Use the parametric equations x = a( - sin) and y = a(1 - cos ), a
Question:
Use the parametric equations x = a(θ - sinθ) and y = a(1 - cos θ), a > 0 to answer the following.
(a) Find dy/dx and d2y/dx2.
(b) Find the equation of the tangent line at the point where θ = π/6.
(c) Find all points of horizontal tangency.
(d) Determine where the curve is concave upward or concave downward.
(e) Find the length of one arc of the curve.
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 62% (8 reviews)
a b c a2n 1 2a d Co...View the full answer
Answered By
Akshay Singla
as a qualified engineering expert i am able to offer you my extensive knowledge with real solutions in regards to planning and practices in this field. i am able to assist you from the beginning of your projects, quizzes, exams, reports, etc. i provide detailed and accurate solutions.
i have solved many difficult problems and their results are extremely good and satisfactory.
i am an expert who can provide assistance in task of all topics from basic level to advance research level. i am working as a part time lecturer at university level in renowned institute. i usually design the coursework in my specified topics. i have an experience of more than 5 years in research.
i have been awarded with the state awards in doing research in the fields of science and technology.
recently i have built the prototype of a plane which is carefully made after analyzing all the laws and principles involved in flying and its function.
1. bachelor of technology in mechanical engineering from indian institute of technology (iit)
2. award of excellence in completing course in autocad, engineering drawing, report writing, etc
4.70+
48+ Reviews
56+ Question Solved
Related Book For
Calculus Of A Single Variable
ISBN: 9781337275361
11th Edition
Authors: Ron Larson, Bruce H. Edwards
Question Posted:
Students also viewed these Mathematics questions
-
Use the parametric equations x = - 3t + 1 and y = 2/t + 1 to answer each question. a. Find the x- and y-coordinates of the points that correspond to the values of t = 3, t = 0, and t = - 3. b. Find...
-
A mortgage pool is worth $10 million. Each mortgage has interest rate of 6%, term of 30 years and monthly payments based on full amortization. Mortgage servicing fee is an annual 1.2% of the mortgage...
-
Use the parametric equations of an ellipse, x = a cos , y = b sin , < < 2, to find the area that it encloses.
-
Express the quantity of 3.225 kJ in calories.
-
The balance sheet for a small firm shows total assets of $429,500 and total liabilities of $379,000. What is the shareholders equity?
-
Elegant Decor Companys management is trying to decide whether to eliminate Department 200, which has produced losses or low profits for several years. The companys 2013 departmental income statement...
-
A purpose of tests of controls over billing is to determine whether: a. Billed goods have been shipped. b. Sales orders agree to shipping documents. c. Sales orders have been approved by Credit...
-
Holiday Entertainment Corporation (HEC), a subsidiary of New Age Industries, manufactures go-carts and other recreational vehicles. Family recreational centers that feature not only go-cart tracks...
-
Sue receives a yearly salary of $32000 She is paid bi-weekly and her regular workweek is 37.5 hours. What is the hourly rate of pay?
-
Mary Losch operates a travel agency called Mary's Luxury Travel. She has five employees, all of whom are paid on a weekly basis. The travel agency uses a payroll register, individual employee...
-
Describe how to test whether a polar graph is symmetric about (a) The x-axis (b) The y-axis.
-
Write an integral that represents the area of the surface generated by revolving the curve about the x-axis. Use a graphing utility to approximate the integral. Parametric Equations x = 1, y = 1 + 2...
-
Seasons Construction is constructing an office building under contract for Cannon Company. The contract calls for progress billings and payments of $1,240,000 each quarter. The total contract price...
-
Is this 2-Tail test? Or 1-Tail test? In this case what I use for H0? I know the standard deviation, what number represent The mean in the equation is it 1955? Or 1800? For the Bank the average...
-
A person deposited $500 in a savings account that pays 5% annual interest that is compounded yearly. At the end of 10 years, how much money will be in the savings account?
-
Does the FTB require payers to file 1 0 9 9 - NEC forms under the information reporting requirement rules that exist for, for instance, 1 0 9 9 - MISC and Form W - 2 ?
-
Franca has AGI of $130,000 this year. After applying the $100 floor, she has $26,000 of federal disaster losses on personal assets, $12,000 of nonfederal casualty losses on personal assets, and...
-
What directed you to become a project manager? Why not stay in engineering or some other form of business management? Discuss examples of the project managers role as a team leader and a team member.
-
Can the income yield from an investment be negative? Explain or give an example
-
The vapor pressure of the liquid NH, is measured at different temperatures. The following vapor pressure data are obtained. Temperature, K P, mmHg 217.1 223.4 234.7 588.1 Calculate the enthalpy of...
-
In Exercises sketch the space curve represented by the intersection of the surfaces. Then represent the curve by a vector-valued function using the given parameter. Surfaces z = x + y, z = 4...
-
In Exercises evaluate the definite integral. TT/2 [(a cos t)i + (a sin t)j + k] dt
-
In Exercises find the vectors T and N, and the binormal vector B = T N, for the vector-valued function r(t) at the given value of t. r(t) = i + sin tj + cos tk, to || 4
-
ABC company retains about half of its earnings each year and pays the rest out as dividend. Recently, the company paid a $3.25 dividend. Investors expect the company's dividends to grow modestly in...
-
Lara Williams is interested in purchasing the ordinary shares of Nillahcoote Ltd which is currently priced at $38.45. The company is now on a fast growth phase and experts its dividends to grow at a...
-
Hardmon Enterprises is currently anall-equity firm with an expected return of 16%. It is considering a leveraged recapitalization in which it would borrow and repurchase existing shares. Assume...
Study smarter with the SolutionInn App