The volume of a cube with sides of length s is given by V = s^3. Find the rate of change of the volume with respect to s when s = 8 centimeters.​

The Volume Of A Cube With Sides Of Length S Is Given By V = S^3. Find The Rate Of Change Of The Volume

Answers

Answer 1

Answer:

[tex]V'(8)=192\text{ cm}^2[/tex]

Step-by-step explanation:

We have the volume of a cylinder:

[tex]V=s^3[/tex]

To find the rate of change of the volume with respect to s, we will take the derivative of both sides with respect to s. So:

[tex]\frac{d}{ds}[V]=\frac{d}{ds}[s^3][/tex]

Differentiate. Use the power rule:

[tex]V'(s)=3s^2[/tex]

So, to find the rate of change of the volume when s is 8 centimeters, substitute 8 for s:

[tex]V'(8)=3(8)^2[/tex]

Evaluate:

[tex]V'(8)=192\text{ cm}^2[/tex]


Related Questions

there are 11 pieces of pie left over in the cafeteria. if the 6 pieces are apple and 5 are cherry , what fraction of the remaining are apple

Answers

Answer:

6/11

Step-by-step explanation: If not this try 12/22

The answer is 6 over 11 (6/11)

This is because 11 is the denominator and both 5 and 6 are numerators. If you were to ask for what the fraction of remaining pie would be cherry, then you would say 5/11

If you roll two six-faced dice together, you will get 36 possible outcomes. 4 pts 1. List all possible outcomes of the experiment. 2 pts 2. What is the probability of getting a sum of 11 in these outcomes? 2 pts 3. What is the probability of getting a sum less than or equal to 4? 2 pts 4. What is the probability of getting a sum of 13 or more?

Answers

Given:

Two dice are rolled together.

Total number of possible outcomes.

To find:

The list of total possible outcomes.

The probability of getting a sum of 11 in these outcomes.

The probability of getting a sum less than or equal to 4.

The probability of getting a sum of 13 or more.

Solution:

If two dice are rolled together, then the total number of possible outcomes is 36 and list of total possible outcomes is

S = {(1,1),(1,2),(1,3),(1,4),(1,5),(1,6),(2,1),(2,2),(2,3),(2,4),(2,5),(2,6),(3,1),(3,2),(3,3),(3,4),(3,5),(3,6),(4,1),(4,2),(4,3),(4,4),(4,5),(4,6),(5,1),(5,2),(5,3),(5,4),(5,5),(5,6),(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)}

Sum of 11 in these outcomes = {(5,6),(6,5),(6,6)} = 3

The probability of getting a sum of 11 in these outcomes is

[tex]P(\text{sum=11})=\dfrac{3}{36}[/tex]

[tex]P(\text{sum=11})=\dfrac{1}{12}[/tex]

Therefore, the probability of getting a sum of 11 in these outcomes is [tex]\dfrac{1}{12}[/tex].

Sum less than or equal to 4 = {(1,1),(1,2),(1,3),(2,1),(2,2),(3,1)} = 6

The probability of getting a sum less than or equal to 4 is

[tex]P({sum\leq 4})=\dfrac{6}{36}[/tex]

[tex]P({sum\leq 4})=\dfrac{1}{6}[/tex]

Therefore, the probability of getting a sum less than or equal to 4 is [tex]\dfrac{1}{6}[/tex].

Sum of 13 or more = empty set because maximum sum is 12.

The probability of getting a sum of 13 or more is

[tex]P(sum\geq 13)=\dfrac{0}{36}[/tex]

[tex]P({sum\geq 13})=0[/tex]

Therefore, the probability of getting a sum of 13 or more is 0.

A study showed that the ratio of the number of people who gets there news from social media to the number of people who got there news from other sources is 3 : 7 based on the ratio, how many people in a town of 900 people get there news from social media

Answers

Answer: 270 people

Step-by-step explanation:

Since the ratio of the number of people who gets there news from social media to the number of people who got there news from other sources is 3 : 7. This can be expressed in a fraction as:

Fraction of people who gets there news from social media = 3/10

Fraction of people who got there news from other sources = 7/10

If there are 900 people, number of people who gets there news from social media will be:

= 3/10 × 900

= 3 × 90

= 270 people

when y= 4x, if y= 36, what is x?

Answers

Answer:

x=9, hope I helped :P

1
Mr. Baker calculated the area of 4 different styles of rugs. The areas of the 4 rugs are shown.
OS
MARULUGARES PARA
P
ALETICO
ZORLUFERITY
A = 50 m2
A5 m2
A = 2 m2
A = 15 m2
Whlch list shows the rugs in order from least area to greatest area?
A
Oval Rug, Square Rug, Circular Rug, Rectangular Rug
B Oval Rug, Square Rug, Rectangular Rug, Circular Rug
C Square Rug, Oval Rug, Rectangular Rug, Circular Rug
D
Circular Rug, Rectangular Rug, Square Rug, Oval Rug

Answers

The answer to your question is c

Renting a small moving truck for a day costs $29.95 plus $0.79 per mile that the truck is driven. Ms. Knowles rented a truck for one day and paid $91.57. The equation 29.95 + 0.79d = 91.57 can be used to model this situation. Choose True or False for each statement. A) The variable d represents the number of miles Ms. Knowles drove. B) The term 0.79d represents the charge in dollars for the distance driven. C) You can isolate the term 0.79d by adding 29.95 to both sides of the equation.

Answers

Given:

Renting a small moving truck for a day costs $29.95 plus $0.79 per mile that the truck is driven. Ms. Knowles rented a truck for one day and paid $91.57.

The equation is

[tex]29.95 + 0.79d = 91.57[/tex]

To find:

Whether the statement are true or false.

Solution:

We have,

[tex]29.95 + 0.79d = 91.57[/tex]

Here,

Fixed cost = 29.95

Variable cost = 0.79d, it depends on the number of miles Ms. Knowles drove.

So, the variable d represents the number of miles Ms. Knowles drove.  Hence, statement A is true.

The term 0.79d represents the charge in dollars for the distance driven. Hence, statement B is true.

You can isolate the term 0.79d by subtracting 29.95 from both sides of the equation.

Hence, statement C is false.

PLEASE HELP and solve

Answers

its A.
The formula is y-y1 = m (x-x1) so by looking at just the slope, (slope is m) , since slope is -7, -7 should be placed where M is

give the numerical coefficient of the term x
the numerical coefficient is?​

Answers

Answer:

1

Step-by-step explanation:

The numerical coefficient of every variable with no visible coefficient in front of it is always 1, since 1 multiplied by a number (or variable) is itself.


There are 5 number cards labeled 1 through 5. What is the probability and its complement of randomly drawing a card from this set that is more than 47

Answers

Answer:

impossible you cant get one that is over 5 if it only goes to 5

Step-by-step explanation:

Simplify 6.9y+2.4y please help me

Answers

Answer:

6.9y+2.4y

= 9.3y

Hope it helps u,

pls put thanks and pls mark as the brainliest

m= 4/5 - 2/5
————- = ?
-1 - -2

Answers

Answer:

2/5 = 4/5 - 2/5 = m

Can someone help me with this math question? First to answer will get Brainliest! :)

Answers

Answer:

A

Step-by-step explanation:

yiu have to rotate it in order to make that

heyyy so like hellpppp me out

Answers

Answer:

gotta be C

Step-by-step explanation:

Question is on a picture ​

Answers

Answer: -9

Step-by-step explanation:

When you plug in the numbers you get the equation 4* (-6) + 5*3

When you solve it out you get -24 + 15. This equals -9.

A rectangle has a length of 64 cm. The rectangle is reduced by a scale factor of 3/4. What is the length of the reduced rectangle?

Answers

Answer:

48 cm

Step-by-step explanation:

64 divided by 4 is 16. multiply 16 by 3 and the answer is 48.

​can someone help me solve this system. thanks
2y = 6
3(x + y) = 12

Answers

Answer

y=3   x=1

Step-by-step explanation:

3(x+3)=12

3x+9=12

subtract 9 from both sides to get...

3x=3

divide 3 from both sides to get...

x=1

Step-by-step explanation:

this is very easy

2y=6

y=2/6=3

so ,

3(x+y)=12

3x+3y=12

3x+3+3=12

3x+9=12

3x=12-9

3x=3

x=3/3

x=1

In a figure, such as a triangle or parallelogram, this is used to refer to the
length of one side.

Answers

Answer:

The hypotenuse is the side opposite the right angle, or defined as the longest side of a right-angled triangle,

Step-by-step explanation:

Refer to the given sets information Y U Z

Answers

Answer:

i hate biden

Step-by-step explanation:

Why do people think maths as a hard subject
Do you feel math is hard

Answers

No, math is the easiest subject for me and my favorite ! But sometimes it can be hard if u don’t understand.
math is different for everyone. i personally enjoy math. also can you please thank this i need points lol

Heyyy yugiii :)) what’s 20 times 50 minus 16 plus 28?

Answers

Answer:

hey do you want to do a zoom

Step-by-step explanation:

i am done with my basketball game

What is the solution for the system of equation
Y=-2x+8 y=x-4

Answers

Answer:

(x , y) = (28/5 , 8/5)

Step-by-step explanation:

Answer:

Step-by-step explanation:

(x , y) = ( 28/5 , 8/5 )

               

In the video game Stunt Pilot, players gain and lose points based on how well they perform tricks in their airplanes. Kirk had 33 points in the game before getting – 18 points for losing control of his plane during a stunt. What is Kirk's score now?

Answers

Answer: 15

Step-by-step explanation: Well first you have to minus 33-18=15


Convert y = x2 - 4x + 1 to vertex form by completing the square.

O y= (- 1)2 + 4
O y= (1 - 2)2 +5
O y= (x - 2)2 – 3
O y = (x - 4) + 1

Answers

Answer:

vertex: (-2, -3)

Step-by-step explanation:

y = x2 + 4x                 + 1  

y = x2 + 4x + 22          + 1 - 22  

y = (x + 2)2 + 1 - 4  

y = (x + 2)2 - 3            in y = (x - h)2 + k, (h, k) is the vertex.  

 

Answer:

y = (x - 2)² - 3

Step-by-step explanation:

Given

y = x² - 4x + 1

To complete the square

add/subtract ( half the coefficient of the x- term )² to x² - 4x

y = x² + 2(- 2)x + 4 - 4 + 1

   = (x - 2)² - 3

HELP WHOEVER IS FIRST GETS BRAINLIST!!!

Answers

Answer:

y = (-2/5)x + 3

Step-by-step explanation:

(2/5)x + y = 3

y = (-2/5)x + 3

PLEASE ANSWER FAST
A principal spent $1560 total on "c" calculators for his school. Which
expressions shows the cost of ONE calculator.
A. c+ 1560 B. 1560c C. 1560- c D. 1560/c

Answers

Answer:

1560/c

Step-by-step explanation:

if you divide 1560 by c the value you get will be the cost of one calculator.

Answer:

The answer is D. 1560/c

Step-by-step explanation:  

If you divide 1560 by c you will get the cost of one calculator.

Which of the following equations has a solution of x = 5
10x/2=1


2 (x – 3) + 8 = 6x – 18
2x – 5 + 3x = 8 + 14
O 4(1 - 2) + 3 = -2 (2 + 2) + 1

Answers

Answer:

equals 345762819

Step-by-step explanation:

i dont know for short i just want a points

Pls help me!!!!!!!!!!!

Answers

Answer:

1) y-4+1(x-5)

Step-by-step explanation:

With point-slope form, you just have to substitue the information that is given to you into the generic formula.

y-y1= m(x-x1)

so the y1 is the y value of the point that is given to you and x1 is the x value of the point that is given to you

m is the slope (also given)

and x and y just stay the same; x &y

A portion of a map with cities A and B is shown. The map uses a scale of 1 inch =15 miles. You are making a map with a scale of 2 inches = 25 miles How far apart are cities A and B on your​ map?

Answers

1in=15 then it’s 75. For 2in=25 then it’s 62.5

Please help me solve this problem!

Answers

Answer:

The line would be a diagonal line that is negative(pointing down).

You can use Desmos Graphing Calculator to help you even more! :)

Use the graph to find the midpoint between O and H.
(4, -1)


(-2, 8)


(8, -2)


(-1, 4)

Answers

Answer:

(-1, 4)

Step-by-step explanation:

-5+3/2 = -1

6+ 2/2 = 4

(-1, 4)

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