A quadratic equation that has a vertex of (0, 4) passes through the point (2, 7). Determine the stretch/compression factor (This is the "a" value). Show all work for complete marks

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A: According to given question we have where AB = 14 , BC = 12EF =BD = x and FD=EB = yArea of the…

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Q: A total of x feet of fencing is to form three sides of a level rectangular yard. What is the maximum…

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Q: Find the point P on the line y=2xthat is closest to the point (25,0). What is the least distance…

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Q: A quadratic equation that has a vertex or (0,4) passes through the point (2,7). Determine the…

A: Given A quadratic equation that has a vertex is (0,4)  and passes through the point (2,7)

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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…

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A: To find the dimensions to obtain minimum fencing

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A: Let x be the distance down the shore where the boat is landed. t1= time to row to the shore = 52+x23…

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

A: According to the question, we have a rectangular box and the sum of the lengths of its 12 edges is…

Q: Find the dimensions of the rectangle with max area that can be inscribed in a circle of radius 10.

A: Find the dimensions of the rectangle with max area that can be inscribed in a circle of radius 10.

Q: A rectangle is inscribed in a parabola y²=8x with one of its vertical side passes through the point…

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Q: An open box is to be made from a square piece of material, 12 inches, by cutting equal squares from…

A: Here we use the concept of APPLICATIONS OF DERIVATIVES

Q: 13. Of all numbers whose difference is 6, find the two that have the minimum product.

A: Let x and y be such numbers. x-y=6 P=xy. Substitute x=6+y in P=xy and obtain that P=y6+y=6y+y2.

Q: A rectangle is bounded by the x-axis and the semi-circle y = √(36 − x^2). What length and width…

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Q: Find the minimum distance from the point to the plane x - y + z = 9. (Hint: To simplify the…

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Q: Find the triangle whose perimeter is constant and has the largest area using Lagranges Multiplier…

A: Perimeter of triangle = Constant  Area of triangle = maximum

Q: A rectangular pen is built with one side against a bam. # 200 mof fencing are used for the other…

A: Given: A rectangular pen is built with one side against a barn.

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: Find the minimum distance from the point to the plane x - y + z = 6. (Hint: To simplify the…

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Q: A rectangular playing field is to have an area of 400 sq. meters. Fencing is required to enclose the…

A: Concept: Area of the rectangle is  A=length×width Fencing of the rectangle means covering its…

Q: A courtyard at the corner Of two buildings is to be enclosed using z = 86ft of redwood fencing. Find…

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Q: A package in the shape of a rectangular box can be sent by post as a postal order if the sum of its…

A: Solution by using Lagrange multipliers as follows :

Q: Find the simple closed curve of a given parameter which encloses a maximum area

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Q: Find the minimum distance from the point to the plane x - y + z = 5. (Hint: To simplify the…

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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: 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…

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Q: A rectangle field is formed using a building as 1 side. The other 3 sides are to be fenced with…

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Q: A box with an open top is to be constructed out of a rectangular piece of cardboard with dimensions…

A: Here, the volume of the box is given by: V=lbh Here, for the given box, l=9-2x, w=10-2x,h=x. So,…

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: When will the ball reach its maximum height? And determine the maximum height that the ball reached.

A: h=-16t2+128t+5 h=-16t2-8t+5 add and subtract 16 h=-16t2-8t+16-16+5 h=-16t2-8t+42-16+5 h=-16t-42-16+5…

Q: Determine two positive numbers whose product is 4 such that the sum of their squares is minimum.

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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 –…

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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: 3. A line of negative slope through (1, 2) cuts off a triangle in the first quadrant. For which such…

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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: 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: A rectangular tank that is 20482048 ft cubedft3 with a square base and open top is to be constructed…

A: Let w be the width and length of the square base and h be the height of the tank.

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: A farmer has 3000 m if fencing on hand. Determine the dimensions of a rectangular fencing that…

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Q: 4. Four identical bricks are stacked up on top of each other. Each has a length of a and a mass of…

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Q: A printed page is to contain 60 cm2 of printed material (not including the margins) with margins (on…

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