Find the dimensions of the isosceles triangle of least area that circumscribes a circle of radius r.

Q: What is the area of the shaded region of the circle, bounded by the x-axis and the line y=-x,…

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Q: Show that a rectangular box of given volume and minimum surface area is a cube.

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Q: Sketch the region in the xy-plane defined by the inequalities x- 4y 0, 2- x - 7lyl 20 and find its…

A: Given region are   x-4y2≥0 and 2-x-7|y|≥0

Q: What is the area of the largest rectangle that can be drawn with one side along the x-axis and the…

A: given curve is y=e-x2 find the largest area of a rectangle which has one side along the x-axis and…

Q: Find the longer dimension of the rectangle enclosed in a semicircle y=V144- x2 with the largest…

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Q: Find the area bounded by the arc square root x + square root y = 7, the x axis, and the line joining…

A: Given curves are                                                   1x+y=7, y=0, points (16, 9) &…

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: Sketch the region in the xy-plane defined by the inequalities x - 2y2 ≥ 0,   1 - x -| y| ≥ 0, and…

A: Now the graph is,

Q: Find the area of the regions enclosed by the two curves, y =x +3 and y = 4x+8. %3D

A: From the given problem:   y=x2+3 & y=4x+8       Now finding a point of intersection:…

Q: Sketch the region in the xy-plane defined by the inequalities x - 5y2 > 0, 2 – x – 9\y| > 0 and find…

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Q: A piece of wire 10 m long is cut into two pieces. One piece is bent into a 30°-60°-90° triangle and…

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Q: Find the area oF the loop OF the curve. given

A: Integration is the process of finding the anti-derivative function of the given function. The…

Q: composed

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Q: Find the area between the curves. 3x х%3 -2, х%34, у%33е3X, у%3D2е 3X +1

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Q: Determine the dimensions of a rectangular box with a volume of 1 ft ^ 3 that has a minimum surface…

A: Given a rectangular box with volume 1 ft^3

Q: What is the largest possible area such a region can have if its perimeter is to be 20 units?

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Q: Show that the rectangular parallelepiped with fixed surface area and maximum volume is a cube.

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Q: Determine the dimensions of the inscribed rectangle of maximum area. y = e¯*

A: Let the point on the curve for the rectangle with maximum area is (x,y) It can be written as: so…

Q: A rectangular storage container with a square base and an open top is to have a fixed volume of…

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Q: Of all boxes with square base and a volume of 512 cm, which one has the minimum surface area? (Give…

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Q: what is the minimum possoble perimeter for a rectangle whose area is 100 in^2

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Q: Find the area of the reglon bounded by the graphs of the equations. y = 5x +5, x = 0, x = 2, y = 0

A: Required area is…

Q: A rectangular lot having an area of 5000 sq meters is to be fenced on three sides Find the minimum…

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Q: find the dimension of a cylinder that can be inscribed in a given sphere if it's convex surface area…

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Q: A poster is to contain 300 cm? of printed matter with margins of 10 cm at the the top and bottom and…

A: Assume some variable to be length and breadth of the poster then find its area. Derivative of area…

Q: Find the volume of the parallelepiped defined by the inequalities 0≤2x−3y+z≤5,1≤x+2y≤4,−3≤x−z≤6.

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Q: 3 and y=X %3D 2

A: The equation of the curve is x=12y2-3 The equation of the curve is y=x-1

Q: A cylinder with no top is to have a volume of 100π cubic centimeters. Find the minimum possible…

A: To find the minimum possible surface area of the given type of cylinder.

Q: If a closed tin can of volume 16x cubic inches is to be in the form of a right circular eylinder,…

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Q: A closed rectangular box has volume 20 cm³. What are the lengths of the edges giving the minimum…

A: Solution is given below:

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Q: what is the minimum perimeter that a rectangle with an area of 32 ft2 can have?

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Q: Suppose that a pentagon is composed of a rectangle topped by an isosceles triangle. If the length of…

A: We have to find the maximum area.

Q: A company that manufactures dog food wishes to pack the food in closed cylindrical tins.  What…

A: Given volume of the can is (128)πcm3 Let height=h radius=x

Q: A triangle is formed by the positive coordinate axes and a straight line through (6,3) . How large…

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Q: A fencing is limited to 120ft length. What is the maximum rectangular area that can be fenced in…

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Q: Use Lagrange multipliers to find the dimensions of a box with volume 1000 cm3 that has minimal…

A: the surface area of the box is  S=2xy+2yz+2xz................(1) the volume of the box is given by…

Q: Find the dimensions of the rectangular box, open at the top, which has a minimum surface area if the…

A: Let us consider the width, length and height of the rectangular box are x, y and z respectively.…

Q: Find the rectangular parallelepiped of fixed total edge length with maximal surface area.

A: The rectangular parallelepiped has all faces in rectangular face. Let a,b,c be the edge lengths for…

Q: Consider a rectangle of sides x and y with fixed perimeter of 40 units. Find the maximum and minimum…

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Q: Find the minimum cost of a rectangular box of volume 200 cm³ whose to

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Q: What are the dimensions of a closed recrangular box that has a square cross section a capacity of…

A: Given that the dimensions of a closed rectangular box that has a square cross sections a capacity of…

Q: Find the dimensions of a rectangle with area 100 m? whose perimeter is as small as possible? Find…

A: to find:- dimensions of the rectangle. minimum perimeter.

Q: should the box have in order to minimize the surface area?

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Q: How do I find the epxression for the perimeter of a rectangel with a length of x2 - x + 4 and a…

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Q: Determine the dimensions of the inscribed rectangle of maximum area.

A: Determine the dimensions of the inscribed rectangle of maximumarea.