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.

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Related Questions

solve please :3 will mark brainliest !!

Answers

>> Answer

__________

[tex] \: [/tex]

6f = $15

8f = $20

10f = ?

Soo :

2f = 5

f = 2,5

10f = 10(2,5) = $25

The cost of the wire of the third length in the table is, 25 dollars

We have to give that,

The cost of a certain type of wire varies directly with its length.

Now, From the table the equation between cost and length is,

y - 15 = (20 - 15)/(8 - 6) (x - 6)

y - 15 = (5/2) (x - 6)

y - 15 = 2.5x - 15

y = 2.5x

Where y represents the cost and x represent the length.

Hence, At x = 10 feet

y = 2.5 (10)

y = 25 dollars

So, The cost of the wire is, 25 dollars

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Find the missing angle measures.
What is m∠2?
a 40
b 60
c 50
d 100

Answers

I think C.50 is the answer

The points ​(​18,21​) and ​(42,​49​) form a proportional relationship. Find the slope of the line through the points. Then use the slope to graph the line.

Answers

Answer: 5/2

Step-by-step explanation: 49 - 42/ 21 - 18

how do you do this, thanks for helping

Answers

Answer:

A: (-7, -4)

B: (-3, 8)

Step-by-step explanation:

Ordered pairs are (x,y).

Count the lines and see:

A is 7 to the left and 4 down so (-7, -4)

B is 3 to the left and 8 up so (-3, 8)

REMEMBER X IS ALWAYS FIRST!!

Does this answer make sense? YES! Because quadrant II all the pairs will be (-#, #) and in quadrant III the pairs will be (-#, -#)

Hope that helps!

Martin finds a shirt on sale

Answers

Hmmm how much is the shirt

What's the answer guys?

Answers

Answer: 14.4p - 2.2q + 4.3r

Step-by-step explanation:

(8.8p + 5.6p) + (6.2q - 8.4q) + (-1.8r + 6.1r)

= 14.4p - 2.2q + 4.3r

please give me a brainliest answer

help is very much needed

Answers

Answer:

IT'S NEGATIVE 3. HOPE THIS HELPS...

Marc solves the equation Latex: (\sqrt[4]{x})^3=5\textsf{.} His work is shown below. Step 1: Latex: (\sqrt[4]{x})^3=5 ( √ [ 4 ] x ) 3 = 5 Step 2: Latex: x^{\frac{3}{4} }=5 x 3 4 = 5 Step 3: Latex: x^{\frac{3}{4} \cdot \frac{4}{3} }=5^{\frac{4}{3} } x 3 4 ⋅ 4 3 = 5 4 3 Step 4: Latex: x=\sqrt[3]{5 \cdot 5 \cdot 5 \cdot 5} x = √ [ 3 ] 5 ⋅ 5 ⋅ 5 ⋅ 5 Step 5: Latex: x=5\sqrt[3]{\not{5} \cdot \not{5} \cdot\not {5} \cdot 5} x = 5 √ [ 3 ] ¬ 5 ⋅ ¬ 5 ⋅ ¬ 5 ⋅ 5 Step 6: Latex: x=5\sqrt[3]{5} x = 5 √ [ 3 ] 5 Explain what Marc did in steps 4 and 5. Why did he do this? Create your own radical equation and explain how to solve it. Is there an extraneous solution to your equation?

Answers

Based on the calculation, we can say that there is an extraneous solution to the equation

Given the equation solved by Marc expressed as:

[tex](\sqrt[4]{x})^3=5[/tex]

We are to check if the indices equation has an extraneous equation.

According to the law of indices [tex](\sqrt[n]{m} )^a=m^{\frac{a}{n} }[/tex], the expression becomes:

[tex](\sqrt[4]{x})^3=5\\x^\frac{3}{4}=5\\[/tex]

Raise both sides to the power of 4/3 as shown:

[tex](x^\frac{3}{4} )^\frac{4}{3} = 5^\frac{4}{3}\\x^1 = 5^\frac{4}{3}\\x = 5^\frac{4}{3}\\[/tex]

This shows that there is an extraneous solution to the equation

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The table shows a set of values for x and y

Answers

a) Assume y = [tex]x^{2}[/tex]

[tex]1b=\frac{k}{1^{2} }[/tex] k = 1b

[tex]y=\frac{1b}{x^{2} }[/tex]

b) y = 25

[tex]x^{2}=\frac{16}{25}[/tex]

[tex]x=\sqrt{\frac{4}{5} ^{2} }[/tex]

x = ±[tex]\frac{4}{5}[/tex]

x > 0, x = 4/5

{ Equation }

y=16/x² is required equation for y in terms of x and x=4/5 when y=25.

What is Equation?

Two or more expressions with an Equal sign is called as Equation.

The table of values are

x         1         2         3         4

y        16        4        16/9      1

Given that y is inversely proportional to square of x.

y=k/x²

Let us consider

y=16 and x=1

16=k/1

k=16.

y=16/x²

So y=16/x² is equation for y in terms of x

b) We need to find value of x when y=25

25=16/x²

Use cross multiplication

x²=16/25

Take square root on both sides

√x²=√16/25

x=±4/5

If x>0 , so x=4/5

Hence y=16/x² is required equation for y in terms of x and x=4/5 when y=25.

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Does the graph represent a function? Why or why not? ​

Answers

Answer:

The vertical line test can be used to determine whether a graph represents a function. ... If we can draw any vertical line that intersects a graph more than once, then the graph does not define a function because that x value has more than one output. A function has only one output value for each input value.

Step-by-step explanation:

Can i get braineist pls

-x^4+2x^3+8x=0. solve by factoring

Answers

2.93114246

Step-by-step explanation:

Solve for x.

(x÷2)+6=50


x = 22

x = 28

x = 38

x = 88

Answers

The answer is x = 88

A square has a area of 121 square centimeters. what is the length of each side

Answers

Answer is so 100-8 is square root of 100

What are the differences and similarities between the the graphs and equations of circles and ellipses?

Answers

Space Environment

A circle is a closed curved shape that is flat. That is, it exists in two dimensions or on a plane. In a circle, all points on the circle are equally far from the center of the circle. An ellipse is also a closed curved shape that is flat.

HELP ME ASAP!!!!!!!!!!!!!!!!!

Answers

Answer:

good luck i need to conquer europe

answer po plss plssplsss

Answers

Answer:

I'll answer 6 to 10 cuz that's only what I'm able to see

Step-by-step explanation:

6.

Y-Z

= {6,4,7,2,8,3} - {2,7,8,9,10}

= {6,4,3}

7.

( Y ∪ Z ) ∩ X

= ( {6,4,7,2,8,3} ∪ {2,7,8,9,10} ) ∩ {1, 2,3,5,8}

= { 2,3,4,6,7,8,9,10} ∩ {1, 2,3,5,8}

= {2,3,5,8}

8.

( X ∪ Y ) ∩  ( Y ∪ Z )

= ( {1, 2,3,5,8} ∪ {6,4,7,2,8,3} ) ∩ ( {6,4,7,2,8,3} ∪ {2,7,8,9,10} )

= {1,2,3,4,5,6,7,8} ∩ {2,3,4,6,7,8,9,10}

= {2,3,4,6,7,8}

9.

( X ∩ Z ) ∪ ( X ∩ Y )

= ( {1,2,3,5,8} ∩ {2,7,8,9,10} ) ∪ ( {1,2,3,5,8} ∩ {6,4,7,2,8,3} )

= {2,8} ∪ {3,8}

= {2,3,8}

10.

( X ∪ Y ) ∩ Z

= ( {1,2,3,5,8} ∪ {6,4,7,2,8,3} ) ∩ {2,7,8,9,10}

= {1,2,3,4,5,6,7,8} ∩ {2,7,8,9,10}

= {2,7,8}

Jon is 3 years younger than Laura. The product of their ages is 1,330. If j represents Jon’s age and represents Laura’s age, what value of j could be Jon’s age?

Answers

Answer:

35

Step-by-step explanation:

The factors chosen are 35 and 38 which multiplied = 1330(the product) Laura is 3 years older than jon so she is 38 and Jon is 35.

Please help !!! Will mark as brainliest !!!

Answers

Answer:

So the answer would be (A.

Step-by-step explanation:

The period of the function, y=cos(4x)is how many degrees?

Answers

Y—cos 4. 4.0 hope this helps

What is the value of 5+6−32(8÷14)?

Answers

Answer:

-7.3

Step-by-step explanation:

Solve the equation, y = 7x + 10, using the x-values, 3, 5, and 8.
Which of the following T-tables represents the ordered pairs?

Please help !!

Answers

Answer:

y=7%283%29%2B10

y=21%2B10

y=31

(3,31)

Step-by-step explanation:

Answer:

the answer is A

Step-by-step explanation:

Which inequality best represents that icecream at -3⁰C is cooler than icecream at 1⁰C?​

Answers

Answer:

Ice cream at -3 c is cooler than 1 C therefore since you are looking to know which one is cooler > would be the best option.

Step-by-step explanation:

Have a wonderful day!

Make y the subject of this equation:
P-3=qy

Answers

Answer: (P - 3)/q = y

how do i write 5z in expanded notation

Answers

Here you go i don’t know what the z meant

what is the ratio of 22 and 8

Answers

4:11. Here we will simplify the ratio 8:22 for you and show you how we did it.

To simplify the ratio 8:22, we find the greatest common divisor of 8 and 22, and then we divide 8 and 22 by the greatest common divisor.

Your classmate says the triangles below are not congruent by SSS. She explains that congruent sides do not correspond explain the error in her reasoning.

Answers

Congruent triangles are triangles with equal corresponding sides.

The triangles are congruent

From the question (see attachment), we have the following observations.

Two corresponding sides are marked with ITwo corresponding sides are marked with IITwo corresponding sides are marked with III

The above highlights mean that:

The corresponding sides are congruent by SSS theorem

Hence, your classmate's claim is incorrect.

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Clay gave four friends seven ball cards
each. How many cards did he give to his
friends?

Answers

Gave 4, kept 3. You can’t split the cards.

Multiply and simplify

Answers

Answer and explanation:

1. 2 × 3/10 = 6/10 = 3/5

2. 8 × 4/8 = 32/8 = 4

3. 9 × 3/9 = 27/9 = 3

4. 12 × 2/11 = 24/11 = 2 2/11

5. 3 × 5/7 = 15/7 = 2 1/7

6. 2 × 3/5 = 6/5 = 1 1/5

7. 11 × 4/8 = 44/8 = 5 4/8 = 5 1/2

8. 10 × 1/4 = 10/4 = 2 2/4 = 2 1/2

9. 5 × 1/4 = 5/4 = 1 1/4

10. 11 × 2/7 = 22/7 = 3 1/7

Hope this helps!


Find the 11" term of the following geometric sequence.
5, 15, 45, 135, ...

Answers

5*3^0 = 5,

5*3^1 = 15,

5*3^2 = 45,

5*3^3 = 135,

5*3^4 = 405
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5




Related Questions (More Answers Below)
the 11th term is 295,245.
I did the calculations

If an area of a circle is 65.71cm*2 what is the radius? Round the answer to 2DP.

Answers

Answer:

4.57

Step-by-step explanation:

square root of 65.71 divided by pie

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