Let the sides of square base be "x" and height be "h" first come up with expressions for surface area and volume<span>SA=2<span>x2</span>+4hx=600</span>
<span>V=h<span>x2</span></span>Next get h in terms of x and sub it into Volume equation<span>h=<span><span>300−<span>x2</span></span><span>2x</span></span></span>
<span>→V=(<span><span>300−<span>x2</span></span><span>2x</span></span>)<span>x2</span></span>
<span>V=150x−<span>12</span><span>x3</span></span>maximize volume by setting derivative equal to 0<span><span><span>dV</span><span>dx</span></span>=150−<span>32</span><span>x2</span>=0</span>solve for x<span>x=10</span><span> which means h =10 max volume occurs when box is a cube 10^3 = 1000 cm^3</span>
You put a one becuse it repusents a 10 and your tencly adding a 10
Answer:
General Formulas and Concepts:
<u>Pre-Algebra</u>
- Order of Operations: BPEMDAS
<u>Algebra I</u>
- Slope Formula:
Step-by-step explanation:
<u>Step 1: Define</u>
<em>Find points from graph.</em>
Point (0, -2)
Point (-2, 0)
<u>Step 2: Find slope </u><em><u>m</u></em>
- Substitute:
- Add/Subtract:
- Divide:
And we have our final answer!
