Thread: Help with an algebra problem

1. Help with an algebra problem

Hello everyone. I need some help with this problem on my homework. Maybe just some tips in what to do first. This is my first time taking a math course in a few years and this is part of a review chapter before we get started with the actual text. I would really like to have a better understanding of the material before we start.

A gas station stores its gasoline in underground tanks that are right circular cylinders lying on their sides. The volume V of the gasoline in the tanks(in gallons) is given by the following formula:

$v=40\,{h}^{2}\sqrt {96\,{h}^{-1}- 0.608}$

If h = 29 inches, how much gasoline is in the tank?

thank you

2. Originally Posted by blackwrx
...
A gas station stores its gasoline in underground tanks that are right circular cylinders lying on their sides. The volume V of the gasoline in the tanks(in gallons) is given by the following formula:

$v=40\,{h}^{2}\sqrt {96\,{h}^{-1}- 0.608}$

If h = 29 inches, how much gasoline is in the tank?

...
Plug in the value h = 29 into the given equation:

$v=40\cdot {h}^{2}\sqrt {96\,{h}^{-1}- 0.608}~\implies~v(29)= 40\cdot {29}^{2}\sqrt {\dfrac{96}{29}- 0.608}\approx 55300$

But the unit of the result confuses me a bit: v has the dimension $\dfrac{(inch)^2}{\sqrt{inch}}$

Normally the volume should have the dimension $(inch)^3$

3. could you care to expand anymore on the process of solving it? I am really not understanding it.

4. Originally Posted by earboth
Plug in the value h = 29 into the given equation:

$v=40\cdot {h}^{2}\sqrt {96\,{h}^{-1}- 0.608}~\implies~v(29)= 40\cdot {29}^{2}\sqrt {\dfrac{96}{29}- 0.608}\approx 55300$
There really is nothing more to solving it. You are given the equation $v=40\cdot {h}^{2}\sqrt {96\,{h}^{-1}- 0.608}$ with the variable 'h' and then you are give a value for 'h'. Just substitute the 'h' value into the given equation and either plug what you get in your calculator or solve it by hand. So in this case you would enter this $v(29)= 40\cdot {29}^{2}\sqrt {\dfrac{96}{29}- 0.608}\approx 55300$ into your calculator and voila you have an answer.