A leaky 10-kg bucket is lifted from the ground to a height of 12 m at a constant speed with a rope that weighs 0.5 kg/m. Initially the bucket contains 36 kg of water, but the water leaks at a constant rate and finishes draining just as the bucket reaches the 12-m level. Find the work done. (Use 9.8 m/s2 for g.) Show how to approximate the required work by a Riemann sum. (Let x be the height in meters above the ground. Enter xi* as xi.)

Answers

Answer 1

Answer:

The work done is 3645.6 J or 3.6 kJ

Step-by-step explanation:

M1 = (0.5 kg/m)(12 - x m) = (6 - 0.5x) kg

At the height of x meters (0<=x<=12), the mass of the rope is,

M2 = (36kg/12m)(12 - x m) = (36 - 3x m) kg

At the height of x meters (0<=x<=12), the mass of the water is,

M3 = 10 kg

The mass of the bucket is 10 kg

Then, Total mass M is,

M = M1 + M2 + M3 = (6 - 0.5x) + (36 - 3x) + 10 = (52 - 3.5x) kg

From Force F = mass m * acceleration due to gravity g

Force = mass x gravity

F = 9.8(52 - 3.5x) Newtons

To get the work done W,

Follow the attached file,

The work done is 3645.6 J or 3.6 kJ

A Leaky 10-kg Bucket Is Lifted From The Ground To A Height Of 12 M At A Constant Speed With A Rope That

Related Questions

The cost of a set of DVDs after a 25%
markup can be represented by the
expression c + 0.25c. Simplify the
expression.

Answers

Answer:0.75c

Step-by-step explanation

So for this problem, 100% - 25% = 75%.

The equivalent equation will be 0.75c.

A tailor has 100 square yards of cotton and 120 square yards of wool material. it takes 2 square yards of each type to make a sports coat. It takes 1 square yard of cotton and 3 square yards of wool to make a pleated skirt. The tailor already has orders for at least 15 sport coats and 5 skirts. If the tailor sells each coat for $40 and each skirt for $45, how many of each garment should be made in order to fill the orders and maximize profit.

Answers

Answer:t  

Takes 2 Square Yards Of Each Type To Make A Sports Coat. It Takes 1 Square Yard Of Cotton And 3 Square Yards Of Wool To Make A Pleated Skirt.

Step-by-step explanation:

hope that is what you were needing

what's 2 + 2?
plzzzzzz help​

Answers

Answer:

4 ;)

Step-by-step explanation:

Answer: 4

Step-by-step explanation:

The equation of a function is
y = 12x - 7. What is the output when the input is 5?

A. 50
B. 53
C. 56
D. 60

Answers

the answer is B. 53
12 times 5 then sub 7
hope it helps
the answer is D
hope this helped

(5.25) An owner of a home in the Midwest installed solar panels to reduce heating costs. After installing the solar panels, he measured the amount of natural gas used y (in cubic feet) to heat the home and outside temperature x (in degree days, where a day's degree-days are the number of degrees its average temperature falls below 65 degrees F) over a 23-month period. He then computed the least-squares regression line for predicting y from x and found it to be

Answers

This question is incomplete, the complete question is;

An owner of a home in the Midwest installed solar panels to reduce heating costs. After installing the solar panels, he measured the amount of natural gas used  y (in cubic feet) to heat the home and outside temperature x (in degree-days, where a day's degree-days are the number of degrees its average temperature falls below 65oF) over a 23-month period.

He then computed the least-squares regression line for predicting y from x and found it to be:   y^=80+16x.  

How much, on average, does gas used increase for each additional degree-day?

Answer : ______ cubic feet.

(Give your answer as a whole number.)

Answer:

Amount of natural gas used increased by 19 cubic feet.

Step-by-step explanation:

Given the data in the question;

Let the dependent variable y be the amount of natural gas used ( ft³ )

Also let an independent variable x be be the degree days temperature ( in °F)

So the least squares regression equation is;

[tex]y^{bar}[/tex] = 80 + 16x

or

amount_of_natural_gas_used = 80 + 16(degree_days_temperature

Th slope or the standardized regression coefficient of the given regression equation is;

b₁ = 16

the slope coefficient b₁ = 16 is tells us that for each additional one-degree days temperature, an amount of natural gas used increased by 19 cubic feet.

Therefore, amount of natural gas used increased by 19 cubic feet.

ASAP!!!! HELP!!!! Will mark you brainliest

Answers

Answer:

f(1) = 2

Step-by-step explanation:

Since f(x) = x^4 + 4 x^3 + 5 x^2 - 4 x - 4

When we evaluate this for x = k = 1, we replace x with the value 1 as shown below:

f(1) = 1^4 + 4 * 1^3 + 5 * 1^2 - 4 * 1 - 4 = 1  + 4 + 5 - 4 - 4 = 10 - 8 = 2

A jar contains n nickels and d dimes. There are 22 coins in the jar and a total value of the coins is $1.50. How many nickels and how many dimes are in the jar?

Answers

Answer:

1.50 + 22

Step-by-step explanation:

23.5

Answer:

12 nickels. 9 dimes

Step-by-step explanation:

12 nickels is equal to 60 cents

9 dimes equals 90 cents

90 plus 60 equals 150 which is $1.50

The difference of sixteen and four is greater than ten






Write the sentence as an equation

Answers

16-4>10

Difference means subtracting

2. What is the
meaning of the
slope in this
situation?

Answers

Answer: The value of the intercept represents the predicted highway mileage for gas city mileage of 0 mpg, and such a prediction would be invalid, since 0 is outside of the range of data.

Step-by-step explanation:

Answer:

The meaning of slope is like the middle number.

The solving equation for the slope is

y2-y1 and x2-x1

Step-by-step explanation:

Which figure best represents a rhombus?

Answers

Answer:

it's the second one a rhombus is a diamond

It’s the first one I believe

The value of 2^3 + 3^3 = .

Answers

Answer: (2^3) +  3^3

2^3 +  3^3

35

Step-by-step explanation:

you most likely just have to add 8 and 27 together im guessing

help pls i'll give brainliest, are they inverses or not explain why or why not

Answers

Is that algebra,????????

How many square feet of outdoor carpet will
we need for this hole?
?
6 ft
2 ft
2 ft
3 ft)
5 ft
3 ft)
12 ft
Please

Answers

Answer:48 ft to the second power

Step-by-step explanation:

I just got it right on iready

The area of the outdoor carpet that needed for the hole should be considered as the  48 ft².

Calculation of the area:

Since

we know that

Area of the rectangle = Length (breadth)

here,

L = 12 ft

b =  5 ft

So,

area = 12 × 5  

= 60 ft²

Now

The cut off triangle area

area = 1/2 × base × height

= 1/2 × 4 × 3

= 12/2

= 6 ft²

Now

The cut off rectangle area should be

area = Lb

= 3 × 2

= 6 ft²

Now finally

The area of the outdoor carpet should be

= 60 - 6 - 6

= 48 ft²

learn more about an area here: https://brainly.com/question/17971267

Somebody please help pleaseeeee I’ll make brainlest please help anybody .

Answers

Answer:

C Is The Correct Answer

The correct answer would be C :)

20 POINTS
look at the rectangle below. the sum of the measures of the 3 interior angles of any triangle is always 180° . What is the measure of A - 30°
B - 45°
C - 60°
D - 120°

Answers

Answer: i think its 30°

Step-by-step explanation:

11. The coordinate grid shows points P, Q, R, and S. All the coordinates for these points
are integers.


What is the value of the x-coordinate of point P?

Answers

Answer:

-6

Step-by-step explanation:

Answer: -6

Step-by-step explanation:

A. 504 units(squared)

B. 436,8 units(squared)

C. 218 units(squared)

D. 283,2 units(squared)

Answers

Answer:

D. 283.2 units²

Step-by-step explanation:

Surface area of the triangular prism = 2×Base Area + Perimeter of triangular base×height of prism

Base Area = ½*bh

b = 6 km

h = 5.2 km

Base area = ½*6*5.2 = 15.6 km²

Perimeter of triangular base = 6+6+6 = 18 km

Height of prism = 14 km

Plug in the values into the equation

Surface area of triangular prism = 2×15.6 + 18×14

= 31.2 + 252

= 283.2 km²

Write
360 000 in standard form.​

Answers

Answer:

300 + 60 + 000

Step-by-step explanation:

Just break these up easy answer. Your welcome :)

work out yhe value of 6.105×10^8/3.7×10^3 give your answer in standard form​

Answers

1.65 x 10^11

Hope this helps

Please please help!! I really need help on this question

Answers

Answer:

They purchased 20 ounces of candy total

Step-by-step explanation:

just add 12 + 8

=20 ounces

What is the surface area of the solid...?​

Answers

580 square units !!
hope this helps you :))

Consider the following hypothesis test: H 0: 50 H a: > 50 A sample of 50 is used and the population standard deviation is 6. Use the critical value approach to state your conclusion for each of the following sample results. Use = .05. a. With = 52.5, what is the value of the test statistic (to 2 decimals)? Can it be concluded that the population mean is greater than 50? Select b. With = 51, what is the value of the test statistic (to 2 decimals)? Can it be concluded that the population mean is greater than 50? Select c. With = 51.8, what is the value of the test statistic (to 2 decimals)? Can it be concluded that the population mean is greater than 50? Select

Answers

Answer:

Part a:

The calculate value of Z = 2.946 lies in the critical region so the null hypothesis is rejected and alternate hypothesis is accepted that population mean is greater than 50.

Part b:

The calculate value of Z = 1.17851 does not lie in the critical region so the null hypothesis is accepted that population mean is not greater than 50.

Part c:

The calculate value of Z = 2.1213  lies in the critical region so the null hypothesis is rejected and concluded that population mean is greater than 50.

Step-by-step explanation:

Data as given

H 0: μ ≤ 50 against the claim H a:  μ> 50  one tailed test

Z (0.05)= ± 1.645

Sample size n= 50

Using the central limit theorem

Population Standard Deviation= σ=s=6

X= 52.5 , 51 and 51.8

Part a:

Z= x-μ/ s/ √n

Z= 52.5- 50 / 6/ √50

Z= 2.5/0.84853

z= 2.946

The calculate value of Z = 2.946 lies in the critical region so the null hypothesis is rejected and alternate hypothesis is accepted that population mean is greater than 50.

Part b:

Z= x-μ/ s/ √n

Z= 51- 50 / 6/ √50

Z= 1/0.84853

z= 1.17851

The calculate value of Z = 1.17851 does not lie in the critical region so the null hypothesis is accepted that population mean is not greater than 50.

Part c:

Z= x-μ/ s/ √n

Z= 51.8- 50 / 6/ √50

Z= 1.8/0.84853

z= 2.1213

The calculate value of Z = 2.1213  lies in the critical region so the null hypothesis is rejected and concluded that population mean is greater than 50.

Using your answer from #3, how many hours will
Victoria need to babysit if she raises her hourly
charge to $15 per hour and she still wants to
earn at least $75?

Answers

Answer:

5 hours cuz 75 divided by 15 is 5 or 15 x 5 is 75

I don’t know what the answer from number three was, but 75÷15 = 5 hours

PLEASE HELP MATH MIDTERM
Find the measure of angle A. Round only your final answer to the nearest hundredth.

Answers

Answer:

73.74 degrees

Step-by-step explanation:

what do i do with this

Answers

Answer: you should plot it a -3.2

Step-by-step explanation:

Fill in the blanks. See picture and give answers please as quickly as possible.

Answers

Concave down
Max is 4
Vertex is (1,4)
Axis of symmetry is x=1
Y intercept is 3

A letter home to the parents of seniors at Westgate High School says, "a simple random sample of 30 Westgate seniors that took the SAT-M test this year produced a mean of 512 and a standard deviation of 95. A confidence interval for the true mean for all WHS seniors is 512.00 ± 47.8." The confidence level for this interval is Group of answer choices

Answers

Answer:

It's 99%

Step-by-step explanation:

It just is.

A confidence interval for the true mean for all WHS seniors is 512.00 ± 47.8." The confidence level for this interval is 99%. The correct option is D.

What is the percentage?

The percentage is defined as "out of 100." Similar to fractions and decimals, percentages are used in mathematics to represent subsets of a whole. When expressing a sum as a percentage, 100 equal components are regarded to make up the whole.

A percentage is a figure or ratio stated as a fraction of 100 in mathematics. Divide the amount by the total value to get the percentage, then multiply the resulting number by 100.

Since one percent (symbolized as 1%) is equal to one-hundredth of something, 100 percent stands for everything, and 200 percent refers to twice the amount specified.

Therefore, the correct option is D, 99%.

To learn more about percentages, refer to the link:

https://brainly.com/question/28269290

#SPJ5

The question is incomplete. Your most probably complete question is given below:

90%

92%

95%

99%

over 99.9%

What is the percent of change of 14 to 10, rounded to the nearest 10th of a percent

Answers

Answer:

jnjnj

Step-by-step explanation:

yes

j jlnjknjkl.n

njn

jnjnjnjn

8 ÷ one third = ___. one twenty fourth alt=twenty four twenty fourths 24 48

Answers

Answer:

Twenty four (24)

Step-by-step explanation:

8 ÷ one third

one third = 1/3

8 ÷ 1/3

= 8 × 3/1

= 24/1

= 24

I need help plz ❤️️️

Answers

Answer:

x= 273

Step-by-step explanation:

Answer:

273

Step-by-step explanation:

3549/13=23

(Hope this helps u and u get it correct!)

-AestheticSnowy

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