Find the points on the surfaces x^2-yz=25 that are closest to origin

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

A: To Find: The surface area of the portion of the half ball with a radius a which cuts off by the…

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: A frustum of a cone is generated by revolving the graph of y = 2x on the interval [2, 8] about the…

A: GIVEN FRUSTUM cone generated by revolving  the graph of y=2x on interval [2,8] about x axis  we need…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis.   y = 5− x, 3 ≤…

A: To find the exact area of the surface obtained by rotating the curve about the x-axis.  y = 5− x, 3…

Q: A container with a height of 3/2 is made by rotating the curve y = 3/2x^2, Osx<1, about the axis x =…

A:

Q: What is the area bounded by the curve x² = -9y and the line y + 1 = 0?

A: Given curve is x2=-9y Line is y+1=0 We need to find the area bounded by the curve

Q: Calculate the area of the segment cut from the curve y = x(3 – x) by the line y = x.

A: here we have to find the area of the region bounded by the curve and line.

Q: You are given a y=sqrt(36-x^2) curve that rotates about the x-axis. What is the area of the…

A: To find the surface area of rotation of the below curve about the x-axis. y=36−x2

Q: Find the area between the curves. 3x х%3 -2, х%34, у%33е3X, у%3D2е 3X +1

A:

Q: Find the area of the surface formed by revolving the graph of y = 2√x on the interval [0, 9] about…

A: given that f(x)=2x . we need to find the area of the surface formed by revolving the graph y=2x on…

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: Find the area of the surface generated by revolving the curve y /2x-x, 0.25 sxs1.5, about the…

A: Use surface area formula about x asis

Q: The area bounded by the parabola y = 4x2, y-axis and the lines y = 1, y = 4 is

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Q: What is the surface area generated by revolving the parabola y = x squred from x = 0 to x = square…

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Q: Find the area of the surface formed by revolving the graph of f (x) = x³ on the interval [0,1]…

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Q: Find the area of the surface generated by revolving the curve y=x^3/18, 0(<=)x(<=) 2 square root 2,…

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Q: Find the area of the bounded region between the parabola y = 2x + 3 and the line y = x2. Sketch the…

A: A detailed solution is given below.

Q: Find area enclosed by curves y=2x, y=4x^2

A: Area enclosed by two curves is the measure of the area occupied by their intersection.

Q: Find the area of the surface generated by revolving the curve y = 2x -x² , 0.25 sxs0.75, about the…

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Q: the solid cut from the first octant by the surface z = 81-x2-y

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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 lateral (side) surface area of the cone generated by revolving the line segment y = x/2, 0…

A: The given line segment is y=x2 where 0≤x≤4. The line segment is revolved around x-axis, thus it…

Q: What is the area of the region bounded by the parabola y^2 = 2x and the line x-y-4 = 0? *

A: See the details solution in below

Q: Find the area between the curves -4x + y = 16 and -2x2 = -y+ 10.

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

A: The region is bounded by y=116x3-34x2+3x and the line y=x.

Q: Find the points on the surface y2 = 4 + xz that are closest to the origin. (Enter your answers from…

A: Consider the given surface equation y2=4+xz.  The distance d between the origin 0,0,0 and any point…

Q: Sketch the region enclosed by the curves. x + y = 3, y + 3x = 3, x - y = 0 f(x) = + 10- -8-

A: Drawing the given line.

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

A:

Q: find the areas of the surfaces generated by revolvingthe curves about the given axes. x = √4y - y2,…

A:

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: What are the new coordinates of the point (-10, 10) under the dilation (x, y) (4x, 4y)? O (40, 40) O…

A:

Q: There is a line through the origin that divides the region bounded by y = x − x^2 and the x-axis…

A: Area between curves

Q: find the area between the two curvesx=2-y^2x=y^4

A: Given thatx = 2-y2         ...(1)x = y4            ...(2)

Q: Find the exact area of surface obtained by rotating the curve about the x-axis. y=sqrt5-x   3< x <…

A: consider the equation

Q: Find the area of the surface generated by revolving the curve Y = 8/x, 2 < x < 7 around the -axis.

A: The given surface is generated by y=8x,  2≤x≤7 around the x axis. The area of the surface generated…

Q: Find the area of one side of the “winding wall” standing orthogo-nally on the curve y = x2, 0 &lt;=x…

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Q: Show that the surfaces S1 : 4x + y° + 9z² = 108 and S2 : xyz = 36 are tangent at the point (3, 6,…

A:

Q: Find the area of the surface generated by revolving the curve: y = V4 -x, -1sxs1 about x-axis.

A: The given curve is: y=4-x2,-1≤x≤1 about x-axis. The formula of surface area=∫ydx

Q: What is the area of the region bounded by the parabola y = x^2 and the line y = x?

A:

Q: Find the area of the segment of a sphere formed by revolving the graph of y = V9 - x2, 0 sxs 2,…

A: We need to find area.

Q: A frustum of a cone is generated by revolving the graph of y = 4x on the interval 32, 64 about the…

A: The surface area A=∫ab2π f(x) 1+f'(x)2dx

Q: 9. y = x', 0< x< 2

A:

Q: Find the area of the surface generated by revolving the curve y = Osxs2, about the x-axis. 9

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Q: Determine the enclosed area by the curve 9x² + 25y² - 225 = 0

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Q: = 4x y = 2x – 4

A:

Q: find the areas of the surfaces generated by revolvingthe curves about the given axes. y = x3/3, 0 ≤…

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Q: Find the area of the surface generated by revolving the curve y=2/x 18xs2, about the x-axis.

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Q: The region is bounded by the curve y = 4x – x², y = 4 and the y-axis.

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

A:

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