Figure 20 shows one arch of a cycloid. Its parametric equations (see Problem 18) are given by
Question:
x = a(t - sin t), y = a(1 - cos t), 0 s t s 2Ï
(a) Show that the area of the surface generated when this curve is revolved about the x-axis is
(b) With help of the half-angle formula 1-cost = 2sin2 (t/2), evaluate A.
Transcribed Image Text:
2 (1 cos t) dt 0 2a πα 2
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 66% (12 reviews)
a b 1cost ...View the full answer
Answered By
Gabriela Rosalía Castro
I have worked with very different types of students, from little kids to bussines men and women. I have thaught at universities, schools, but mostly in private sessions for specialized purpuses. Sometimes I tutored kids that needed help with their classes at school, some others were high school or college students that needed to prepare for an exam to study abroud. Currently I'm teaching bussiness English for people in bussiness positions that want to improve their skills, and preparing and ex-student to pass a standarized test to study in the UK.
5.00+
1+ Reviews
10+ Question Solved
Related Book For
Question Posted:
Students also viewed these Calculus questions
-
(a) Show that the parametric equations x = x1 + (x2 x1)t y = y1 + (y2 y1) t where 0 < t < 1, describe the line segment that joins the points P1(x1, y1) and P2(x2, y2). (b) Find parametric equations...
-
Find the area under one arch of the trochoid of Exercise 40 in Section 10.1 for the case d < r. In Exercise 40 Let P be a point at a distance from the center of a circle of radius r. The curve traced...
-
1. In the investigation you used the parametric equations for a circle, x = 3cos t and y = 3 sin t, to graph other geometric shapes on your calculator. Mathematically, do you think it is correct to...
-
Consumers commonly focus on the price when buying auto insurance. They feel less pain from buying auto insurance when they pay as little as possible However, this strategy can backfire because the...
-
The following executive summary has faults in grammar, punctuation, spelling, wordiness, parallelism, and possessives. You may either (a) Use standard proofreading marks (see Appendix B) to correct...
-
Franco Ltd. purchased $ 400,000 of Gentron Company 5% bonds. The bonds pay semi- annual interest each 30 June and 31 December. The market interest rate was 6% on the date of purchase. The bonds...
-
In some instances, a temporary restraining order can be granted ex parte (i.e., without notice to the other side) until a hearing for a preliminary injunction can be held. Further investigate CCP 527...
-
Johnson Electronics makes calculators. Consumer satisfaction is one of the top priorities of the companys management. The company guarantees the refund of money or a replacement for any calculator...
-
Week 3 Activities Solution QUESTION 1: Given below is a list of costs: Max Furniture Company manufactures wooden chairs and reported the following costs for January 2024: COST ITEM AMOUNT (AED)...
-
The T. Boom Pickens Corporation has a $1 million capital structure and always maintains this book value amount. Pickens currently earns $250,000 per year before taxes of 50 percent, has an all-equity...
-
Show that the area of the part of the surface of a sphere of radius a between two parallel planes h units apart (h < 2a) is 2irah. Thus, show that if a right circular cylinder is circum-scribed about...
-
The circle x = a cos t, y = a sin t, 0 t 2, is revolved about the line x = b, 0 < a < b, thus generating a torus (doughnut). Find its surface area.
-
In Exercises use the shell method to set up and evaluate the integral that gives the volume of the solid generated by revolving the plane region about the x-axis. || 1 | | - 34 2 - - + +
-
Customers arrive an average of 10 per hour and an average of 16 customers can be served in an hour. Assuming this is an M/M/1 model, what is the average length of the line?
-
What is thermodynamics?
-
Explain the scope and limitations of thermodynamics.
-
How do units and dimensions play an important role in characterizing the physical quantities of thermodynamic systems?
-
Distinguish between absolute pressure and gauge pressure. How is it related to the other in case of vacuum?
-
Determine and sketch or graph the sets in the complex plane given by < |z - 4 + 2i| < 3
-
Assume a simple Keynesian depression economy with a multiplier of 4 and an initial equilibrium income of $3,000. Saving and investment equal $400, and assume full employment income is $4,000. a. What...
-
In the study of ecosystems, predator-prey models are often used to study the interaction between species. Consider populations of tundra wolves, given by W(t), and caribou, given by C(t), in northern...
-
Graphs of the velocity functions of two particles are shown, where is measured in seconds. When is each particle speeding up? When is it slowing down? Explain. (a) (b) VA 1
-
Graphs of the velocity functions of two particles are shown, where is measured in seconds. When is each particle speeding up? When is it slowing down? Explain. (a) (b) VA 1
-
gross margin? Joseph Company recorded sales of $39000 and Cost of Goods Sold of $14000. What is Joseph Company's
-
What are some examples of a difficult situation that due care may face? What would an ethical response be to those examples be ? And lastly why might a practitioner be tempted to or accidentally not...
-
You are starting a business and as part of your business plan you need to develop a break - even analysis. Your fixed costs ( overhead ) associated with your store are $ 1 , 0 0 0 , 0 0 0 annually,...
Study smarter with the SolutionInn App