Water is filling a cylindrical water tank. As it is filled the radius of the tank expands at 0.2cm/s and the height decreases at the rate of 0.5cm/s. Find the rate at which the volume of the tank is changing at the instant the radius equals 1.8cm and height equals 65 cm. What is the volume of water at this point? Show all working. Volume, V, of the cylinder is given by V = ϖr2h.
Recall that V is a function of both r (radius of the cylinder) and h (the height of the cylinder). This is a partial differentiation problem. The volume is also changing with time.

Answers

Answer 1

Answer:

141.94 cm³/s

Step-by-step explanation:

Since the volume of the tank V = πr²h, and both the height and radius of the tank change with time, we find the rate of change of the volume with time, dV/dt from

dV/dt = dV//dr × dr/dt + dV/dh × dh/dt

where dV/dr = 2πrh, dr/dt = + 0.2 cm/s (since the radius of the tank expands), dV/dh = πr² and dh/dt = -0.5 cm/s (since the height of the tank decreases)

So,

dV/dt = dV/dr × dr/dt + dV/dh × dh/dt

dV/dt =  2πrh ×  + 0.2 cm/s +  πr² ×  -0.5 cm/s

dV/dt =  0.4πrh cm/s -  0.5πr² cm/s

dV/dt =  πr(0.4h - 0.5r) cm/s

We now find the rate at which the volume is changing when r = 1.8 cm and h = 65 cm.

So,

dV/dt =  π(1.8 cm)(0.4 × 65 cm - 0.5 × 1.8 cm) cm/s

dV/dt =  π(1.8 cm)(26 cm - 0.9 cm) cm/s

dV/dt =  π(1.8 cm)(25.1 cm) cm/s

dV/dt =  π(45.18 cm²) cm/s

dV/dt = 141.94 cm³/s


Related Questions

so i am hqving trouble with a particular question and hoping somebody could help me with it. this is the particular question 47 + 10x = -10x + 7​

Answers

Step-by-step explanation:

given 47 + 10x = -10x + 7

[tex]47 + 10x = - 10x + 7 \\ 47 + 10x + 10x = 7 \\ 47 + 20x = 7 \\ 20x = 7 - 47 \\ 20x = - 40 \\ x = - 40 \div 20 \\ = - 2[/tex]

Evaluate each expression if a = 6, b = 3, and c = 2.

A | 6 + c
B | a - b
C | 2 c
D | a - 1
E | c + 4
F | a/b
G | b ÷ 3
H | ab

Answers

A: 9
B: 3
C: 4
D: 5
E: 6
F: 2
G: 1
H: 18

please answer this question

Answers

3/8 because half of 8/8 is 4/8 and 4/8-1/8 equals 3/8

Answer:

0.3

Step-by-step explanation:

Find the perimeter
xin
X + 4 in
Select the correct response:
• P= x2 + 4x in?
O P = 4x + 8 in
O P = 2x + 4 in
O P = 4x + 8 in?

Answers

Answer:

p=X^2+4x

aaaaaaaa is corect a

It depends. If the object is a square, then the perimeter is 4 times the length of the given side. 4x + 16

If it’s a quadrilateral and one side is x and the other side is x + 4, then the perimeter is x + x + (x +4) + (x +4). 4x + 8 inches

Just onve more question
same as the other one

Answers

multiply out the brackets 4(5-2x)
4*5=20
4*2x=8x
put this into the equation
20-8x+3=7
- which can also be written as 23-8x=7
by minusing 7 from both sides you get:
16-8x=0
minus 16 from both sides
-8x=-16
from this we can see that x=2

Answer:

x = 2

Step-by-step explanation:

4(5 - 2x) + 3 = 7

Distributive property ,    multiply (5-2x) by 4:

20 -8 x + 3 = 7

Combine like terms:

23 - 8x = 7

Inverse add and subtract:

23 - 7 - 8x + 8x = 7 - 7 + 8x

16 = 8x

Inverse divide:

16/8 = 8x/8

x = 2

pls help asap no wrong answer pls

Answers

Answer:

Answer in explanation

Step-by-step explanation:

Probability of Magic elf =

[tex]p(elf) \times p(magic) \\ = \frac{1}{3} \times \frac{1}{5} \\ = \frac{1}{15} or \: 0.66667[/tex]

Answer:

6.66%

Step-by-step explanation:

There is a 1/3 chance of getting the character you want and 1/5 chance of getting the weapon you want. So the probability is 1/3*1/5=1/15 or 6.66%.

BRAINLIEST TO CORRECT

Answers

Answer:

Step-by-step explanation:

Can anyone turn this fraction to a decimal i have to have this full sheet of work done by 12:00pm tonight so I need quick answers ASAP!!

Answers

Answer:

6/10 = 0.6

3/25 = 0.12

1/5 = 0.2

14/20 = 0.7

24/50 = 0.48

1/2 = 0.5

8/25 = 0.32

4/10 = 0.4

17/20 = 0.85

6 x 4/8 = 3

6 x 4/12 = 2

8 x 18/8 = 18

Step-by-step explanation:

Maria is training to be a long distance runner. She runs once every day. On the average, each day that Maria has run, she has improved her time by 20 seconds. Today she ran for the fifth time. Her time was 10 minutes 48 seconds. What was Maria's running time the first day she ran?

Answers

Answer:

9 mins and 8 secs

Step-by-step explanation:

Mark wants to paint a mural. He has 1 1/8 gallons of yellow paint, 1 1/9 gallons of green paint, and 7/8 gallons of blue paint. Mark plans to use 3/4 a gallon of each paint color. How many gallons of paint will he have left after painting the mural? Enter your answer as a simplified fraction.

Answers

Answer:

We have 31/36 gallons of paint left after painting the mural.

Step-by-step explanation:

"Mark wants to paint a mural. He has 1 1/8 gallons of yellow paint, 1 1/9 gallons of green paint, and 7/8 gallons of blue paint. Mark plans to use 3/4 a gallon of each paint color. How many gallons of paint will he have left after painting the mural? Enter your answer as a simplified fraction."

==================================================================

First change each number into a improper fraction:

1 1/8 = 9/8

1 1/9 = 10/9

7/8 = 7/8

=================================================================

"If Mark has 9/8 gallons of yellow paint, and he uses 3/4 gallons"

  -We have to multiply 3/4 by 2/2 to make the denominators same.

3/4 × 2/2 = 6/8

Now subtract 6/8 from 9/8.

9/8 - 6/8 = 3/8

We will have 3/8 gallons of yellow paint.

==================================================================

"If Mark uses 10/9 gallons of green paint, and he uses 3/4 gallons"

     - We have to multiply 10/9 by 4/4, and 3/4 by 9/9, to get a common denominator.

10/9 × 4/4 = 40/36

3/4 × 9/9 = 27/36

Now subtract 27/36 from 40/36

40/36 - 27/36 = 13/36

We will have 13/36 gallons of green paint.

==================================================================

"If Mark uses 7/8 gallons of blue paint, and he uses 3/4 gallons"

        -We have to multiply 3/4  by 2/2 to get a common denominator.

3/4 × 2/2 = 6/8

Now subtract 6/8 from 7/8.

7/8 - 6/8 = 1/8

We will have 1/8 gallons of yellow paint.

==================================================================

Now, we will add the leftover amounts of paint to find the answer.

3/8 + 13/36 + 1/8

Add "like terms".

4/8 + 13/36

Simplify 4/8 into 1/2

1/2 + 13/ 36

Multiply 1/2 by 18/18 to get a common denominator.

1/2 × 18/18 = 18/36

Substitute 18/36 as 1/2 in the expression.

18/36 + 13/36 = 31/36

So, We have 31/36 gallons of paint left after painting the mural.

==================================================================

Hope I helped, Have a nice day!

              -Aadi x

NEED HELP ASAP

What type of function is this: y = 4X ?

1:Quadratic

2:Exponential Growth

3:Exponential Decay

4:Linear

Answers

Answer:

linear

hope this was helpful

PLEASE HELP THIS IS MY LAST QUESTION!

Triangle JKL is an equilateral triangle with two of its vertices at points J and K. What are the coordinates of point L? Round to the nearest tenth as needed.

Answers

Answer:

The X coordinate is 6, since it's midway between J and K. If you draw a midline from L, and running to the midpoint of the line JK, you make two right angled triangle. The length of the midline would be the square root of the difference of the squares of six and three, which is 5.20, which is the offset of the Y coordinate of L from the Y coordinate of J and K, which is 2. Add 5.20 to 2 to get the Y coordinate of L as 7.20. L is therefore (6,7.20)

Answer:

(6, 7.2)

Step-by-step explanation:

Since it is an equilateral triangle, all of the side length must be equal.

Therefore, we know the lengths JK = 6 and JL = 6. If h is the height of the triangle, the Pythagoras's theorem says

(JK/2)² + h² = JL²

putting in the values of JK and JL gives

(6/2)² + h² = 6²

3² + h² = 6²

subtracting 3^2 from both sides gives

h² = 6² - 3²

h² = 27

Taking the square root of both sides gives

h =

[tex] \sqrt[3]{3} [/tex]

h = 5.2

With the value of h in hand, we can now read off the coordinates of L.

The x coordinates of L is 6 (count the boxes along the x-axis until you are under L or halfway between J and K).

The y-coordinates of L is 2 + h = 2 + 5.2 = 7.2 ( how far above the x-axis the triangle is plus the height of the triangle).

1 of 6
©
Solve
x² - 23x + 132 < 0​

Answers

Answer:

11<x<12

Step-by-step explanation:

You Spin The Spinner The Numbers on it are: 1,2,2,2,3,3,3,1, in how many ways can spinning 1 occur

Answers

Answer:

1/4

Step-by-step explanation:

Probability (spinning 1) = 2/8

= 1/4

Answer:

2 over 8

Step-by-step explanation:

so there are 8 numbers altogether. there are 2 1s in all so it would be 2 over 8

given f(x) = X^2 – 5x + 6 state discriminant # of solutions

Answers

The discriminate formula is b^2+4ac so -5^2+4(1)(6)=49

To control an​ infection, a doctor prescribes a dosage of 200 mg of medicine every 8 hours for an infant weighing 12.1 lb. At this​ rate, what would the dosage be for an infant weighing 20.8 ​lb?

Answers

Answer:

To control an infection, a doctor prescribes a dosage of 200 mg of medicine every 8 hours for an infant weighing 12.1 lb. At this rate, what would the dosage be for an infant weighing 20.8 lb?

Step-by-step explanation:

ans :- 7.5 ml

I need help, find the area

Answers

*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆

Answer: 45.5

Explanation:

5 x 7 x 1/2 = 17.5

18 x 7 x 1/2 = 63

63 - 17.5 = 45.5

I hope this helped!

<!> Brainliest is appreciated! <!>

- Zack Slocum

*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆

Answer:

45.5

Step-by-step explanation:

I assume you need the area of the shaded triangle.

area = base * height / 2

A = 13 * 7 / 2

A = 45.5

Q. You do lawn work for $13 an hour, but charge a $7.5 transportation cost. What rule
represents your business model?
answer choices
Cy=13x + 7.5
f y=13x - 7.5
By=20.5%
Dy=7.5x + 13

Answers

Answer:

Cy

Step-by-step explanation:

x is the number of hours

The answer to your question is Cy

Can someone please help!!! i really need it

Answers

Answer:

Step-by-step explanation:

6. 8

7. 21

8. 18

Circle with the center at (2,4) which goes through the point (-1,0). What is the equation of that circle?

Answers

Answer:

(x-2)²+(y-4)² = 25

Step-by-step explanation:

Standard equation of a circle is expressed as

(x-a)²+(y-b)² = r²

Center = (a, b)

Radius = r

Get the radius

r² =(0-4)²+(-1-2)²

r² = (-4)²+(-3)²

r² = 16 + 9

r² = 25

Centre = (2, 4)

Substitute into the equation

(x-2)²+(y-4)² = 25

This gives the required equation

Shirt is $45 but is on sale for 20% off. What is the discount

Answers

Answer:

$15 dollars off so the original price is $60!!!

Step-by-step explanation:

Answer:

$36

Step-by-step explanation:

45 x 0.20

= 9

Total price - sale

= 45 - 9

= 36

Please find the area of this rectangle.

Answers

Answer: third choice  A=6x^2-7x-3 inches squared

Step-by-step explanation:

Area = (2x - 3)(3x + 1)

Multiple terms: first x first, first by second, second by first, second by second
Area = (2x • 3x) + (2x • 1) + (-3 • 3x) + (-3 • 1)

Simplify each term
Area = 6x^2 + 2x - 9x - 3

Combine like terms
Area = 6x^2 -7x -3 squared inches

Evaluate 8d, when d=12

Evaluate 75/d (75 divide by d), when d = 5

Evaluate 6p^2 + 8(6 times p to the second power plus 8), when p = 4

Answers

Answer:

9615104

Step-by-step explanation:

Given:

d = 12 find 8dd = 5 find 75/dp = 4 find 6p² + 8

Computation:

d = 12 find 8d

8(12)

96

d = 5 find 75/d

75 / 5

15

p = 4 find 6p² + 8

6(4)² + 8

6(16) + 8

96 + 8

104

Someone help plz I only have 5 questions and plz make sure it’s right :)

Answers

Answer:

That question is easy you can use simple logic for this no math needed the answer is B 4.2mi if you need a reason why it is i will provide one

Step-by-step explanation:

Naomi plotted the graph below to show the relationship between the temperature of her city and the number of popsicles she sold daily:

A scatter plot is shown with the title Naomis Popsicle Stand. The x axis is labeled High Temperature, and the y-axis is labeled Number of Popsicles Sold. Data points are located at 90 and 20, 85 and 17, 70 and 14, 75 and 20, 60 and 16, 50 and 14, 60 and 12, 40 and 10, 50 and 12, 80 and 8.

Part A: In your own words, describe the relationship between the temperature of the city and the number of popsicles sold. (2 points)
Part B: Describe how you can make the line of best fit. Write the approximate slope and y-intercept of the line of best fit. Show your work, including the points that you use to calculate the slope and y-intercept. (3 points)

Answers

Answer:

Answer:

A.  The temperature of the city and the number of popsicles sold are positively correlated

B.

Slope: 0.1233

Y-Intercept: 6

Step-by-step explanation:

Being dead honest with you less people will answer if there isn;t a photo, But I can't be 100% sure of my answer being there isn't one.

(90,20)

(40,10)

40-90= -50

10-20= -10

-10/-50= 0.2

Thats the slope line I used 2 random numbers, I don't know the order so it might be wrong.

Well look at your graph are the lines going up or down as x increases?

From my assighment it is a increase.

(I'll mark brainliest)Sam is planning a birthday celebration for his coworker. He drew the map below to show the places he needs to drive to get party supplies. The 'nap has a scale 1 inch to 25 miles.


Sam is currently at the bakery and his next stop is the florist. What is the actual distance, in miles, between the two places?

A. 10.0

B. 27.5

C 62.5

D.75 0

Answers

The correct answer is letter C

. The perimeter of a square is 8y – 12. The area of the square is 100 square units. What is the value of y?

Answers

Answer:

y = 6.5 units

Step-by-step explanation:

Let L be the length of sides of the square.

Given the following data;

Perimeter of square = 8y - 12

Area of square = 100 square units

To find the value of y;

Area of a square = L²

Substituting into the formula, we have;

100 = L²

L = √100

L = 10 units

Mathematically, the perimeter of a square is given by the formula;

Perimeter of a square = 4L

Substituting into the formula, we have;

8y - 12 = 4*10

8y - 12 = 40

8y = 40 + 12

8y = 52

y = 52/8

y = 6.5 units

What is the result of −14⋅−1249?

Answers

Answer:

138

Step-by-step explanation:

Hope you have a wonderful day!

1. a line that is parallel to y=3/4x-9 has slope m=___________

Answers

parallel means same slope so it’s also 3/4

Answer:

Hi! The answer to your question is [tex]\frac{3}{4}[/tex]

Step-by-step explanation:

This equation is in y=mx+b or -b which is Slope Intercept form for Graphing basically y is the y intercept and b means slope, you don't have to do anything extra to find the slope when its in Slope Intercept Form all you have to do is look for usually its a fraction but it can also be a number but all you have to look for is the number that comes before b in the equation! If this has helped you please say that this has helped, if it hasn't please tell me what confuses you and i can quickly clear up that confusion! Have a nice day!

Can someone please help me with this question

Answers

1065 ft^2
Hope this helps
Other Questions
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