The radius of a sphere is increasing at a rate of 5 mm/s. How fast is the volume increasing when the diameter is 100 mm?

Answers

Answer 1

Answer:

157,143 mm/s

Step-by-step explanation:

Formula for the volume of a sphere is;

V = 4/3 * pi * r^3

dv/dr = 4 pi r^2

dv/dt = dv/dr * dr/dt

dr/dt = 5 mm/s

dr/dt = 4 * pi * r^2

r = d/2 = 100/2 = 50 mm

dr/dt = 4 * 22/7 * 50^2 = 220,000/7

dv/dr = 220,000/7 * 5 = 157,142.8571428571

Approximately 157,143 mm/s


Related Questions


Please get back to ASAP I really need help with this

Mrs. Hopkins made four different pies for Thanksgiving dinner at her house. Each pie was the same size.
She cut the blueberry pie into 6 equal slices, the apple pie into 5 equal slices, the peach pie into 3 equal
slices, and the chocolate pie into 4 equal slices.
Her grandchildren. Alyssa, Bobby, Caitlin, and Dylan, each had one slice of pie but only ate a portion of
that slice. Each grandchild chose a different kind of pie.
Alyssa had the largest slice available and ate 1/4 of it
Bobby had the smallest slice available and ate 3/4 of it.
(The slice Caitlin had was larger than the slice Dylan had.)
Caitlin ate 1/2 of her slice.
• Dylan ate 2/3 of his slice.

What kind of pie did each person choose? And what fraction of the total pie did each person eat?

Answers

Answer:

Step-by-step explanation:

How do you graph the solution to inequality? y≤−2x+3

Answers

Answer:

Step-by-step explanation:

Y would equal 8 so then 2x+3 would be 10 so you multiply and get your answer!

Apply the Distributive Property to the following expression.
4(x+10)


A.4x + 14
B.4x + 10
C.4x + 40
D.x+ 40

Answers

The answer
is 4x+40 so C

12x + 4x + 25y + 15y A. 2(8x + 10 B. 4(4x + 10) C. 5(3x + 5y D. 8(2x + 5y​

Answers

Answer:

The answer is D.

Answer:

D. [tex]8(2x + 5y)[/tex]

Step-by-step explanation:

STEP 1: Add 12x and 4x.

[tex]16x+25y+15y[/tex]

STEP 2: Add 25y and 15y.

[tex]16x+40y[/tex]

STEP 3: Factor 8 out of 16x+40y.

[tex]8(2x+5y)[/tex]

PLEAASSSE HELP ASAP I WILL MARK →BRAINLIEST← AND 5 STARS!!!


Marni has 11 ounces of walnuts. She needs 6 ounces for one recipe and 14\frac {1}{4}41​ pound for another. There are 16 ounces in 1 pound.
Does she have enough?

Answers

Answer:Yes she has enough

Step-by-step explanation:

Total ounces=11

1st recipe=6 ounces

2nd recipe=1/4 ounces

1 pound =16 ounces

= 1/4 pounds × 16 ounces/1 pound

= 4 ounces

First recipe + Second recipe

= 6 ounces + 4 ounces

= 10 ounces.

10 ounces of walnuts and Marni has 11

12 times x tell me sponge

Answers

Answer: 12x

Step-by-step explanation:

Answer:

12x

Step-by-step explanation:

1. One week a student exercised 3 hours at school and 1/4 hour at home. If 1/4 of the student's total exercise came from playing basketball, how much time did the student spend playing basketball that week?

2. One week a student exercised 2 hours at school and 1/4 hour at home. If 1/4 of the student's total exercise came from playing soccer, how much time did the student spend playing soccer that week?

Answers

Answer:

1- The student spent 48 minutes and 45 seconds playing basketball.

2- The student spent 33 minutes and 45 seconds playing soccer.

Step-by-step explanation:

1- If during a week the student exercised for 3 hours at school, and for 1/4 hour at home, it could be said that the student exercised for a total of 195 minutes (60 x 3 + 60/4) . Now, if I exercise 1/4 of that time playing basketball, the student spent 48 minutes and 45 seconds playing that sport (195/4).

2- If during a week the student exercised for 2 hours at school, and for 1/4 hour at home, it could be said that the student exercised for a total of 135 minutes (60 x 2 + 60/4) . Now, if I exercise 1/4 of that time playing basketball, the student spent 33 minutes and 45 seconds playing soccer (135/4).

Can somebody solve number 5

Answers

hiiihere's your answer 4×2 8---------- = ------ 5×2 104×20 80---------- = ----------5×20 100

HOPE IT HELPS YOU OUT PLEASE MARK IT AS BRAINLIEST AND FOLLOW ME PROMISE YOU TO FOLLOW BACK ON BRAINLY.IN

Which of the following is not a characteristic of permanent life insurance?
O A. Paid out when you die
O B. Must be renewed periodically
O C. Lifetime coverage
O D. Ability to access cash value

Answers

The statement's ability to access cash value is not characteristic of permanent life insurance.

We have given that

The characteristic of permanent life insurance

We have to determine which statement is not correct.

A. Paid out when you die

B. Must be renewed periodically

C. Lifetime coverage

D. Ability to access the cash value

What is the characteristic of permanent life insurance?

Permanent life insurance refers to coverage that never expires, unlike term life insurance, and combines a death benefit with a savings component.

The two primary types of permanent life insurance are whole life and universal life.

Permanent life insurance policies enjoy favorable tax treatment.

Therefore the statement's ability to access cash value is not characteristic of permanent life insurance.

To learn more about the permanent life insurance visit:

https://brainly.com/question/27023711

#SPJ2

Answer:

B Must be renewed periodically

Step-by-step explanation:

Jenna goes fishing every Saturday morning. She is only allowed to catch a maximum of 222 fish each trip. The table below displays the probability distribution of XXX, the number of fish that Jenna catches in a trip. X= \# \text{ of fish}X=# of fishX, equals, \#, start text, space, o, f, space, f, i, s, h, end text 000 111 222 P(X)P(X)P, left parenthesis, X, right parenthesis 0.040.040, point, 04 0.320.320, point, 32 0.640.640, point, 64 Given that \mu_X=1.6μ X ​ =1.6mu, start subscript, X, end subscript, equals, 1, point, 6 fish, find the standard deviation of the number of fish that Jenna catches. Round your answer to two decimal places.

Answers

Answer: 0.57 fish. Khan academy told me.

Answer:

0.83

Step-by-step explanation:

step by step on Khan

which geometric series converges?

Answers

Answer:

Option (1)

Step-by-step explanation:

In a geometric series,

[tex]\sum_{n=0}^{\infty}ar^n=a+ar^1+ar^2+....[/tex]

Here r = [tex]\frac{a_n}{a_{n-1}}[/tex]

For |r| < 1, series will converge.

For |r| > 1, series will diverge.

Option (1)

Given geometric series is,

[tex]\frac{1}{2}+\frac{1}{4}+ \frac{1}{8}+ \frac{1}{16}.......[/tex]

Common ratio = [tex]\frac{\frac{1}{4}}{\frac{1}{2} }[/tex]

                        = [tex]\frac{1}{2}[/tex]

Since, [tex]\frac{1}{2}<1[/tex]

Series will converge.

Option (2)

[tex]\frac{1}{2}+1+2+4+......[/tex]

r = [tex]\frac{1}{\frac{1}{2}}=2[/tex]

Since, 2 > 1,

Series will diverge.

Option (3)

[tex]\frac{1}{2}+ \frac{3}{2}+ \frac{9}{2}+ \frac{27}{2}+......[/tex]

Common ratio 'r' = [tex]\frac{\frac{3}{2} }{\frac{1}{2} }=3[/tex]

Since, 3 > 1,

Series will diverge.

Option (4)

[tex]\frac{1}{2}+3+18+108+.....[/tex]

Common ratio 'r' = [tex]\frac{3}{\frac{1}{2}}=6[/tex]

Since, 6 > 1

Series will diverge.

Therefore, Option (1) will be the correct option.

Which expression is equivalent to 4−7?

A). 4 + 7

B). 4−( −7)

C). 4+(−7)

D). 7+(−4)

Answers

C. It’s 4 + (-7)
Since when you add a negative, it’s the same as subtracting

Answer:

-3

Step-by-step explanation:

Y/11=8


PLEASE ASAP ....

Answers

Answer:

y=88

Step-by-step explanation:

88÷11=8

8x11=88

....

Answer:

Y=88

Have a nice day and drink water!

select all numbers equivalent to -1 ?

Answers

Answer:

-1 / 0 + -1 and the list goes on

Step-by-step explanation:

Write the slope-intercept form of the equation of the line

4x + y = 2

Answers

Answer:

The equation in slope intercept form is y= 2 - 4x

Finish the distance formula. | P 1 P 2 | = d =

Answers

Answer:

d=2P^2

Step-by-step explanation:

Answer:

sqrt  (x2 - x1)^2 + (y2 - y1)^2

what is the value of y in the solution to the system of equations?
4x-2y=5
y=3x-1

Answers

Answer:

-5.5

How I solved it:

A helpful website that I use is called Desmos. It makes the graph for you.

Just type in your equation and it is good to go. My teacher showed it to me so you know that it is good.

8^1/6 x 2^x= 32^1/2
Work out the exact value of x.

Answers

Answer:

8^1/6 x 2^x= 32^1/2

Step-by-step explanation:

1/6 x 2^x= 32^1/2

factoring expression using GCF of 84+28

Answers

Answer:

The answer to yours is incorrect the answer is 112.

Step-by-step explanation:

Answer:

the answer would be 28(3+1).

Step-by-step explanation:

first you would try to find the GCF of the two numbers, which is 28. to find this you need to divide the two numbers by the GCF, which may take a few tries. then you would have to divide those two numbers by the GCF. your answer should look like this: 28(3+1)

If 1/4 is .25, what is the mixed number 6 1/4 in a decimal form?

PLZ HELP I'LL GIVE BRAINLIEST!

Answers

Answer:

6.25 is the answer

Step-by-step explanation:

PLEASE MARK BRAINLIEST

Rock that is formed by melting then cooling is which type of rock?
Question 9 options:

A Metamorphic

B Igneous

C Sedimentary

D Mineral

Answers

Answer:

B Igneous

Step-by-step explanation:

Igneous rock is formed by melting and then cooling.

Answer:

B

Step-by-step explanation:

Igneous

The point (3, y) lies on the line y = 4x + 5. Find the value of y.

Answers

Answer:

y = 17

Step-by-step explanation:

y = 4x + 5

since the x value is 3 you substitute it in

y = 4(3) +5

y = 12 +5

y = 17

mark me brainliest by clicking the crown at the bottom of this answer : )

Any two lines lie in exactly one plane true or false

Answers

Answer:

true

Step-by-step explanation:

Answer is true buceause the statmentis 100% true

7ft = __ inches. Show work

Answers

Answer:

Step-by-step explanation:

12 inches is in a foot

10 x 7= 70

2 x 7= 14

70+14=84

Find the time it takes for a rocket following the path, h(x) = - 3x2 + 18x, to reach a maximum. In your final answer, include all of your calculations and a verbal explanation of the process that you followed in your solution.

Answers

Answer:

it takes 3 seconds for it to get the the maximum height

Step-by-step explanation:

well this is easy bc it is negative so we know it goes down, meaning the vertex will be at the top/highest point.

so all u gotta do is find the vertex which is x=-b/2a

now we gotta plug the numbers in and solve

h(x)=-3x^2+18x

x=-18/2(-3)=-18/-6=3

voilà there is the answer, 3 seconds

Express this number in scientific notation. 0.0048

Answers

Answer

4.8 x 10^-3

Step-by-step explanation:

Find the missing measures. Write your numerical answers only with a comma in between.

Answers

Answer:

m∠T = 72°

m∠U = 54°

Step-by-step explanation:

Property of an isosceles triangle,

Opposite angles of two equal sides of an isosceles triangle are equal in measure.

By this property, in the given triangle STU,

Since, ST ≅ TU,

m∠S = m∠U = 54°

Since, sum of interior angles of a triangle is 180°

m∠T + m∠S + m∠U = 180°

m∠T + 54° + 54° = 180°

m∠T = 180° - 108°

m∠T = 72°

What is the rate of change ? Please help!

Answers

Answer:

It is 1000

Step-by-step explanation:

To find the unit rate, we divide y/x. In this case our y is the height (ft) and the x is the time(min).

If we divide 1000/1, we get 1000

If we divide 2000/2, we get 1000

and so on...

Hope it helps :^)

Tom bought a comic book for $5 at a discount of 20%. How much did the comic book
cost originally?

Answers

Answer:

0.4cents

Step-by-step explanation:

Is it possible to prove DOG is con to GED?​

Answers

Answer:

Yes

Step-by-step explanation:

The angles are identical, so they are congruent.

Hope I helped! Plz leave a comment and a rating!

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