1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Vinil7 [7]
3 years ago
12

If

dle" class="latex-formula">300 cm of material is available to make a box with a square base and an open top, find the maximum volume of the box in cubic centimeters. Answer to the nearest cubic centimeter without commas. For example, if the answer is 2,000 write 2000.

Mathematics
1 answer:
Artist 52 [7]3 years ago
6 0
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

You might be interested in
HELP ME I WILL GIVE BRAINLIEST California has a population of approximately 4 × 10^7 people and South Dakota has a population of
GaryK [48]

Answer:

40000000 800000

Step-by-step explanation:

whats the question here?

4 0
2 years ago
Read 2 more answers
The Rawesome Cafeteria manufactures round metal tabletops for restaurants. The machinist uses ¼ sheet of metal for each tabletop
Serjik [45]
Prime cost is the combination of a manufactured product's costs of direct materials and direct labor. In other words, prime cost refers to the direct production costs.
Prime cost=direct material cost+direct labor cost

Direct material cost of a tabletop is
380×(1÷4)=95 for each tabletop

Direct labor cost
The question says The machinist cuts and polishes five tabletops each hour
Which means 27.50 of direct labor to cut and polish 5 tabletops So direct labor cost for each tabletop is
27.50÷5=5.5

Finally the prime cost of cutting and polishing a tabletop is
Prime cost=95+5.5=100.5
5 0
3 years ago
Martha buys a surfboard that cost $405 for 40% off. How much money does she save?
alukav5142 [94]

Answer:

$162

Step-by-step explanation:

Discount = percentage discount ÷ 100 × original cost

Discount = \frac{40}{100} × $405 = $162

7 0
2 years ago
13 = m/4 + 7 can you show work too
lukranit [14]

The correct value of this equation is <u>m = </u><u>24</u>

<h3>Resolution method</h3>

This equation contains a fractional term. We note that the denominator of this equation is the <u>term 4</u>. Therefore, we will multiply the sides by <u>4</u>:

13 = m/4 + 7

13 . 4 = 4(m/4) + 7 . 4

52 = m + 28

Now, let's isolate the variable "as negative" and after the equality - we'll be subtracting the terms:

52 = m + 28

-m = 28 - 58

-m = -24

<u>m = 24</u>

Therefore, the correct value of this equation will be <u>m = 24</u>

7 0
1 year ago
A=1/2bh. A=200ft. H=10. What is b
Svetllana [295]

Answer:

B= \frac{2A}{H}

Step-by-step explanation:

If you noticed, A= \frac{1}{2}BH is the formula for finding the area for a triangle. Your goal is to get B by it's self. Your first step will be to clear of the fraction first, so you will multiply both sides by 2.   2(A)=2(\frac{1}{2}BH).    On the left, you have 2×A= On the right side, you have     2(\frac{1}{2}BH),     but since you have a number in the equation, you will only use 2×\frac{1}{2}. To solve  2×\frac{1}{2}, you will cnacel out both 2's and you have 1. 1×BH will still equal BH, so you are now left will B×H.

(Your new equation looks like this by the way).    2A=BH

Since you need to get B by its self, the way to clear the H away from the B is by dividing.  You will now divide the B and H aswell as 2A and H. (It will look like this) \frac{2A}{H} = \frac{BxH}{H} . (Again when you have the same number or letter, you cross it out. When you divide, you won't change anything on the left side, and all you have to do on the right id to cross out the H next to the B and cross out the H on the bottom of the equation). You should be left with \frac{2A}{H} = B. Now you can turn it around for your final answer. B= \frac{2A}{H}.

Please let me know if i helped, how I did, and if you have any questions.

3 0
3 years ago
Other questions:
  • Explain defined and undefined terms in geometry
    9·1 answer
  • Which of the expressions is rational?
    6·1 answer
  • Which value of x would make NO || KJ?<br> 1<br> 6<br> 8<br> 10
    6·2 answers
  • Identify the conic section represented by the equation y^2 -3x +4y +7 = 0
    15·2 answers
  • Simplify the expression 3(x + 3) - 2x
    11·1 answer
  • Find the volumes of the solids whose bases are bounded by the circle x^2 + y^2 = 9, with the indicated cross sections taken perp
    5·1 answer
  • Can anybody help me with this number 9 ? show work please and thank you
    12·1 answer
  • Could anyone help me on this? Thanks.
    13·2 answers
  • Simplify ((c∧6)÷(c-d))-3
    15·1 answer
  • Question 9 of 10
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!