Determine the maximum area of a rectangle inscribed in the ellipse x^2/49+y^2/81=1.

Q: Find the height of the right circular cylinder of maximum volume that can be inscribed in a sphere…

A: Given, A sphere of radius 15 cm  We have to find the height of the right circular cylinder of…

Q: There is a line through the origin that divides the region bounded by the parabola y = 5z – 2z and…

A:

Q: A long metal sheet with a width of L meters is formed into a gutter by bending up two of its sides…

A: We will use the basic knowledge of 3D solid geometry and applied differential calculus to answer…

Q: Find the minimum cost of a rectangular box of volume 140 cm³ whose top and bottom cost 2 cents per…

A:

Q: A farmer uses 2000 feet of fence to enclose a rectangular region and also to subdivide the region…

A: Let the width of the fence be:  w Let the length of the fence be:  l

Q: what are the dimensions of the right hexagonal prism of minimum surface whose volume is 36 cubic…

A: This is a problem of optimization.

Q: There is a line through the origin that divides the region bounded by the parabola y = 2x and the…

A: Answer

Q: There is a line through the origin that divides the region bounded by the parabola y = 8z – 32 and…

A: According to question given :There is a line through the origin that divides the region bounded By…

Q: A solid has a base in the form of an ellipse with major axis 10 and minor axis 8. Find its volume if…

A: Disclaimer: Since you have asked multiple questions, we will solve the first question for you. If…

Q: A rectangle sheet of cardboard measures 16 cm by 6 cm . equal squares are cut out of each corner and…

A: We need to find maximum volume.

Q: An open box is formed by cutting identical squares from each corner of a 22 inches by 22 inches…

A:

Q: An isosceles triangle of maximum area is inscribed in an ellipse with major axis 10cm and minor axis…

A: An isosceles triangle of maximum area is inscribed in an ellipse with major axis 10cm andminor axis…

Q: A rectangle with perimetee 18 cm is rotated about one of its sides forming a a right circular…

A:

Q: A rancher with 220 meters of fence intends to enclose a rectangular region along a river​ (which…

A: A fence will be only on 3 sides of the rectangular region. Assume l= length of rectangle and w=…

Q: A farmer has enough money to build only 150 meters of fence. What are the dimensions of the field he…

A: We know that, The perimeter of a rectangle is 2l+b where l is the length and b is the breadth of the…

Q: An open-top bin is to be made from a 15-centimeter by a 40-centimeter piece of plastic by removing a…

A: Assume that side of square which should be cut from each corner is a.Given the dimension of piece of…

Q: A right triangle who's hypotenuse is square root 3 m long is revolved around one of its legs to…

A: Given data is : Hypotenuse is 3 m To find the radius, height, and the volume of a cone of greatest…

Q: Find the maximum and minimum volumes of a rectangular box whose, surface area is 1300 cm² and whose…

A:

Q: There is a line through the origin that divides the region bounded by the parabola y = 3x – 4x² and…

A: The given equation of the parabola is,

Q: A right triangle whose hypotenuse is sqrt3m long is revolved about one of its legs to generate a…

A: In the question it is given a right angled triangle with the length of the hypotenuse as 3m. The…

Q: A farmer wants to secure a certain part of his land. Calculate the maximum area of a rectangular lot…

A: Given: total length of fencing material of rectangular plot = 1000m

Q: A rectangular piece of paper with a perimeter of 100 cm is to be rolled to form a cylindrical tube.…

A:

Q: An open box will be made by cutting a square from each corner of a 10-cm by 16-cm piece of cardboard…

A: To find: The size of square to be cut from the corner of cardboard to maximize volume and also find…

Q: A landowner wishes to use 2 miles of fencing to enclose a rectangular region of maximum area. 1.…

A:

Q: An open box is to be made from a 3-ft by an 8-ft rectangular piece of sheet metal by cutting out…

A: An open box is to be made from a 3-ft by an 8-ft rectangular piece of sheet metal by cutting out…

Q: An architect was commissioned to design a nuclear explosion resistant building in the shape of a…

A: The given dimenssions of ellipsoid area=25 mb=20mc=40 mthickness t = 1 m

Q: A farmer is constructing a rectangular pen with one additional fence across its width. Find the…

A: Let the width of rectangular pen is x m and length is y m. So, perimeter of rectangular pen is…

Q: A manufacturer wants to design an open box having a square base and a surface area of 244 square…

A:

Q: Determine the dimensions of a rectangular solid (with a square base) with maximum volume if its…

A:

Q: A 63-inch by 168-inch pieceof cardboard is used to make an open-top container by removing a square…

A:

Q: There is a line through the origin that divides the region bounded by the parabola y 7z 5x and the x…

A:

Q: Find the dimensions of the box of maximum volume with its sides parallel to the coordinate planes…

A: Given :                    The ellipsoid is :                           xa2 + yb2 + zc2 = 1…

Q: A rain gutter is made from sheets of aluminum that are 12 inches wide by turning up the edges to…

A: Given that, The three sides of the rain gutter is add up to 12 inches              2x+y=12⇒y=12-2x…

Q: A rectangular field is to be covered by 800-meter of hog wire in such a way that one side has a…

A: The Perimeter of rectangular field = 800 m Let length of field = x m Width of field = y m

Q: A bridge was built in the shape of a semi-elliptical arch, with span of 210 feet and maximal height…

A: Given that a bridge which is in semi-elliptical shape and span of 210 feet and maximum height 75…

Q: Determine the dimensions of a rectangular solid (with a square base) with maximum volume if its…

A: Follow the procedure given below.

Q: A wire of length Lis cut into pieces, one being bent to form a square and the other form an…

A: Let the length of the portion of the wire to form a square is x, then the length of wire to form a…

Q: A garden is in the form of an ellipse with semi-major axis 4 and semi-minor axis 3. If the axes are…

A:

Q: A parkway 20 meters wide is spanned by a parabolic arc 30 meters long along the horizontal. If the…

A:

Q: What are the dimensions of the rectangular field of maximum area that can be fenced with exactly 500…

A:

Q: An open box is formed by cutting identical squares from each corner of a 4 inches by 4 inches sheet…

A:

Q: Find the maximum volume of a rectangular box with no top that has a surface area of 48 square…

A:

Q: The roof of a tunnel is a semi-deck, if the tunnel is 100 m wide and the maximum height from floor…

A:

Q: Using the side of a building as one side and fencing for the other three sides, a rectangular garden…

A: Given: Using the sides of a building as one side and fencing for the other three sides,a rectangular…

Q: A right triangle whose hypotenuse is 15 m long is revolved about one of its legs to generate a right…

A:

Q: Determine the dimensions of a rectangular solid (with a square base) with maximum volume if its…

A:

Q: Brittany needs to construct a cylinder from a single sheet of metal with a perimeter of 2,148 mm.…

A: Given that a single sheet with perimeter 2148 mm.

Q: find the maximum volume of a rectangular box that a post office will accept for delivery of the sum…

A:

Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.