Question

100 Points! Algebra question. Photo attached. Please show as much work as possible. Thank you!

Answer 1

Explanation:

Ok so, as given in the table, the cost of the 3rd tank is 800$, we can thus determine the cost of 1 cubic inch for a tank and use that to determine the cost of the other tanks.

`volume =L* W* H\\=24* 24* 24\\=13824 in^3`

thus, to compute the cost of one cubic inch, we can divide the cost by the volume of the 3rd tank (in cubic inches)

`(800)/(13824)=0.0579`
`usd/in^3`

now, we can determine the dimensions of the second tank that will make it cost 150$

`0.0579* 18* W* 24=150`

`W=(150)/(0.0579* 18* 24) =6 in.`

Now to determine the cost of the first tank, we can multiply its volume by the cost per cubic inch:

`cost=0.0579*36* 36* 36=2700`$

As of question B, the cost will increase as the width increases.

For Question C, we can find the volume of the sphere by the formula:

`volume=(4)/(3)\pi r^3 =(4)/(3)\pi * 24^3=57905 in^3`

To find the cost of that tank, we just multiply its volume by the cost per unit volume:

`cost=57905* 0.0579=3352`$ (roughly)