, P= 300, find P when u= 1 and B= 11.

## Directly Proportion

When a variable varies either directly or inversely with two or more variables, the variable is said to vary jointly with both variables. An example is the area of a rectangle which varies jointly with the width and the length.

## Answer and Explanation:

As P varies jointly, the relationship can be written as:

\begin{align} &P\propto uB^2\\ &\text{Introducing a constant of proportionality,}\\ &P=kuB^2 \end{align}

We need to find the value of k using the fact that when u= 4 and B= 5, P= 300.

\begin{align} &300=4*5^2k\\ &300=100k\\ &k=3 \end{align}

The value of P when u=1 and B=11 will be:

\begin{align} &P=100*1*11^2\\ &P=121000 \end{align}