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
Anna [14]
3 years ago
6

A box with a square base and open top must have a volume of 296352 c m 3 . We wish to find the dimensions of the box that minimi

ze the amount of material used. First, find a formula for the surface area of the box in terms of only x , the length of one side of the square base. [Hint: use the volume formula to express the height of the box in terms of x .] Simplify your formula as much as possible.
Mathematics
1 answer:
mestny [16]3 years ago
5 0

Answer:

  • Base Length of 84cm
  • Height of 42 cm.

Step-by-step explanation:

Given a box with a square base and an open top which must have a volume of 296352 cubic centimetre. We want to minimize the amount of material used.

Step 1:

Let the side length of the base =x

Let the height of the box =h

Since the box has a square base

Volume, V=x^2h=296352

h=\dfrac{296352}{x^2}

Surface Area of the box = Base Area + Area of 4 sides

A(x,h)=x^2+4xh\\$Substitute h=\dfrac{296352}{x^2}\\A(x)=x^2+4x\left(\dfrac{296352}{x^2}\right)\\A(x)=\dfrac{x^3+1185408}{x}

Step 2: Find the derivative of A(x)

If\:A(x)=\dfrac{x^3+1185408}{x}\\A'(x)=\dfrac{2x^3-1185408}{x^2}

Step 3: Set A'(x)=0 and solve for x

A'(x)=\dfrac{2x^3-1185408}{x^2}=0\\2x^3-1185408=0\\2x^3=1185408\\$Divide both sides by 2\\x^3=592704\\$Take the cube root of both sides\\x=\sqrt[3]{592704}\\x=84

Step 4: Verify that x=84 is a minimum value

We use the second derivative test

A''(x)=\dfrac{2x^3+2370816}{x^3}\\$When x=84$\\A''(x)=6

Since the second derivative is positive at x=84, then it is a minimum point.

Recall:

h=\dfrac{296352}{x^2}=\dfrac{296352}{84^2}=42

Therefore, the dimensions that minimizes the box surface area are:

  • Base Length of 84cm
  • Height of 42 cm.
You might be interested in
Let f(x)=(x-2)^3+8 Find the inverse of f(x). Please show steps in written form would be gladly appreciated
Tatiana [17]

Hello from MrBillDoesMath!

Answer:

(x-8)^(1/3) +2

Discussion:

To find the inverse of a function swap the values of x and y in the original equation y = (x-2)^3 +8  and solve for y.

y = (x-2)^3 +8          =>  original function. swap x and y values

x = (y-2)^3 + 8        =>  subtract 8 from both sides

x - 8  = (y -2)^3        =>  take cube root of both sides

(x-8)^(1/3) = y - 2     => add 2 to both sides

(x-8)^(1/3) +2 = y      => y is the inverse



Thank you,

MrB

4 0
3 years ago
pranav's school is selling tickets to a play. On the first day of tickets sales the school sold 8 adult tickets and 4 child tick
viva [34]
Adult tickets are $8 and child tickets are $4
3 0
3 years ago
Jaime wrote 4.4_0.33=1.1 is his answer reasonable?why're why not?
shusha [124]
No you have to make sure to line up the decimals when subtracting them. Do not just line of the numbers, this wills get you the wrong answers. Hope this helps. If you need anything else just call for a helping hand.

7 0
3 years ago
PLEASE HELP ME IM STUCKK!!
galben [10]
I don’t know the answer I jus need to answer 2 questions
7 0
3 years ago
Which refers to a material that causes a wave to bounce off of it?
Stolb23 [73]

Answer:

A barrier, a surface or a boundary

Step-by-step explanation:

Reflection is the property waves that occurs due to the bouncing back of a wave after it strikes a barrier.

Reflection involves change in direction of a wavefront at an interface between two different media such that the wavefront returns into the medium from which it originated. In other words, the direction of the wave changes when they bounce of a barrier or a surface.

8 0
3 years ago
Other questions:
  • How do you add and subtract indices?
    15·2 answers
  • Each visitor at the Wacky World Water Park gets a free towel to use at the park. At the entrance, workers arrange the towels in
    12·1 answer
  • I need helpp plss ///:
    8·1 answer
  • Cuánto es -2+(-3)+4-(-3)-5
    13·2 answers
  • When it comes to money, you are either_____<br> or a_______
    13·1 answer
  • I NEED THE RIGHT ANSWER ASAP NO LINKS!!!
    5·2 answers
  • Pleasee helppp meee i’ll give 14 points! :)
    10·2 answers
  • 1?
    9·1 answer
  • 14) Write the scientific notation.<br> 12 million
    9·2 answers
  • Algebra 2 unit 5 lesson 6 homework
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!