1. [20 points] Find the points on the ellipse, 4x² + y² = 4 that are farthest away from the point (1,0). 2. [20 points]

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1 20 Points Find The Points On The Ellipse 4x Y 4 That Are Farthest Away From The Point 1 0 2 20 Points 1 (70.66 KiB) Viewed 8 times

1. [20 points] Find the points on the ellipse, 4x² + y² = 4 that are farthest away from the point (1,0). 2. [20 points] A box with a square base and an open top must have a volume of 32,000 cu. cm. What dimensions will minimize the amount of materials? [To receive full credit, solve with Calculus!] 3. [30 points] A Norman window has the shape of a rectangle surmounted by a semicircle. The diameter of the semicircle is equal to the width of the rectangle. If the perimeter of the window is 30 feet, find the dimensions of the window so that the greatest possible mount of light is admitted. 4. [30 points] Two vertical poles are secured by a rope going from the top of one pole to a point on the ground and then to the top of the second pole, as shown in the figure. Show that the shortest length of such a rope occurs when the angles at the point on the ground are equal.