Answer:
Please see the attached file for the complete answer.
Step-by-step explanation:
A) Volume = l * w* h --> V = 7 * 5 * 4 --> V = 140 units³
B) 140 units³: Prism B has the same length, width, and height as A, just rotated.
C) As long as the tree numbers' product is 140 units³, it works.
Prism C: 140 * 1 * 1
Prism D: 14 * 2 * 5
From the ratio given you can determine that m is proportional to 1/(r^3). You can write this as m = k * 1/(r^3), k being your constant of proportionality. Then use this to calculate the next parts of the question.
<em><u>To </u></em><em><u>find:</u></em>
<em><u>=</u></em><em><u>></u></em><em><u> </u></em><em><u>The</u></em><em><u> </u></em><em><u>value</u></em><em><u> of</u></em><em><u> </u></em><em><u>x</u></em>
<em><u>=</u></em><em><u>></u></em>
<em><u>
</u></em>
<em><u>Now,</u></em><em><u> we'll</u></em><em><u> </u></em><em><u>move </u></em><em><u>-</u></em><em><u>8</u></em><em><u> </u></em><em><u>to </u></em><em><u>the</u></em><em><u> </u></em><em><u>other</u></em><em><u> </u></em><em><u>side </u></em><em><u>i.e </u></em><em><u>the </u></em><em><u>RHS </u></em><em><u>side,</u></em>
<em><u>which</u></em><em><u> </u></em><em><u>results</u></em><em><u> </u></em><em><u>in </u></em><em><u>the </u></em><em><u>change</u></em><em><u> </u></em><em><u>of </u></em><em><u>it's</u></em><em><u> </u></em><em><u>sign(</u></em><em><u>-</u></em><em><u> </u></em><em><u>converts</u></em><em><u> </u></em><em><u>into </u></em><em><u>+</u></em><em><u>)</u></em>
<em><u>=</u></em><em><u>></u></em>
<em><u>
</u></em>
<em><u>Now </u></em><em><u>,</u></em><em><u> we'll</u></em><em><u> </u></em><em><u>add </u></em><em><u>the </u></em><em><u>Numbers</u></em>
<em><u>=</u></em><em><u>></u></em>
<em><u>
</u></em>
<h2><em><u>Hence</u></em><em><u>,</u></em><em><u>-</u></em><em><u>3</u></em><em><u> </u></em><em><u>is </u></em><em><u>the</u></em><em><u> </u></em><em><u>required</u></em><em><u> </u></em><em><u>answer</u></em><em><u>.</u></em></h2>
<em><u>^</u></em><em><u>-</u></em><em><u>^</u></em>
She gonna need to buy 32 boxes because 315 divided by 10 is 31 r 5 and also you can't buy 31 boxes because 5 kids aren't gonna have pencils so she needs to buy 32 boxes of pencils