Question

What is the area of the largest rectangle which can be inscribed in the ellipse given by x^2/16 + y^2/4 = 1?

Answer #1

Find the area of the largest rectangle that can be inscribed in
a semicircle of radius r = 2.

Determine the largest possible area for a rectangle that can be
inscribed in a circle of radius 7.8 cm.

Use a Lagrange multiplier to find the maximum possible area of a
rectangle inscribed in the ellipse x2 + 4y2 =
32. Assume the sides of the rectangle are parallel to the
coordinate axes. Note that the area of the rectangle is not xy

Find the circular cylinder of largest lateral area which can be
inscribed in a sphere of radius 4 feet. (Surface area of a cylinder
of radius r and height h is 2πrh.)

Find the dimensions of the rectangle of maximum area with sides
parallel to the coordinate axes that can be inscribed in the
ellipse 128xsquaredplus2ysquaredequals128. Let length be the
dimension parallel to the x-axis and let width be the dimension
parallel to the y-axis.

A rectangle is inscribed with its base on the x-axis and its
upper corners on the parabola y= 1x^2. What are the dimensions of
such a rectangle with the greatest possible area?

Find the area of the largest trapezoid that can be inscribed in
a circle of radius 2 and whose base in as diameter of the
circle.

Find the dimensions of the rectangular solid of largest volume
which can be inscribed in the ellipsoid
x2/16+y2/4+z2/9=1
Hint: Let (?, ?, ?) represent one of the eight vertices of the
solid. Then by symmetry the volume of the solid is ? =
(2?)(2?)(2?).

a rectangle that is x feet wide is inscribed in a circle of
radius 7 ft. .
a)express the area of the rectangle as a function of x.
b) find the domain of the function
c) graph the function with a graphing calculator
d) what dimensions mazimize the area of the rectangle
a(x) =

Find the area of the largest rectangle in the first quadrant
with one side on the x-axis, one side on the y-axis, and one vertex
on the curve y = e −x .

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