A rectangle is inscribed in a parabola y²=8x with one of its vertical side passes through the point (6,0). Find its maximum area?

Q: There is a line through the origin that divides the region bounded by the parabola y = 6x x-axis…

A: We will find the slope

Q: There is a line through the origin that divides the region bounded by the parabola y = 7x X-axis…

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: There is a line through the origin that divides the region bounded by the parabola y=4x−6x2y=4x-6x2…

A:

Q: A machinist in an engineering machine shop has ordered a sheet of plastic with dimensions of 5 m × 6…

A: Dimensions of plastic sheet = 5m×6m×50mm            Dimensions of door  = 3m×4m where Length of…

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

A: Answer

Q: What is the maximum vertical distance between the line y = x + 6 and the parabola y x2 for -2 < x<…

A:

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: There is a line through the origin that divides the region bounded by the parabola y = 7x – 3? and…

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

Q: Find the orthogonal trajectories of family of hyperbola with center at the original and the length…

A:

Q: A rectangle is bounded by the x-axis and the parabola y=9-x². What length and width should the…

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

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

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Q: (c) cut from each corner of length x cm, a maximum volume for the resulting open-top cake tin will…

A:

Q: What is the maximum vertical distance between the line y =x +2and the parabola y =x2 for     -1 ≤ x…

A:

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: The slope of the tangent line to the parabola y=4x2+2x+6y=4x2+2x+6 at the point (-3,36) is: ?

A:

Q: What is the maximum vertical distance between the line  y = x + 30  and the parabola  y = x2 for…

A: Definition used -                  Vertical distance is given by -…

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

A:

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

A: we have been given the parabola y=3x-4x2 to find the points put 3x-4x2=0⇒x(3-4x)=0⇒x=0, 34…

Q: There is a line through the origin that divides the region bounded by the parabola y = 4x - 5x² and…

A: Given that equation of parabola y=4x-5x2let ,equation of line y=mx   where slope=m which is devide…

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 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: Find the largest possible area of an isosceles triangle with two vertices in the curve y=4-x^2 and…

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Q: Find the orthogonal trajectories of the family of parabolas through origin and foci on axis.

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

A: Shown below

Q: There is a line through the origin that divides the region bounded by the parabola y = 5x – 7x² and…

A:

Q: There is a line through the origin that divides the region bounded by the parabola y = 2x – 3x2 and…

A: According to company rule, we can answer only first question and rest can be reposted.

Q: What is the maximum vertical distance between the line y = x + 2 and the parabola y = x2 for -1 <x<…

A:

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

A:

Q: what is the minimum vertical distance between parabolas y = x2 + 4 and y = x -x2

A: Given: The equations of two parabolas are: y1=x2+4 y2=x-x2 We have to find the minimum vertical…

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

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Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 1 –…

A:

Q: The size of the rectangle that can be made from 200 cm long wire so that the area is maximum is ….

A: We have to find the maximum area of given rectangle.

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

A:

Q: The semi-hyperbola H(X)=(sqrt(x^2-1)) is continous at which x interval?

A:

Q: There is a line through the origin that divides the region bounded by the parabola y = 7x- 3x2 and…

A: Given the parabola : y=7x-3x2Let the line through the origin be : y=mx   , where m is the slope of…

Q: There is a line through the origin that divides the region bounded by the parabola y=8x−6x2 and the…

A:

Q: A rectangle is inscribed with ts base on the z-axis and its upper comers on the parabola y= 12-r Fre…

A:

Q: What is the average distance between the parabola y = 7x(16-x) and the x-axis on the interval…

A:

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

A: Given data: The given equation of the parabola is y=8-x2. The below figure shows a rectangle is…

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: A long suspension bridge 180 meters from end,has towers 60 meters tall,where suspension cables are…

A: Given : from the data given above  the graph of the parabola is:

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: A rancher has 400 feet of fencing with which to enclose two adjacent rectangular corrals. What…

A:

Q: There is a line through the origin that divides the region bounded by the parabola y = 2x-6x and the…

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Q: Find the parabola y = ax2 + bx + c that passes through (2,1) and be tangent to the line y = 2x + 4…

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Q: What is the average distancebetween the parabola y = 30x(20 - x) and the x-axis on theinterval [0,…

A: The equation of parabola is given by y=30x20-x on [0, 20] The expression to evaluate the average of…

Q: What is the maximum vertical distance between the line y = x + 6 and the parabola y = x< for -2 <x<…

A: To Find

Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.