A cylindrical tank with radius 5 m is being filled with water at a rate of 3 m^3/min. How fast is the height of the water increasing

Answers

Answer 1

Answer:

[tex]\frac{3}{25\pi}[/tex] meters per minute

Step-by-step explanation:

Given:

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

[tex]r=5[/tex]

[tex]\frac{dV}{dt}=3[/tex]

[tex]\frac{dh}{dt}=?[/tex]

Substitute r=5:

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

[tex]V=\pi(5)^2h[/tex]

[tex]V=25\pi h[/tex]

Differentiate both sides:

[tex]\frac{d}{dt}V=\frac{d}{dt}(25\pi h)[/tex]

[tex]\frac{dV}{dt}=25\pi\frac{dh}{dt}[/tex]

Solve for dh/dt:

[tex]3=25\pi\frac{dh}{dt}[/tex]

[tex]\frac{3}{25\pi}=\frac{dh}{dt}[/tex]

Therefore, the height of the water is increasing at a rate of [tex]\frac{3}{25\pi}[/tex] meters per minute.


Related Questions

Kashira has 3/9 of a pizza and Laila gave her 1/3 of a pizza. How much pizza does Kashira have now? Please provide your answer in simplest form. (NVM FIGURED IT OUT)

Answers

Answer:4/9 pizzas

Step-by-step explanation:

A dress originally priced at 8080 dollars was put on sale for 25\%% off. If 10\% tax was added to the sale price, then the total selling price (in dollars) of the dress was

Answers

Answer: If the dress orginially priced at 8080 dollars and put for 25 percent, that means that you have to move the decimal point to the left twice which will result as 0.25 and 10 percent tax ends up as 0.10. Multiply the two and the product, you have to add to the 8080!

Step-by-step explanation:

9 13 / 16 + 10 3 / 8 =

Answers

It equals 20 3/16, or 20.1875

A salesperson's commission rate is 4% what is the commission from the scale of 39,000 worth of furnaces?


Suppose sales would double. What would be true about the commission?

Answers

Answer:

3,120

Step-by-step explanation:

hope it will help you

please help,I WILL GIVE BRAINLIEST.
Ben participated in a race. During the first half of the race, he walked 3 miles and ran at a rate of 5 miles per hour for x hours. During the second half of the race, he walked for 2 miles and ran at a rate of 5.5 miles per hour for x hours. What equation could you write to solve for the number of hours Ben ran during each half of the race? Let y represent the number of miles in half the race. Write two equations, one for the first half of the race and one for the second half. How could you transform these two equations to be the same as the original equation you wrote to solve for x? What do you think this means about solving for the variables in a situation represented by two equations?

Answers

Answer:

During the first half of the race, he walked 3 miles and ran at a rate of 5 miles per hour for x hours.y = 5x + 3

During the second half of the race, he walked for 2 miles and ran at a rate of 5.5 miles per hour for x hours. y = 5.5x + 2

Then using both equations will be:

y = 5x + 3

y = 5.5x + 2

Subtract the equations

0.5x = 1

x = 1/0.5 = 2

Therefore, the value of y will be:

y = 5x + 3 = 5(2) + 3 = 13

pls help due soon i’ll mark brainliest

Answers

I can't see anything dude, you on something?

The cost of a jacket increased from $60.00 to $71.40. What is the percentage increase of the cost of the jacket?

Answers

Answer:

19%

Step-by-step explanation:

Percentage increase = ( (final value - original value) / original value ) x 100

= ( ($71.40 - $60.00) / $60.00 ) x 100

= 19%

[tex]71.40 - 60 = 11.40[/tex]

to find the increase of percentage, divide the amount of increasing price with intial price and multiply with 100%

[tex] \frac{11.40}{60} \times 100\% = 19\%[/tex]

so the cost of jacket has increased 19%

A moneylender’s income decreased by $60 When the rate of interest dropped from 8% per annum to 7 3/4 % per annum . What was his principal?

Answers

Answer:

  $24,000

Step-by-step explanation:

The difference for principal amount P is ...

  (8% × P) - (7 3/4% × P) = $60

  0.0025P = $60

  P = $24,000 . . . . . multiply by 400

His principal was $24,000.

Need Help....
I can't understand the question so please help me.....

[tex]for \: x \: such \: that \: 0 < x < \frac{\pi}{2}[/tex]
It is the expression
[tex] \frac{ \sqrt{1 - {cos}^{2}x } }{sin \: x} \:- \frac{ \sqrt{1 - {sin}^{2}x } }{cos \: x} \\ \\ is \: equivalent \: to:[/tex]
[tex]f.0 \\ g.1 \\ h.2 \\j. - tan \: x \\ k. \: sin \: 2x[/tex]
Don't spam and Don't copy
Don't answer if you don't know
Thank You!

Answers

If 0 < x < π/2, then both sin(x) and cos(x) are positive.

From the Pythagorean identity, we then have

cos²(x) + sin²(x) = 1

⇒   cos(x) = + √(1 - sin²(x))   and   sin(x) = + √(1 - cos²(x))

Then

√(1 - cos²(x))/sin(x) = sin(x)/sin(x) = 1

and

√(1 - sin²(x))/cos(x) = cos(x)/cos(x) = 1

so that the overall expression reduces to

1 - 1 = 0

Expand the following expressions and write in standard form. Show your work.

a) (3x + 2)(1 - 4x)
b) (x - 5)^2(2x + 7)

Please help!!!!

Answers

3x(1-4x)+2(1-4x)

3x-12x²+2-8x

-5x-12x²+2

Write the name of a polynomial (using the degree) with the sequence of the
outputs: (5,2,-1,-4, ...}*
Type ONE word

Answers

Answer:

pentagon

Step-by-step explanation:

5 degree angle

Pentagon is the answer i think

Unit Rate
Madison can eat 12 eggs in 20 minutes. How many
eggs can she eat in 35 minutes?

Answers

Answer:

37

Step-by-step explanation:

38 + u actually thought lol

four water bottles can hold 8 gallons of water how much water can ten big water bottles hold

Answers

Answer:

20 gallons of water.

Step-by-step explanation:

4 water bottles = 8 gallons

1 water bottle = 2 gallons

X = Number of Water bottles

N = Gallons Per Water Bottle

X * N

10 * 2

20

If 12g of a radioactive substance are present initially and 8yr later only 6g remain, how much if the substance will be present after 13 years?

Answers

The weight of substance remaining after 13 years is 2.25 g.

Given:

Present weight of substance = 12 g

After 8 years weight remains = 6 gm

Now, weight loss in 8 year will be,

12-6=6 gm

So, weight loss in 1 year will be,

[tex]\dfrac{6}{8} =\dfrac{3}{4}[/tex]

Total weight loss in 13 year will be,

[tex]\dfrac{3}{4}\times13=9.75[/tex]

The weight of substance remaining after 13 years will be,

[tex]12- 9.75 = 2.25 \;\rm g[/tex]

Therefore, the weight of substance remaining after 13 years is 2.25 g.

To know more about radioactive decay, refer to the link:

https://brainly.com/question/12116123

a
The eighth-grade class has a total of 162 students. The students need to be
divided evenly into homerooms. There needs to be at least 20 students in
each homeroom. List all the possible combinations. Which combination
makes the most sense? Explain.

Answers

Answer:

162/20 Would be your answer, however, it wouldn't make sense as you can not switch students into decimals. Therefore, you could make 7 classes of 20, and one of 22, and 6 classes of 20, and two of 21. Therefore, there are two combinations that are possible.

Step-by-step explanation:

Refer to the answer.

Answer:

56

Step-by-step explanation:

The standard configuration for a Colorado license plate is 3 letters followed by 3 digits. How many different license plates are possible if letters and digits can be repeated?

Answers

Answer:

17,576,000 different combinations possible.

Step-by-step explanation:

Brian has DVDs and CDs. The number of CDs he has can be modelled with the formula C = 2D + 11, where C represents the number of CDs and D represents the number DVDs. If he has 41 CDs, how many DVDs does he have?​

Answers

Answer: 15 DVDs

Step-by-step explanation:

C = 2D + 11

41 = 2D + 11

2D = 30

D = 15 DVDs

(03.02) If g(x) = x2 + 2, find g(3). (2 points) Group of answer choices 9 8 11 6

Answers

this answers is 8 am I right

Shawna wanted to boat across the river, but did not know how wide it was. She walked along the shore for 90 feet and sighted across the water to the point she wanted to go. The angle that the sight line made with the shoreline was 65°. What was the distance across the river?​

Answers

The distance across the river, given the angle of the line of sight and the

distance along the shoreline is found using trigonometric ratios.

The distance across the river is approximately 193 feet.

Reasons:

The distance along the the shore Shawna walked before sighting across the river = 90 feet

The angle made by the line of sight and the shoreline, θ = 65°

Required:

The distance across the river.

Solution:

Taking the initial location of Shawna to be the closest place to point she wanted to go across the river, we have;

The shortest distance across the river = A perpendicular line

Therefore, the following sides, form a right triangle;

The line of sight.The distance along the shoreline Shawna walked, andThe closest distance across the river.

Where:

The line of sight = The hypotenuse side

The distance she walked = The adjacent side to angle 65° angle

The closest distance across the river = The opposite side to the 65° angle

By trigonometric ratio, we have;

[tex]\displaystyle tan(\theta) = \frac{Opposite \, side \, to\ angle}{Adjacent\, side \, to\, angle} = \mathbf{\frac{Distance \ across \ the \ river}{Distance \ along \ the \ shoreline}}[/tex]

Which gives;

Opposite side to angle = tan(θ) × Adjacent side to angle

Therefore;

Distance across the river = tan(65°) × 90 feet ≈ 193.0 feet

The distance across the river is approximately 193 feet

Learn more about trigonometric ratios here:

https://brainly.com/question/10270672

https://brainly.com/question/2560921

Please answer both please please I’ll give brainly

Answers

Answer:

4.  9  

5.    5x

Step-by-step explanation:

its an isocoles

Q6 (i) please i don’t know what i’m doing wrong

Answers

Start by squaring the numbers on both sides to get rid of the square root on both the left and right sides to get:

x + 5 = 5^2 – x

x + 5 = 25 – x

Then rearrange to make x the subject.

x + 5 = 25 – x

2x + 5 = 25

2x = 20

x = 10

Answer:

x = 4

Step-by-step explanation:

Square both sides

x+5 = 25-10sqrt(x)+x

20 = 10sqrt(x)

sqrt(x) = 2

Square both sides again

x=4

Verify sol

x = 4

Determine the intercepts of the line.

Answers

Answer:

y-intercept: (0,5)

x-intercept: (5/2,0)

Step-by-step explanation:

[tex]-4x+7=2y-3[/tex]

[tex]-4(0)+7=2y-3[/tex]

[tex]0+7=2y-3[/tex]

[tex]7=2y-3[/tex]

[tex]10=2y[/tex]

[tex]5=y[/tex] <-- y-intercept: (0,5)

[tex]-4x+7=2y-3[/tex]

[tex]-4x+7=2(0)-3[/tex]

[tex]-4x+7=-3[/tex]

[tex]-4x=-10[/tex]

[tex]x=\frac{5}{2}[/tex] <-- x-intercept: (5/2,0)

HELP GIVING BRAINLIEST!

Answers

Answer:

C

Step-by-step explanation:

Answer:

y = 1/4x

Step-by-step explanation:

Jim has 44 nickels and dimes totaling $2.95. How many nickels does he have?

Answers

29 Nickels

15 Dimes

Hope this is helpful!

Can someone please help me with 54? It’s the last one and it’s due in 1 hour Tysm if you do!!

Answers

Answer:

The awnser should be 4. (3x4 = 12, 12 x 4 = 48, 48 x 12 = 192, 192 x 4 = 768. )

Step-by-step explanation:

(Hope this helps, Happy holidays!!)

4. But what happened to the paper? Looks like it’s been through stuff.

The ratio of three number is 5:6:7. If the sum of the numbers is 54. What
are the numbers?

Answers

Let the numbers be 5x, 6x and 7x respectively.Therefore, by the problem

[tex]5x + 6x + 7x = 54 \\ = > 18x = 54 \\ = > x = 3[/tex]

So, the numbers are (5 × 3) i.e., 15, (6 × 3), i.e., 18, (7 × 3), that is 21.

Answer:

The numbers are 15, 18 and 21.

Hope you could get an idea from here.

Doubt clarification - use comment section.

What is the coefficient of the term x°ys in the
expansion of the binomial expression
(2x - y)8?

Answers

Answer:

if it is (2x-y)8

then it is 16x - 8y

[tex]x^0[/tex]y = 1.y = y

so the co efficient of y is -8

Step-by-step explanation:

A T-shirt company charges $4 per T-shirt, plus a
flat shipping fee of $5. Terry bought some
T-shirts. How can you write an algebraic
expression to represent the total cost of Terry's
order including shipping?
Plz help plz

Answers

Answer:

y = 4x + 5

Step-by-step explanation:

4 times the number of shirts, which is unknown, +$5 no matter how many.

Answer:

4x + 5

Step-by-step explanation:

Four multiplied by the number of shirts purchased (x) plus five dollars for shipping.

I hope this helps!!

y = 2x + 7
3x - 4y = -13

Answers

The answer would be (x,y) = (-3, 1)

A ball is thrown upward from a height of 15 feet with an initial upward velocity of 5 feet per second. Use the formula b(t)= -16t^2 + 5t + 15 to find the time it takes for the ball to reach the maximum height of the ball. Round to the nearest tenth

A. 0.2 seconds

B. 0.1 seconds

C. 0.3 seconds

D. 0.9 seconds​​

Answers

Answer:

0.2 seconds

Step-by-step explanation:

The graph of b(t) = -16t^2 + 5t + 15 is a parabola opening downward.  The maximum value of b(t) occurs at the vertex.  The t-coordinate of the vertex is t = -5 / (2(-16)) = 5/32 = 0.15625 sec ≈ 0.2 sec.  

Answer:

A) 0.2 seconds

Step-by-step explanation:

[tex]b(t)=-16t^2+5t+15[/tex]

[tex]v(t)=-32t+5[/tex] <-- Take the derivative

[tex]0=-32t+5[/tex] <-- Set equal to 0

[tex]-5=-32t[/tex]

[tex]\frac{5}{32}=t[/tex]

[tex]t=\frac{5}{32}[/tex]

[tex]t\approx0.2[/tex]

Therefore, it will take the ball about 0.2 seconds to reach its maximum height (which happens to be about 15.4 feet BTW).

Alternatively, another non-calculus approach is the fact that the parabola opens downward, and as such, the maximum of [tex]b(t)[/tex] occurs at the vertex where [tex]t=-\frac{b}{2a}[/tex], therefore [tex]t=-\frac{5}{2(-16)}=\frac{-5}{-32}=\frac{5}{32}\approx0.2[/tex]

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