Find the number b such that the line y = b divides the region bounded by the graphs of y = 9x2 and y = 16 into two regions with equal area.

Q: What is the maximum vertical distance between the line y = x + 30 and the parabola y = x2 for -5 s x…

A: given, equation of line is y = x + 30 and equation of parabola is  we have to find maximum vertical…

Q: The area of the region bounded by the two curves y = x²and y 25 is Square Units

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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: What is the area of the largest rectangle that can be drawn with one side along the x-axis and the…

A: given curve is y=e-x2 find the largest area of a rectangle which has one side along the x-axis and…

Q: Find the aren of the region in the tirst quadrant baunded by the line y=27, e the line X-4, the…

A: We first sketch the region using a graphing calculator.

Q: Find b such that the line y = b divides the region bounded by the graphs of the y = 9 − |x| and y =…

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Q: What is the area (in square units) of the region bounded by the graphs of y=r²+2, and the x axis…

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Q: The area of the region bounded by the two curves y = x and y = 64 is Square Units

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Q: The region between the graphs of y = x² and y = 3x is rotated around the line x = 3.

A: Given data:   The expression first curve is: y=x2. The expression for the second curve is: y=3x. The…

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: Find a vertical line x=k that divides the area enclosed by y=x^2, x=2, and y=0 into two equal parts.

A: Given,

Q: over the triangular region Cut from the * quadrant by the line x+y =1.

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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: Given,

Q: 5. Consider the two curves y = x° - 3x + 20x + 88x² + 71x – 74 and y = 2a+ 50x – 22x + 42.x + 31. |…

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Q: Find the total area of the shaded region (area constrained by curves) y = -2r4 -2

A: The area of the shaded region is given by  ∫abf(x)-g(x)dx Where a and b are limits of x f(x) and…

Q: Find the number 6 such that the line y = 6 divides the region bounded by the curves y = x2 and y =…

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Q: The area bounded by the curve y = 6x and the lines x = 9 ,x = 11 and x %3| axis is - O 486 square…

A: Consider the curves, y=6x,  x=9,  x=11   and   x-axis To draw the bounded region:

Q: Find the areas of the regions enclosed by the curves x3 - y = 0 and 3x2 - y = 4

A: The given curves are x3-y=0   and  3x2-y=4. Rewrite the above equations as  y=x3  and  y=3x2-4. Now…

Q: What is the area of ​​the region between the parabola y=x^2-1 and the line y+2x=2?

A: The solution is given below in the next step:

Q: The area bounded by the curve y = 10x and the lines z = 7,x = 11 and a – axis is O 850 square units…

A: Given y=10x,x=7,x=11 and x-axis  Area= integral a to b f(x) dx  Let y=f(x)=10x then find area…

Q: Find the area of the region bounded by f(x) =|x^2−5x+ 6|, the x-axis, and the lines x=1 and x= 4.

A:

Q: Sketch the region in the xy  -plane defined by the equation or inequalities. -1 <=y<=3

A: -1≤y≤3

Q: The region in the first quadrant bounded above by the line y = 6, below by the curve y = √6x, and on…

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Q: Find the area bounded by the curve x = y² + 2y and the line  x = 3.

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Q: y = -a(x – h)? +k (-2.1 , 2.9) (1,n)

A: The given curve is y=-ax-h2+k. Here h=-1 and k=11 given. So the curves becomes y=-ax+12+11. Also the…

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: 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: The area of the region bounded by the curves y = 4x? 3 22 and the lines æ = 1 and x = 5 and y is

A: Here is the solution of the given problem

Q: Find the area of the region bounded by the  graph y=2x2-3x+2 the x axis and the vertical lines x=0…

A:

Q: Find the total area of the regions enclosed by the two curves y = 4-x2 and y = -x+2 %3D and the two…

A: The given curves are: y=4-x2, y=-x+2 and the lines x=-2, x=3

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

A:

Q: Find the area enclosed between the x-axis, the curve y= (x-15)(7-x)(x+12) and the lines x=-12 and…

A: We have to find the area enclosed between the x-axis, the curve y=(x-15)(7-x)(x+12) and the lines…

Q: The area of the region enclosed by the parabola y =2 -X and the line y = - xis equal to:

A: Given that that a parabolic equation and a line equation y = -x. And we find area enclosed by…

Q: Find the area of the region bounded by y=2x2-3x+2 the x-axis and the vertical lines x=0 and  x=2

A:

Q: Find the area of the region enclosed by parabola y=3-x2 and the line  Y=3-2x

A: We have to find the area of the region enclosed by parabola y=3-x2 and the line y=3-2x. The point of…

Q: The area bounded by the parabola x² = 2y, and the line x - y = -4 is 18 square units. %3D

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Q: Consider the region bounded by the function y = 4x, and the lines x = 0 and x = 3. Then the area of…

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Q: Find a horizontal line y = k that divides the area between y = x² and y = 9 into two equal parts.

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Q: Find the equation of a horizontal line that equally cuts the area bounded by the curves 2y=x^2 and…

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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 the area of the region in the first quadrant bounded by the circle (x - 1)² + y² = 1, and the…

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Q: Find the area of the region bounded by the graph of y = 2x2 − 3x + 2 the x-axis, and the vertical…

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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: Sketch the region and find the area of the region bounded by y = 3x + 1, the lines x = 1 and x = 4,…

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Q: The region is bounded by the curve y = 6x – x² and y = x² – 2x – 10

A:

Q: Find the area of the region bounded by the parabola y2 = 2x-2 and the line y = x-5 using (a)…

A: We will find out the required area.

Q: The region shown below is bounded by the curve y = 2x3 and the lines x = 8 and y = 3.

A: Given y=2x13 and lines x=8 and y=3. ax=y38when x=8⇒y=4 when y=3 ⇒x=278 By washer method,…

Q: Find the area of a triangle bounded by the yy-axis, the line f(x)=10−2xf(x)=10−2x, and the line…

A: Now, from the graph we have the points of intersection of the lines

Q: The area of the region enclosed by the parabola y =2-x and the line y = – xis equal to:

A: