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
Tanzania [10]
3 years ago
5

A rectangular storage container with an open top is to have a volume of 10 m3. the length of this base is twice the width. mater

ial for the base costs $10 per square meter. material for the sides costs $6 per square meter. find the cost of materials for the cheapest such container. (round your answer to the nearest cent.)

Mathematics
1 answer:
BartSMP [9]3 years ago
7 0
Refer to the diagram shown below.

The volume of the container is 10 m³, therefore
x*2x*h = 10
2x²h = 10
h = 5/x²        (1)

The base area is 2x² m².
The cost is $10 per m², therefore the cost of the base is
(2x²)*($10) = 20x²

The area of the sides is
2hx + 2(2xh) = 6hx = 6x*(5/x²) = 30/x m²
The cost is $6 per m², therefore the cost of the sides is
(30/x)*($6) = 180/x

The total cost is
C = 20x² + 180/x

The minimum cost is determined by C' = 0.
That is,
40x - 180/x² = 0
x³ = 180/40 = 4.5
x = 1.651
The second derivative of C is
C'' = 40 + 360/x³
C''(1.651) = 120 >0, so x = 1.651 m yields the minimum cost.

The total cost is
C = 20(1.651)² + 180/1.651 = $163.54

Answer: $163.54

You might be interested in
Someone pls help im struggling if you do tysm ! <333 :)
Allisa [31]

Answer:

everything except -1 will be the answer

Step-by-step explanation:

4n + 13 < 9

n < -1

if n is -1, the answer would be 9(INCORRECT)

if n is -2, the answer would be 5(CORRECT)

if n is -3, the answer would be 1(CORRECT)

if n is -4, the answer would be -3(CORRECT)

4 0
3 years ago
Read 2 more answers
Johan found that the equation –2|8 – x| – 6 = –12 had two possible solutions: x = 5 and x = –11. Which explains whether his solu
Effectus [21]
-2|8-x|-6=-12 \ \ \ |\hbox{add 6} \\&#10;-2|8-x|=-6 \ \ \ |\hbox{divide by (-2)} \\&#10;|8-x|=3 \\&#10;8-x=-3 \ \lor \ 8-x=3 \\&#10;-x=-3-8 \ \lor \ -x=3-8 \\&#10;-x=-11 \ \lor \ -x=-5 \\&#10;x=11 \ \lor \ x=5 \\&#10;\boxed{x=5 \hbox{ or } x=11}

It should be x=11 instead of x=-11, so he is not correct because he made a sign error.
6 0
3 years ago
Read 2 more answers
Distribute a negative -7.1h-(-2k-1)
Andrew [12]

Answer:

<h2>=-7.1h+2k+1</h2>

Step-by-step explanation:

-7.1h-(-2k-1)\\-\left(-2k-1\right):\quad 2k+1\\=-7.1h+2k+1

3 0
3 years ago
PLSSSSS HELPPPPPPPPPPPPPPP LOOK AT THE PICTURE
Lera25 [3.4K]
True because the ratios are a comparison of two or more numbers . I think
6 0
3 years ago
According to the line Gregg below what is the total number of tickets sold ?
podryga [215]

Answer:

The answer would be 155 tickets

6 0
3 years ago
Other questions:
  • A dress that normally cost $69.50 is on sale for 45% off what is the sales price of the dress
    10·2 answers
  • A power line is to be constructed from a power station at point A to an island at point C, which is 1 mi directly out in the wat
    15·1 answer
  • In San Jose a sample of 73 mail carriers showed that 30 had been bitten by an animal during one week. In San Francisco in a samp
    9·1 answer
  • Please help correct answer will be marked brainliest answer :)
    7·1 answer
  • Note: T is the midpoint of PO.<br> PT = 6x + 4 and TO = 52.
    15·2 answers
  • Abe deposited $600 in a savings account with simple interest. One year later, he had earned
    9·1 answer
  • hey anyone here! I need some help solving and understanding these please! I tried so hard but don't quite understand
    12·1 answer
  • Grandma Gertrude’s Chocolates, a family owned business, has an opportunity to supply its product for distribution through a larg
    7·1 answer
  • Y = 6x<br> 2х + Зу = -20
    14·1 answer
  • 2 kilometers to 72 meters write each ratio in simplest form
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!