Minimum perimeter rectangles Of all rectangles with a fixedarea A, which one has the minimum perimeter? (Give the dimen-sions in terms of A.)

Q: 5. Find the area of the region enclosed by 2 parabolas: y = * and y = 2x - r. Find the two…

A:

Q: An isosceles triangle is inscribed in a circle of radius R. Find the value of 0 that maximizes the…

A: In this question we have to find which option is good.

Q: An open box of maximum volume is to be made from a square piece of material, s = 36 centimeters on a…

A: An open box of maximum volume is to be made from a square piece of material, s = 36 centimeters on a…

Q: A rectangular tank with a square base, an open top, and a volume of 32ft^3 is to be constructed of…

A: Let side of square base be x ft and height be y ft Given, Volume=32 ft3 X2y = 32, y = 32/x2 – i)…

Q: A certain airline requires that rectangular packages carried on an airplane by passengers be such…

A: According to the problem, we have

Q: Optimal popcorn box A small popcorn box is created from a12" x 12" sheet of paperboard by first…

A: Height of box ⇒12-x2-x2⇒12-xLength ⇒6-xDepth ⇒xSo,V = (12-x)(6-x)(x)V = x3-18x2+72xfor max.…

Q: 1. A rectangular box has a square base. The combined length of a side of the square base, and the…

A:

Q: Eind the dimensions of arect-ongular box the top having of open at -Volume 3 32 m

A: To Determine: The dimensions of a rectangular  box whose volume is 32 m3.

Q: 13. A right circular cylinder is inscribed inside a sphere with radius r = 3 inches. Find the…

A: The radius of the sphere is 3 inches.

Q: 3. A rectangle is bounded by the x-axis and the semi-circle y= v4-x as shown in the diagram below.…

A:

Q: Maximum-volume box Suppose an airline policy states that allbaggage must be box-shaped with a sum of…

A: Modeling of the problem: As the base is square base , let the three dimensions be x, x and y. Since…

Q: 6. Find the area of the region bounded by a parabola and a line: y = r-4x and y = 2x. Find the two…

A: Given       y=x2-4x and y=2x        x2-4x=2x ⇒x2-4x-2x=0                         ⇒x2-6x=0…

Q: Arectangular tank with a square base, an open top, and a volume of 13,500 ft° is to be constructed…

A:

Q: A box with an open top has vertical sides, a square bottom, and a volume of 4 cubic meters. If the…

A:

Q: A A cone-shaped drinking cup is made from a circular piece of paper of radius R by cutting out a…

A: It can be only half filled and hence a cup can have maximum capacity of volume of semi sphere, which…

Q: A box with an open top has vertical sides, a square bottom, and a volume of 4 cubic meters. If the…

A:

Q: 5. A school is constructing a new sports field. Its shape is a rectangle with two semicircles on…

A:

Q: we are constructing an open top box with a square base out of 24 m^2 of material. Find the dimension…

A:

Q: lUse linearization to deteimine the stability.of fixed points in the pitchbik bifureation noimal…

A: Pitchfork bifurcation point: A pitchfork bifurcation is a particular type of local bifurcation where…

Q: A box with an open top has vertical sides, a square bottom, and a volume of 256 cubic meters. If the…

A: Solution: Let x is the base of the box Let y is the width of the box Let z is the height of the box…

Q: A Norman window has the shape of a rectangle with a semi circle on top; diameter of the semicircle…

A: In this question, we need to find the dimensions of Norman window of perimeter 200 inches.

Q: A certain airline requires that rectangular packages carried on an airplane by passengers be such…

A:

Q: 1. A rectangle is bounded by the X-axis and the semicircle in the positive y-region (see figure).…

A:

Q: 10. An open box is to be made by cutting a square from each corner of a 12-inch-by-12-inch piece of…

A: Suppose the side of the square to be cut off from each corner is "x" inch. Therefore, the length of…

Q: Maximum Area Find the dimensions of the largest rectangle that can be inscribed in a semicircle of…

A: Largest rectangle

Q: Maximum Volume Consider the following solids, each of which has a surface area of 150 square inches.…

A: Solution is given below:

Q: A certain airline requires that rectangular packages carried on an airplane by passengers be such…

A:

Q: A rectangular tank with a square base, an open top, and a volume of 10,976 ft is to be constructed…

A:

Q: A rectangie is bounded by the x-axis and the semiorde y- V25 - x (see figure). What length and width…

A: The given equation is  y=25-x2

Q: A certain airline requires that rectangular packages carried on an airplane by passengers be such…

A:

Q: A rectangle is bounded by the x-axis and the semicircle in the positive y-region (see figure). Find…

A: We have to find the dimensions of the largest rectangle that can be inscribed in a semicircle of…

Q: A box with an open top has vertical sides, a square bottom, and a volume of 32 cubic meters. If the…

A: GIVEN DATA : A box withe vertical sides and base of the base is square                         The…

Q: A rectangular tank with a square base, an open top, and a volume of 2,916 ft° is to be constructed…

A: Here I am attaching image so that you understand each and every step.

Q: 5. A trough with trapezoidal cross-section is to be made from a 1,000 cm by 40 cm rectangular sheet…

A: A trough with trapezoidal cross-section is to be made from a 1,000 cm by 40 cm rectangular sheet of…

Q: A rectangle is bounded by the x-axis and the semicircle in the positive y-region (see figure). Find…

A: Given:Assume that the center of the semicircle be (0,0).

Q: 12 A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y What…

A:

Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y the…

A:

Q: 4. The bottom of the legs of a three-legged table are the vertices of an isosceles triangle with…

A: According to the question, we need to determine the minimum length of wire needed to make a brace of…

Q: A Norman window has the shape of a rectangle with a semi circle on top; diameter of the semicircle…

A:

Q: A trough is 4 meters long, 2.5 meters wide, and 2 meters deep. The vertical cross-section of the…

A: Given data, A trough long = 4 meters width (base) =2.5 meters Depth (height) = 2 meters. Density =…

Q: 35. Minimum Distance Find the point on the graph of the equation arigh a lo abea ort 16x = y2 vd…

A: 35. Given, equation of the graph is 16x=y2. To find the point on the graph which is closest to the…

Q: A rectangular box with an open top and one partition is to be constructed from 288 square inches of…

A:

Q: Find the dimensions of the rectangle of maximum area that can be inscribed in a circle of radius  r…

A: To find the dimensions of the rectangle

Q: 1. Find the maximum area A of a triangle whose perimeter is a fixed length P. Show that your answer…

A: Let the two sides of the triangle are x and y. Given that perimeter of the triangle is P then the…

Q: 1. An open-top box with a square base is made from a cardboard of area 75 cm². Find the maximum…

A: given area is 75cm2find the maximum volume of the box

Q: Rectangles beneath a semicircle A rectangle is constructed withits base on the diameter of a…

A: A rectangle whose base on the diameter of circle of radius 5 and its vertices on the semicircle is…

Q: A rectangular solid with a square base has a surface area of 121.5 square centimeters. (Let w…

A: Let w represent the width of the sides of the square base and h represent the height of the…

Q: A Norman window has the shape of a rectangle with a semi circle on top; diameter of the semicircle…

A:

Q: A box with an open top has vertical sides, a square bottom, and a volume of 4 cubic meters. If the…

A: Given: Volume = 4 m3