Find the largest area possible for a rectangle inscribed between the parabola y = 9 – x² and the x- axis, with its base on the x-axis.

Q: Suppose that 208 ft of fencing are used to enclose a corral in the shape of a rectangle with a…

A: Given:  208 ft of fencing is used to enclose a coral From given figure diameter of the semicircle is…

Q: What is the length of the latus rectum (LR) of the parabola y = -÷(x – 2)“ + 5?

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Q: Farmer Jones and his wife, Dr. Jones, decide to build a fence on their farm. Because Dr. Jones is a…

A: Follow the procedure given below.

Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 12 –…

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Q: A rectangle is bounded by the x-axis and a parabola defined by y = 4 – x. What are the dimensions of…

A: Given that, a rectangle is bounded by the x-axis and a parabola defined by y = 4 - x2. The area of…

Q: Find the volume of the largest rectangular box in the first octant with three faces in the…

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Q: 19. Find the area of the largest rectangle with lower base on the x- axis and upper vertices on the…

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Q: Find the length L and W (with W(less than or equal to) L) of the rectangle with perimeter 48 that…

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Q: Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other…

A: We need to find length and width.

Q: 19. Find the total area between the parabola y = x² - 4x, the x-axis, and the ordinates x = -2 and x…

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Q: .כ Find the ared of a parabola which is inscribed in a rectangle 40 cm long and 25 cm wide.

A: We know are of parabola is( 2/3) ×b×h Where b is base of parabola and h is height of parabola.

Q: 19. Find the total area between the parabola y = x2 - 4x, the x-axis, and the ordinates x = -2 and x…

A: We can use integration to calculate the area

Q: A rectangle is inscribed in the parabola y=8– x - such that one side lies on the x-axis and two…

A: Answer

Q: Find the area of the s and the parabola

A: Given curves are: x2+y2=2xy2=x Then the points of intersection of the above curves are obtained…

Q: A rectangle has its two lower corners on the x-axis and its two upper corners on the parabola y = 7…

A: here the width of the rectangle is  w=2x and the right is l=7-x2

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

A:

Q: Find the area of the largest rectangle with sides parallel to the coordinate axis which can be…

A: Draw the curves using tools or by hand.

Q: What is the maximum area of a rectangle that is above the X- axis and below the graph of the…

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Q: Find the area of the largest rectangle with the lower base on the X-axis and the upper vertices on…

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Q: Suppose that 202 ft of fencing are used to enclose a corral in the shape of a rectangle with a…

A: Given that 202 ft of fencing are used to enclose a corral in the shape of a rectangle with a…

Q: An open-top box is to be made by cutting congruent squares of side length x from the cor- ners of a…

A: The box is in the shape of cuboid whose sides are x , 20-2x and 25-2x

Q: Find the shorted distance from the point A(2, to a point on the parabola y = x². And find the point…

A: Let (x,y) = (x,x2) point on the parabola is closest to A Distance between (2 , 1/2) and (x,x2) is:…

Q: The area bounded by the parabola y2 = 4ax, its axis, and its latus rectum revolves  about the x-

A: The given equation of parabola is y2=4ax. The objective is to calculate the area bounded by the…

Q: Given the point P =,(a,b) in the first quadrant, find the downward-opening parabola that passes…

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Q: the maximum area for the rectangular whic

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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 area of the ellipse given that the length of the semi-major axis of 99 and the length of…

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Q: Find the two values of c such that the area of the region enclosed by the parabolas y = x² – c² and…

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Q: Let f (x) = 1x² +6x+8. Find the x-coordinate for the parabola's vertex. Round your answer to the…

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Q: A trough with trapezoidal cross sections is formed by turning up the edges of a 30-inch-wide sheet…

A:

Q: A rectangle has its base on the x-axis and its upper two vertices on the parabola y=6-x² What is the…

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Q: Find the vertex, focus and endpoints of the latus rectum of the parabola  4y^2 - x + 2 y = 0

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Q: What is the largest possible area of a rectangle inscribed in the region bounded by the parabola y =…

A: According to the figure, we have

Q: Suppose that 465 ft of fencing are used to enclose a corral in the shape of a rectangle with a…

A: We are given that 465 ft of fencing is used to enclose a corral in the shape of a rectangle with a…

Q: Show the figure or model of a rectangular object 25 m wide is to pass under a parabolic arch that…

A: given that Parabolic arch has a width 32m at the base and height 24m at the center Vertex of…

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

A: first we have to draw the sketch of y = 1-x2 and draw a rectangle beneath it From the graph we can…

Q: 2. Find the dimensions of the rectangle of largest area that has its base of the x-axis and its…

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Q: The maximum area of the parabola inscribed in a right circular cone having a diameter of 24cm is…

A: Figure of right circular cone and inscribed parabola.

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

A:

Q: A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 10 –…

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Q: Find the area of the enclosed by the parabola y=x2-8x+15 and the x-axis .

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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: A spotlight is made by placing a strong light bulb inside a reflective paraboloid formed by rotating…

A: Let's find how far from the vertex should the bulb be placed.

Q: The area of the parabola x^2=4y-4 cut through its latus rectum is revolved about the horizontal line…

A:

Q: Find the volume of the reqion bauoded the parabolalde2=4-x2-42 3 below the parabolaid aboue by

A: We need to find the volume of the region bounded above by the paraboloid above z = 4 - x2 - y2 and…

Q: The area of the region to the left of the parabola x=2y^2, to the right of the y-axis, and between…

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Q: How long is the latus rectum of the parabola y? + 3x – 12 = 0? O 12 O 6 4 O 3

A: The given parabola is: y2+3x-12=0

Q: A rectangle has its base on the x-axis and its upper two vertices on the parabola y = 12 - x2. What…

A: First draw the situation roughly

Q: Find the dimensions of the rectangle, with the largest possible area, enclosed in the semicircle, y…

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.