A rectangle has its base on the x-axis and its two upper corners on the parabola y = 12 – x. What is the largest possible area of the rectangle? A (x) = A' (x) = Maximum Area is

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A: We will find the slope

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A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

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A: Answer

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

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Q: How do I find the shortest distance between y=x^2 and y=ln(x) ?

A: By using tangent of two curves we find the minimum distance as follows :

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A: The equation of the line passing through the origin is y=mx where m is the slope of the line. The…

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A: Solution :-   Given,A rectangle is bounded by the x-axis and the parabola y=9-x2Since, y aixs is the…

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Q: A wire 57 inches long is cut into two pieces, with the first piece bent into a square and the second…

A: A wire 57 inches long is cut into two pieces, with the first piece bent into a square andthe second…

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A: Let the length of poster ABCD =x cmBreadth of poster =y cmTop margin=2.5cmBottom margin=1.5cmBoth…

Q: 3. What is the height of the right circular cylinder with greatest volume that can be inscribed in a…

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

Q: 2. A closed rectangular box with a volume of 16 ft3 is made from two kinds of materials. The top and…

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Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 2 –…

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Q: A rectangle is constructed with its base on the diameter of a semicircle with radius 16 and with its…

A: A rectangle is constructed with its base on the diameter of a semicircle with radius 16 and with its…

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A: Given that, So, the surface area, S=24π cm2 Let, the radius be r and the height be h. As the…

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A: Fencing = 76m, Since, perimeter of the given rectangle=2x+y and, fencing = perimeter Then,…

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A: We have to find the dimensions of the box.

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Q: A rectangle is bonded by the X axis and the Parabola f(x)=16 - 0.25x^2. What length and width should…

A: NOTE: Refresh your page if you can't see any equations. . the length of the rectangle is  and the…

Q: A rectangular box is to have a square base and a volume of 24ft^3. If the material for the base…

A: Let x denotes the side of the base and y denotes the height of the rectangular box.

Q: What is the average distance between the parabola y = 7x(20 – x) and the x-axis on the interval…

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Q: It is desired to construct a structure like the figure with a volume of V (hemispherical and six…

A: The diagram for the given is, The volume for the diagram is, Assume the total cost is, P

Q: Find the dimensions of a rectangle of maximum area inscribed in a circle of radius 4. (Must show…

A: Let ABCD be the rectangle inscribed in the circle of radius 4. AC and BD are the diameters of length…

Q: A storage box with a square base must have a volume of 70 cubic centimeters. The top and bottom cost…

A:

Q: A rectangle is to be inscribed between the parabola y = 4 -x² and the X- axis, with its base on the…

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Q: What should the dimensions of the box be in order to minimize the surface area?

A: Let,Breadth of the box = b = xLength of the box = l = 2b = 2x        (according to question)Height…

Q: 3. A rectangle is bounded by the x-axis and the parabola y = 8- x2. What length and width should the…

A: In the question it is asked to calculate the dimensions of rectangle for which the area of rectangle…

Q: There is a line through the origin that divides the region bounded by the parabola y=8x−4x2y=8x-4x2…

A:

Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 8 –…

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Q: A cylindrical can is to be made to hold 1000cm^3 of oil. How do you find the dimensions that will…

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Q: What is the average distance between the parabola y = 10x(22 - x) and the x-axis on the interval…

A: From the average of a curve to x axis in an interval.

Q: Find the minimum distance from the parabola x-y2=0 to the point (0,3)(0,3).

A: Given data:   The given expression for the parabola is x-y2=0. The given point is (x1, y1)=(0,3).…

Q: 1. A closed box, with a rectangular base, whose length is twice its width, is to have a surface of…

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Q: A storage box with a square base must have a volume of 90 cubic centimeters. The top and bottom cost…

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Q: A cylindrical can is to be made to hold 2200 cubic inches of oil. Find the radius and height of the…

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Q: A storage box with a square base must have a volume of 90 cubic centimeters. The top and bottom cost…

A:

Q: A picture frame has its length 8 cm longer than its width. It has an inner 1-cm boundary such that a…

A: Consider the figure below. Assume the length of the frame be l cm and width of the frame be w cm.…