Mathematics High School

The radius of a sphere is increasing at a rate of 0.5 centimeters per minute. At a certain instant, the radius is 17 centimeters.


What is the rate of change of the volume of the sphere at that instant (in cubic centimeters per minute)?

Answers

Answer 1

Using implicit differentiation, it is found that the rate of change of the volume of the sphere at that instant is of 1815.84 cubic centimetres per minute.

The volume of a sphere of radius r is given by:

[tex]V = \frac{4\pi r^3}{3}[/tex]

Applying implicit differentiation, the rate of change is of:

[tex]\frac{dV}{dt} = 4\pi r^2\frac{dr}{dt}[/tex]

In this problem, we have that [tex]\frac{dr}{dt} = 0.5, r = 17[/tex], thus:

[tex]\frac{dV}{dt} = 4\pi (17)^2(0.5) = 1815.84[/tex]

The rate of change of the volume of the sphere at that instant is of 1815.84 cubic centimetres per minute.

A similar problem is given at https://brainly.com/question/11496075

Related Questions

need help for 20 points.....plzzzzz



a^2/16-5ab+100b^2

Answers

is it factorization ...

Same I have the same problem

A football field is 360 feet long 160 feet wide. What is the area of the football field?

Answers

Answer:The area of the field is 57600 square feet.

Step-by-step explanation:

Answer:

57600 square feet.

Step-by-step explanation:

360 x 160 = 57600.

95 people went to a convention in San Francisco. They took three large vans and 50 people traveled by car. How many people fit in each large van. Write an equation first, then solve

Answers

Answer:

15

Step-by-step explanation:

95 - 50 = 45

45/3 = 15

Can someone tell me the answer to this please?

Answer choice C is incorrect

Answers

i’m pretty sure it’s A

pls help!!!!! i will give brainliest!!!!!

Answers

Answer:

I believe it to be the first answer. Since, similar triangles always have the same slope.

Step-by-step explanation:

what 5 divided by 475

Answers

Answer:

it's 0.01 (approx.)

Step-by-step explanation:

brainliest plz

Answer:

0.010526315789

OR

0.011

QUICK HELP!!!
Use the table of the probability distribution to find the variance

Answers

The answer is 0.6 to find the variance

Answer:

0.9

Step-by-step explanation:

What is the change from 3 to -2

Answers

-5 because 3 - 5 = -2
-5. 3 to 0 on a number line is 3 units, and 0 to -2 on a number line is 2 units. If you add these together it equals to 5, but the 3 is not being increased and instead decreased by 5 so this results in -5.

hi help pls will mark as brainlist!!!!!!!!!​

Answers

Answer:

The answer would be B.) 30.

Step-by-step explanation:

If it took 15 workers 20 day, and you want to split it so it gets done in 10 days, you would want 15 more workers to get the job done quicker, doing this would have you a total of 30 workers.

easy one - giving brainly!
CREATE 5 TOTAL. YOU CAN USE DECIMALS.​

Answers

Answer:

2:4

3:6

4:8

Step-by-step explanation:

Two numbers have a sum of 12 and a difference of 4. What is the smaller of the two numbers?
Α. 8
B. 6
C. 4
D. 3

Answers

Answer:

8

Explaining :

4/12 is 8

8+4=12

12-4=8

I hope it work :)

PLEASE HELP what is the term what is A in the sequence and what is the common ratio
for 3 9 27 54

Answers

Show me a pic of the question please

can someone pls help me with solving one variable expressions pls show your work too so i can understand thanks

Answers

Step-by-step explanation:

Basically, let's represent the amount of money earned in

July with x

and

August with x+90

x+(x+90)=350

2x+90=350

2x=350-90

2x=260

x=260÷2

x=130

So, Wanda earned $130 babysitting in July and in July, 130+90=$220.

Hope this helps!

PLEASE HELP IT’S DUE TMR

Answers

Answer:

13) 29.75

14) P : P

Step-by-step explanation:

13)

4 ------ 17

7 ------ x

4x = 7*17

4x = 119

x = 29.75

14) A square is a square it has all sides the same, so p : p is the ratio

Order the set of numbers from least to greatest.
-0.62
-0.615
-5/6

Answers

Answer:

5/6, -0.62, -0.615

Step-by-step explanation:

Hope this Help If i got it wrong I'm sorry I tried :(

The coordinates of the vertices of quadrilateral ABCD are A(−5, 1), B(−2, 5), C(5, 3), and D(2, −1).



Drag and drop the choices into each box to correctly complete the sentences.
The slope of AB is ⎯⎯⎯⎯⎯ , the slope of BC is ⎯⎯⎯⎯⎯ , the slope of CD is ⎯⎯⎯⎯⎯⎯ , and the slope of AD is⎯⎯⎯⎯⎯ . Quadrilateral ABCD is ————- because —————

Answers

Answer:

mab-2

mbc1/2

mcd-3/4

mad-3/4

Step-by-step explanation:

PLEASE HELP!!

Which of the following is a complex number?

Answers

Answer:

A

Step-by-step explanation:

not sure if it is correct

find the surface area of a open box of cardboard whose dimensions are 24cm, 18cm and 14cm

Answers

Answer:

hope this helps

Step-by-step explanation:

l = 24 cm

b = 18 cm

h = 14 cm

S.A of cuboid = 2 (l+b) × h

= 2 (42) × 14

= 84 × 14

= 1,176 cm²

Ruben and his friends are celebrating Ruben's birthday at Adventure Zone, which has trampolines, mini golf, laser tag, and an arcade. Ruben's mom gives 18 arcade tokens to each kid at the party. In all, she gives out 144 tokens.
Use an equation to find the number of kids at Ruben's party.

Answers

The number of kids that are at Ruben's party will be 8 kids.

Let the number of kids at the party be represented by x.Number of arcades token given to each person = 18Total number of arcade tokens given out = 144

Based on the information given, the equation to solve the question will be:

18 × x = 144

18x = 144

x = 144/18

x = 8

Therefore, there are 8 kids at the party.

Read related link on:

https://brainly.com/question/25294118

GIVING BRAINLIEST THOSE WHO PROVIDE PICTURES
graph the solution to this system of inequalities in the coordinate plane.
3y>2x+12
2x+y<-5

Answers

Here is the answer, you just simplify the equation to get y alone then graph :)

A square has an area of 4 square feet. What is the perimeter of the square, rounded to the nearest foot?

A. 8
B. 12.5
C. 28
D. 200​

Answers

Answer: A. 8 feet

Explanation:
A = L*W
Since the shape is a square, all sides are the same length. The square root of 4 is +- 2, but the value will be positive 2 because distance can’t be negative. If each side has a length of 2 feet, and a square has 4 sides, 2*4 = 8. The perimeter is 8 feet.

An item is regularly priced at $55. It is on sale for 20% off the regular price. What is the sale price?

Answers

Answer:

44

Step-by-step explanation:

   

Answer:

$44

Step-by-step explanation:

20% changes to 0.2

$55 x 0.2 = $11 ---> this is the sales discount

$55 - $11 = $44 ---> sale price

write the equation
it passes through (0,-2) and is perpendicular to the graph of y=5x+7

Answers

Step-by-step explanation:

the line passes through (0,-2) and perpendicular to the graph of y=5x+7.

solution :

the slope = -1/5

the equation :

y+2 = -1/5 (x-0)

y = -1/5x - 2

6. 2(x + 6) = 3(x + 1)

7. -2(4x+1) = 3(x+3)

8. 2(5x + 9) = 10x + 18

9. -5(x + 6) = -5x + 9

10. (h+20) = -5(h-6)
11. 3(2x-5) = -(x+1)
12. -3(d+1) = -2(3d-9)

Answers

Answer:

Hope this helps you

Step-by-step explanation:

6. x = 9

7. x = -1

8. x = True of all

9. no solution

10. h = 5/3

11. x = 2

12. d = 7

Find the slope, m, and y-intercept, b, for the graph of the linear equation represented by the table below.

Answers

Answer: m=1/2, b=-7

Step-by-step explanation:

(0,-7) is the y-intercept on the line...

i need help
2 x 3 + 4 - 6r2
A : -26
B : -22
C : -2
D : 10

Answers

6+4-36
-26
The answer is -26

what is the domain of the fraction​

Answers

The domain is the set of all x-values in that table:

   { -6, -1, 0, 3}

or

  { x | x = -6, -1, 0, 3 }


The ratio of boys to girls in Mr. Hakeem's class is 64. If there are 18 boys, how many girls
are there? (1 point)
A 2
B. 10
C. 12
D. 24
How many girls

Answers

Answer: C. 12 girls

Step-by-step explanation:

what is the value of Y

Answers

Answer:

150°

Step-by-step explanation:

the sum of the interior angles is 180° (triangle)

your answer in the picture

A rocket needs to reach a speed of 28,300 km/hr in order to get into orbit around Earth. How fast is this in miles per second.

Answers

Answer:

Step-by-step explanation:

1 km = 0. 621371 miles

28,300 km = 28,300* 0. 621371 miles = 17,584.7993 miles

1 hour = 60 *60 seconds  = 3,600 seconds

speed of 28,300 km/hr =

17,584.7993 miles / 3,600 seconds ≈ 4.88 miles / second

Other Questions
100 points will mark BRAINLYEST Define the type of muscle contraction that you experience most throughout your day and the one that you experience most when working out. Give examples to support your answer. A rectangular cake pan has a volume of 234 cubic inches. If the length of the pan is 9 inches and the width is 13 inches, what is the height of the pan? Part AHow does the author develop the central idea that people have varying opinions about how valuable a product is?A. The author discusses how systems for collecting taxes vary according to where people live.B. The author explains that the consumer's willingness to pay a certain price for a given item affects how the retailer sets the price.C. The author says that items such as shoes, bottled water, and garden hoses differ in price from place to place.D. The author explains that value-added tax is collected from manufacturers, retailers, and consumers.Part BWhich evidence from the text best supports the answer in Part A?A. "Once youve found all the parts you need, you could end up spending between $65 and $120 for your new garden hose!"B. "One of Germany's fiscal policies is to collect taxes in many stages during the production of items."C. "We al Need help ASAP ?!!!50 points A 125 mililiter solution of fabric dye contains 5 ml of hydrogen peroxide what percent concentration of hydrogen peroxide? What is the vertex of the graph of f(x) = 4(x+5)-1? Can someone help me with these two questions about the crucible and the author Arthur miller .1.Miller has written about similarities between the Salem trials and the HUAC investigations: Threehundred years apart, both prosecutors were alleging membership in a secret disloyal group; should theaccused confess, his honesty could be proved only in precisely the same way--by naming formerconfederates." Explain how these ideas are developed in each act of The Crucible.2. What is killer saying about those who stood fast against HUAC ( house un-American activities committee) Multiply. Write the answer in the simplest form.4/7 x 4 3/8 x 5/6 simplify 4h^j^-5k^7 Ans My brother lives there into Negative Anthocyanin are an alternative type of chlorophyll that some plants will produce depending on season or their general location. Based on the graph below, if I were to see a plant making strictly anthocyanin what color would it be? Blue Yellow Purple Red Green Find the domain and range of the given rational function f(x) =x+12x2 Solve for X then find the measure of angle B The Conjure-Man Dies Throughout the excerpt, the author spends a lot of time describing physical locations. In a essay wrote atleast 300 words in length,anylize an instance from The Conjure-Man Dies where the author uses a description of place to help create specific mood. Use details from the text to illustrate your answer. what conflict did the passengers on the mayflower face? what might have happened if they didnt agree to the mayflower compact? list the function done by living organisms please help me with this A student graphed f(x) = x and g(x) = -5f(x) + 2 on the same coordinate grid. Which statement describes how the graphs of f(x) and g(x) are related?The graph of f(x) is translated 5 units up to create the graph of g(x).The graph of g(x) is translated 2 units down and is less steep than the graph of f(x).The graph of f(x) is translated 5 units down to create the graph of g(x).The graph of g(x) is translated 2 units up and is steeper than the graph of f(x). An ice climber stands at the edge of a crevasse that is 115 Ft wide. The angle of the depression from the edge where she stands to the bottom of the opposite side is 52 degrees. How deep is the crevasse at this point? Round off to the nearest foot.