Show that the arc length of the catenary y = cosh x over the interval [0, a]

Question:

Show that the arc length of the catenary y = cosh x over the interval [0, a] is L = sinh a.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For answer-question

Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

See More Books

Question Posted: Apr 06, 2019 11:49 AM

See More Questions

a. Show that the arc length integral for the function where a > 0 and A > 0, may be integrated using methods you already know. b. Verify that the arc length of the curve y = f(x) on the interval [0,...
Find the arc length of the function SVIn? t 1 dt on [e, e]. f(x) =
Johann Bernoulli (16671748) evaluated the arc length of curves of the form y = x(2n + 1)/2n , where n is a positive integer, on the interval [0, a]. a. Write the arc length integral. b. Make the...
The Wall Street Journal Corporate Perceptions Study 2011 surveyed readers and asked how each rated the quality of management and the reputation of the company for over 250 worldwide corporations....
As the new intern for the summer, you have been asked to investigate two methods of e-mail encryption: S/MIME and Pretty Good Privacy (PGP). Compare and contrast the two systems. 1. Why do two...
How do you explain the growing popularity of teams in organizations? What are the differences among downward, upward, and lateral communication? How is mentoring valuable to leadership? What are...
Refer to the information in Exercise 22-12. Assume that each of the companys divisions has a required rate of return of 7%. Compute residual income for each division. Data From Exercise 22-12 A food...
The Allen Company is a wholesale distributor of automotive replacement parts. Initial amounts taken from Allens accounting records are as follows: Inventory at December 31, 2007 (based on physical...
Explain Suppose the government grants $2,500 per child to households that have more than two children. Draw a graph and explain whether these child allowances influence the fertility behavior of...
Grants Graphics has a December 31 year end. Grants Graphics records adjusting entries on an annual basis. The following information is available. 1. At the end of the year, the unadjusted balance in...
The portion of the curve y = 17/15 - cosh x that lies above the x-axis forms a catenary arch. Find the average height of the arch above the x-axis.
A power line is attached at the same height to two utility poles that are separated by a distance of 100 ft; the power line follows the curve f(x) = a cosh(x/a). Use the following steps to find the...
Find each integral in Problems 16. np. n I + nan fue"
f(x)= 9/x x= 1, x= a What is the net change? What is the average rate of change?
solve 7 / 3 = 5 / x + 4 for x
find any horistonal asymptoptes of f ( x ) = 3 x - 9 / 2 x - 6
5. A box is dragged along the ground by a rope that applies a force of 14 lb at an angle of 30 with the ground. Find the work done by the force in pulling the box 20 ft.
profitability, liquidity, gearing, efficiency ratios. I am confused on the numbers to use, but also the values for pre-calculation before calculating the actual ratios. For example: calculating...
In its first year of operations, Lima Company manufactured 1,000 widgets, incurring direct materials and labor costs of $227,000. For book purposes, Lima capitalized $260,000 of indirect...
List four items of financial information you consider to be important to a manager of a business that has been operating for a year.
For identify A, B, C, and D for the sine functions and sketch their graphs. f(x) = A sin ( 7 7 (x c ) ) + - C) + D.
Find the function value. sin 2 /12
The accompanying figure shows the graph of a function (x) with domain [0, 2] and range [0, 1]. Find the domains and ranges of the following functions, and sketch their graphs. a. (x) + 2 b. (x) - 1...
Company F shipped 8,000 tons of gold for a total mixed cost of $450,000 in April and 11,000 tons for $555,000 in May. Shipping costs for 13,000 tons to be shipped in June would be expected to be?
After the U.S. Congress passed temporary tax cuts in 2010, U.S. taxpayers who earned up to $50,000 per year had a lower tax rate. On average, these taxpayers retained 2% more of their income than...
At the beginning of the year DRJ Enterprises reported gross fixed assets of $915 million and net fixed assets of $616 million; at the end of the year, it reported gross fixed assets of $882 million...

Show that the arc length of the catenary y = cosh x over the interval [0, a]

Question:

Step by Step Answer:

a L 0 V1 ...View the full answer

Calculus Early Transcendentals

Students also viewed these Mathematics questions