Suspension bridge cables hang in parabolas The suspension bridge cable shown in the accompanying figure supports a uni- form load of w pounds per horizontal foot. It can be shown that if H is the horizontal tension of the cable at the origin, then the curve of the cable satisfies the equation dy dx х. Н Show that the cable hangs in a parabola by solving this differential equation subject to the initial condition that y = 0 when x = 0. y Bridge cable х

Suspension bridge cables hang in parabolas The suspension bridge cable shown in the accompanying figure supports a uni- form load of w pounds per horizontal foot. It can be shown that if H is the horizontal tension of the cable at the origin, then the curve of the cable satisfies the equation dy dx х. Н Show that the cable hangs in a parabola by solving this differential equation subject to the initial condition that y = 0 when x = 0. y Bridge cable х

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter3: Polynomial Functions

Section: Chapter Questions

Problem 9PS: Finding the Equation of a Parabola The parabola shown in the figure has an equation of the form...

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Similar questions

Finding the Equation of a Parabola The parabola shown in the figure has an equation of the form y=ax2+bx+c.Find the equation of this parabola using each method. (a) Find the equation analytically. (b) Use the regression feature of a graphing utility to find the equation.
Calculus The graph of a parabola passes through the points (0,1) and (12,12) and has a horizontal tangent line at (12,12). Find an equation for the parabola and sketch its graph.

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