Question: Using principles from physics it can be shown that when a cable is hung between two poles, it takes the shape of a curve y

Using principles from physics it can be shown that when a cable is hung between two poles, it takes the shape of a curve y = f(x) that satisfies the differential equation where p is the linear density of the cable,

Is the acceleration due to gravity, and T is the tension in the cable at its lowest point, and the coordinate system is chosen appropriately. Verify that the function y = f(x) = T/pg cos (pgx/T) is a solution of this differential equation.

- dy p9 d'y dy 1 + dx

Step by Step Solution

★★★★★

3.50 Rating (153 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

T We differentiate the function twice then substitute into the d... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

M-C-D (168).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

It can be shown that for any data y 1 , y 2 , c , y n the smallest value for is obtained by setting M = y. Explain why this implies that the fitted values in ANOVA are the sample averages of the...

It can be shown that for any real number s. illustrate this equation graphically for s = 2 by graphing y1 = (1 + 2/n)n y2 = 7.389 056 099 e2 in the same viewing window, for 1 ¤ n ¤ 50....

It can be shown that if |d2y / dx2| M on a closed interval with c and c + Ax as end points, then |y - dy| 1/2M(x)2 Find, using differentials, the change in y = 3x2 - 2x + 11 when x increases from 2...

Please answer all the required questions in detail I hope the answer is not copy-paste I hope that the answer will be according to the concepts in the chapter 3 The following article summarizes the...

A computer algebra system is recommended. A manufacturer of corrugated metal roofing wants to produce panels that are 48 in. wide and 2 in. high by processing at sheets of metal, as shown in the...

Consider the following context-free grammar of expressions E ::= n | (E, E) where n ranges over integers. (a) Present a right-most derivation of the expression ((21, 18), 17). [2 marks] (b) List the...

kinetic energy is converted into potential energy. When the ball falls back to the ground, the potential energy is converted back into kinetic energy. The total amount of energy in the system remains...

Set Student Name: 1. Answer true or false for each part, and if false, explain your answer. a. The point estimate for the population mean, , of an x distribution is x-bar, computed from a random...

Complete the following Carolina Biological Lab: Kinematics. Please read the Distance Learning Lab Safety Agreement. By taking part in these labs, you agree to the terms in the Distance Learning...

answer the question clearly You are building a flight-control system for which a convincing safety case must be made. Would you assign the tasks of safety requirements engineering, test case...

Wilbert Heikkila listed eight parcels of real property for sale. David McLaughlin submitted written offers to purchase three of the parcels. Three printed purchase agreements were prepared and...

Suppose the quantity of apples supplied in your market is 2,400. If there are 60 apple producers, each with identical cost structures, how many apples does each producer supply to the market?

Which of the following statements is true with regard to activity - based costing rates? The premise of ABC is that act wvities are what cause costs to be incurred. All cost drivers used to determine...

(Single-step Income, Retained Earnings, Periodic Inventory) Presented below is the trial balance of Mary J. Blige Corporation at December 31, 2004. A physical count of inventory on December 31...

QualSupport Corporation manufactures seats for automobiles, vans, trucks, and various recreational vehicles. The company has a number of plants around the world, including the Denver Cover Plant,...

If a particle is projected vertically upward to a height h above a point on Earths surface at a northern latitude , show that it strikes the ground at a point 4/3 w cos 8h3/g to the west (Neglect air...

An economist has predicted that for the next 5 years, the United States will have an 8% annual inflation rate, followed by 5 years at a 6% inflation rate. This is equivalent to what average price...

A thin rod of length l lies on the + x-axis with its left end at the origin. A string pulls on the rod with a force F directed toward a point P a distance h above the rod. Where along the rod should...

Complete and balance the equations for the following reactions: (a) K(s) + I 2 (g) (b) Ba(s) + O 2 (g) (c) Al(s) + S 8 (s) (d) Si(s) + Cl 2 (g)

Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle and label its height and width. Then find the area of the...

Sketch the region enclosed by the given curves and find its area. y = 12 - x 2 , y = x 2 - 6

Sketch the region enclosed by the given curves and find its area. y = x 2 , y = 4x - x 2

A solutions architect wants to design a solution to save costs for Amaron EC 2 instances that do not need to run during a 2 - week company shutdown. The applications running on the instances store...

Which of the following is NOT a true statement about vector drawables? Group of answer choices Vector drawables look the same on all devices without loss of quality. A vector drawable is specified in...

e theory, what is a Nash equilibrium? he optimal strategy for one player regardless of e other players' strategies. outcome where no player has an incentive to viate from their strategy. e strategy...