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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:

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


Learn more about this topic:

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Directly Proportional: Definition, Equation & Examples

from High School Algebra II: Help and Review

Chapter 1 / Lesson 23
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