x²y²8. A football is in the shape of a solid obtained by rotating an ellipsea² b²1 about its major axis. Aninflated NFL football averages 11.125 inches in length and 28.25 inches in center circumference. If the4volume of the ball isTab², how much air does the football contain? (neglect material thickness)3

Answered: Image /qna-images/answer/9d33108e-39ee-411c-be60-743ebe265d26.jpg

Answered: 3. A football is in the shape of a…

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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Area of the trapezium whose vertices lies on the parabola y = 4x and its diagonals pass through (1, 0) and having length 25 unit each, is 4 625 (A) 5 sq. unit (B) 16 sq. unit 4 (C) 2 sq. unit (D) 5 sq. unit 4 8
a.) Find the dimensions of the large rectangle that can be inscribed in the ellipse 9x^2 + 16y^2 = 144. The sides of the rectangle are parallel to the axes of the ellipse. b.) the sum of the bases and altitude of an isosceles trapezoid is 36cm. Find the altitude if the area is to be a maximum. c.) A Norman window, consisting of a semicircle surmounting a rectangle, has a given perimeter. Find the radius of the semicircle to admit the most light. d.) Find the point the curve y= x^3 which is nearest the point (4,0). e.) the points (3,2) and (1,6) lie on the ellipse y^2 + 4x^2 = 40. Find a point on the ellipse so that the area of the triangle having these three points as vertices is maximum.
5. A highway overpass is in the shape of half an ellipse with the base 200 feet wide. The highway is 120 feet wide and the minimum clearance is 40 ft. Find the height of the overpass at its center.
The plane x + y + 2z = 6 intersects the paraboloid z = x? + y? in an ellipse. Find the points on this ellipse that are nearest to and farthest from the origin. Point farthest away occurs at Point nearest occurs at ).
VI. Assessment Read the following statements. Choose the letter of the correct answer. 1. Give the center of hyperbola represented by the equation А. (0, 9) В. (0, 0) С. (25, 0) D. (9, 25) 2.The equation of a hyperbola that is centered at (3, -1). A. 9(x + 3)2 – 16(y + 1)² = 144 B. 9(x + 3)2 – 16(y - 1)2 = 144 C. (x – 3)2 – (y + 1)2 = 144 D. 9(x - 3)2 —- 16(у - 1)2 %3D144 3. Rewrite the equation of the hyperbola 9x2 – y2 = 81 in the standard form. c. - D. - A.- = 1 = 1 81 В. 81 9. 4. Graph the equation 9y² + 36y – x² + 6x = 54. (y-(-2))² _ (x-3)² (y-2)?_ (x-3)² А. = 1 81 С. = 1 81 9 (y-(-2))² В. (x-3)2 = 1 (y-(-2))² D. (х-3)2 = 1 3 5. Give the coordinates of the vertices of the fundamental rectangle of the hyperbola 25 (x-4) y2 = 1 А. (3, 1), (3, -1), (-1, -1), (1, -1) В. (9, 3), (9, -3), (-1, 3), (-1, -3) С. (9, 9), (9, -9), (-1, -9), (1, -9) D. (9, 1), (9, –1), (-1, –3), (1, -3) 6. Give the coordinates of the vertices of hyperbola represented by the x2 equation 9 (y+1)2 = 1 25 А.…
On each chord of 9?²+ 16?² = 144 perpendicular to the x-axis is erected an isosceles right triangle perpendicular to the plane of the ellipse and with ends of the hypotenuse on the ellipse. Find the volume of the solid thus formed.
A satellite dish is shaped like a paraboloid of revolution. This means that it can be formed by rotating a parabola around its axis of symmetry. The receiver is to be located at the focus. If the dish is 30 feet across at its opening and 14 feet deep at its center, how many feet above the vertex should the receiver be placed? (round to 2 decimal places)
Mercury moves in an elliptical orbit with the sun at one of the foci. The length of the half of the major axis is 56,996,838 kilometers, and the eccentricity is 0.2056. Find the maximum distance (aphelion) of Mercury from the sun. Round your answer to nearest kilometer. Select one: a. 45,278,288 km O b. 68,715,388 km ○ c. 58,136,775 km O d. 55,856,901 km e. 11,718,550 km
Note: Kindly provide a solution pls. The answer is already provided. Thank you! 1.2 The length of the latus rectum of an ellipse is 2/6 of the length of the major axis. If we take thedistances of a point on the ellipse to two fixed points, the sum is always 16. Compute theeccentricity of the ellipse. Ans: 0.82
A viewing spot tower has a shape of a hyperboloid and is 32 meters high. The rooftop and ground floor are 10 meters in diameter and are symmetric with respect to the middle height of the tower. The circular portion between the rooftop and the ceiling has a diameter of 8 meters. Find the diameter of the circular portion of the viewing spot 20 meters above the ground.
デジタル形式で段階的に解決ありがとう!! SOLVE STEP BY STEP IN DIGITAL FORMAT 1. The plane x + y + z = 12 intersects the paraboloid z = x into an ellipse. Find the highest and lowest point of the ellipse. 2 + y²

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