Show that the area of the plane region bounded by the curves,  x - y =7   and    x= 2y² - y + 3    is 9 square units

Q: b) The region is between the curves y horizontal line y = 1. i, y = 1 and x = 0, above the x4 ,

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Q: For numbers 1-2, consider a plane bounded by the curves y=9-x² and y=x+3. 1. What is the desired…

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Q: Find the area of the “triangular” region in the xy-plane that is bounded on the right by the…

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Q: Find the areas of the regions enclosed by the lines and curves x = 2y2, x = 0, and y = 3

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Q: Find the number b such that the line y = b divides the region bounded by the curves y = 16x2 and y =…

A: It is given that, y=16x2y=9   Area under the bounded region can be calculated by using,…

Q: у%3D 2х — х", у%3D 2х — 4х -

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Q: Find the area of the plane region bounded by y = x2 - 4x and y = x(2 - x)

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Q: Find the area of the region bounded by the hyperbola 9x2 – 4y2 = 36 and the line x = 3. %3D

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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: What is the total length of the curve of intersection of the surfaces x2 + y2 + z2 = 4 and y2 + 2z2…

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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: Calculate the area of the plane region bounded by the function Y=X²-4X +5, and the line that passes…

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Q: Find the area of the region bounded by the curve y = Vz – 1, the y-axis and the lines y = 1 and y =…

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Q: Find the number  b such that the line  y = b divides theregion bounded by the curves y = x 2  and y…

A: Given Data The equation of curve is y=x2. The equation of line is y=4. The equation of another line…

Q: The area of the region bounded by the two curves y=z' and y 64 is %3D Square Units

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Q: Find the number a such that the line x = a divides the region bounded by the curves y = x, y = 0,…

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Q: A region in the xy-plane is bounded by y = 2x + 2, X = y + 2, y = -2, 2 y = 2. and

A: Given curves are y=2x+2 and x=y22+2 The limits are y=-2 and y=2 We isolate x from the first curve,…

Q: Find the area bounded by the curve 4 square units 10 square units 8 square units 16 square units 3 y…

A: Area

Q: Find the area of the region in the plane bounded by the circles x2+y2  = 1, x2 + y2 = 2 and the…

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Q: Find a horizontal line y = k that divides the area between y = x and y = 4 into two equal parts.

A: Solution:Given     y=x and y=4T o find a horizontal line y = k that divides the area between y = x…

Q: Find the lateral surface area of the cone generated by revolving the line segment 5x-8y+40=0 about…

A: Find lateral surface area.

Q: Find the exact area of surface obtained by rotating the curve about the x-axis. y=sqrt(5-x)    3<…

A: Given curve is y=5-xdydx=-125-x Now, area of the surface obtained by revolving y=f(x) from x=a to…

Q: Find the surface area of the portion of the half ball with radius a which cuts off by the cylinder…

A: The equation of a ball with radius a is x2+y2+z2=a2. The surface area of the function z=fx,y over…

Q: Find the area of the region cut from the plane x+4y+8z=9 by the cylinder whose walls are x=y2 and…

A: Given, x+4y+8z=9 x=y² x=18−y² Therefore, The surface is  f=0 with f= x+4y+8z-9

Q: Find the area of the region bounded by the curve y2=4x and the lines x = 1 and x = 4. 24 square…

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Q: Find the area of the surface. The portion of the plane y + z = 4 that lies above the region cut from…

A: Given:

Q: Find the area bounded by the following:   A parabolic curve whose vertex is at P(1,4) and its latus…

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Q: The region is bounded by the curves y = x² and y = 4x - x² and is rotated about the line X = 4. %3D…

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Q: Find the number b such that the line y = b divides the region bounded by the curves y = 9x² and y =…

A: Given, The curves are y =9x2 y =25 y = b Let's draw the curve y =25 and y = b are straight lines…

Q: Calculate the surface area of the surface given by z=x^2+y^2 over the region 0<x<2 and 0<y<min(x,…

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Q: How many square units is the area of the region bounded by the two curves y = x^2 - 4x and y = x^3 -…

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Q: Sketch the region and find its area. 36 and y 1 9+x2 The region bounded by y= -

A: Given     y=369+x2,  y=1

Q: Find the number b such that the line y = b divides the region bounded by the curves y = 25x2 and y =…

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Q: Find the area of the region bounded by the parabola x^2 + y + 4 = 0 and the line y = −8 by taking…

A: Find the area of the region bounded by the parabola x^2 + y + 4 = 0 and the line y = −8 by taking…

Q: Find the area of the triangular region in the first quadrant bounded on the left by the y axis and…

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Q: What is the solid formed when the area bounded by

A: Given: 2x+y=2 The  coordinate axis is revolved about the y axis. To find: What is the solid form.

Q: Find the area of the region bounded by the curve y^2 = 4x and the lines x = 1 and x = 4.

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Q: Find the Area of a Surface of Revolution. y=1/3(x3), [0,3]

A: Given, y=13x3   interval :0,3

Q: Show that the area of the plane region bounded by the curves,  x=y^2 -1,  x= 1 - y^2  is 8/3 square…

A: Given equation of cyrves, x=f(y)=y2-1,x=g(y)=1-y2

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

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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: Find the area of the region bounded by the curves y^2= 2px, y^2= 2qx, x^2= 2ry, x^2=2sy (0<p<9, 0<r…

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Q: ola y  x  x2 and the x-axis. Find the equation of the line y  mx that divides this region into…

A: Let y=2x-x2 The graph of y=2x-x2 and y=mx intersect the origin and limit of x is 0 to 2

Q: region bounded by y =x1/2 , y = 0 and x = 9. Use disks or washers to find the volume generated by…

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Q: Find the volume of the solid formed when the area of the region bounded by the curves x²- 3y-5 and…

A: Solution

Q: find the are of the plane region bounded by the urves y=3x2 and y=16-x2

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Q: Find the areas of the regions enclosed by the lines and curves y = sec2 (πx/3) and y = x1/3, -1 ≤ x…

A: Given the curve  y=sec2πx3 and y=x13 and -1≤x≤1

Q: Find the area of the plane region bounded by y=-x+2 and y=x²-2x

A: The given curves are y=-x+2 and y=x2-2x. The main objective is to find the area of the plane region…