The graph of the equation (x/a) + (y/b) = 1, with a x a,b y b...

 

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The graph of the equation (x/a) + (y/b) = 1, with a x a,b y b is an ellipse. i. Find the enclosed area of this ellipse. Hint: First find the area of the first-quadrant portion, y = b (1-(x/a))/,0 x a, and multiply it by 4. Then, with a = 3 and b = 5, plot the enclosed area of the ellipse using the built-in syntax of Mathematica. ii. Find the length of this ellipse. Hint: First find the length of the first-quadrant portion, y = b(1 - (x/a))/2,0 x a, and multiply it by 4. Then, with a = 3 and b = 5, plot the ellipse using the built-in syntax of Mathematica. iii. Find the volume of the solid by rotating this ellipse about the x-axis. Hint: First find the volume of the solid of revolution of the first-quadrant portion, y = b(1-(x/a))/2,0 x a, about the x-axis and multiply it by 2. Then, with a = 3 and b = 5, plot the solid of revolution about the x-axis using the built-in syntax of Mathematica. iv. Find the area of the surface by rotating this ellipse about the x-axis. Hint: First find the area of the surface of revolution of the first-quadrant portion, y = b(1-(x/a))/2,0 x a, about the x-axis and multiply it by 2. Then, with a = 3 and b = 5, plot the surface of revolution about the x-axis using the built-in syntax of Mathematica. The graph of the equation (x/a) + (y/b) = 1, with a x a,b y b is an ellipse. i. Find the enclosed area of this ellipse. Hint: First find the area of the first-quadrant portion, y = b (1-(x/a))/,0 x a, and multiply it by 4. Then, with a = 3 and b = 5, plot the enclosed area of the ellipse using the built-in syntax of Mathematica. ii. Find the length of this ellipse. Hint: First find the length of the first-quadrant portion, y = b(1 - (x/a))/2,0 x a, and multiply it by 4. Then, with a = 3 and b = 5, plot the ellipse using the built-in syntax of Mathematica. iii. Find the volume of the solid by rotating this ellipse about the x-axis. Hint: First find the volume of the solid of revolution of the first-quadrant portion, y = b(1-(x/a))/2,0 x a, about the x-axis and multiply it by 2. Then, with a = 3 and b = 5, plot the solid of revolution about the x-axis using the built-in syntax of Mathematica. iv. Find the area of the surface by rotating this ellipse about the x-axis. Hint: First find the area of the surface of revolution of the first-quadrant portion, y = b(1-(x/a))/2,0 x a, about the x-axis and multiply it by 2. Then, with a = 3 and b = 5, plot the surface of revolution about the x-axis using the built-in syntax of Mathematica.