Find the points on the cone z = x² + y that are closest to the point (-3,-2,0) %3D

Q: Find c > 0 such that the area of the region enclosed by the parabolas y = x² – c and y = c² – a² is…

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Q: Use Lagrange multipliers to find the points on the cone z2 = x2 + y2 that are closest to (8, 2, 0)…

A: Given: Equation of the cone: z2 = x2 + y2 Given point: (8, 2, 0)   To find: The points on the cone…

Q: Find the area of the surface. The portion of the cone z = 4V+ y² inside the cylinder x? +y² = 16

A: Consider the provided cone z=4x2+y2 inside the cylinder x2+y2=16. Find the area of the surface. The…

Q: Find the area of the segment of a sphere formed by revolving the graph of       y = √(r2 − x2) , 0 ≤…

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Q: The axis of symmetry of the cylinder is parallel to the z-axis. х-ахis. O y-axis.

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Q: 4.) y = VT, y = 3, x = 0 around the y axis %3D

A: Given, y = x1/2, y = 3, x = 0, we have to find the volume by rotating about the y-axis.

Q: Find the point in the plane x – 2y + z = 4 that is closest to the origin.

A: Solution)                   Given                           plane  x-2y+z =4

Q: Find the points on the cone z = x+y' that are closest to the point (-2,3,0) 22

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Q: Find the areas of the shaded regions

A: The area of the shaded region of the left is:

Q: Find the area of the cap cut from the sphere x2 + y2 + z2 = 2 by the cone z = sqrt(x2 + y2).

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Q: Find the points on the surface x² + y² + z² = 4 farthest from the point (1,–1,1), 2 %D

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Q: Find the area of the portion of the paraboloid z=x^2+y^2 that lies inside the cylinder x^2+y^2=4.

A: Given that ,  paraboloid   z=x2+y2 cylinder        x2+y2=4

Q: B) Use Lagrange multipliers to find the the points on the circle a² + y? = ry has its extreme…

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Q: Convert to standard from and give the center and radius: x^2+ Y^2 - 2x +6y - 1=0

A: x-h2 +y-k2 =r2 (h , k) is centre and r is radius .

Q: FIND THE AREA OF THE SURFACE FOR THE PORTION OF THE PARABOLOID Z = 49-x² - y² IN THE FIRST OCTANT

A: Formula: The surface area of the function z=fx, y over the region D is: SA=∫∫D1+zx2+zy2 dA The given…

Q: Standardize the cone with equation 7x2+4xy+4y2-8x-12y+9=0

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Q: Evaluate [. 2y² + 4z² ds, where o is the first octant portion of a cone z = x² + y2 with height of…

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Q: Find the average height of the paraboloid z = x + y over the square 0sxs2,0sys2. The average height…

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Q: Find the area of the surface. The part of the cylinder y2 + z2 = 9that lies above the rectangle…

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Q: Graph the first-octant portion of each plane. x + y + z = 15

A: Given a Plane, x+y+z=15 We need to graph the above plane.

Q: Find the isogonal trojecdories of x*+y² =r² at 45",

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Q: PICTURE

A: We are given that the cone ax2+by2+z2 = 0 and the ellipsoid 2x2+4y2+z2 = 42 intersect and are…

Q: Find the points on the cone z = x +y? that are closest to the point (3,-2,0)

A: Solve the following

Q: Find the point on the surface x2 − 2xy + y2 − x + y = 0 closest to the point (3, 4, −5).

A: Consider the provided surface

Q: Find the area of the surface. The part of the paraboloid z = x² + y2 that lies inside the cylinder…

A: Area of the surface f(x ,y) above a region R of the xy-plane is given by…

Q: 6. Use the Lagrange multiplier method to find the points on the cone z? = x² +y² that are closest to…

A: given the constraint function z2=x2+y2. Use the Lagrange's multiplier method to find the points on…

Q: Q6/ Find the volume of the parallclogram-sided determined by: u- -3i +7j +5k, v -3i + 7j-3k, and w-…

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Q: Find the points on the cone z2 = x² + y² nearest the point P(6,8,0).

A: Here, we need to find the points on the cone z2=x2+y2 nearest the point P(6,8,0).

Q: Find the area of the cap cut from the sphere x2 + y2 + z2 = 2 by the cone z = √(x2 + y2).

A: to find the area

Q: Consider the data: 0 1 2 3 4 f(x) -4 -3 -2 5 12 a) Applying the Composite Trapezoidal Rule with all…

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Q: 2 Find the points on the cone z = x´ + y´ that are closest to the point (2,-3,0)

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Q: Find the points on the cone z2 = x² + y² that are closest to the point (-2,2,0)

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Q: 3. Find the centroid of the region bounded by the parabola y? = 4x, the y-axis, and the line y = 4.

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Q: Find the average height of the paraboloid z = x2 + y2 over the square 0<= x <= 2, 0…

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Q: Find the area of the cap cut from the paraboloid y2 + z2 = 3x by the plane x = 1.

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Q: = x² + y² that are Find the points on the cone z? closest to the point (1,-1,0)

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Q: XydA, D is the triangular region with Vertices (0,0), Cu,0], and Cor) SketchD onthe XY planel

A: 8/3

Q: Find the points on the cone z = x + y2 that are closest to the point (8, 2, 0). %3D (x, y, z) =…

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Q: ...) The figure below shows contours of g(x, y) on the region R, with 9 < x < 15 and 2 < y < 8. 7 6…

A: Consider the provided question, R=x,y| 9⩽x⩽15 and 2⩽y⩽8Using ∆x=∆y=2, break the region R into 9…

Q: Evaluate f, (2x? + 2y2) dS, where S is the portion of the cone z2 = 8x2 + 8y2 for 0szs 4V2.

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Q: Find the point on the line y = x closest to the circle of radius 1 and center (5, 2) using Lagrange…

A: First I have find the function f(x,y) and then decide the constraint.Then using Lagrange multipliers…

Q: What is the center of X x² + y² – 30x + 221 = 0? Show all work for full credit.

A: Topic = Geometry

Q: Find the point on the circle x2 + y2 = 1 that is closest to the point (1, 3/4) by using the method…

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Q: Find the points on the cone z? = x² + y² that are closest to the point (4,2,0).

A: Given :       z2 = x2 + y2  at (4 , 2 , 0)   Minimize the distance function is   f(x ,y ,z) =  (x -…

Q: Find the absolute maximum and minimum values of f(r, y) = r-3r-y+12y, closed region D, where D is…

A: Given problem:-  Find the absolute maximum and minimum values of f(x, y) = x²-3x-y³+12y, on the…

Q: Find the Võlumé of thé šólid generated by revolving the shaded region about the given axi About the…

A: Explanation: If we rotate the shaded region about the x-axis, we will get the cone shape. Height of…

Q: Find the minimum distance from the surface to the given point. (Hint: Start by minimizing the square…

A: The minimizing function is, d2=(x-8)2+y2+z2

Q: Let a = 2 and b = 3. Find (x, y ,z) the closest point from the cone z = V ax+by to the point…

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Q: Find the area of the part of the cone S = {(x, y, 2); z = Vx² + y?, x²+y² < 1}.

A: Given surface is S=x,y,z:z=x2+y2,x2+y2≤1 We have to find the area of the surface. Here, z=x2+y2…