A rectangle is bounded by the x and y axes and the graph of y= (6-x)/2 (see figure). What length and width should therectangle have so that its area is a maximum? (x, y)

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A: Let say that(a,b,c) is point in plane 4x+3y+z=12 and it is one vertex of requested rectanglar box.…

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Q: A rectangle is to be inscribed inside a circle of radius 1. Find the dimensions of the rectangle…

A: Given : Radius of the rectangle inscribed in a circle = 1

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

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: A sheet of cardboard 16 in. square is used to make an open box by cutting squares of equal size from…

A: Given, a sheet of cardboard 16 in. square is used to make an open box by          cutting squares of…

Q: A waterway in a theme park has a semicircular cross section with diameter 11 ft. The boats that are…

A: Consider the figure for the water way and the boat. The circumference of the boat is the equation of…

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: A box with a square base and open top must have a volume of 32 000 cm³. Find th dimensions of the…

A: Given: The Volume of square box =32000cm3 To find its dimention

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 right triangle is formed in the first auadrant by the x- and y- axes and a line through the point.…

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Q: A rectangular sheet of metal having dimensions 20cm by 12cm has squares removed from each of the…

A: A rectangular sheet of metal having dimensions 20cm by 12cm has squares removed from each of the…

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

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Q: The area of region bounded by the parabola y2 = 4x and the line %3D y = 2x – 4 is

A: We have to find the area of the region bounded by the parabola y2=4x and the line y=2x-4 .

Q: The area bounded by the parabola y = 4x2, y-axis and the lines y = 1, y = 4 is

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Q: We want to construct a box with a square base and we only have 10 m² of material to use in…

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Q: Calculate the total area of the semiregular polyhedron of the image knowing that its edge is a.…

A: We can find the answer as below.

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

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Q: All boxes with a square​ base, an open​ top, and a volume of 200ft^3 have a surface area given by…

A: We differentiate S(x) with respect to x. S(x)=x2+800xS(x)=x2+800x-1S(x)=2x-800x-2S'(x)=2x-800x2

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…

Q: A rectangle is constructed with its base on the diameter of a semicircle with radius 30 and with its…

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Q: The diagram on the side show a cross-section of hollow shaft. Determine the maximum volume of h…

A: Lagrange's multiplier method can be used to calculate the maximum or minimum value of the function…

Q: A rectangle is bounded by the x-axis and the semicircle y=sqrt(81-x^2) what length and width should…

A: Given that A rectangle is bounded by the x-axis and the semicircle y=sqrt(81-x^2) To find what…

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Q: The base of a three-dimensional figure is bound by the graph x = y3 on the interval [1, 2]. Vertical…

A: answer is in next step.

Q: (1 point) A closed rectangular box has volume 26 cm³. What are the lengths of the edges giving the…

A: let length x and width y  and height z of the box the total surface Area S=2xy+xz+yz  -----(1) Given…

Q: Find the maximum area of the largest rectangle that can be inscribed in the region bounded as shown…

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Q: A rectangle is constructed with its base on the diameter of a semicircle with radius 21 and with…

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Q: perimeter of the region bounded

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Q: A rectangle has one corner at the point (0,0), a second corner on the posit below. What is the…

A: Let the length of the rectangle be "y" and breadth be "x". The expression for the area of the…

Q: Find the dimensions of a rectangular box of maximum volume such that the sum of the lengths of its…

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Q: A closed rectangular box with faces parallel to the coordinate planes has one bottom corner at the…

A: Let x , y, z donate  the length, width and the height of the rectangular box.  Volume of the box is…

Q: A rectangular box has three of its faces on the coordinate planes and one vertex in the first octant…

A: Given,The box's volume is  V = xyz  but we know that   z = 4 − x2 − y2V = xyz    = xy ( 4 − x2 − y2…

Q: An Inscribed rectangle Is bounded by the x - axls and the semicircle y =V25-x2. What length and with…

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Q: |An open storage bin with a square base and vertical sides is to be constructed from a given amount…

A: According to the question, Let the length, breadth and depth of the open tank be x, x and y,…

Q: Sketch the region in the xy-plane defined by the inequalities x- 5y 2 0, 2 - x - 9lyl 20 and find…

A: Graph of the curves÷

Q: Two factories are located at the coordinates (−x, 0) and (x, 0), and their power supply is at (0,…

A: To Determine: Find y such that the total length of power line from the power supply to the factories…

Q: An open top box is to be made from 48 m of wood with dimensions x, y and z as shown in figure. Using…

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

Q: The area bounded by the parabola x² = 2y, and the line x - y = -4 is 18 square units. %3D

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Q: As a hardworking student, plagued by too much homework, you spend all night doing math homework. By…

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Q: here having a radius of 3cm. is cut in the shape of a circular cone of maximum volume. is the…

A: Topic:- application of derivatives

Q: Find b such that the line y = b divides the region bounded by the graphs of the equations into two…

A: Given: y = 9 - x2,  y = 0 To find: The value of b such that the line y = b divides the region…

Q: An Architect Plans To Build A Triangular Enclosure With A Fence On Two Sides And A Wall On The Third…

A: The given triangle is sketched below.

Q: A rectangular  box has a square base with edges at least 10cm long.  It has no top, and the total…

A: Given: let's side of base of rectangular box is x+10cm, x+10cm and height is h cm

Q: An architect plans to build a triangular enclosure with a fence on two sides and a wall on the third…

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Q: The area of the region bounded by x = /9- y2, the y-axi first quadrant is:

A: Here we have to find the area bounded by the region x=9-y2 .....................(1), the y-axis, and…

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.…

Q: Find the length L and width W (with W < L) of the rectangle with perimeter 72 that has maximum ar L…

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Q: Find the area of a triangle bounded by the yy-axis, the line f(x)=10−2xf(x)=10−2x, and the line…

A: Now, from the graph we have the points of intersection of the lines