1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
spin [16.1K]
3 years ago
11

A heavy rope, 60 ft long, weighs 0.3 lb/ft and hangs over the edge of a building 130 ft high. (Let x be the distance in feet bel

ow the top of the building.)
a. How much work W is done in pulling the rope to the top of the building?
b. Express the work as an integral.
c. Evaluate the integral.
d. How much work W is done in pulling half the rope to the top of the building?
Mathematics
1 answer:
Murljashka [212]3 years ago
8 0

Answer:

half the rop to the top of the building = W = 423.75

top of the building = W = 423.75

Step-by-step explanation:

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

When a length of rope xi has been pulled to the top of the building, then the force  required to move the remaining rope is 1/2(g(60− xi)), the weight of the rope.

The work to pull  an additional small length of rope, ∆x, to the top of the building is 1 /2 ((60 − xi)∆x).

Note that  the relationship between xi and ∆x is that for n constant lengths of rope equal to ∆x, then  xi = i∆x. The Riemann sum for the work is:

W=  ∑ n,i = 1  (1/2(60 - xi). ∆x) = ∑ n,i = 1  (1/2(60 - i∆x). ∆x)

Note that xi = i∆x will not limit to zero as n → ∞. The corresponding integral is:

W =  \int\limits^3_0 {0. 1/2 (60 - x)} \, dx

W = 1/2. [60x - 1/2. x^2]^3_0

W = 423.75

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

This requires almost the same Riemann sum except the upper limit on the sum  changes:

W=  ∑ n/2,i = 1  (1/2(60 - xi). ∆x) = ∑ n,i = 1  (1/2(60 - i∆x). ∆x)

The corresponding integral is:

W = \int\limits^{1.5}_0 {5. 1/2 (60 - x)} \, dx

W = 1/2. [60x - 1/2. x^2]^{1.5}_0 . 5

W = 423.75

You might be interested in
Doug entered a conoe race he rowed 3.5 miles in .5 hrs what is his average speed
vichka [17]
7 miles per hour.

if you multiply the distance and time by 2 you get 7 miles in 1 hour, or 7 mph
4 0
3 years ago
2. Today Carly’s bank account contains $82. Yesterday she made a withdrawal of $25. What was the bank account balance before Car
Slav-nsk [51]
Is it together or different questions to the reading
4 0
3 years ago
The tangent of an angle is 3.4. what is the measure of the angle to the nearest tenth?
Amiraneli [1.4K]

To answer this question, you first need to know what SohCahToa is.

S- opposite over hypotenuse

C- adjacent over hypotenuse

T- opposite over adjacent

In this situation, they have made it easier for you as they have given you the quotient of the opposite and adjacent sides (3.4) . Now in order to find an angle, you take the inverse of your expression. So instead of just Tan, you would plug in Tan^-1. So plug it in:

Tan^-1 (3.4)

Answer is 73.6 degrees.

3 0
3 years ago
Which expression is equivalent to 9 p minus 3 p + 2?
Snezhnost [94]

Answer:

Didn't know how far I was needed to go, but I hope something there helps you.

Step-by-step explanation:

9p - 3p +2 = 0

6p +2 = 0

6p = -2

p = -2/6

p = -1/3

5 0
3 years ago
Read 2 more answers
If six girls can finish sweeping the floor of a hall in 45mins,how long will the same work take ten girls to do
AleksandrR [38]

Answer:

15 minutes i think

Step-by-step explanation:

45÷6=7.5

meaning 7.5 minutes per girl

so 4 girls would be 30 minutes of work

so 45-30=15

4 0
3 years ago
Other questions:
  • Suppose a spider moves along the edge of a circular web at a distance of 3cm from the center.
    8·1 answer
  • A photographer charges a sitting fee of $15, and charges $4 for each 5-in by 7 in photograph the customer orders. The linear
    10·1 answer
  • write an expression to describe the sequence below.Use n to represent the position of a term in the sequence, where n=1 for the
    13·1 answer
  • Which choices are equivalent to the expression below? Check all that apply. 6√3
    7·1 answer
  • Which equation shows how the properties of numbers extend to negative whole numbers by the Distributive Property?
    11·1 answer
  • Rewrite the product (3x2)(2x5) as a equivalent expression in simplest exponential form?
    15·1 answer
  • Please help me out! And please show your work!
    11·2 answers
  • Select the three ratios that represent the number of blue marbles to red marbles.
    12·1 answer
  • Jake Visits his relatives on Thanksgiving. He first travels to his parents'
    10·2 answers
  • The​ U-Drive Rent-A-Truck company plans to spend ​$16 million on 320 new vehicles. Each commercial van will cost ​$​25,000 each
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!