Answer 29 to 33......

If <img src="https://tex.z-dn.net/?f=%20300cm%5E%7B2%7D%20" id="TexFormula1" title=" 300cm^{2} " alt=" 300cm^{2} " align="absmid

Artist 52 [7]

Check the picture below. Recall, is an open-top box, so, the top is not part of the surface area, of the 300 cm². Also, recall, the base is a square, thus, length = width = x.

$\bf \textit{volume of a rectangular prism}\\\\
V=lwh\quad 
\begin{cases}
l = length\\
w=width\\
h=height\\
-----\\
w=l=x
\end{cases}\implies V=xxh\implies \boxed{V=x^2h}\\\\
-------------------------------\\\\
\textit{surface area}\\\\
S=4xh+x^2\implies 300=4xh+x^2\implies \cfrac{300-x^2}{4x}=h
\\\\\\
\boxed{\cfrac{75}{x}-\cfrac{x}{4}=h}\\\\
-------------------------------\\\\
V=x^2\left( \cfrac{75}{x}-\cfrac{x}{4} \right)\implies V(x)=75x-\cfrac{1}{4}x^3$

so.. that'd be the V(x) for such box, now, where is the maximum point at?

$\bf V(x)=75x-\cfrac{1}{4}x^3\implies \cfrac{dV}{dx}=75-\cfrac{3}{4}x^2\implies 0=75-\cfrac{3}{4}x^2
\\\\\\
\cfrac{3}{4}x^2=75\implies 3x^2=300\implies x^2=\cfrac{300}{3}\implies x^2=100
\\\\\\
x=\pm10\impliedby \textit{is a length unit, so we can dismiss -10}\qquad \boxed{x=10}$

now, let's check if it's a maximum point at 10, by doing a first-derivative test on it. Check the second picture below.

so, the volume will then be at $\bf V(10)=75(10)-\cfrac{1}{4}(10)^3\implies V(10)=500 \ cm^3$

6 0

3 years ago

$248.62 rounded to the nearest dollar

nata0808 [166]

$249.......................................

7 0

3 years ago

Read 2 more answers

a recipe calls for 12 ounces of raisin. raisins come in boxes of 170 g. how many boxes of raisins are needed for the recipe?

Olin [163]

Hi there! Hope this helps, and if it does, please mark brainliest!

Answer:

2 boxes

Step-by-step explanation:

There are roughly 28 grams in an ounce. So if you have 12 ounces, times 28 by 12, which is 336, so you need 336 grams of raisins. Divide by 170, the number of grams in one box, which would be 1.98 boxes, but you have to round up, so you would need two boxes.

5 0

3 years ago

How to get to the answer

Ilia_Sergeevich [38]

Answer:

$\large\boxed{C)\ F(x)=2^x+1}$

Step-by-step explanation:

$C)\ F(x)=2^x+1\\\\\text{Put the values of x from the table to the equation of a function:}\\\\F(3)=2^3+1=8+1=9\qquad\ CORREC\\F(4)=2^4+1=16+1=17\qquad CORRECT\\F(6)=2^6+1=64+1=65\qquad CORRECT\\F(7)=2^7+1=128+1=129\qquad CORRECT\\F(8)=2^8+1=256+1=257\qquad CORRECT$

7 0

2 years ago

6a-2(4a-5)=40<br>How do I solve it

Elza [17]

Answer:

Distribute, then combine like terms, subtract 10 from both sides of the equation, simplify, divide both sides of the equation by the same term, and simplify to get your solution.

Step-by-step explanation:

1.) Distribute

6−2(4−5)=40

6−8+10=40

2.) Combine like terms

6a-8a+10=40

-2a+10=40

3.) Subtract 10 from both sides of the equation

-2a+10=40

-2a+10-10=40-10

4.) Simplify

subtract the numbers

-2a+10-10=40-10

-2a=40-10

subtract the numbers

-2a=40-10

-2a=30

5.) Divide both sides of the equation by the same term

-2a=30

$\frac{-2a}{-2} =\frac{30}{-2}$

6.) Simplify

cancel terms that are in both the numerator or denominator

$\frac{-2a}{-2} =\frac{30}{-2}$

a= $\frac{30}{-2}$

Divide the numbers

a= $\frac{30}{-2}$

a=-15

a=-15

7.) Solution

a=-15

8 0

3 years ago