spherical water tank of radius R = 5m is emptied through a small circular hole of radius r = 0.03 m at the bottom. The top of the tank is open to the atmosphere. The instantaneous water level h in the tank (measured from the bottom of the tank, at the drain) can be determined from the solution of the following ODE:
dh /dt =r²(2gh)^0.5/ 2hR-h²
where g = 9.81 m/s². If the initial (t = 0) water level is h=6.5 m, compute the time required to drain the tank to a level of h= 0.5m. Use the fourth-order Runge-Kutta method.

Answers

Answer 1

Answer:

water level is h=6.5 m, compute the time required to drain the tank to a level of h= 0.5m. Use the fourth-order Runge-Kutta method.

Step-by-step explanation:

water level is h=6.5 m, compute the time required to drain the tank to a level of h= 0.5m. Use the fourth-order Runge-Kutta method.


Related Questions

which one is greater 7 pounds or 70 ounces

Answers

Answer:

7 pounds is greater

Step-by-step explanation:

1 lb = 16 oz

7 lb = 112 oz

70 oz is 70 oz

Answer:

7 pounds is greater

Step-by-step explanation:

1 lb = 16 oz

7 lb = 112 oz

70 oz is 70 oz

You should be able to figure out the answer

Find the length of the diagonal.

Answers

Answer:

     D.  34 in

Step-by-step explanation:

You are given the formula for the diagonal in terms of the edge lengths of the cuboid. To find the diagonal, use the given numbers in the given formula.

  Diagonal = √((24 in)² +(18 in)² +(16 in)²) = √(576 +324 +256) in = √1156 in

  Diagonal = 34 in

A supply company manufactures copy machines. The unit cost C (the cost in dollars to make each copy machine) depends on the number of machines made. If
x machines are made, then the unit cost is given by the function C(x) = 0.5x^2- 150x +20,960. How many machines must be made to minimize the unit cost?
Do not round your answer.

Answers

The supply equation of the company is an illustration of a quadratic function

The number of machines that must be made to minimize the unit cost is 150

How to determine the number of units?

The equation of the function is given as:

[tex]C(x) = 0.5x^2- 150x +20960[/tex]

Differentiate the function

[tex]C'(x) = x - 150[/tex]

Set to 0

[tex]x - 150 = 0[/tex]

Add 150 to both sides of the equation

[tex]x = 150[/tex]

Hence, the number of machines that must be made to minimize the unit cost is 150

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If z varies directly with the square of x and inversely with the cube of y, when x = 8, y = 2, and z = 12, what is x when y = 1 and z = 24?
PLEASE HELP!!! :))))

Answers

Step-by-step explanation:

it just means

z = k×x²/y³

12 = k×8²/2³ = k×64/8 = k×8

k = 12/8 = 3/2

24 = k×x²/1³ = 3/2 × x²/1 = 3/2 × x²

24/(3/2) = x²

48/3 = x²

16 = x²

x = 4 or

x = -4

Answer the questions below about the quadratic function. g(x)=-2x^2+16x-31

Answers

Answer:

Hope it helps!!!Brainliest pls!!!

Show how you got the answer, giving brainliest :)

Answers

Answer:

Step-by-step explanation:

Volume of a rectangular prism: l*w*hVolume of a triangular prism: 1/2*b*h*l

For the rectangular prism:

L (length) = 5 cmW (width) = 8 cmH (height) = 3 cm

V = l*w*h <== substitute the values (from above) for the variables

V = 5*8*3

V = 40*3

V = 120 cm^3 (cubed)

For the triangular prism:

B (base) = 6 cmH (height) = 3 cmL (length) = 2 cm

V = 1/2*b*h*l <== substitute the values (from above) for the variables

V = 1/2*6*3*2

V = 3*3*2

V = 9*2

V = 18 cm^3 (cubed)

Hope helps!

draw a diagram and explain how you can use it to find 3 ÷ 1/5​

Answers

Answer:

3/1/5

3×5/1

15/1

15 you don't need diagram

You randomly choose one of the morales.Without replacing the first marble, you choose a second marble. What is the probability of choosing red and then green?
P(Red and green)=1/4*1/4=1/16

(I really need help) ​

Answers

Let’s say, hypothetically speaking, you chose the second marble without replacing the first marble so, events are hypothetically dependent. Events are dependent if the occurrence of one hypothetical event hypothetically does affect the likelihood that the other events occur. The probably of two or more dependent events A and B is the probability of A times the probability of B after A hypothetically occurs

P(A and B) = P(A) x P(B after A)

Choose the first marble

The total number of hypothetical marbles are, hypothetically speaking, 4 on a hypothetical basis, and there is one red marble.

P(red)=1/4

Choose the second marble

Without hypothetically replacing the hypothetical first marble, you choose the hypothetical marble, hypothetically speaking. So, the total hypothetical number of marbles are, hypothetically, 3, and there is, hypothetically, one green marble.

P(green) = 1/3

The probability of choosing red and then, hypothetically, green is:

P(red and green) = P(red) x P(green)
=1/4 x 1/3

= 1/12

P(red and green) is hypothetically equal to 1/12 on a hypothetical account.

Final hypothetical answer: 1/12

7. Frank wants to paint his room in the school colors of maroon and white. The floor and
ceiling will be white, and all the walls will be maroon. The door will also be white. If one
gallon of paint covers 400 sq ft, how many gallons of each color will he need?
A. 1 gallon white, 1 gallon maroon
B. 1gallon white, 2 gallons maroon
C. 2 gallons white, 2 gallons maroon
D. 2 gallons white, 3 gallons maroon
10 ft
3 ft
7 ftlo
12 ft
12 ft

Answers

Frank would need two gallons of maroon painting and one gallon of white painting to paint all his room.

How much white painting is required?

Area of the ceiling:

12 feet x 12 feet = 144 squared feet

Assuming the floor has the same area, the total area for the floor and ceiling is 288 square feet.

Area of the door:

3 feet x 7 feet = 21 feet

Total area in white 144 feet + 21 feet = 165 square feet

Total of gallons

1 gallon equals 400 square feet, which means only one gallon of white painting is required.

How much maroon painting is required?

Area of one wall:

12 feet x 10 feet = 120 feet120 feet x 4 walls = 480 square feet480 square feet - 21 feet (door) = 459 square feet

Considering 1 gallon equals 400 square feet, a total of 2 gallons would be required.

Note: This question is incomplete because the image of the room is missing; below I attach the missing section.

Learn more about area in: https://brainly.com/question/16151549

Need help with this geometric question ASAP, Thank you

Answers

Because LP squared plus PM squared must equal LM therefore LP cannot be less.

Towns Kand L are shown on a map.
N
a) Work out the actual distance
between towns Kand L.
b) A third town, M, is 150 km due
South of town K.
Mark M on the map with X.
c) Measure the bearing of town L
from town K.
Scale: 1 cm represents 50 km

Answers

I’m not sure but is it C?

Woody has a lasso is 11ft long. No peep has a lasso that is 23ft longer than wordy how long is no peep lasso

Answers

Answer:

Bo Peep's lasso is 34ft long.

Step-by-step explanation:

Simply add 11 to 23.

Hope that helps!

Answer:

no peep lasso: 34ft

Step-by-step explanation:

11 + 23 = 34

Write the equation in standard form for the circle with center (0, -3) passing through (15/2 , 1)

Answers

Check the picture below, so the green line is really the radius of the circle, and we know its center.

[tex]~~~~~~~~~~~~\textit{distance between 2 points}\\\\(\stackrel{x_1}{0}~,~\stackrel{y_1}{-3})\qquad(\stackrel{x_2}{\frac{15}{2}}~,~\stackrel{y_2}{1})\qquad \qquadd = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}\\\\\\\stackrel{radius}{r}=\sqrt{[\frac{15}{2} - 0]^2 + [1 - (-3)]^2}\implies r=\sqrt{\left( \frac{15}{2} \right)^2 + (1+3)^2}\\\\\\r=\sqrt{\left( \frac{15}{2} \right)^2 +4^2}\implies r=\sqrt{\frac{225}{4} + 16}\implies r=\sqrt{\cfrac{289}{4}}\implies r=\cfrac{17}{2}\\\\[-0.35em]\rule{34em}{0.25pt}[/tex]

[tex]\textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{0}{ h},\stackrel{-3}{ k})\qquad \qquad radius=\stackrel{\frac{17}{2}}{ r} \\\\\\\ [x-0]^2~~ + ~~[y-(-3)]^2~~ = ~~\left( \cfrac{17}{2} \right)^2\implies x^2+(y+3)^2 = \cfrac{289}{4}[/tex]

the box plot shoes the lengths of the songs on two digital music players

Answers

Hello, it seems your questions didn't upload correctly. Are you able to resend it?

Jason drew a square with a side length of 8 cm. and Bella drew a rhombus with a side length of 8 cm. Jason says the perimeter of the square is smaller than the perimeter of the rhombus. Bella says they have the same perimeter. Which of them is correct and why? A. Jason is correct because a square is always smaller than a rhombus. B. Bella is correct because the rhombus and square have equal side lengths. C. Jason is correct because a square has fewer sides than a rhombus. D. Bella is correct because a square is half the perimeter of the rhombus. 5 / 18 4 of 18 Answered

Answers

Answer:

B

Step-by-step explanation:

to find the perimeter of a square its side*number of sides

which would be 8*4

to find the perimeter of a rhombus its 4*side length

which would be 4*8

therefore, its b they both have the same perimeter

Given the function
[tex]f(x) = (x + 4){(x - 2)}^{2} [/tex]
Determine the end behavior of the graph of the function. Show all/any work​

Answers

[tex]lim \: f(x) = ( \infty + 4)( \infty - 2) {}^{2} \\ x - > \infty [/tex]

[tex]lim \: f(x) = \infty \times \infty \\ x - > \infty [/tex]

[tex]lim \: f(x)= \infty \\ x - > \infty [/tex]

[tex]lim \: \frac{f(x)}{x} = \frac{x(1 - \frac{4}{x})(x - 2) {}^{2} }{x} \\ x - > \infty [/tex]

[tex]lim \: \frac{f(x)}{x} = (1)( \infty - 2) {}^{2} \\ x - > \infty [/tex]

[tex]lim \: \frac{f(x)}{x} = \infty \\ x - > \infty [/tex]

We can then say that the function f(x)=(x-4)(x-2)² admits an asymptotic direction parallel to the y-axis at + and - as well since we have to follow the same steps.

HELLPPPP REALLLLYYY NEEDDD
THISS ANSWER

Answers

Answer:

we need a picture to help

Step-by-step explanation:

Answer:

what is the question man stop messing around

Find the question. 1/3 +(5/7)=

Answers

Answer:

22/21

Step-by-step explanation:

1/3 + 5/7

LCM of 3,7 = 3 x 7 = 21

1/3

= 1/3 x 7/7

= ( 1 x 7 )/( 3 x 7 )

= 7/21

5/7

= 5/7 x 3/3

= ( 5 x 3 )/( 7 x 3 )

= 15/21

1/3 + 5/7

= 7/21 + 15/21

= ( 7 + 15 )/21

= 22/21

22/21 is the answer I think

WILL MARK BRAINLIEST
Rewrite the equation in Ax+By=C form.
Use integers for A, B, and C.
y-6= -5(x-3)

Answers

y - 6 = - 5 * x - 5 * (-3)

y - 6 = -5x + 15

y + 5x = 15 + 6

5x + y = 21

Answer:

5x + y = 21.

Step-by-step explanation:

y - 6 = -5(x - 3)

y - 6 = -5x + 15

5x + y - 6 = 15

5x + y = 15 + 6

5x + y = 21.

List and describe the characteristics of a perfectly competitive market.

Answers

The three primary characteristics of perfect competition are (1) no company holds a substantial market share, (2) the industry output is standardized, and (3) there is freedom of entry and exit. The efficient market equilibrium in a perfect competition is where marginal revenue equals marginal cost.

A market system with perfect competition is one in which there are several buyers and sellers interacting with the same goods.

A perfectly competitive market structure is widely found a market in the Indian economy. This market often accepts prices as a single seller cannot change the market price in the economy. Together with other characteristics, this trait sets this market apart from other types of markets.

Let's discuss the characteristics of the perfectly competitive market in detail which are as follows:

1. Large number of buyers and sellers- A commodity has a high number of buyers and sellers when there is ideal competition. Because there are so many customers, each one only purchases a very little portion of the available supply.

2. Homogeneous Products- Products in this market are homogenous in nature which means the products are identical in nature. This suggests that each company's output, in terms of quantity, quality, colour, size, features, etc., is a perfect substitute for the work of the others. This suggests that consumers don't care about what different companies produce.

3. Free entry and exit of firms- In the economy, there are 2 periods: long run and short run. In the long run, there is completely free entry and exit of firms while in the short run, some factors may contribute to the obstruction of entry and exit of firms. This guarantees that all businesses will ultimately make a regular profit or no economic profit, which evaluates the opportunity cost of the business to either continue operating or close.

4. Perfect Knowledge- In this market structure both the sellers and buyers have perfect knowledge of the market factors like price prevailing in the market because of this feature no seller can charge a higher price in the market to any customer.

5. No transportation cost- The products sold in this market structure are generally sold locally so there incur no transportation cost. Also because the same price is prevailing in the market sellers not require to transport anything.

6. No promotion cost- Homogeneous product is sold and uniform prices prevail so the sellers do not need to incur any selling cost like advterisemt for such a product. So the promotional cost incurred by firms is zero.

7. Price Taker- Firms are generally price takers in this structure of the market as sellers cannot influence the price of the goods so they need to accept the price that is prevailing in the market.

8. Perfect mobility of factors of production- Factors of production like Land, Labour and Capital are perfectly mobile in this market structure. These factors can freely move in and out of industry making demand and supply equal to each other.

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If 24% of the Skittles in the bag are red, what percentage of the Skittles are not red?

Answers

Answer:

76%

Step-by-step explanation:

Given:

If 24% of the Skittles in the bag are red, what percentage of the Skittles are not red?

Solve:

Percent - Out of 100

100 - 24 = 76

Hence, 76% of the skittles are not red.

~~Lenvy~~

Answer:

76% are not red

Formula:

(Total Skittle %)-(Red Skittle %)=(Non-Red Skittle %)

Work:

100%-24%=76%

Kylie brought 5 pears to soccer practice to share with her teammates. She cuts each pear into thirds. How many slices of pears does she have to share with her teammates? Which equations can you use to solve the problem? Select two equations.
A. 5 × 3 = 15
B. 1/5 × 1/3= 1 /15
C. 1/5 × 3 = 3/5
D. 5 ÷ 1/3 =15
E. 1/3 ÷ 5 = 1/15

Answers

Answer :D

A (or) 5 * 3= 15

Question explanation:

5 pears.

3 pieces

[tex](1 * 3) + (1 * 3) + (1 * 3) + (1 * 3) + (1 * 3)[/tex]

Which is:

[tex](3) * (3) * (3) * (3) * (3)[/tex]

Which, simplified:

[tex]3 * 5[/tex]

Which equals:

[tex]3 * 5 = 15[/tex]

Hope this helps :)  - Answered by Lilo

Put the following investment options in order of least to greatest risk:

starting a business
B-rated bond
speculative stock
property

Answers

The order of investment options from least to greatest risk is:

B rated bond.Property.Speculative stock. Starting a business.

How risky are some investment options?

A B rated bond is considered safer than the rest because there is a high chance that the owners of the bond will redeem it. Property is not very risky but can be susceptible to market shocks.

Speculative stock is the third riskiest because its prices are prone to fluctuation. Starting a business is by far the riskiest because a lot of new businesses fail.

Find out more on risky investments at https://brainly.com/question/25219850.

Answer:

B-rated bond

property

starting a business

speculative stock

Step-by-step explanation:

Select the correct answer from each drop-down menu.
On the day the link was emailed, trailer
Two days after the link was emailed, trailer
Four days after the link was emailed, trailer
had the most views.
had the most views.
had the most views.

Answers

Answer:

k

[tex]2xyy15 { { \div - \\ \sqrt[ {x. - - {?}^{?} }^{2} ]{?} }^{2} }^{2} [/tex]

Answer:

On the day the link was emailed, trailer

A

had the most views.

Two days after the link was emailed, trailer

A

had the most views.

Four days after the link was emailed, trailer

B

had the most views.

Step-by-step explanation:

The total number of views on the day the email was sent, two days later, and four days later are represented by the values of the functions when x = 0, 2, and 4.

Substitute these values into the equation:

Find these values in the table:

Apply the described rule:

So, on the day the link was emailed, trailer A had the most views.

Two days after the link was emailed, trailer A had the most views.

Four days after the link was emailed, trailer B had the most views.

There are caterpillars in two greenhouses. Greenhouse A has 4 times the number of caterpillars Greenhouse B has. A bird came into the two greenhouses and devoured many caterpillars. After the bird ate 41 caterpillars in Greenhouse A and 5 caterpillars in Greenhouse B, both greenhouses have the same number of caterpillars. How many caterpillars did Greenhouse A have in the first place?

Answers

there will be your 1000 caterpillars

Answer:

12

Step-by-step explanation:

4a = b and A-41=b-5

a-41+5=b

a-36 =b

which means a+36 =4a

so 3a=36 and a=12

Working alone, Mr. Tough can grade the final exams in 12 hours. His assistant, Mrs. Nice, cam grade the same exams in 15 hours. What fraction of the exams can Mr.Tough and Mrs.Nice grade in 1 hour if they work together?

Answers

Answer:

9n/60

Step-by-step explanation:

add 1/12 + 1/15 which = 5/60 + 4/60.

= 9/60

YAY!!!!!!!

The fraction of the exams that Mr Tough and Mrs Nice grade in 1 hour if they work together is 3/20

What are fractions?

In Maths, a fraction is used to represent the portion/part of the whole thing. A fraction has two parts, namely numerator and denominator. There are proper fractions, improper fractions and mixed fractions.

Example: 2/5, 1/4 etc.

How to solve Work and Time problems:

We will this equation,

rate × time = work done

For this problem:

             Mr Tough's rate:

                          Mr Tough's rate × 12 hours = final exam

                          Mr Tough's rate = 1/12

             Mrs.Nice's' rate:

                            Mrs .Nice's' rate × 15 hours = final exam

                            Mrs .Nice's' rate = 1/15

To make this into a solvable equation,  find the total time (T) needed for Mr Tough and Mrs.Nice to grade the final exam. This time is the sum of the rates of Mr Tough and Mrs.Nicea, or:

Total time:

T(1/12 hours + 1/15 hours) = final exam

T =  final exam / (1/12 + 1/15)

Simplifying we get,

T =  final exam / (0.15)

Now, to finish in 1 hour we will find what fraction of the final exam they can grade, so taking T = 1 hour,

1 hour =  final exam / (0.15)

By further simplifying,

final exam = 1 × 0.15

                 = 0.15

                 = 15/ 100

                 = 3/20

Therefore, 3/20 fraction of the final exam they can grade if they work together for 1 hour.

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The fuel tank of chris new lawn mower holds 1/2 gallon of gasoline chris poured 0.4 gallons into the tank did chris fill the tank explain?

Answers

Sry I can’t explain it but it should be 0.9 I checked with a Scientific calculator

What is the value of x?
13 m
15 m

Answers

Answer:

which one?

Step-by-step explanation:

Mrs. Lennon has 100/275/50 liability insurance and $50,000 PIP (Personal Injury Protection) insurance. During an ice storm, she hits a fence and bounces into a store front with 11 people inside. Some are hurt and sue her. A passenger in Mrs. Lennon’s car is also hurt. A) The store front will cost $24,000 to replace. There was $1,450 worth of damage to the fence. What insurance will cover this, and how much will the company pay? B) The passenger in the car had medical bills totaling $20,000. What type of insurance covers this, and how much will the insurance company pay?

Answers

The property damage will convert the insurance regarding the damage and the insurance company will pay $25450.

How to compute the insurance?

From the question, the store front will cost $24,000 to replace and there was $1,450 worth of damage to the fence.

The amount paid by the insurance company will be:

= $24000 + $1450

= $25450

When the passenger in the car had medical bills totaling $20,000, the PIP insurance will cover this and the company will pay $20000.

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a cyclist travels 108m in 12 seconds.what is her speed in km/h

Answers

Step-by-step explanation:

=108÷12

=9m/s

=9x0.001x1/3600

=2.5x10^6km/h

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Geoffrey measures the width of his bedroom to determine the largest size bed frame he can have. The wall he plans to place the bed frame against is 13.65 feet wide. He wants there to be 2.25 feet between the wall and the bed frame on each side. What is the maximum width bed frame, in inches, that Geoffrey can put in his bedroom? Which part of Japan's land was usable for farming? Why? How to solve this please What is the volume of this right prism? 96 in 60 in 48 in 44 in Which pair shows equivalent expressions? 2x + 10 = -2(x-5)-2(x+5) = 2x-10-2x-10 = -2(x+5)-2(x-5) = -2x-10 what was the bloody Sunday? During May, 2021, Breakfront Corporation announced a 2-for-1 stock split. This brought the number of shares outstanding from 25,000,000 shares to _____ shares, and its $2.00 par value to _____ per share. HELP ASAP ITS DUE SOON!!!!! pls help french with this Why was it important for the colonial regions to band together against Great Britain? How did Andrew Jackson's election illustrate the growth of democracy in the United States?A. He was chosen by African Americans In their first opportunity to vote.B. He was the first president elected without the Electoral College.C. He was able to attract women's votes.D. He represented voters that were not wealthy or aristocratic. There are values of t so that sin t= 5/4 ?.7,000 dollars is placed in a savings account with an annual interest rate of 3%. If nomoney is added or removed from the account, which equation represents how muchwill be in the account after 7 years?A. M= 7,000(0.03)B. M= 7,000(1 + 0.03)(1 + 0.03)C. M= 7,000(1 - 0,03)D M= 7,000(1.03) Decide which measurement is greater. Place the correct symbol ( , =) on the line between the measurements. 5 gallons _______ 18 quarts1 pint 4 cups _____ 32 fl oz 3 pints ______ 8 cups 13 quarts _______ 4 gallons 4 quarts _______ 9 pints 38/-97 latitude/longitude Chipman Sofware recently reported the following amounts in its unadjusted trial balance at its year-end:1. Prepare the adjusting journal entry required for the year. Assume Chipman uses 1/2 of 1 percent of sales to estimate its Bad Debt Expense for the year and no Bad Debt Expense has been recorded yet.2. Prepare the adjusting journal entry required for the year. Assume instead that Chipman uses the aging of accounts receivable method and estimates that $82 of its Accounts Receivable will be uncollectible.3. Assume instead that Chipman uses the aging of accounts receivable method and estimates that $82 of its Accounts Receivable will be uncollectible. Prepare the year-end adjusting journal entry for recording Bad Debt Expense. Assume Chipman's year-end unadjusted balance in Allowance for Doubtful Accounts was a debit balance of $22.4. If one of Chipman's main customers declared bankruptcy after year-end, what journal entry would be used to write off its $20 balance? HELP ASAP The existence of comets provides possible evidence for _____.solar origin of cometsa young solar systeman ancient solar system Based on the image below, what can you conclude about travelers on the Underground Railroad?A painting depicting a scene in which slaves are getting off of a wagon with some belongings in their arms. In the foreground two children, an adult white woman, and a dog stand. Behind them, a white woman helps an elderly African-American man who is carrying a cane and rubbing his back. Behind this pair, a larger group of African-American adults and children are climbing down from a hay-filled wagon. The larger scene includes a barn and some trees all of which are covered with snow.Library of Congress LC-USZ62-28860 The routes to the North offered many comforts and places of rest. The journey to freedom was quite educational for young people. The escape would have been difficult for the elderly. The travelers were lucky if they found their way to a main road. Rotate shape A 90 clockwise with centre of rotation (0,0).What are the coordinates of the vertices of the image? help. will give brainliest. please hurry!!!