The volume of a sphere is decreasing at a constant rate of 23 cubic centimeters per
second. At the instant when the volume of the sphere is 7 cubic centimeters, what is
the rate of change of the radius? The volume of a sphere can be found with the
equation V 28. Round your answer to three decimal places.

Answers

Answer 1

The rate of change of the radius is 1.32cm²/s

The formula for calculating the volume of a sphere is expressed as:

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

The rate of change of the volume is given as:

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

Given the following paramters;

dv/dt = 23cm³/s

Volume = 7cm³

Get the radius of the sphere:

7 = 4/3 πr³\

21 = 4πr³

r³ = 21/4π

r = 1.18 cm

Get the rate of change of the radius to have:

[tex]23 = 4(3.14)(1.18)^2 \frac{dr}{dt} \\23 = 17.48 \frac{dr}{dt} \\\frac{dr}{dt}=1.32cm^2/s[/tex]

Hence the rate of change of the radius is 1.32cm²/s

Learn more on volume of a sphere here: https://brainly.com/question/22807400


Related Questions

Lee's Leather Store marked down leather jackets 10 percent. What is the sale price of a
leather jacket regularly priced at $130?
O $103
O $113
O $123
O $117

Answers

$117 is the correct answer to that question !

Combine the like terms to create an equivalent expression.
\large{9y+y}9y+y

Answers

Answer:

20y

Step-by-step explanation:

Estimation Rita goes to the mall. If x is the number of items she ​bought, the expression 18.54x+23 gives the amount she spent in dollars at one store. Then she spent 25 dollars at another store. Find the expression which represents the amount Rita spent at the mall. Then estimate how much Rita spent if she bought 2 items.

Answers

Answer:

18.54x +48$85

Step-by-step explanation:

The total amount Rita spent is ...

  (18.54x +23) +(25) = 18.54x +48 . . . total spent

__

When x=2, that is approximately ...

  (18.5)(2) + 48 = 37 +48 = (40 -3) +(50 -2) = (40 +50) -(3 +2) = 90 -5 = 85

Rita spent about $85 if she bought 2 items.

_____

Additional comment

Estimation is often done using 1 significant figure. In this case, that would mean rounding the equation to 20x+50, so it would give a value of 90 when x=2.

An additional task when estimating is to estimate the error in the estimate. Here, using 20x+50 has an error of approximately 1.5x+2 (too high), so the error for 2 items will be about (1.5(2)+2) = 5. That is, the estimate of 90 is approximately 5 too high. Even this estimate has a remaining small error of 0.04x (too low).

Please help meeee! Need the answer for the first box, no phony answers please! Thanks for your help, and happy holidays!

Answers

Answer:

y=2(x+5)^2-4.

Step-by-step explanation:

By solving a little bit, we get the vertex to be (-5, -4). Plugging the info given and the vertex into the vertex form, we get y=2(x+5)^2-4. You have a happy holiday season, too!

Sam paid $50 for her new skateboard. In addition, she paid $3.50 in taxes. What was the tax rate on Sam's purchase?

Answers

Answer: $53.50 ?

Step-by-step explanation:

Please help in this!

Answers

Step-by-step explanation:

Correct option is C)

41−

21+

19−

9

=

41−

21+

19−3

=

41−

21+

16

=

41−

21+4

=

41−

25

=

41−5

=

36

=6

[tex] \sqrt{41 - \sqrt{21 + \sqrt{19 - \sqrt{9} } } } \\ = \sqrt{41 - \sqrt{21 + \sqrt{19 - 3} } } \\ = \sqrt{41 - \sqrt{21 + \sqrt{16} } } \\ = \sqrt{41 - \sqrt{21 + 4 } } \\ = \sqrt{41 - \sqrt{25} } \\ = \sqrt{41 - 5} \\ = \sqrt{36} \\ = 6[/tex]

Answer:

a) 6

Hope you could get an idea from here.

Doubt clarification - use comment section.

Please someone help meee! It’s advanced algebra

Answers

Answer: I think it would be 80 feet I hole I’m correct.

Step-by-step explanation: So to explain 20 + 50 is 80 and that’s how I got the answer I am not 100% sure but I wanted to help you :-)

Anand's garden is 70m long. If it is a square type and he has to fence with barbed wire of 3 rounds. What is the total length of the wire?

please give a valid and step by step explanation and answer this will give u an extra 5 points

Answers

Answer:

If her garden is 70m long, and it's a square type, wouldn't that suggest that her garden is 280m long?(70m X 4) And if this is the case, her garden would be 280 X 3=840 since there are 3 rounds?

Step-by-step explanation:

Answer: 840m

what percent increase is 1/3 to 1/6

Answers

Answer:

50% increase

Step-by-step explanation:

half of 6 is 3 thus 50%, and vise versa.

Triangle J K L is shown. Point M is the midpoint of side K L and point J is the midpoint of side J L. The length of K J is 12.8 meters, the lengths of J N and N L are 3.7 meters, and the lengths of K M and M L are 5.9 meters. Which statements about triangle JKL are true? Select two options. M is the midpoint of line segment KJ. N is the midpoint of line segment JL. MN = One-halfKJ MN = 4.4m MN = ML

Answers

Answer:

1 and 3

Step-by-step explanation:

Answer:

B) N is the midpoint of line segment JL.

D) MN = 1/2 KJ

Step-by-step explanation:

edgeeee

The sales tax on a surfboard is $12 what is the percent of sales tax?

Answers

The percent of the sales tax would be 5%.

Find the size of unknown angles ​

Answers

Answer:

hope it helps.

plzz give me brainliest

Help me pleaseeeeeeeeeeeeeee

Answers

The formula to find the volume of a cube is:

volume= a^3

OR

volume= a*a*a

(a stands for the side length)

The way you would write it is:

V=2.8^3

Then you solve.

You would get 21.952

But since you need to round to the tenth place it would be:

22

Hope this helps! :)

Adam eats 2 apples in 5 minutes, at this rate how many apples will Adam eat in a hour?
6
10
24
120

Answers

Answer:

24 apples

Step-by-step explanation:

60 divided by 5 is 12 then you multiply 2 which is 24:)

Maria earns $12/hour as a store clerk. This week she worked 49 hours. Estimate her
gross wage for her 2 week pay period, assuming she worked 40 hours last week?

Answers

Answer:

a= $1,068 without overtime pay

b= $1,122 with overtime pay

Step-by-step explanation:

[tex]a = (12 \times 49) + (12 \times 40) \\ = 1068[/tex]

[tex]b = (9(12 \times 1.5) + (12 \times 40)) + (12 \times 40)\\ = 1122[/tex]

This is my last question I need help please

Answers

Answer:

.11

Step-by-step explanation:

it is correct

Answer:

A) $.11

Step-by-step explanation:

A dozen = 12

To find unit cost you divide cost of items by # of items

In this case we have 12 eggs that cost 1.35

So unit cost = 1.35 / 12 = .11

What is the mass of a litter of 9 baby opossums?

Answers

Answer:

It is approximately 0.13 grams.

the other two options are…
c. Function A and function B both have two real solutions.
d.The vertex of function A is lower on the graph than the vertex of function B.
GIVING BRAINLIEST IF FAST

Answers

It’s B

Explanation: use desmos or trust me lol

* 5.) Write the following in standard form.* 5.8709 x 107
58, 709
58,709,000
5,870,900
587,090​

Answers

Answer:

5.8709 x 10 to the 4th power = 58,709

5.8709 x 10 to the 7th power = 58,709,000

5.8709 x 10 to the 6th power = 5,870,900

5.8709 x 10 to the 5th power = ​​​​587,090

Step-by-step explanation:

Hoped that helped:P

What is the quotient? StartFraction 3 y 2 Over 3 y EndFraction divided by StartFraction 6 y squared 4 y Over 3 y 2 EndFraction StartFraction 1 Over 2 y EnDfraction StartFraction 3 y 2 Over 6 y squared EndFraction StartFraction 1 Over y EndFraction StartFraction 2 (3 y 2) Over 3 EndFraction.

Answers

The quotient of the expression is [tex]\frac{1}{2y}[/tex]

The expression is given as:

[tex]\frac{3y^2}{3y} \div \frac{6y^4}{3y^2}[/tex]

Divide 3y^2 by 3y

[tex]\frac{3y^2}{3y} \div \frac{6y^4}{3y^2} = y \div \frac{6y^4}{3y^2}[/tex]

Rewrite the equation as a product

[tex]\frac{3y^2}{3y} \div \frac{6y^4}{3y^2} = y \times \frac{3y^2}{6y^4}[/tex]

Divide 6 by 3

[tex]\frac{3y^2}{3y} \div \frac{6y^4}{3y^2} = y \times \frac{y^2}{2y^4}[/tex]

Multiply y and y^2

[tex]\frac{3y^2}{3y} \div \frac{6y^4}{3y^2} = \frac{y^3}{2y^4}[/tex]

Divide y^3 by y^4

[tex]\frac{3y^2}{3y} \div \frac{6y^4}{3y^2} = \frac{1}{2y}[/tex]

Hence, the quotient of the expression is [tex]\frac{1}{2y}[/tex]

Read more about quotients at:

https://brainly.com/question/12217706

Answer:

its B

Step-by-step explanation:

What is the value of (225 ÷ 0.25) – 11.875 written to two decimal places.(2d.p.)​

Answers

888.125 is the answer just use your calculator

Answer:

Step-by-step explanation:

888.13

-3(3 - 10x) please help, distributive property.

Answers

Answer:

-9 +30x

Step-by-step explanation:

-3(3) = -9

-3(-10x) = 30x

-9 +30x

Hope that helps

a number cube is rolled.what is the probability of rolling a number greater than 4​

Answers

Answer: 2/6

Step-by-step explanation:

There’s only 2 numbers greater than 4 on a die, so two would be the numerator and the denominator would be the number of possibilities you could roll, which is 1-6.

2/6, 1/3, or approx. 33.3%

A number cube will have six sides and two out of six will be greater than four, therefore, there is around a 33.3% chance you will roll a number greater than 4. :)

40% of 58 and 34% of 76

pls subscribe to aphmau it'll help her alot

Answers

Answer:

See below

Step-by-step explanation:

40% of 58 = 0.40(58) = 23.2

34% of 76 = 0.34(76) = 25.84

Answer:

23.2

25.84

Step-by-step explanation:

To calculate percentage, multiply the number by the percentage's decimal.

for example, 20% of 300

20%-->20/100---->0.20

300×0.20=60

40% of 58--->

40/100--->0.40

58×0.40=23.2

34%--->34/100--->0.34

0.34×76=25.84

Find the 63rd term of the arithmetic sequence 17, 26, 35

Answers

Answer:

a₆₃ = 575

Step-by-step explanation:

The nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 17 and d = a₂ - a₁ = 26 - 17 = 9 , then

a₆₃ = 17 + (62 × 9) = 17 + 558 = 575

Write the inequality represented by the graph below. (0,-2) (0,1)

Answers

The line is solid, and the shaded region is up. Therefore, it is > (with the line at the bottom, greater than or equal to. I am on mobile, so I do not have it.) We can see the y-intercept is -2. We can easily see the slope is 2. However, we can check by using x2-x1/y2-y1. 0+2/1-0 is 2/1. That is 2. (Your coordinate is wrong. It should be (1, 0).)

Our answer is y > (with the line at the bottom) 2x - 2.

5x/2 - 3x/4 = 10 1/2
how to solve this? ​

Answers

[tex] \frac{5x}{2} - \frac{3x}{4} = 10 \frac{1}{2} \\ [/tex]

[tex] \frac{5x}{2} - \frac{3x}{4} = \frac{21}{2} \\ [/tex]

Multiply both sides by 4

[tex]4 \times ( \frac{5x}{2} - \frac{3x}{4} ) = 4 \times \frac{21}{2} \\ [/tex]

[tex]10x - 3x = 42[/tex]

[tex]7x = 42[/tex]

Divide both sides by 7

[tex] \frac{7x}{7} = \frac{42}{7} \\ [/tex]

[tex]x = 6[/tex]

please help i will give brainliest

Answers

Answer:

because AB//DE

so DÊC=BÂC ( 2 straight lines are parallel and have the same internal angle)

because ACD is the outer angle of the triangle ABC so ACD= ABC+BÂC

because DÊC=BÂC

so ACD= ABC+ DÊC

CAN SOMEONE HELP ME PLEASE ASAP!?

Answers

Answer:

i think its b

Step-by-step explanation:

Which is an example of nonverbal communication?

O A. Test questions

O B. An outline

O C. Words like please

O D. Body posture

Answers

Body posture, because when you are slouching while listening to someone it is likely that you are uninterested or bored as an example.
Hope this helps. Pls give me the brainliest if it does.
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