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
Margaret [11]
3 years ago
5

A rectangular box with a square base and a cover is to be built to contain 640 cubic feet. If the cost per square foot for the b

ottom is $15 and for the top and the sides is $10, what is the minimum cost of the constructed box?

Mathematics
1 answer:
mixer [17]3 years ago
8 0

Answer:

  $4800

Step-by-step explanation:

The cost is minimized when any pair of opposite faces of the box costs the same as any other pair. Since the top+bottom total $25 per square foot and the sides (left+right or front+back) total $20 per square foot, the area of a side must be 25/20 = 5/4 times the area of the top or bottom.

If we let x represent the length of one side of the square bottom, then 5/4x will be the height of the box. Its volume will be ...

  (5/4x)(x²) = 640 ft³

  x³ = (4/5)(640 ft³) = 512 ft³ . . . . . . multiply by 4/5

  x = 8 ft . . . . . . . . . . . . . . . . . . . . . . . take the cube root

The base area is then (8 ft)² = 64 ft², and the cost of the top+bottom is ...

  64 ft² × $25/ft² = $1600

The three pairs of opposite sides will cost 3×$1600 = $4800.

The minimum cost of the constructed box is $4800.

_____

You can also write an equation for the total cost in terms of x, the side length of the base. That cost function will be ...

  c(x) = 15x² + 10x² + 10·4x(640/x²)

This simplifies to ...

  c(x) = 25x² +25600/x

A graph shows the minimum is c(8) = 4800 (as above).

__

Algebraically, you can set the derivative to zero to find the value of x.

  dc/dx = 0 = 50x -25600/x²

  512 = x³ . . . . multiply by x²/50 and add 512

  8 = x . . . . . . . take the square root. Same solution as above. <em>Cost is minimized when the side length of the base is 8 ft</em>.

You might be interested in
Write answer in slope intercept form (3,-8); slope= -3
Slav-nsk [51]

Answer:

y=-3x-8

Step-by-step explanation:

The slope intercept form is y=mx+b.

The "mx" is the slope; which in this case is -3. So -3x.

The "b" is the y-intercept, which is this case is the -8 because it is the 2nd number in the coordinate point.

This is why the answer is y=-3x-8.

4 0
2 years ago
Read 2 more answers
Shawn graphed the points listed below.
Semenov [28]

Answer: A. (4, 4) and (4, 5)

Step-by-step explanation:

The same x value maps onto more than one y value.

6 0
2 years ago
A 14 inch pizza (diameter is 14) was cut in to 8 pieces. What is the angle measure of each slice? *
Luda [366]

Answer:

The angle for each slice is 45 degrees.

Step-by-step explanation:

In order to calculate the angle of each slice, we first need to calculate the total area of the pizza, because we will use that to find the area of each slice and as a result it's angle. To calculate the area of the pizza we must use:

pizza area = pi*r²

r = d / 2 = 14 /2 = 7 inches

pizza area = pi*(7)² = 153.86 square inches

Since the pizza was divided in 8 pieces, the area of each piece is given by the area of the pizza divided by the number of slices. We have:

slice area = pizza area  / 8 = 153.86 / 8 =19.2325 square inches

Each slice is a circle sector, therefore it's area is given by:

slice area = (angle*pi*r²)/360

Therefore we can solve for angle:

19.2325 = (angle*pi*7²)/360

angle*pi*49 = 6923.7

angle = 6923.7 / pi*49 = 45 degrees

The angle for each slice is 45 degrees.

4 0
3 years ago
What is 50+15d=125 equivalent to
zlopas [31]

Step-by-step explanation:

50-50+15d =125-50

15d = 75

15d/15=75/15

d=5

7 0
3 years ago
Read 2 more answers
How do I simplify this?
kakasveta [241]
I believe this would be the solution.

4 0
3 years ago
Read 2 more answers
Other questions:
  • One common system for computing a grade point average​ (GPA) assigns 4 points to an​ A, 3 points to a​ B, 2 points to a​ C, 1 po
    13·1 answer
  • I really need help please dont put a crazy answer for points I NEED HELP! WILL MARK BRAINLIEST!!! If Pam works more than 40 hour
    13·1 answer
  • Multiply the polynomials *<br> –6w(2w2 - 5)
    11·1 answer
  • A rental car company charges $60.00 just to rent a car, and $70.00 for each day you keep the car.
    13·2 answers
  • All I need are four equations of perpendicular lines that is all
    14·1 answer
  • What is the value of x?
    14·2 answers
  • Sharon has a carton of quilting notions. She has a total of 52 notions. She has 16 patterns. She has three times as many thimble
    11·1 answer
  • 15, 60,240,...<br> 15,60,240,...<br> \text{Find the 6th term.}<br> Find the 6th term.
    11·1 answer
  • Please help<br> pictures are down below
    7·1 answer
  • I don't understand would this be a linear function,quadratic function,or exponential function
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!