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
iris [78.8K]
2 years ago
11

A rectangular box has a square base. The combined length of a side of the square base, and the height is 20 in. Let x be the len

gth of a side of the base of the box.
a. Write a polynomial function in factored form modeling the volume V of the box.
b. What is the maximum possible volume of the box?
Mathematics
1 answer:
aniked [119]2 years ago
7 0

Answer:

a. V = (20-x) x^{2} in^{3}  

b . 1185.185 in^{3}

Step-by-step explanation:

Given that:

  • The height:  20  - x (in )
  • Let x be the length of a side of the base of the box (x>0)

a. Write a polynomial function in factored form modeling the volume V of the box.

As we know that, this is a rectangular box has a square base so the Volume of it is:

V = h *x^{2} in^{3}

<=> V = (20-x) x^{2}  in^{3}

b. What is the maximum possible volume of the box?

To  maximum the volume of it, we need to use first derivative of the volume.

<=> dV / Dx = -3x^{2} + 40x

Let dV / Dx = 0, we have:

-3x^{2} + 40x  = 0

<=> x = 40/3

=>the height h = 20/3

So  the maximum possible volume of the box is:

V = 20/3 * 40/3 *40/3

= 1185.185 in^{3}

You might be interested in
Packages of laundry soap are labeled 70 oz, but they are actually filled with mean contents of 70.2 oz and standard deviation 0.
kozerog [31]

Answer:

Step-by-step explanation:

3 0
3 years ago
Amir has RM565. He spent all his money buying b pieces of clothing which cost Rm70 per piece and k pairs of shoes which cost RM9
agasfer [191]

Answer:

70b+95k=565. I think it's like this

6 0
2 years ago
Read 2 more answers
Given F(x) =x^2, choose whether the graph moves up down left or right.
malfutka [58]

Answer:

Left 7

Step-by-step explanation:

f(x)=a(x-h)^2+k

f(x)=(x-(-7))^2

-7 of x is to the left

8 0
3 years ago
2 rectangles are shown. The second rectangle is flipped. Li transformed rectangle ABCD. The image is shown. Does Li’s transforma
Over [174]

Answer:

the answer is c

Step-by-step explanation:

edge 2020

7 0
2 years ago
Read 2 more answers
25= 5(3X-4)^1/3<br> PLEASE HELP AND SHOW WORK!<br> THANKS SM
Effectus [21]

Answer:

x=43

Step-by-step explanation:

Given equation:

25=5(3x-4)^{\frac13}

Divide both sides by 5:

\implies 5=(3x-4)^{\frac13}

Cube both sides:

\implies 5^3=((3x-4)^{\frac13})^3

\implies 125=(3x-4)^{\frac33}

\implies 125=(3x-4)^1

\implies 125=3x-4

Add 4 to both sides:

\implies 129=3x

Divide both sides by 3:

\implies x=43

8 0
2 years ago
Read 2 more answers
Other questions:
  • Jasmine swims 12 laps every afternoon, Monday through Friday. How many laps does she swim in one week?​
    10·2 answers
  • Dixon is performing stunts for a show where he launches off from the edge of a ramp on his motorbike. The graph shown below trac
    10·1 answer
  • Geometry!!!!!!!!!!!!!!!!!!!!
    5·1 answer
  • How many solutions can be found for the system of linear equations represented on the graph?
    15·1 answer
  • Does anyone know the answer?
    10·1 answer
  • Write an equation of the line with the given slope and y-intercept
    10·1 answer
  • Hi I would really appreciate some help fast! This is 8th grade scatter plot question
    7·1 answer
  • Please someone I need the right answer will give brainiest if right​
    12·2 answers
  • Joseph has $620 to spend at a bicycle store for some new gear and biking outfits.
    9·1 answer
  • An artist has completed 1/4<br> of a penting in 2 weeks. At what rate is she working?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!