A right circular cylinder is changing shape. The radius is decreasing at the rate of 2 inches/sec while it's height is increasing at the rate of 5 inches/sec. When the radius is 4 inches and the height is 6 inches, how fast is the volume changing? Round your answer to three decimal places

Answers

Answer 1

The volume of the right circular cylinder is changing at a rate of approximately 50.265 cubic inches per second.

Given that a right circular cylinder is changing shape.

The radius is decreasing at the rate of 2 inches/sec

dr/dt = -2 inches

The radius is increasing at the rate of 2 inches/sec

dh/dt=5 inches

We have to find dv/dt when r is 4 inches and h is 6 inches.

Volume=πr²h

Differentiate with respect to 't' to find the change of volume:

[tex]\frac{dV}{dt}=\pi(2rh\frac{dr}{dt}+r^2\frac{dh}{dt})[/tex]

Plug in the values:

[tex]\frac{dV}{dt}=3.14(2(4)(-2)(6) + 16(5))[/tex]

[tex]=3.14(-96+80)[/tex]

[tex]=3.14(-16)[/tex]

[tex]=-50.265[/tex] inch³/sec.

Hence, the volume change is -50.265 inch³/sec.

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Related Questions

does 3,34 satisfy the equation y= 8x + 10

Answers

8(3)+10=34
24+10=34
34=34

It does

Answer:

Let y=34 and x=3

Step-by-step explanation:

y = 8x + 10

34 = 8 (3) + 10

34 = 24 + 10

34 = 34

Hence,3 and 34 satisfies this equation.

Y=-2x+9 answer to this question

Answers

Answer:

5.5

Step-by-step explanation:


Dinner at your grandfather's favorite restaurant now costs $25.25 and has been increasing steadily at 4% per year. How much did it cost 35 years ago when he was courti
your grandmother?

Answers

Why would my grandfather charge me to eat at his restaurant? I’m family aren’t I?

SOMEONE PLEASE HELP ME ASAP

Answers

Answer:

its 2

Step-by-step explanation:

Answer:

-13

Step-by-step explanation:

9 + -13= -4

add nine on both sides

then subtract -13 from 9

and you will get -4

Plssssss help ASAP
And thx it u do :)

360 students in the 6th grade voted for class president. The loser received 108 votes. What percentage of the vote did the winner receive?
A) 20%
B) 30%
C) 60%
D) 70%

Answers

B

Convert fraction (ratio) 108 / 360 Answer: 30%

Find the perimeter of the shaded region of this composite figure. ​

Answers

Answer:

perimeter of shaded region:

area of rectangle- area of semicircle

l×b‐(pie r²) diameter of circle‐6m; Radius‐3

8×6‐(3.14×3×3)

42— 28.26=13.74m

HOPE IT WILL HELP YOU

Divide 6 divided by 3/5


Answer only if u know please:)

Answers

Answer:

The answer is 10 or 10/1

Simplify the following equation (2^3)^-2

Answers

Multiply the exponents
3 * -2 = -6
It would be 2^-6
Format: a^-b = 1/a^b
1/2^6 = 1/64
The solution is 1/64

30 cents in each dollar is a paid tax. what fraction is paid in tax? what percentage is not paid in tax?please i need an answer within 10 minutes I'm In an exam ​

Answers

Answer:

30 cents of a dollar is 30% tax paid and 70% not paid.

A dollar is 100 cents.

Step-by-step explanation:

9y - 1 = -10y + 227

Answers

Answer: y=12

Step-by-step explanation:

help plzzzzzzzzzzzzzz ​

Answers

Answer:

i am not sure try 56

Step-by-step explanation:

Hope this helps!:)

What is the initial value in this question y=8x+6 8 or 6?

Answers

Answer:

it should be an 8

Step-by-step explanation:

The initial value in this question y = 8x+6 will be 8 .

What is a system of equations?

A system of equations is two or more equations that can be solved to get a unique solution. the power of the equation must be in one degree.

The equation is given as;

y = 8x+6

We can see that the equation contains two terms that are 8x and 6.

The initial value is the first number of the first term in the equation.

Here, the first term is 8x.

Hence, the initial value in this question y = 8x+6 will be 8 .

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A ladder that is 21 feet long is propped against a building. The bottom of the ladder was placed 4 feet from the base of the building. How high up on the building does the ladder reach? Round the answer to the nearest tenth of a foot

Answers

Answer:

20.62 feet

Step-by-step explanation:

The ladder propped against a building forms a right angle triangle

Height of the ladder (hypotenuse) = 21 feet

Base of the ladder from the building (adjacent) = 4 feet

Height of the building (opposite) = x feet

Hypotenuse ² = opposite ² + adjacent ²

21² = x² + 4²

21² - 4² = x²

441 - 16 = x²

425 = x²

x = √425

= 20.62 feet

Answer: 20.62 ft or rounding it to 20.6 ft

Step-by-step explanation:

I need help please ​

Answers

Answer: SAS

Explanation: There are two sides that are congruent and there is one vertical angle between them which are always congruent.

A password is 4 characters long, consisting of 2 letters and 2 numbers. The password must begin and end with a
letter. If numbers can be repeated but letters cannot, how many possibilities are there?
a. 65,000
b. 60,840
c. 58,500
d. 52,650

Answers

Answer:

a.

65,000

Step-by-step explanation:

There are 65000 possibilities of 4 character-password

What is a password?

A password is a security code that is used for verifying identities

The password has 4 characters.

The password must begin and end with a letter.

So the selections are:

First = 26

Last = 25

The other selections are:

Second = 10 digits

Third = 10 digits

So, the number of password is:

Password = 26 * 10 * 10 * 25

Evaluate

Password = 65000

Hence, there are 65000 possibilities of 4 character-password

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What is the slope of the line that passes through the points M (4,-5) and N (0, -8)?

A.) -3/4
B.) 13/4
C.) -4/3
D.) 3/4​

Answers

Answer:

D. 3/4

Step-by-step explanation:

using the y2-y1/x2-x1 to find the slop: -8--5/0-4 = 3/4

Answer:D

yee

Step-by-step explanation:

What is the sum of the exterior angles, one at each vertex, of any polygon?

Answers

Answer:

Polygon Exterior Angle Sum Theorem. If a polygon is convex, then the sum of the measures of the exterior angles, one at each vertex, is 360° .

Can an isoceles triangle be an obtuse triangle? Explain. ​

Answers

Answer:

it can and cant at the same time.

Yes, the hypotenuse must be longer than both of the other sides though for it to be obtuse.

It is Friday and you and your friends are going to hit up
the local amusement park. The park costs $30 dollars
to enter and then the tickets for the rides each cost
$3.50. Write an equation when y is total price of
amusement park and x is the number of tickets bought.
Interpret the slope and y-intercept when asked to
explain your answer

Helpp plss

Answers

Answer:

y= 30 + 3.50

Step-by-step explanation:

lol I think you're Giselle for my school but that's what the answer it im pretty sure.

What is the x- intercept of y+ 12 =3 (x-9)?

Answers

Answer:

13,0

Step-by-step explanation:

12=3(x-9)

divide both sides by three

4=x-9

add 9 to both sides

x=13

so, the x intercept is (13,0)

Answer:

x-intercept: (13,0)

y-intercept: (0,-39)

Step-by-step explanation:

To find the x-intercept, substitute in  0  for  y  and solve for  x .

To find the y-intercept, substitute in  0  for  x  and solve for  y .

At one gas station, gas costs $2.75 per gallon. Complete the equation that relates the total cost, C, to the number of gallons of gas purchased, g.



C = __

Answers

Answer:

C = 2.75

Step-by-step explanation:

it does not tell how much there for it is 1 gallon

zora recently got an afterschool job to save money to buy a car. She opened a savings account and deposits a fixed amount each week so that she can quickly meet her savings goal. The table below shows the relationship.

Answers

Answer:

40

Step-by-step explanation:

The initial value of the function is 40, which represents the amount of money she deposits each week

are you smarter than a 7th grader get your answers by answering this question please please please please please

Answers

Answer:

F

Step-by-step explanation:

8 - (2-3) -1 = 8

6 - (-2) = 8

8-(2-3)-1=6-(-2)

can someone please answer this

Answers

Answer:

y = -0.6x + 24.6

Step-by-step explanation:

A model car is built to a scale of 1 in. : 2.5 ft. If the model is 5.8 in. Long how long is the car in real life?

Answers

Answer:

14.5 ft

Step-by-step explanation:

We are told that the model car is built to a scale of 1 in. : 2.5 ft.

That means 1 inches represents 2.5 ft in actual measurement.

Thus, for a 5.8 inch long model, the real life measurement is;

(5.8 inch × 2.5 ft)/1 inch = 14.5 ft

The height of a firework shot upward from the ground with the initial velocity of 10meters per second is represented by the function h(t) = - 16t2 + 4t How long did it take the firework to reach the ground

Answers

Answer:

0.375 seconds

Step-by-step explanation:

In simple terms, to find the time it took to reach the ground, we need to find t from the equation.

If we differentiate h with respect to t we will get the velocity with which the fireworks is moving at.

[tex]h(t) = - 16t^2 + 4t.\\dh/dt =-32t +4[/tex]

We can now equate this to its velocity and solve for t

10 = -32t +4

t = 0.1875 ( time cannot be negative in value, so we ignore the negative sign)

Therefore, the time it took the fireworks to reach the ground is = 2 x 0.1875= 0.375 seconds.

(We need to account for the fact that the fireworks went up and came down)

PLEASE HELP ME ASAP!!!! My entire grade depends on these questions and I need to show the work that go me there
I know it is a long one, but I am giving away all of my points!!! I know most of the answers, but for all exept the graphing questions the work needs to be shown!
Consider the quadratic function.
f(x)=-(x+4) (x-1)
(a) What are the x-intercepts and y-intercept?
(b) What is the equation of the axis of symmetry?
(c) What are the coordinates of the vertex?
(d) Graph the function on the coordinate plane. Include the axis of symmetry.


Based on a poll of 1000 residents, a newspaper article claims that 62% of the residents in town favor the
development of a recreational park on the west side of town. A community action group interested in
preserving the environment claims that 45% of the town’s residents favor the development of a recreational
park.
To determine whether the sample supports the population proportion, a simulation of 100 trials is run, each
with a sample of 200, using the point estimate of the population. The minimum sample proportion from the
simulation is 0.46 and the maximum sample proportion is 0.76.
(a) What is the point estimate of the population?
(b) The margin of error of the population proportion is found using an estimate of the standard deviation.
What is the interval estimate of the true population proportion?
(c) The margin of error of the population proportion is found using the half the range.
What is the interval estimate of the true population proportion?
(d) Is the community action group’s claim likely based on either interval estimate of the true population
proportion? Explain.

Solve the system of equations. Show your work.
y=x^2-3x+4
x+y=4

Answers

Answer:

Answers are in bold

Step-by-step explanation:

Part 1A

Use the Zero Product Property to find the x-intercepts:

0=-(x+4)(x-1)

0=(x+4)(x-1)

0=(x+4)

-4=x

x=-4

0=(x-1)

1=x

x=1

So the x-intercepts are x=-4 and x=1 which is also (-4,0) and (1,0)

For the y-intercepts, plug in x=0:

f(x)=-(0+4)(0-1)

f(x)=(-4)(-1)

f(x)=4

So the y-intercept is y=4 which is also (0,4)

Part 1B

In general, the axis of symmetry is equal to x=h in the equation y=(x-h)^2+k

For a parabola, the axis of symmetry is equal to x=-b/2a, so we expand the given equation and then plug in the values of "a" and "b" to get the axis of symmetry:

f(x)=-(x+4)(x-1)

f(x)=-(x^2+3x-4)

f(x)=-x^2-3x+4

So now we know a=-1 and b=-3, therefore we can plug them in:

x=-b/2a

x=-(-3)/2(-1)

x=3/-2

x=-3/2

x=-1.5

So the equation of the axis of symmetry is x=-1.5

Part 1C

We'll use the equation x=-b/2a to get the x-coordinate for the vertex (which we already know is x=-1.5), then plug in that value of x in the original equation to get the y-coordinate for the vertex:

f(x)=-(-1.5+4)(-1.5+1)

f(x)=-(2.5)(-0.5)

f(x)=-(-1.25)

f(x)=1.25 <-- y-coordinate

So the coordinates of the vertex are (-1.5,1.25)

Part 1D

See the image below

I'll let someone else do the last 4 questions as I am unable to answer them.

1/3+ 1/8 show your work a with equation
please hurry ​

Answers

Answer: 11/21

Step-by-step explanation:

Answer:

11/24 or 0.453

Step-by-step explanation:

1/3 + 1/8

1/3 × 8/8 = 8/24

1/8 × 3/3 = 3/24

8/24 + 3/24 = 11/24

Is this a function? Yes or No?!

{(1, 14), (2, 28), (3, 42), (4, 52), 5, 52)}

Answers

Answer:

Yes

Step-by-step explanation:

This is a function because each x value is given one y value. More simply, no x value was repeated.

Prove that (x+y)(x-y)+(y+z)(y-z)+(z+x)(z-x)=0

Answers

Answer:

x=0 x=y=z. with these presumed variable amounts, one can conclude that the equation you asked is equivalent to 0

Answer:

Step-by-step explanation:

(x+y)(x-y)+(y+z)(y-z)+(z+x)(z-x)

=x²-y²+y²-z²+z²-x²

=0

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