The height of a cylinder is decreasing at a constant rate of 1 centimeters per minute, and the volume is decreasing at a rate of 2341 cubic centimeters per minute. At the instant when the height of the cylinder is 1010 centimeters and the volume is 577 cubic centimeters, what is the rate of change of the radius? The volume of a cylinder can be found with the equation V=pi r^2 h. Round your answer to three decimal places.

Answers

Answer 1

Let's organize our given information.

[tex]\frac{dh}{dt}=-1[/tex]

[tex]\frac{dV}{dt}=-2341[/tex]

[tex]\frac{dr}{dt}=?, h=1010, V=577[/tex]

[tex]V=\pi r^2h[/tex]

What I'd like to do is solve for [tex]r[/tex] first, it'll help later.

[tex]577=\pi r^2(1010)[/tex]

[tex]r=\sqrt{\frac{577}{1010\pi}}[/tex]

[tex]r=0.426[/tex]

Now, we can differentiate our formula for the volume of a cylinder to find the rate of change of the radius.

[tex]V=\pi r^2h[/tex]

Use the product rule of differentiation.

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

Plug in the information we are given.

[tex]-2341=2\pi (0.426)(1010)\frac{dr}{dt}+\pi (0.426)^2(-1)[/tex]

Solve for [tex]\frac{dr}{dt}[/tex].

[tex]-2341=860.52\pi\frac{dr}{dt}+(0.426)^2\pi[/tex]

[tex]-2341.57=860.52\pi\frac{dr}{dt}[/tex]

[tex]\frac{dr}{dt}=-0.866[/tex]

The rate of change of the radius is -0.866 centimeters per minute.

Hope this helps!


Related Questions

need these 2 questions answer fast pls

Answers

Answer:

4a) The sides are not scaled up equally for the sides. Plus, B is not a right triangle since it does not satisfy the pythogorean theorem.

4b) 6, 8, 10

an athlete takes 10 rounds of a rectangular path, 70m long and 40m in wide. find the total distance covered by him.

Answers

Answer:

2,200 meters.

Step-by-step explanation:

Given that an athlete takes 10 rounds of a rectangular path, 70 meters long and 40 meters wide, in order to find the total distance covered by him the following calculation must be performed:

((40 + 70) x 2) x 10 = X

(110 x 2) x 10 = X

220 x 10 = X

2,200 = X

Thus, the total distance covered by the athlete was 2,200 meters.

K + 20% of k
k = Rs
Rs 180​

Answers

Answer:

216........................

A rectangle has an area of 54 square inches and a length of 6 in what is the width in inches of the rectangle?​

Answers

[tex]\mathfrak{\huge{\orange{\underline{\underline{AnSwEr:-}}}}}[/tex]

Actually Welcome to the Concept of the Areas and Volumes.

We know that, Area of a Rectangle = length * Width.

Since,here Length = 6 inch and Area = 54 square inches,

==> Width = Area / length

==> Width = 54/6

=> Width = 9 inches.

Hence the width of the rectangle is 9 inches.

Write as a square of a binomial

4.8xy+36y^2+0.16x^2

Answers

Rearrange 0.16x^2+4.8xy+36y^2
Take 4 out 4(0.04x^2+1.2xy+9y^2)
Now its a square 4(0.2x+3y)^2
If we multiply it out
0.04x^2+0.6xy+0.6xy+9y^2
0.04x^2+1.2xy+9y^2

Answer:

(6y+0.4x)^2

Step-by-step explanation:

What is an exponent?
I am just confused. I need the definition. Thx

Answers

Answer:

a quantity representing the power to which a given number or expression is to be raised, usually expressed as a raised symbol beside the number or expression (e.g. 3 in 23 = 2 × 2 × 2).

Answer:

an exponent is how many times you multiply a number by itself.

Step-by-step explanation:

For example, if there is a 4 with a 3 as an exponent, you would solve 4x4x4, also known as 4 cubed. or if there was a 2 with a 4 as an exponent , you would do 2x2x2x2. Hope this helps :)

2 points
7) My savings account increases in value by 4% every year. I started with
$10,000. Which of the following equations can be used to represent the
value of my account over time. *
f(x) = 10000(0.04)^x
f(x) = 10000(1 -0.04)^x
Of(x) = 10000(1.04)^x
O f(x) = 10000(0.96)*x

Answers

Answer: 10000(1.04)^x

Step-by-step explanation: every year your interest increases 4%

And you get multiplier 1.04. After first year you have 10400 and next year you multiply it by 1.04 again.

Determine whether the relation is a function
10
21
18
9
6
Is this relation a function?

Answers

Answer:

pppppp

Step-by-step explanation:

ppppppp

Two families went to Rollercoaster World. The Garcia family paid $170 for 3 children and 2 adults. The McGruder family paid $360 for 4 children and 6 adults.

If x is the price of a child’s ticket in dollars and y is the price of an adult’s ticket in dollars, write a system of equations the models this situation.

Answers

Answer:

3x +2y  =170  ---equation 1

4x +6y  =360 ---equation 2

Price of child 's ticket =$30

price of an adult’s ticket  =$40

Step-by-step explanation:

Let x represent  the price of a child’s ticket in dollars

and y represent  the price of an adult’s ticket in dollars

Such that

3 children and 2 adults for the cost of $170 be represented as

3x +2y  =170  ---equation 1

4 children and 6 adults for the cost of $360 be represented as

4x +6y  =360 ---equation 2

3x +2y  =170  ---equation 1

4x +6y  =360 ---equation 2

bY Elimination method  Multiplying equation 1 by 4 and equation 2 by 3

12x+8y =680---equation 3

12x +18y =1080---equation 4

Subtracting equation 3 from 4

10 y=400

y =400/10

y=40

Puting the value of y=40 in equation 1 to foind x

3x +2y  =170  

3x+2 x 40=  170

3x+80 =170

3x=170-80

3x=90

x=90/3=30

Price of child 's ticket =$30

price of an adult’s ticket  =$40

can i get some help plz? God bless ❤️

Answers

Answer:

Step-by-step explanation:

a, i took this quiz a while ago


Find the range for the measure of the third side of a triangle given the measures 5 and 9 for two of its sides.

Answers

the answer is 4.....

Imogene's car traveled 504 mi averaging a certain speed. If the car had gone 9 mph faster, the trip would have taken 1 hour less. Find the average speed.
The average speed of the car was mph.

Answers

The answer is 6.3782

2x=11 need the answer plss

Answers

Answer:

x=11/2 = 5 1/2

Step-by-step explanation:

Answer:

5.5 =x

Step-by-step explanation:

2x=11

1. Start by dividing by ten since its a even number

2. Then you'll get 5

3. With the last number you'll divide it that'll end up with

.5

4. Just combine both 5 and .5 and you'll get your answers 5.5



Evaluate:
UV
2
if u=4 and v=3

Answers

The answer would be 1 1/2 (one and one half)

look at the picture nd hurry please it needs to be done by 3 I have to do reading too!

Answers

Answer:

First one

Step-by-step explanation:

Even numbers

2 is tossed 10 times

4 is tossed 10 times

6 is tossed 9 times

10 + 10 + 9 = 29

Odd numbers

1 is tossed 8 times

3 is tossed 6 times

5 is toosed 7 times

8 + 6 + 7 = 21

write the word sentence as an quotation:
the sum of the number k and 5 is 11

Answers

Answer:

k+5=11

Step-by-step explanation:

Answer:

k=6

Step-by-step explanation:

k+5=11 (this is an algebraic expression)

k=11-5 (you move 5 to the left)

k=6

I need help please with number 5 and 6

Answers

Answer: #5 = -3    #6 =  0, there is no x

Step-by-step explanation:  #5 -   first you have to turn it into slope-intercept form. So, 3y+12=-9x will become y= -3x -4 because you divide all sides by 3 and you transpose 12 so it becomes negative... then you will pick out you slope which is the number in front of x so slope = -3

#6 - the slope is zero because there is no x in that equation.

5. The slope is -3 and the y intercept is (0,-4)

6. I got Y=-4

Which equation represents a line with slope -1/2
that passes through (-3, 4) ?

Answers

Answer:

y=-1/2x+5/2

Step-by-step explanation:

y-4=-1/2(x-(-3))

y-4=-1/2(x+3)

y-4=-1/2x-3/2

y=-1/2x-3/2+4

y=-1/2x+5/2

PLEASEEEEEEEEEEEEEEE HELPPP

Answers

Answer:

88, A

Step-by-step explanation:

16 x 4 = 64

3 x 8 = 24

64+24 = 88

This is a question my friend asked me help

Cranberry juice is made with a 16:3:1 ratio of water:sugar:cranberries. How much water, in gallons, is needed in order to make three gallons of cranberry juice? Express your answer as a common fraction.

Answers

Answer:

12 / 5 gallons

Step-by-step explanation:

cost of 4 dozen bananas is rupees 180 how many bananas can be purchased for rupees 30 unto ​

Answers

Answer:

8 bananas

Step-by-step explanation:

4 dozen is equal to 48 and 180 divided by 48 is 3.75 then 30 divided by 3.75 is 8

600 students attend Ridgewood Junior High School. 10% of students bring their lunch to school everyday. How many students brought their lunch to school on Thursday?

Answers

Answer:

60

Step-by-step explanation:

10% of 600 is 60

Answer= 60

10% of 600
10 ÷ 100 = 0.1
0.1 x 600 = 60

( 3 + 1/2/) x 14= Thanks for the assistance......

Answers

Answer:

49

Step-by-step explanation:

3+1/2= 3.5

3.5 x 14= 49

hope I helped. :)

Find the slope of a line that passes through the points (8, 7) and (-8,
-1).

Answers

Answer:

m = 1/2

Step-by-step explanation:

What do I do for this

Answers

Answer:

its 7 or B.

Step-by-step explanation:

7 is the number being repeated the most (dunno if that makes sense so the mode is the most common number in a data set.)

Omar deposited $4000 into an account with 3.3% interest, compounded semiannually. Assuming that no withdrawals are made, how much will he have in the account after 5 years? Do not round any intermediate computations, and round your answer to the nearest cent.

Answers

Answer:

4711.22

Step-by-step explanation:

[tex]A=P(1+\frac{r}{n} )^{nt}\\\\A=4000(1+\frac{0.033}{2}) ^{2*5}\\\\A=4711.22[/tex]


A baby girl weighed 6 pounds at birth and 8
pounds one month later. How many ounces
did the baby gain in her first month of life?
A. 16 ounces
В.
64 ounces
C. 32 ounces
D. 48 ounces

Answers

The answer is c 32 ounces

Answer: C

Step-by-step explanation:

1 pound is equivalent to 16 ounces. She earned 2 pounds in 1 month, meaning that you have to multiply 16 times 2, which gives 32 ounces. Hope this can help you! Have a great day/night!

Write The Equation on the line.​

Answers

Answer:

Check pdf

Step-by-step explanation:

The equation is :-y=-2/3x-4 ( co - ordinates are (-6,0) , (0,-4) )

True or False: Cold air is more dense than warm air, causing it to sink and hover near the ground.

Group of answer choices

False

True

Answers

Answer:

True! :)

Step-by-step explanation:

Complete the equation of the line through (-10.-7) and (5.9).


15 POINTS PLEASE

Answers

Answer:

y=16/15x-11/3

Step-by-step explanation:

(9--7)/(5--10)

slope = 16/15

y=16/15(x)+b

-9=(16/15)(-5)+b

b=-11/3

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