A heavy rope, 50 ft long, weighs 0.6 lb/ft and hangs over the edge of a building 120 ft high. Approximate the required work by a Riemann sum, then express the work as an integral and evaluate it.

Exercise (a)

How much work W is done in pulling the rope to the top of the building?

Exercise (b)

How much work W is done in pulling half the rope to the top of the building?

Answers

Answer 1

Answer:

Exercise (a)

The work done in pulling the rope to the top of the building is 750 lb·ft

Exercise (b)

The work done in pulling half the rope to the top of the building is 562.5 lb·ft

Step-by-step explanation:

Exercise (a)

The given parameters of the rope are;

The length of the rope = 50 ft.

The weight of the rope = 0.6 lb/ft.

The height of the building = 120 ft.

We have;

The work done in pulling a piece of the upper portion, ΔW₁ is given as follows;

ΔW₁ = 0.6Δx·x

The work done for the second half, ΔW₂, is given as follows;

ΔW₂ = 0.6Δx·x + 25×0.6 × 25 =  0.6Δx·x + 375

The total work done, W = W₁ + W₂ = 0.6Δx·x + 0.6Δx·x + 375

∴ We have;

W = [tex]2 \times \int\limits^{25}_0 {0.6 \cdot x} \, dx + 375= 2 \times \left[0.6 \cdot \dfrac{x^2}{2} \right]^{25}_0 + 375 = 750[/tex]

The work done in pulling the rope to the top of the building, W = 750 lb·ft

Exercise (b)

The work done in pulling half the rope is given by W₂ as follows;

[tex]W_2 = \int\limits^{25}_0 {0.6 \cdot x} \, dx + 375= \left[0.6 \cdot \dfrac{x^2}{2} \right]^{25}_0 + 375 = 562.5[/tex]

The work done in pulling half the rope, W₂ = 562.5 lb·ft


Related Questions

How many groups of 5 can you make
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Answer:

5 groups

Step-by-step explanation:


25/5 is 5
So the answer
Would be
5

a clothing store is having a sale on tshirts. the first tshirt you buy costs $7, and every additional shirt costs only $5

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Answer:

12

Step-by-step explanation:

bc I added 7+5 equals 12

PLS HELP DUE SOON WILL MARK BRAINLIEST
A store owner asks each person to write "Yes" or "No" on a slip of paper as
they leave, secretly writing down whether they were happy with their
experience. At the end of the day, the owner selects 12 slips at random and
looks at them. These were the results:
yes, yes, yes, no, yes, no, yes, yes, no, yes, no, yes
Part 1: Estimate the proportion of all shoppers who were haphy with their
experience that day. Enter your response as a decimal.

Answers

The estimated proportion of all shoppers who were happy with their experience that day and said yes is 0.667.

What is random sample?

Random sample is the way to choose a number or sample in such a manner that each of the sample of the group has an equal probability to be chosen.

A store owner asks each person to write "Yes" or "No" on a slip of paper as they leave, secretly writing down whether they were happy with their experience.

At the end of the day, the owner selects 12 slips at random and looks at them. These were the results:

yes, yes, yes, no, yes, no, yes, yes, no, yes, no, yes=12yes=8

To estimate the proportion is the following formula:

[tex]p'=\dfrac{x}{n}[/tex]

Here, x is the number of success and n is the sample size. Here, the sample size is 12 and number of success (yes) is 8. Thus, the estimated proportion is:

[tex]p'=\dfrac{8}{12}\\p'=0.667[/tex]


Thus, the estimated proportion of all shoppers who were happy with their experience that day and said yes is 0.667.

Learn more about the random sample here;

https://brainly.com/question/17831271

#SPJ1

What is the m∠J, to the nearest tenth? JLK is right angle triangle. The length of JL is 9.4 and length of LK is 15.1.

Answers

Answer:

58.1

Step-by-step explanation:

istribute and simplify these radicals square root 12 times (-1+ square root 5)

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Here's link to the answer:

tinyurl.com/wpazsebu

Zynga and Walmart which balance sheet items does the two have in common

Answers

need more context pls

Write an expression that is equivalent to 30(x + y + 1)

Answers

30(x+y+1)
Well you can simply just distribute and it’s an equivalent expression.
So
30x+30y+30
30x+30y+30
hope this helps

A particular fruit's weights are normally distributed, with a mean of 372 grams and a standard deviation of 26 grams. If you pick 36 fruit at random, what is the probability that their mean weight will be between 365 grams and 380 grams

Answers

Answer: 90.93%

Step-by-step explanation:

M= 372

s= 26

n=36

P(365<x<380)

1. Find Z ----> 365-372 [tex]\sqrt{36}[/tex] = -1.6     Next Z---->  380 - 372 [tex]\sqrt{36}[/tex]=  1.8

                           26                                               26

2.  plug into calculator to find probablity: normalcdf(-1.6 , 1.8 ) = .90927 or 90.93% that the prob is between 365 and 380

Mrs Sogiba is catering for her son's birthday party. She has invited some of
her son's friends to theparty. The number of friends is a compositemultiple of her
son's age on his birthday. She has baked 48 cup cakes and each childwill receive
exactly the same number of cupcakes. Use your knowledge of factors and multiples
to find out how old her son will be on this birthday.

Answers

Answer:

48 cupcakes divided by the boys age equals amout of cupcakes per person.

Step-by-step explanation:

I need help I'll give out 40 points quickly ​

Answers

Answer:

The figure in the upper right corner.

A trapezoid has two parallel sides

Step-by-step explanation:

Answer:

The answer would be the shape on the right side on the top! NOT THE Rectangle (on the right bottom side)  or the rhombus (on the left top side). The shape on the left bottom side IS a trapezoid.

Hope that helps. And this wasnt worth 40 points, it was only 5 points!?

PLZ HELP I WILL MARK BRIANLIST Complete the table for 11, 15, and 19 days. Input your
answers. Then click done.
Number of Days
Total Number of
Trophies Won
80
slope
3
100 trophies
4 days
25 trophies
1 day
7
180
11
15
19
DONE

Answers

Answer:

275, 375, 475

Step-by-step explanation:

First, find the slope using the two pairs of values given.

Number of days = x

Total number of trophies = y

Using (3, 80) and (7, 180),

Slope = ∆y/∆x = (180 - 80)/(7 - 3) = 100/4 = 25

Slope/unit rate = 25 trophies per day

Multiply 25 by each given number of days to get each corresponding total number of trophies won.

Thus:

✔️Number of days = 11

Total number of trophies won = 11*25 = 275

✔️Number of days = 15

Total number of trophies won = 15*25 = 375

✔️Number of days = 19

Total number of trophies won = 19*25 = 475

Answer:

280

380

480

Step-by-step explanation:

If he gets 100 trophies every 4 days then you just add 100 to each column because in each one the days are increasing by 4

Your welcome ;)

1, 3, 5, 7, 9, 9, 11, 11, 13, 14 }

Which box plot represents the data set?

Answers

It should be the second one

Please Help!!!!! Ill give thanks and rate best!

Answers

Answer:

1/216

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Did you only need the answer for the one on the top right?? Or all of them because If you need all of them I can do that too I am just assuming you just needed that one because it was selected.

2 of 8
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Answers

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A 12m by 12m square garden has a 1m wide path through the centre, parallel to one side of the square. calculate the area of the garden left for planting.​

Answers

Answer:

132 m²

Step-by-step explanation:

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Answers

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Please help!!!!!!!!!!!!!!!!!!!!!!

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the right answer is B.

ANSWER FAST!! All of the following angle pairs are ALWAYS congruent when a transversal passes through 2 parallel lines EXCEPT:

Adjacent angles

Alternate Interior Angles

Alternate Exterior Angles

Corresponding Angles

Answers

Answer:

Adjacent angles

Step-by-step explanation:

Select the correct answer from each drop-down menu.


A camp director developed the function m(c) = 12c + 80 to model the total cost of taking c campers on a field trip to the movies.


In the camp director’s function, the number of campers is the _______ variable and the total cost of the trip _________


1. ( independent, dependent )

2. ( changes by a constant factor per camper, Changes by a constant amount per camper )

.

Answers

Answer:

(a) Independent variable

(b) The constant factor is 12

Step-by-step explanation:

Given

[tex]m(c) = 12c + 80[/tex]

c = campers

m = total cost

Solving (a) What type of variable is the number of campers (c)

The total cost (m) is dependent on the number of campers (c) for its own value.

In other words, if c changes from 5 to say 7, the value of m will also change.

This implies that the number of campers is an Independent variable

Solving (b): Constant factor

This in other words means, rate of change (or slope)

A linear function is:

[tex]y = ax + b[/tex]

Where a represents the slope

By comparison with: [tex]m(c) = 12c + 80[/tex]

Hence, the constant factor is 12

Answer:

dependent, changes by a constant factor per camper.

Step-by-step explanation:

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Answers

Answer:

Perimeter: 50.27

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Step-by-step explanation:

The perimeter (circumference) is radius times pi times 2

This would be 8 times pi tomes 2 and when you do that you get 50.27

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One interior angle of a triangle is 60⁰. The other angle measures are x⁰ and y⁰. Which of the following could be the values of x and y? Select all that apply. A. x = 50, y = 90 B. x = 45, y = 45 C. x = 40, y = 80 D. x = 100, y = 20 E. x = 60, y = 60

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Answer:

B,C,D

Step-by-step explanation:

What is the slope of the line below? Be sure to scroll down first to see all
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10
10
118
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Answer:

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Step-by-step explanation:

4. 5/16 +6/16
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Answers

Answer:

11 / 16

Step-by-step explanation:

5/16 + 6/16

5 + 6 = 11

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11 / 16

Answer:

4.5/16+6/16=4.5+6/16

=10.5/16

Step-by-step explanation:

Here you can see denominator in both the side are same and operation sign between them is plus, therefore you can take denominator as is it.

Then add numerator and divide by denominator which is 16. Answer is 10.5/16 since you have to simplify only.

The television show 50 Minutes has been successful for many years. That show recently had a share of 15, which means, that among the TV sets in use, 15% were tuned to 50 Minutes. An advertiser wants to verify that 15% share value by conducting its own survey, and a pilot survey begins with 15 households have TV sets in use at the time of a 50 Minutes broadcast.

Required:
a. Find the probability that none of the households are tuned to Lindsay and Tobias. (Round to three decimal places as needed)
b. Find the probability that at least one household is tuned to Lindsay and Tobias.
c. Find the probability that at most one household is tuned to Lindsay and Tobias.
d. If a most one household is tuned to Linday and Tobias, does it appear that the 15% share value is wrong? Why or wh not?

Answers

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Step-by-step explanation:

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Answers

Answer: 2000 hope this helps. Can u give me brainliest

Step-by-step explanation:

Answer:

2,000

Step-by-step explanation:

Since there's a 9 before the 1 you would round up the 1,987 to 2,000

A design engineer wants to construct a sample mean chart for controlling the service life of a halogen headlamp his company produces. He knows from numerous previous samples that this service life is normally distributed with a mean of 500 hours and a standard deviation of 20 hours. On three recent production batches, he tested service life on random samples of four headlamps, with these results.

Sample Service Life (hours)
1 495 500 505 500
2 525 515 505 515
3 470 480 460 470

1. What is the sample mean service life for sample 2?

a. 460 hours
b. 495 hours
c. 515 hours
d. 525 hours

2. What is the mean of the sampling distribution of sample means for whenever service life is in control?

a. 250 hours
b. 470 hours
c. 495 hours
d. 500 hours
e. 515 hours

Answers

Answer:

1. c. 515 hours

2.  c. 495 hours

Step-by-step explanation:

Sample mean:

Sum of all values in the sample divided by the number of values.

1. What is the sample mean service life for sample 2?

Sample 2 has four values, which are:

525 515 505 515

So

[tex]M = \frac{525+515+505+515}{4} = 515[/tex]

The answer is given by option C.

2. What is the mean of the sampling distribution of sample means for whenever service life is in control?

3 samples, 12 total values. We find the mean of all these values. So

[tex]M = \frac{495+500+505+500+525+515+505+515+470+480+460+470}{12} = 495[/tex]

The answer is given by option C.

First one to answer gets BRAINLIEST no cap look at the picture.

Answers

Answer:460

Step-by-step explanation:

Convince yourself that there are 3 similar triangles in the diagram. Choose the
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Please only answer if your sure

Answers

The correct answer is the second option.

Answer:

second option.

Step-by-step explanation:

Georgia brought a snow cone shaped like the cone below what is the height of the snow cone

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Answer:

Step-by-step explanation:

Use the Pythagorean Theorem.

h² = 5² - 3² = 4²

h = 4 in

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