#62.Civil engineers often design road surfaces with paraboliccross sections to provide water drainage. Assume a roadsurface on level ground is 32 feet wide and is 0.4 foothigher at its center point than at its edges.(a.) Derive in standard form the equation of that(b.)surface's parabola, assuming the parabola's vertexis at the origin of your coordinate system.Use that equation to calculate the distance from theroad's centerline to the point at which the roadsurface is 0.1 foot lower than at the centerline.

Given: Width of the road (w) =32 feet radius of the road (r)=322=16 feet rise at center of road 0.4…

Answered: #62. Civil engineers often design road…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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1. Use the equation x2 +18x – 2y -85 = 0 to determine the following for a parabola:a. equation in vertex form,b. coordinates of vertex,c. focus,d. equation of axis of symmetrye. Sketch the graph of parabola. Thank you so much.
3. Reason Jupiter's gravity changes a spacecraft's path to a hyperbola as it approaches. The focus of the hyperbola nearest the spacecraft's path is the center of Jupiter. The diameter of the planet is 139,822 km. Suppose the path of an approaching spacecraft has an equation with a = 80,000 km and c= 170,000 Km. Assuming the transverse axis.js horizontal, write the equation that models the path of the spacecraft as it approaches Jupiter. What is the distance from the spacecraft to the planet at the vertex of the hyperbola?
Classify the following parabola as horizontal and vertical, indicate where they open.
answer number 13 and 14 13. What are the center and radius of the circle (x−7)^2+(y+6)^2=4 A.C: (7,-6); r= 16 B.C: (7,-6); r=2 C.C: (-7,6) ; r=4 D.C: (-7,5); r=8 14.A parabola defined by the equation x+3=18(y+2)2 is translated 44 units down and 3 units to the right. What is the vertex of the resulting parabola? A.(−6,0)(−6,0) B.(6,−6)(6,−6) C.(0,−6)(0,−6) D.(−6,−6)(−6,−6)
1. Find the equation of the parabola with its axis parallel to the y-axis, vertex at (-3, 2) and passing through the point (1, 0). State the focus and equation of the directrix line. Hence, sketch the parabola.
Write the equation of the hyperbola centered at the origin, with length of the horizontal transverse axis 6 and the curve passes through the point (7, -4).
Determine the standard form of the parabolic equation x = 1/2 (y + 5)2 − 2. Further, characterize this parabola by indicating its vertex, focus, directrix, and endpoints of the latus rectum.

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