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
Which of the following values are solutions to the inequality 10+ x &gt; 7?
Tanzania [10]

Answer:

II

Step-by-step explanation:

All the other options create a number that is smaller than 7, while the inequality suggests otherwise.

While, II create the number 9 - which is indeed bigger then 7

Glad to help ÷)

7 0
3 years ago
Help, please!!!<br><br> Simplify. (4/9)^2=
alina1380 [7]

Answer:

Exact form: \frac{16}{81}

Decimal form: 0.1975308

8 0
1 year ago
What is the slope of the line given by the following equation? Give an exact number.  -13x 5y=-7
Black_prince [1.1K]
The slope should be 13/5x
8 0
3 years ago
Write the equation of a line with a slope of 4 and a y-intercept of −3.
olga_2 [115]

Answer:

D. y = 4x − 3

Step-by-step explanation:

Just took the test and got 100%

7 0
3 years ago
What is the y-intercept Of the function Represented by the table of values belowX -2 1 2 4 7 y 15 6 3 -3 -12
Kipish [7]

Given:

The table of values.

To find:

The y-intercept of the given function.

Solution:

The table of values represents a linear function because the rate of change is constant.

Consider any two points from the given table. Let the two points are (-2,15) and (1,6). Then the equation of the linear function is

y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)

y-15=\dfrac{6-15}{1-(-2)}(x-(-2))

y-15=\dfrac{-9}{1+2}(x+2)

y-15=\dfrac{-9}{3}(x+2)

y-15=-3(x+2)

Adding 15 on both sides, we get

y=-3x-6+15

y=-3x+9

Putting x=0, we get

y=-3(0)+9

y=0+9

y=9

The y-intercept is 9. Therefore, the correct option is C.

8 0
2 years ago
Read 2 more answers
Other questions:
  • Does the product of diagonals of trapezoid equal to its area
    7·1 answer
  • HELP!!!In the expression 100 a/b, if a is greater than b, which statements are true? b ≠ 0. Select all that apply.
    7·1 answer
  • The streptococci bacteria population N at time t (in months) is given by N = N0e 2t where N0 is the initial population. If the i
    10·1 answer
  • Find the distance between the two points.
    15·1 answer
  • Emily is a diver. Today she descended to a
    11·2 answers
  • Text Jim Belushi Lanka Lanka ​
    6·1 answer
  • What is the area of the base ? / / / / /
    8·1 answer
  • What is the sum of the measures of the interior angles of a decagon?​
    11·1 answer
  • True or False: An outlier is a point for which the actual value of y is far from the predicated value.
    15·1 answer
  • Select the symbol = (equal to) or ≠ (not equal to) to make the expression true. <br> {0} ? { }
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!