|35. Find the maximum area of a rectangle inscribed in the region bounded by the graph of y | (Figure 20). and the axes 2+x y = FIGURE 20

Q: 1. Find the area bounded by the parabola y=4ax, the x-axis, and the lines x=4a, x=9a.

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Q: Find the area of the region bounded by the parabola y² = 2x - 2 and the line y = x - 5. 16 17 18 19…

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Q: Sketch the region in the xy-plane defined by the equation or inequalities. (a) -1sys3 (b) |지 < 4 and…

A: Since we only answer up to three sub parts. We’ll answer the first three. Please resubmit the…

Q: D={(1,y) | + 등아 < 6}. 25

A: Use lagarange multipliers

Q: Consider the region bounded by the graph of y = 4x + 3, the x-axis, and the lines x = 2, x = 7. A…

A: Given area bounded by the curve y=4x+3, x-axis and the lines x=2, x=7

Q: The area bounded by the curve y = 4x and the lines a = 4 and a = 6 above the a - axis is_ O 208.00…

A: Here we use washer's method to find the area between given curves. The answer is given as follows:

Q: find the are bounded by the given curves y^2=2ax,y^2=4ax-a^2

A: The two equations represent parabolas. First both parabolas will have origin as vertices. The region…

Q: Find the extreme values of f on the region described by the inequality. f(x, y) = 2x2 + 3y2 - 4x -…

A: we use langrange multiplier method

Q: A new auditorium is built with a foundation in the shape of one-fourth of a circle of radius 50…

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Q: Find the extreme values of f on the region described by the inequality. f{x, y) = e-Xy; x2 + 4y2 < 1

A: We will lagrange's multiplier here

Q: Consider the accompanying graphs of y = 2x + 3 and y = In x. Determine the %3D a. minimum vertical…

A: (a) Given information:

Q: Find the values of such that the area of the regionbounded by the parabolas  y  = x 2 - C 2  and…

A: given : the two parabolas are: y=x2-C2y=C2-x2 the area bounded by the parabolas is 576.

Q: A new auditorium is built with a foundation in the shape of one-fourth of a circle of radius 50…

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Q: EXAMPLE 2 Find the area of the region R enclosed by the parabola y = x² and the line y = x+ 2.

A: We have to find area

Q: In the given question  find b such that the line y b divides the region bounded by the graphs of the…

A: Given :           Equation of curves as :                  y = 9 - x , y = 0 Formula :           A =…

Q: Find the maximum value of f(x, y) = 4x + 6y subject to being on the circle = 13. 5. x² + y

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Q: Find the region bounded by the parabola x = y - 8 and the line y = x - 12. O 163.5 121.5 103.5…

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Q: Find 3 numbers x, y, and z such that their sum is 32 and P=xy^2z is a maximum.

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Q: 3 Find the area bounded by the curve y= -x3x2+3x and the line y=x. 16 O 16 square units O 8 square…

A: Please follow the next step.

Q: Find the area of a triangle bounded by the y axis, the line f(x) = 5 - r, and the line perpendicular…

A: Triangle bounded by the y-axis, the line f(x)=5-(x/7) , and the line perpendicular to f(x) which…

Q: Find the area of a triangle bounded by the y axis, the line f(z) 1 z, and the line perpendicular to…

A: Area of triangle = (1/2)*base*height

Q: Let r be the region in the first quadrant bounded by the graphs of y=x^3 and y=4x

A: Find the region in the first quadrant bounded by the graphs

Q: Find the area bounded by the graph y = 30x − 3x^2 and the x-axis (18A) 2,000 (18B) 250 (18C) 500…

A: Area bounded by curve f(x) A=integration a to b f(x) dx

Q: Show that the maximum value of f (x, y) = x 2 y3 on the unit circle is

A: We should maximize f(x,y)=x2y3 under the constraint gx,y=x2+y2 where x2+y2=1. Now, ∇f=2xy3,…

Q: Area of the region under the graphs? Integral related question

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Q: Find c 0 such that the area of the region enclosed by the parabolas y- x- c and y = c-a2 is 100.

A: Given the region enclosed by the curve y=x2-c2 and y=c2-x2 To find the value of c such that area of…

Q: The area bounded by the curve y = 3x and the lines x = 4 and x = 6 above the x - axis is O 30.00…

A: Given that y=3x at x=4 and x=6  find out area bounded by the curve

Q: The area of the finite region enclosed by the curve xy = 4, the x-axis and the ordinates x= 2 and x…

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Q: The area under the curve y = 5x bounded by the lines a = 3 and æ = 6 above the a – axis is_ 225.00…

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Q: Consider the following functions. f(y) = y2 + 5 g(y) = 0 y = -1 y = 2 Sketch and shade the region…

A: We have to first sketch the given region.

Q: Sketch and shade the region bounded by the graphs of X = y? +1 and x + 2y = 4 and find the area of…

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Q: Find each of the two areas bounded by the curve y = x³ – 4x and y = x² + 2x. Solve in two ways.

A: Given curves are, and Comparing both,

Q: y = x2-4r + 5 y y=x +5

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Q: Figure 4.6 shows the curves y = Vx, x= 9, y = 0, and a rectangle with its sides parallel to the axes…

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Q: The area bounded by the curve y = 2x – x² and the %3D ordinates x = 0; a = 4 is: 14 sq. units - 3.…

A: area between curves

Q: A new auditorium is built with a foundation in the shape of one-fourth of a circle of radius 50…

A: It is given that radius of circle is 50 feet.  The equation of the region is x2+y2=502; x≥0 and y≥0.…

Q: Evaluate fxydxdy over the region bounded by x axis, ordinate x =2 and the curvey2 = 4y O A. 3 O B.…

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Q: Use a change of variables to find the area of the curved rectangle above the x-axis bounded by…

A: Given,Area bounded by:y24-1≤x≤4-y216 , y264-16≤x≤9-y236 , x≥0

Q: The area bounded by the curve y 3x and the lines x = 4 and x = 36 above the x – axis - is O 3888.00…

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Q: Find the absolute maximum of f(x,y) = 9x²y² + 4y2 + 4x² bounded by y = x, y = 0 anC Answer:

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Q: Consider the following equations. f(y) = y2 g(y) = y + 2 Sketch and shade the region bounded by the…

A: We have to find the area of the enclosed portion.

Q: The area bounded by the curve Y 4x and the lines x 6 and a 14 above the x axis is O 640.00 square…

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Q: (b) Find the areas of the regions enclosed by the line Y=* and curve y=x-3x

A: Given: Curves y=x and y=x2-3x Definition: The area between curve f(x)≥g(x) on the interval [a, b] is…

Q: Find the value of c > 0 such that the area of the region bounded by the parabolas x² - c and c2 -x²…

A: Sketch the region and integrate in x variable.

Q: graph and find the area of the loop bounded by the curve a^3y^2 = x^2 (a-x)^3

A: The given curve is a3y2=x2a-x3y2=x2a-x3a3y=x2a-x3a3y=xaaa-x3 The graph is shown below.

Q: The area under the curve y = 8x bounded by the lines a = 4 and a = 9 above the a – axis is_ 648.00…

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Q: Consider the following equations. 4 f(x) = y = 0 X = -3 X = -1 Sketch the region bounded by the…

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Q: Find the area of a triangle bounded by the y axis, the line f(x) = 3 – z, and the line perpendicular…

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