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
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

You might be interested in
Do yall know any easy way to do slope​
mart [117]

Answer:

To find the slope of two given points, you can use the point-slope formula of (y2 - y1) / (x2 - x1). With the points plugged in, the formula looks like (3 - 2) / (4 - 1). Simplify the formula to get a slope of ⅓.

Step-by-step explanation:

7 0
2 years ago
Read 2 more answers
What is the perimeter of a rectangle which measures 300m long and 78m 60 cm wide?​
Paraphin [41]

Answer:

75720cm or 757.2m

Step-by-step explanation:

300m = 30000cm

78m & 60cm=7860cm

perimeter of rectangle = 2(length) + 2(width)

2(30000) + 2(7860) = 75720cm or 757.2m

8 0
3 years ago
The length of a rectangle is 7 inches more than twice the width. The
solmaris [256]

Answer:

Length: 25

Width: 9

Step-by-step explanation:

3 0
3 years ago
in a final exam you have four multliple choice questions left to do. each questions has five suggested answers and only one of t
kompoz [17]

Answer:

The probability that you get zero questions correct is 0.4096

The probability that you get one questions correct is 0.4096

The probability that you get three questions correct is 0.0256

Step-by-step explanation:

These probability can be describe with a Binomial Distribution. These distribution can be used when we have n identical and independent situations in which there is a probability p or probability of success and a probability q or probability of fail. Additionally q is equal to 1 - p. The probability of x for a situation in which we can apply binomial distribution is:

P( x,n,p) = n Cx * p^{x } * q^ {n-x}

Where x is the variable that says the number of success in the n situations

And nCx is calculate as:

nC x = \frac{ n!}{ x! (n-x)! }

From the question we can identify that:

  • n is equal to 4 multiple choice question
  • p is 1/5 or 0.2, the probability of get one question correct
  • q is 4/5 or 0.8, the probability of get one question incorrect

Then the probability of get zero questions correct of 4 questions is:

P( 0, 4, 0.2) = 4 C0 * p^{0 } * q^ {4-0}= 0.4096

The probability of get one question correct of 4 questions is:

P( 1, 4, 0.2) = 4 C1 * p^{1 } * q^ {4-1}= 0.4096

The probability of get three questions correct of 4 questions is:

P( 3, 4, 0.2) = 4 C3 * p^{3 } * q^ {4-3}= 0.0256

8 0
3 years ago
Draw a set of objects where you can find a fractional part of the group using the total number of objects by using subgroups
lara31 [8.8K]
We divide the total set into several sub-sets (subgroups) that contain the exact same number of members. This way we know the number of total members by adding the number of total subsets.
5 0
2 years ago
Read 2 more answers
Other questions:
  • A square has side lengths of 2x inches. An equilateral triangle has side lengths of (2x+1/3) inches. If the square and the trian
    10·2 answers
  • Sports City is having a blowout sale on sports equipment. You have a total of $450 to spend. What discount would have to be offe
    10·1 answer
  • Multiplying a number by 4/5 then dividing by 2/5 is the number same as multiplying by what number ?
    5·1 answer
  • Flower pots cost $60.25 each.
    10·1 answer
  • 5x - 4y = 1 <br> 2x + 3y = 5<br> show your work
    13·2 answers
  • Please help me find the answer
    11·1 answer
  • governor A earns 52,035 more than governor b. total of their salaries is 291,035 find the salaries of each.
    5·1 answer
  • 6p = -42 what is the answer???????????
    12·2 answers
  • I’ll give brainliest
    7·1 answer
  • Find the axis of symmetry and the vertex of the graph of y=3x^2+2x
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!