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
Mumz [18]
3 years ago
12

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

rial for the base costs $10 per square meter. material for the sides cost $6 per square meter. find the cost of materials for the cheapest such container.
Mathematics
1 answer:
katrin [286]3 years ago
7 0

Answer:

The cost of materials for the cheapest such container is $163.54.

Step-by-step explanation:

A rectangular storage container with an open top is to have a volume of 10 m³.

The volume of the rectangle is

\text{Volume} =\text{Length} \times \text{Width} \times \text{Height}

Length of its base is twice the width.

Let Width be 'w'.

Length is l=2w.

Height be 'h'.

10 =2w\times w\times h

10=2w^2h

The height in terms of width is represented as,

h=\frac{10}{2w^2}

h=\frac{5}{w^2}

According to question,

The cost is 10 times the area of the base and 6 times the total area of the sides.

i.e. Cost is given by,

C=10(L\times W)+6(2\times L\times H+2\times W\times H)

C=10(2w\times w)+6(2\times 2w\times \frac{5}{w^2}+2\times w\times \frac{5}{w^2})

C=20w^2+\frac{120}{w}+\frac{60}{w}

C(w)=20w^2+\frac{180}{w}

To get the minimum value,

Differentiate the cost w.r.t 'w',

C'(w)=20\frac{d(w^2)}{dw}+180\frac{d(w^{-1})}{dw}

C'(w)=20\times 2w-180 w^{-2}

C'(w)=40w-\frac{180}{w^2}

To find critical points put derivate =0,

40w-\frac{180}{w^2}=0

40w=\frac{180}{w^2}

w^3=\frac{180}{40}

w=\sqrt[3]{4.5}

w=1.65

We find the second derivative to minimize,

C''(w)=40\frac{d(w)}{dw}-180\frac{d(w^{-2})}{dw}

C''(w)=40+360(w^{-3})

C''(w)>0

As C''(w)>0 it is the minimum cost.

The cost is minimum at w=1.65.

Substitute the values in the cost function,

C(1.65)=20(1.65)^2+\frac{180}{1.65}

C(1.65)=54.45+109.09

C(1.65)=163.54

Therefore, the cost of materials for the cheapest such container is $163.54.

You might be interested in
The square below represents one whole.
kupik [55]

Answer:

\text{Shaded area as fraction}=\frac{81}{100}

\text{Shaded area as decimal}=0.81

\text{Shaded area as percent of the whole}=81\%

Step-by-step explanation:

Please consider the attached image as the given square.

We are asked to express the shaded area as a fraction, a decimal, and a percent of the whole.

We can see that in our figure there are 100 squares as there are 10 rows and each row contains 10 squares.

We can also see that there are 81 shaded squares out of 100 squares, so we can represent it as a fraction as:

\frac{\text{Shaded squares}}{\text{Total squares}}

\text{Shaded area as fraction}=\frac{81}{100}

To convert the shaded area into decimal, we need to divide 81 by 100.

\text{Shaded area as decimal}=0.81

To convert the shaded area into percent, we need to multiply 0.81 by 100.

\text{Shaded area as percent of the whole}=0.81\times 100\%

\text{Shaded area as percent of the whole}=81\%

7 0
3 years ago
Read 2 more answers
PLEASE PLEASE PLEASE HURRY!
MariettaO [177]
I believe it might be A or C. Not really sure
5 0
2 years ago
A square is always a parallelogram.<br> True False
agasfer [191]

Answer:

yes,

Step-by-step explanation:

because of them being quadrilaterals

8 0
3 years ago
Read 2 more answers
Gabriela 30 in of ribbon to make bows each bow uses 5 in of ribbon how many ribbons dose Gabriela make
Shalnov [3]

Answer:

Gabriela Can Make 6 Bows.

Step-by-step explanation:

30 ÷ 5 = 6

So Gabriela Has Enough Ribbon To Make 6 Bows.

3 0
2 years ago
What equation represents the nth term of the sequence {2, -1, -4, -7, ...}
user100 [1]
You got a picture??????
7 0
2 years ago
Other questions:
  • Solve the proportion x+1/x-1 = 14/20
    7·2 answers
  • CHECK MY WORK PLEASE
    13·2 answers
  • What is the length of side BC?
    9·1 answer
  • Which statement about parallel lines is true?
    15·1 answer
  • If 75% of a number is 60 what is the number
    11·1 answer
  • Use a graphing calculator to solve (1/4) ^ x+2 = 6:
    14·1 answer
  • The eight segments from the center of a cube to the eight corners of the cube form the edges of six pyramids. If one edge of the
    13·1 answer
  • Which pairs of angles in the figure below are vertical angles?<br> Check all that apply.
    6·2 answers
  • Your long distance service provider charges you $.06 per minute plus a monthly access fee of $4.95. For referring a friend, you
    12·1 answer
  • Select the correct answer.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!