Mathematics High School

The radius of a right circular cylinder is increasing at the rate of 7 in./s, while the height is decreasing at the rate of 3 in./s. At what rate is the volume of the cylinder changing when the radius is 17 in. And the height is 5 in.?

Answers

Answer 1

Answer:

1014.73 in³/s

Step-by-step explanation:

We know the volume of a cylinder, V = πr²h where r = radius of cylinder and h = height of cylinder.

Now, to find the rate of change of volume, we differentiate it with respect to time. So

dV/dt = d(πr²h)/dt

= πhdr²/dr × dr/dt + πr²dh/dh × dh/dt

= 2πrh × dr/dt + πr² × dh/dt

when r = 17 in, dr/dt = rate of change of radius = + 7 in/s, h = 5 in and dh/dt = rate of change of height = - 3in/s (negative since it is decreasing).

So, dV/dt = 2πrh × dr/dt + πr² × dh/dt

= 2π × 17 in × 5 in × (+ 7 in/s) + π(17 in)² × (- 3 in/s)

= 1190π - 867π

= 323π in³/s

= 1014.73 in³/s

Related Questions

The set of ordered pairs below represents a function.
(5,8) , (-8,1) , (15,-4), (-1,16), (17,7)
Mariela claims that she can add any point to the set and it will still represent a function.
Which of the following points can be used to show that Mariela's claim is incorrect?
Select all that apply.
(1,1)
(-8,6)
(17,-3)
(-5,8)
(-1,-16)

Answers

(1,1)

(-1,-16)

(-5,8)

(-8,6)

(17,-3)

WILL MARK BRAINLIST!!! only for correct answer
NEED CORRECT ANSWER ASAPPP

Answers

Answer:

B

Step-by-step explanation:

The answer is B because the slope is [tex]\frac{4}{1}[/tex] and there is no y- intercept

Answer:

A.

Step-by-step explanation:

It starts from 32 on the y-axis and goes up 4 times on x-axis.

please help, choose the correct equation

Answers

Equations 4 and 5
Hope this helps

A family of five people has $200 to spend on fishing rods and fishing licenses. They spend a total of $20 on licenses. Assuming they buy 5 identical rods, what is the maximum amount they can spend on each rod?

how do you solve this?????

Answers

Answer:

36

Step-by-step explanation:

200-20=180

180/5=36

you do 200-20=180 the 180 divided by 5 which is 36

If you were to buy a municipal bond for $100 and it returned 1% per year for four years how much interest would you have after four years?

$100
$4
$40
$400

Answers

Answer:

$4

Step-by-step explanation:

As, interest = PTR /100

= 100 x 1 x 4/ 100

= $4

Total Interest = $4

(0,4) F (-40) (40) (0, -4) What is the length of FG ? 811 units O OD. units 3 units units 3 Ос. units 13​

Answers

The answer is C

Hope it helps

If "k" is a negative number, then k + 2 is a negative number.

Answers

Answer:

Not exactly, if a possitive and a negetive are added together the number that was larger will choose its symbol. Say "k" is -3, so -3 + 2 = -1, or if "k" was -1, then -1 + 2 = 1.

Step-by-step explanation:

I hope that makes sense

Please help!!!

composition of functions

g(x)=2x-5 h(x)=x^2-2

find g(h(-8))

Answers

Answer:

g(h(-8)) = 119

Step-by-step explanation:

Given

g(x)=2x-5h(x)=x²-2

To determine

g(h(-8)) = ?

In order to determine g(h(-8)), we need to determine h(-8) first

substituting x = -8 in h(x)=x²-2

h(-8) = (-8)² - 2

h(-8) = 64 - 2

h(-8) = 62

so

g(h(-8)) = g(62)

now substituting x = 62 in g(x)=2x-5

g(62)=2(62)-5

g(62) = 124 - 5

g(62) = 119

so

g(h(-8)) = g(62) = 119

Therefore,

g(h(-8)) = 119

Linear or nonlinear

Answers

Answer:

Linear

Step-by-step explanation:

Linear is a straight graph

Answer:

Linear

Step-by-step explanation:

The easiest way to recognize this from a graph is that its a straight line. If not then its non linear. If you aren't given a graph to go off of another way is to see if it has a constant rate of change, if it does its linear.

What are the roots of the equation 5x^2=-17x-165x in simplest a+bi form?

Answers

Bdbdhd Snsnsn d d d did dbdbdbd

Help me out please an thank you

Answers

This answer is the third choice, C

I need help asap pls

Answers

you can use HL to because the triangles have 2 sides and an angle similar

NEED HELP PLZ!!!!!!!!!!!!!

Answers

Answer:

1st Option is correct

Step-by-step explanation:

Just keep adding 150 to see the results

Help!!!!!! Find x and y so the quadrilateral is a parallelogram.

Answers

Answer:

Conclusion:

The value of x = 7The value of y = 4

Step-by-step explanation:

Given

The parallelogram PQRS

We know that the diagonals of a parallelogram bisect each other.

Therefore,

RT = TP

Given RT = x and TP = 5x-28, so

x = 5x-28

5x = x+28

5x-x = 28

4x = 28

divide boh sides by 4

4x/4 = 28/4

x = 7

Thus, the value of x = 7

Similarly,

QT = TS

Given QT = 5y and TS = 2y+12, so

5y = 2y+12

5y-2y = 12

3y = 12

divide both sides by 3

3y/3 = 12/3

y = 4

Thus, the value of y = 4

Conclusion:

The value of x = 7The value of y = 4

(-81) + 70=
Uhhhh answer someone-

Answers

Answer:

-11

Step-by-step explanation:

Francie lives 1_5 mile from the school. Jake lives 2_10 mile from the school. Do they live the same distance from the school? Explain.

Answers

Answer:

Yes

Step-by-step explanation:

So, we see that both Francie and Jake lives miles from the school. Hence, they both live the same distance from the school.

the giraffe is the worlds tallest land mammal. if the scale is 1/2 inch represents 5 feet . the giraffe is 20 feet tall . how many inches is the giraffe?

Answers

Answer:

The giraffe will be 2 inches

Step-by-step explanation:

If we know that if the scale is 1/2 inch to 5 feet we simply just have to divide the height of the giraffe by 5 feet and then multiply it by 1/2 inches. So we do...

20feet / 5 feet x 1/2 inches = 4 x 1/2inches = 2 inches

-3/4 x (-12)= I need help please this is hard

Answers

Answer:

9

Step-by-step explanation:

Hope this helps and have a great day : )

Answer:

hiiioiofffffrrrrrtttttttt

Which phrase describes the algebraic expression n + 14?.

Answers

Isn’t it addition I’m guessing but I could be wrong

plz I need a help expand:(5x+4y)(5x-4y) ​

Answers

Answer:

25xwith an exponent of 2 minus 16y with an exponent of 2

I need help, I don't quite understand

Answers

Answer:

1

Step-by-step explanation:

so we have:

f+2>5 2 goes the other side, so

f>5-2

f>3

f+4<9 4 goes to the other side, so

f<9-4

f<5

we have two inequality

f>3

f<5

f belongs (3,5), we have only one value for this, it is 4

F can be equal to both 1 and 2. Reason why: If you input 1 or 2 to replace f on either inequality, it will never be greater than or equal to 5 or 9.

16 + 13p -- 9p
how do you do this?

Answers

16 + 13p - -9p
= 16 + 22p

REALLY EASY MATHS QUESTION PLS HELP
(I think it easy lol)

Answers

Answer:

no.2 no.5

Step-by-step explanation:

i don't know how to explain

have a good rest of your day

Answer:

question (1) c^2=a^2+b^2

Step-by-step explanation:

pythagoras theorem

Lee filled several jars with 1/4 cup of water in each jar .He used a total of 8 cups of water. Let j represent the number of jars that Lee filled. Write and Solve an equation to find out how many jars lee filled.

Answers

Answer: 32

Step-by-step explanation:

8x4 = 8 / 0.25

Help please! worth a lot of points! Screenshot included

Answers

Answer:

x=44444444444444444444444444444444

Step-by-step explanation:

Answer:

.2

Step-by-step explanation:

SOMEONE HELP ME PLSS !

Answers

5 x 8 x 2 = 80 .
volume = length x width x depth
I think it’s 80 I’m sorry if you get it wrong though:)

What is the acceleration of the bike from 0 seconds to 6 seconds?

Answers

Answer:

3mph

Step-by-step explanation:

this is math pls help 3x + 2(5x − 7)

Answers

Answer: 13x - 14

Step-by-step explanation:

3x + 10x - 14

13x -14

Answer:

13x-14

Step-by-step explanation:

PLEASE HELP ME FAST!!! Monica's bicycle wheel has a radius of 16 inches. Kevin's tricycle wheel has a radius of 8 inches. How many times larger is the circumference of Monica's wheel that the circumference of Kevin's tricycle wheel? Show your work

Answers

Answer:

50.2 inches

Step-by-step explanation:

The wheel of a tricycle is circular in shape.

The circumference of a circle = 2πr

For Monice

Monica's bicycle wheel has a radius of 16 inches.

The circumference of her bicycle wheel = 2 × π × 16

= 100.53096491 inches

Approximately = 100.5 inches

For Kevin

Kevin's tricycle wheel has a radius of 8 inches.

The circumference of his wheel =

2 × π × 8

= 50.265482457 inches

Approximately = 50.3 inches

How many times larger is the circumference of Monica's wheel that the circumference of Kevin's tricycle wheel?

This is calculated as:

Circumference of Monica's wheel - Circumference of Kevin's wheel

= 100.5 inches - 50.3 inches

= 50.2 inches

Hence: Monica's wheel is 50.2 inches larger than Kevin's wheel

Answer: All I know is I got a 1/2 points on my open ended question. Monica’s bicycle wheel is 2 times larger than Kevin’s.

Step-by-step explanation: I think you add or multiply or divide. I gotta figure it out myself.


18. A figure is said to be regular if its sides are equal in length and angles are equal in
measure. What do you mean by a regular quadrilateral?​

Answers

Answer:

If its 4 sides need to be equal and 4 angles need to be equal then it is a square.

Step-by-step explanation:

[tex]\huge\sf\fcolorbox{green}{pink}{Answer}[/tex]

Properties of regular quadrilateral :-

All sides are equal

All angles are 90° ( equal)

Square is only the regular quadrilateral

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