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
Snowcat [4.5K]
3 years ago
6

A rectangular storage container with an open top is to have a volume of 24 cubic meters. The length of its base is twice the wid

th. Material for the base costs 13 dollars per square meter. Material for the sides costs 9 dollars per square meter. Find the cost of materials for the cheapest such container.
Mathematics
1 answer:
Mariana [72]3 years ago
4 0

Answer:

419.25

Step-by-step explanation:

The calculation of the cost of materials for the cheapest such container is shown below:-

We assume

Width = x

Length = 2x

Height = h

where, length = 2 \times width

Base area = lb

= 2x^2

Side area = 2lh + 2bh

= 2(2x)h + 2(x)h

= 4xh + 2xh

Volume = 24 which is lbh = 24

h = \frac{24}{2x^2} \\\\ h = \frac{12}{x^2}

Now, cost is

= 13(2x^2) + 9(4xh + 2xh)\\\\ = 13(2x^2) + 9(4x + 2x)\times \frac{12}{x^2} \\\\ = 26x^2 + \frac{648}{x}

now we have to minimize C(x)

So, we need to compute the C'(x)

= 52x - \frac{648}{x^2}

C"(x)  = 52x - \frac{1,296}{x^3}

now for the critical points, we will solve the equation C'(x) = 0

= 52x - \frac{648}{x^2} = 0\\\\ x = \frac{648}{52}^{\frac{1}{3}}

C" = ((\frac{648}{52} ^{\frac{1}{3} } = 52 + \frac{1296}{(\frac{648}{52})^\frac{1}{3} )^3}\\\\ = 52 + \frac{1296}{\frac{648}{52} } >0

So, x is a point of minima that is

= (\frac{648}{52} )^\frac{1}{3}

Now, Base material cost is

= 13(2x^2)\\\\ = 26(\frac{648}{52} )^\frac{2}{3}

= 139.75

Side material cost is

= \frac{648}{x} \\\\ = \frac{648}{(\frac{648}{52})^\frac{1}{3}  }

= 279.50

and finally

Total cost is

= 139.75 + 279.50

= 419.25

You might be interested in
Complete the square to determine the minimum or maximum value of the function defined by the expression.
Igoryamba
Depends how you were taught to solve it but if it were me I’d choose B) minimum value at -6
7 0
3 years ago
What is the difference of the rational expressions below?
Stolb23 [73]

Answer: A

Step-by-step explanation:

We need to get the denominators to be same first before we can do anything to the numerator.

<em>The LCD (lowest common denominator) is </em>3x^{3}<em>. To find the LCD, multiply the denominators together: </em>x^{3}<em> · </em>3x<em> = </em>3x^{3.

Below, we are trying to get the denominators to equal the same or to 3x^{3}.

\frac{3}{3}  (\frac{4}{x^{3} } ) - \frac{x^{2} }{x^{2} }  (\frac{2x-1}{3x} )

\frac{12}{3x^{3} } - \frac{2x^{3}-x^{2} }{3x^{3} }

Now that the denominators are the same, we can subtract the numerators from each other.

\frac{ 12 - (2x^{3} -x^{2})\\}{3x^{3} } \\

\frac{12-2x^{3} +x^{2} }{3x^{3} }

Now, we can just reorganize the variables.

Answer:  A or \frac{-2x^{3} + x^{2}+12 }{3x^{3} }

7 0
3 years ago
ANSWER ASAP
Brut [27]
Honestly i have no clue
6 0
3 years ago
I will give you brainly if help
Vesnalui [34]

Answer:

i think its D im not sure tho

Step-by-step explanation:

3 0
2 years ago
The sum of two numbers is 27. The larger number is 3 more than the smaller number. What are the two numbers? PLEASE DO NOT GIVE
Contact [7]
Let x and y be the two numbers

Saying "The sum of two numbers is 27" means x+y = 27. The term "sum" is the result of adding. So the first equation is x+y = 27

The second equation is y = x+3 where we assume that y is the larger number of the pair. 

So your system of equations will be
x+y = 27
y = x+3

Use substitution to solve this system. 
x+y = 27
x+( y ) = 27
x + (x+3) = 27 ... notice how y has been replaced with x+3 (since y = x+3)
x+x+3 = 27
Solve for x and then use this to find y. I'll let you finish up.

If you need more help, then please let me know. 
4 0
3 years ago
Other questions:
  • What is the slope of the line that passes through (-2, 7) and (4, 9)?
    11·2 answers
  • Help please thank you
    6·2 answers
  • Solve for y in terms of w, x, and z.<br> x = żyw
    5·1 answer
  • Ryan isn’t riding his bike he bikes a distance of12 miles at a rate of4 miles per hour rearrange the distance formula d=rt to ao
    9·2 answers
  • translate into an algebraic expression and simplify if possible. what number exceeds m by five more than n
    6·1 answer
  • Which ordered pair is not a solution of y = 2x + 1?
    9·2 answers
  • Translate into algebra,<br> the sum of twice the number x and 25 more than 3 times the number y
    13·1 answer
  • 1/5x1/3 as a fraction please
    8·1 answer
  • There was a back ….
    7·1 answer
  • The figure shows a circle within a square. Find the circumference of the circle let π = 3.14. <br> ​
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!