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.
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
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