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patriot [66]
3 years ago
14

A circular cylindrical container, open at the top, and having a capacity of 24pi cubic inches, is to be manufactured. If the cos

t of the material used for the bottom of the container is three times that used for the curved part and if there is no waste of material, find the dimensions which will minimize the cost
Mathematics
1 answer:
otez555 [7]3 years ago
5 0

Answer: radius r = 2 inches

height h = 6 inches

Step-by-step explanation:

Given;

Volume V = 24πin3

Volume of a cylinder is given by

V = πr^2h

h = V/πr^2. ....1

Where, h = height and r = radius of cylinder

For the surface area of the cylinder with open top. we have,

S = 2πrh + πr^2

For the cost of materials used, let k represent the cost of materials used for the body of the cylinder.

Then, for the bottom will be 3k

Total cost will be represented by C, which gives

C = 2πrhk + 3πr^2k. .....2

Substituting eqn 1 to 2, we have;

C = 2πrVk/πr^2 + 3πr^2k

C = 2Vk/r + 3πr^2k

The material cost is minimum at dC/dr = 0

dC/dr = -2Vk/r^2 + 6πrk =0

6πrk = 2Vk/r^2

r^3 = 2V/6π

r = (2×24π/6π)^-3

r = (8)^-3

r = 2

Substituting r = 2 into eqn1

h = 24π/π(2^2)

h = 24/4 = 6

h = 6

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4 0
3 years ago
What is the perimeter of the actual garden?
Lilit [14]

Answer: 576 inches or 48 feet

Step-by-step explanation:

set up a proportion where \frac{drawing AB}{actual AB} =\frac{drawing perimeter}{actual perimeter}

so you get drawingAB = 24 in

actualAB = 18 feet = 18 * 12 in = 216 in

drawing perimeter = 64 in

so plug these in to get\frac{24}{216} =\frac{64}{actual perimeter}

rearrange to get actual perimeter = \frac{216 * 64}{24}

and solve to get 576 inches or 576/12 = 48 feet

4 0
3 years ago
3 (2x-1 ) +7 = - 44 ( solve for x)
s344n2d4d5 [400]

Answer:

x = - 8

Step-by-step explanation:

To solve for x, isolate it by "moving" everything else over to the other side. This is done in reverse BEDMAS order using the reverse operations of number you want to move.

3 (2x-1 ) +7 = - 44   Simplify first using distributive property over the brackets

6x - 3 + 7 = - 44    Combine like terms, terms that have the same variables

6x + 4 = - 44

6x + 4 - 4 = - 44 - 4   Subtract 4 from both sides to cancel it out on the left side

6x = - 48

6x/6 = - 48/6   Divide by sides by 6 to cancel out the 6 from 6x

x = - 8    Final answer

8 0
3 years ago
HELP!!!
Tom [10]

Answer:

x + (x + 2) = 30

Step-by-step explanation:

Number of Pennies = x

Number of Nickels = x + 2

Total = 30

x + (x +2) = 30

Hope it helps

8 0
2 years ago
Read 2 more answers
Tom has 25 bumblebee marbles and Marcus has a few more than Tom. If they have 56 marbles in all, how many bumblebee marbles does
vodomira [7]

Answer:

56-25

= 31

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
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