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
Assoli18 [71]
3 years ago
6

Among all right circular cones with a slant height of 24​, what are the dimensions​ (radius and​ height) that maximize the volum

e of the​ cone? The slant height of a cone is the distance from the outer edge of the base to the vertex. Let V be the volume of the cone. What is the objective function in terms of the height of the​ cone, h?
Mathematics
1 answer:
aleksklad [387]3 years ago
4 0

Answer:

5571.99

Step-by-step explanation:

We need to use the Pythagorean theorem to solve the problem.

The theorem indicates that,

r^2+h^2=24^2 \\r^2+h^2=576\\r^2=576-h^2

Once this is defined, we proceed to define the volume of a cone,

v=\frac{1}{3}\pi r^2 h

Substituting,

v=\frac{1}{3} \pi (576-h^2)h\\v=\frac{1}{3} \pi (576h-h^3)

We need to find the maximum height, so we proceed to calculate h, by means of its derivative and equalizing 0,

\frac{dv}{dh} = \frac{1}{3} \pi (576-3h^2)

\frac{dv}{dh} = 0 then \rightarrow \frac{1}{3}\pi(576-3h^2)=0

h_1=-8\sqrt{3}\\h_2=8\sqrt{3}

<em>We select the positiv value.</em>

We have then,

r^2 = 576-(8\sqrt3)^2 = 384\\r=\sqrt{384}

We can now calculate the maximum volume,

V_{max}= \frac{1}{3}\pi r^2 h = \frac{1}{3}\pi (\sqrt{384})^2 (8\sqrt{3}) = 5571.99

You might be interested in
So it says change the following fractions and mixed numbers to decimal numbers
puteri [66]

Answer:

2.16666666667 or rounded to 2.17

Step-by-step explanation:

first you have to change the mixed number to an improper fraction which would be 13/6 and then divide the numerator by the denominator

6 0
3 years ago
Which of these numbers has exactly four factors?<br>A6<br>B 12<br>C 18<br>D 24​
coldgirl [10]

Answer: 6

The factors of 6 are 1,2,3 and 6

5 0
3 years ago
1- find the first term= ?, 90, 540, 3240
Luda [366]

Answer:

1. 15

2. 8

Step-by-step explanation:

The two sequence are geometric progression GP, because they follow a constant multiple (common ratio)

The nth term of a GP is;

Tn = ar^(n-1)

Where;

a = first term

r = common ratio

For the first sequence;

The common ratio r is

r = T3/T2 = 540/90 = 6

r = 6

T2 = ar^(2-1) = ar

T2 = 90 = ar

Substituting the values of r;

90 = a × 6

a = 90/6

a = 15

First term = 15

2. The sam method applies here.

Common ratio r = T3/T2 = 128/32 = 4

r = 4

T2 = ar^(2-1) = ar

T2 = 32 = ar

Substituting the values of r;

32 = a × 4

a = 32/4

a = 8

First term = 8

4 0
3 years ago
What’s 23-(+25)-(-7)
Tamiku [17]

Answer: It =5

Can I get brainliest please and thank you :)

4 0
3 years ago
What is the third quartile of this data set? 21,24,25,28,29,35,37,39,42
tangare [24]

Answer:

121.5

Step-by-step explanation:

Find the mean of the last 4 numbers.

8 0
3 years ago
Other questions:
  • This is worth 20 points please help now it is an emergency. Please do 1 through 10
    14·1 answer
  • In a test of a particular weight loss program, weights of 40 subjects are recorded before and after the program. The before-and-
    10·2 answers
  • Solution for 2x + x + 5 = 4x +3
    10·2 answers
  • 1. Change each fraction to a percent. a. 6/100 b. 3/8 c. 357/100 d. 100/100
    5·1 answer
  • What is the answer to this equation 13-3/2x=34
    11·2 answers
  • The sum of 5 consecutive integers is 70 what are the numbers
    6·1 answer
  • Please help help help help​
    9·2 answers
  • THE PICTURE Is Up THERE PLEASE HELP ME WTHH
    11·1 answer
  • What two numbers have a product of -36 and a sum of<br> 5?
    6·1 answer
  • 19) The sales tax on a $105 digital camera is $7.15. What is the sales tax rate? (Round your answer to the nearest tenth.)​
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!