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
Alex_Xolod [135]
3 years ago
12

A rectangular box with a volume of 684 ftcubed is to be constructed with a square base and top. The cost per square foot for the

bottom is 20cents​, for the top is 10cents​, and for the sides is 2.5cents. What dimensions will minimize the​ cost?
Mathematics
1 answer:
umka21 [38]3 years ago
3 0

Answer:

The dimensions of the rectangular box is 29.08 ft×29.08 ft×4.85 ft.

Minimum cost= 26,779.77 cents.

Step-by-step explanation:

Given that a rectangular box with a volume of 684 ft³.

The base and the top of the rectangular box is square in shape.

Let the length and width of the rectangular box be x.

[since the base is square in shape,  length=width]

and the height of the rectangular box be h.

The volume of rectangular box is = Length ×width × height

                                                       =(x²h) ft³

According to the problem,

x^2h=684

\Rightarrow h=\frac{684}{x^2}.....(1)

The area of the base and top of rectangular box is = x² ft²

The surface area of the sides= 2(length+width) height

                                                =2(x+x)h

                                                =4xh ft²

The total cost to construct the rectangular box is

=[(x²×20)+(x²×10)+(4xh×2.5)] cents

=(20x²+10x²+10xh) cents

=(30x²+10xh) cents

Total cost= C(x).

C(x) is in cents.

∴C(x)=30x²+10xh

Putting h=\frac{684}{x^2}

C(x)=30x^2+10x\times\frac{684}{x^2}

\Rightarrow C(x)=30x^2+\frac{6840}{x}

Differentiating with respect to x

C'(x)=60x-\frac{6840}{x^2}

To find minimum cost, we set C'(x)=0

\therefore60x-\frac{6840}{x^2}=0

\Rightarrow60x=\frac{6840}{x^2}

\Rightarrow x^3=\frac{6840}{60}

\Rightarrow x\approx 4.85 ft.

Putting the value x in equation (1) we get

h=\frac{684}{(4.85)^2}

  ≈29.08 ft.

The dimensions of the rectangular box is 29.08 ft×29.08 ft×4.85 ft.

Minimum cost C(x)=[30(29.08)²+10(29.08)(4.85)] cents

                                =29,779.77 cents

You might be interested in
Please help I’m doing points
-Dominant- [34]

3 7/8

Hope this helps! :D

6 0
3 years ago
Find thee consecutive even integers such that the sum of twice the smallest number and three times the largest is 42
tekilochka [14]

Answer:

7,8,9

Step-by-step explanation:

The closest you can get to 42 with that equation and it has to use consecutive intergers is 41 and these numbers get you there.

4 0
2 years ago
If AB = 4 centimeters, which is closest to BC?
Misha Larkins [42]

Answer:

The correct answer AC = 11.52

Step-by-step explanation:

From the figure attached with this answer shows the triangle ABC.

BC=4 centimeters, m angle B=m angle c, and m angle a = 20 degrees

To find AC

From the figure we can see that D is the mid point and AD⊥BC

Then BD = CD = 4/2 = 2 cm

<BAD = 10° and <CAD = 10°

By using trigonometric ratio,

sin 10 = CD/AC = 2/AC

AC = 2/sin 10 = 2/0.1736 = 11.52

Therefore the value of AC = 11.52 cm

4 0
3 years ago
Read 2 more answers
I need Help with this pls
Ainat [17]

Answer: A

Step-by-step explanation:

4 0
2 years ago
11to the power of 3 multiply by 21 to the power of three
julia-pushkina [17]

Answer:

12326391

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
Other questions:
  • The angles shown in the illustration are complementary. the measure of the larger angle is 30° more than three times the measure
    8·1 answer
  • The price of gold is often reported per ounce. At the end of 2005, this price was $513. At the end of 2015, it was $1060. By wha
    14·1 answer
  • I just need help with the last part. the c) part<br> Describe the end behavior of the function:
    11·2 answers
  • What is the equation of a circle with center (8, 6) and radiuss5?
    8·1 answer
  • There was a surplus of office space in a city, with 400,000 square feet, or 16% of the total office space, vacant. How much offi
    12·1 answer
  • Show how to solve (3X+2)-(2X-1)
    13·1 answer
  • Pools are not selling well at Jay’s Store. So, he decides to put them on clearance for $19.99, plus an extra 20% off. Approximat
    8·2 answers
  • Ryan is making biscuits. The recipe call for 0.25 quart of milk and 2.5 cups of flour. He has 1/5 quart of milk and 9/4 cups of
    11·2 answers
  • How many solutions does this equation have?<br> 4(-3b - 14) = -12b
    9·1 answer
  • 5. Complete the following statement. Write your answer as a decimal or
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!