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
sam and jose mowed 2/3 of the yard. jose mowed 3/4of that amount. whta part of the yard did jose mow?
guapka [62]

Answer:

09

Step-by-step explanation:

34

3 0
2 years ago
Factor 3x 2 - 15x - 42. 3(x - 2)(x - 7) 3(x - 2)(x + 7) 3(x - 7)(x + 2)
Anna71 [15]
3*(x-7)*(x+2)
last option
7 0
3 years ago
Read 2 more answers
Help me please this is due today
mojhsa [17]

Answer:

your answers obviously 210

6 0
3 years ago
Read 2 more answers
There are 1,994 strawberries picked from the farmif the strawberries are sorted equally into six bins, how many strawberries wil
irakobra [83]

Answer:

332

the reason why I think it's $332 is because if you do 1,994 / 6 then that equals 332 I don't know if you get it right if you do great job if you don't I understand

7 0
2 years ago
Which graph shows the equation v=4+2t
ehidna [41]
You need to give options for future reference
5 0
3 years ago
Other questions:
  • Solve the formula for the variable y.
    9·1 answer
  • Pls help me guys! This is super hard
    6·2 answers
  • Define negative integer. Give an example of a negative integer and then give its opposite
    15·1 answer
  • The function f(t) represents the cost to connect to the Internet at an online gaming store. It is a function of t, the time in m
    9·2 answers
  • A sugar mixture has 3 parts water and 2 parts sugar. Suppose the chef adds one more part to each. What is the new ratio of sugar
    10·2 answers
  • NEED HELP ASAP!!! Solve 0 = (3x - 4) / 5
    8·1 answer
  • In the grade 9, the ratio of girls to boys is 17:8. What percent of the grade 9 are boys?
    9·1 answer
  • URGENTTTT! please help me with these four problems! having trouble I will give thanks and brainliest.
    6·2 answers
  • Write an equation to model each problem. Solve the equation.
    8·1 answer
  • Identify the terms and like terms in the expression 2x2 – 3+6+4r.
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!