Mathematics, 08.04.2020 04:22 Travisbennington

A storage shed is to be built in the shape of a box with a square base. It is to have a volume of 686 cubic feet. The concrete for the base costs $5 per square foot, the material for the roof costs $9 per square foot, and the material for the sides costs $3.50 per square foot. Find the dimensions of the most economical shed.

Answers: 2

Show answers

Answers

Answer from: oof40

Therefore the dimension of box is 7 ft by 7 ft by 14 ft.

Step-by-step explanation:

Given that, a storage shade is be built in the shape of a box with a square base.

Let the height of the box be h and the length of one side of the square base be x.

The area of the square base is = side²

=x²

The volume of the box is = area of the base × height

=x²h

According to the problem,

x²h=686

$\Rightarrow h=\frac{686}{x^2}$ .......(1)

The concrete for the base costs $5 per square foot.

The material for the base costs =$ 5x²

The material for the roof costs $9 per square foot.

The material cost for roof is =$9x²

The material for the sides costs $3.50 per square foot.

The material cost for sides =$(3.50× 4xh )

=$14xh

Total cost =$(5x²+9x²+14xh)

=$(14x²+14 xh)

Let

C = 14x²+14 xh

Putting $h=\frac{686}{x^2}$

$C=14x^2+14 x.\frac{686}{x^2}$

$\Rightarrow C=14x^2+\frac{9604}{x}$

Differentiating with respect to x

$C'= 28x-\frac{9604}{x^2}$

Again differentiating with respect to x

$C''= 28+\frac{19208}{x^2}$

To find the dimension set C'=0

$28x-\frac{9604}{x^2}=0$

$\Rightarrow 28x=\frac{9604}{x^2}$

$\Rightarrow x^3=\frac{9604}{28}$

$\Rightarrow x=7$

Now,

$C''|_{x=7}= 28+\frac{19208}{7^2}0$

Since at x=7, C''>0, So at x=7 , The cost of material will be minimum.

The height of the box is $h=\frac{686}{x^2}$

$=\frac{686}{7^2}$

=14 foot

Therefore the dimension of box is 7 ft by 7 ft by 14 ft.

The cost of the material is $=14x^2+\frac{9604}{x}$

$=14(7)^2+\frac{9604}{7}$

=$2,058

Answer from: Quest

what does muffins have to do with anything?

step-by-step explanation:

Answer from: Quest

solution:

→c= a b , that is product of a and b is possible only when when a is m × n matrix and b is n × p matrix.

that is, number of columns of a= number of rows of b.

so, size of matrix , c= a b is , if a = (m × n)matrix

b= (n × p)matrix

then a b = [ (m × n)matrix] ×[ (n × p)matrix ]

→→c= a b= [m × p ] matrix

→→size of product a b will be equal to = number of rows of a × number of columns of b

Another question on Mathematics

Mathematics, 21.06.2019 18:00

Me, prove a quadrilateral with vertices g(1,-1), h(5,1), i(4,3) and j(0,1) is a rectangle using the parallelogram method and a rectangle method.

Answers: 3

Answer

Mathematics, 21.06.2019 19:00

Samantha is growing a garden in her back yard. she spend $90 setting up the garden bed and buying the proper garden supplies. in addition, each seed she plants cost $0.25. a. write the function f(x) that represents samantha's total cost on her garden. b. explain what x represents. c. explain what f(x) represents. d. if samantha plants 55 seeds, how much did she spend in total?

Answers: 2

Answer

Mathematics, 21.06.2019 20:30

Steve had 48 chocolates but he decided to give 8 chocolats to each of his f coworkers. how many chocolates does steve have left

Answers: 1

Answer

Mathematics, 21.06.2019 22:00

Problem situation: caren is making rice and beans. she can spend no more than $10 on ingredients. she buys one bag of rice for $4.99. beans cost $0.74 per pound. how many pounds of beans, x, can she buy? inequality that represents this situation: 10≥4.99+0.74x drag each number to show if it is a solution to both the inequality and the problem situation, to the inequality only, or if it is not a solution.

Answers: 1

Answer

You know the right answer?

A storage shed is to be built in the shape of a box with a square base. It is to have a volume of 68...

Questions