Let a = 2 and b = 3. Find (x, y ,z) the closest point from the cone z = V ax+by to the point (3,3,0). Write the value of x

Q: 1. Let S be the part of the cone z? = x? +y² that lies between the planes z = 1 and z = 2. Compute…

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Q: If KN=2x+1 and NJ=3x+5, what value of x makes point N the centroid? K, J M

A: (1).   If in the given triangle N is the centroid then the point N divides the line HL, JK and LM in…

Q: (7) Let D be the solid above the cone z = r and below the sphere of radius 2, and let fla, 4, 7) =…

A: To convert the cartesian coordinates into cylindrical coordinates put  And the integral will be…

Q: Evaluate x² + y? – z dS where S is the part of the cone z? = x² + y² that lies between the planes Z…

A: To evaluate :  Where , S is the part of the cone , that lies between the plane   and .…

Q: Find the points on the cone z² = x² + y² that are closest to the point (-5,4,0)

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Q: Let B be the ball with center at the origin and radius 1 SS $3(x² + y? + z²)dV = B

A: Solve integral by using Cylindrical cordinates

Q: Verify Green's theorem for F =, where C is the part of the parabola y = x², and the line y = 4 for…

A: If be a positively oriented,  closed curve  enclosing the region D Then for a vector field F→=P,Q…

Q: Suppose the temperature at the point (x, y, z) on the sphere x2 + y2 + ?2 = 16 is T= 800xy2z3 .…

A: Solution is given below:

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: Let C be the curve of intersection of the parabolic cylinder x² = 2y, and the surface 3z = xy. Find…

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Q: Find the points on the cone z2 = x² + y² that are closest to the point (1,-1,0) %3D

A: Given that, z2=x2+y2 and the point is (1, -1,0). Form the equation of distance as follows.…

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

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Q: Use Lagrange multipliers to find the points on the given surface that are closest to the origin. y2…

A: Use Lagrange multipliers to find the points on the given surface that are closest to the origin.…

Q: .2 y = z, -2 < z < 2 %3D (x - 2)² + 4y2 = 4

A: (b)  The given equation is y=z2, -2≤z≤2. Observe that y-coordinate will always be positive and…

Q: Find the equation of the tangent plane to the surface z = 4 +y? at the point (2,-3, 10) Ox+ 4y- z =…

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Q: Let a = 3 and b = 3. Find (x, y ,z) the closest point from the cone Z = V ax²+ by² to the point…

A: The cone is z=ax2+by2To find x*,y*,z*, the closest point from the cone z to the point 9,2,0The value…

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: Evaluate x2 + y? – z dS where S is the part of the cone z? = x2 + y² that lies between the planes z…

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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: W and Z are the midpoints of the legs, VX and UY, of trapezoid UVXY. If UV = p 15, WZ = p + 2, and…

A: Using mid point theorem of trepazium

Q: Verify Green's theorem for Q7 [x(x? + y²)dx – y(3x² – y²)]dy Where C is the boundary of the triangle…

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Q: Use Lagrange multipliers to find the points on the given cone that are closest to the following…

A: Given:  The equation of cone is z2=x2+y2. To determine: The points on the given cone that are…

Q: Calculate /| xz dS, where K is the part of the cone z = Va2 + y? where z < 2.

A: Given the surface

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: Let a = 3 and b = 3. Find (x, y",z") the closest point from the cone z =V ax²+ by to the point…

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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: 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: Let C be the intersection curve of the parabolic cylinder √2x2 = 2y and the surface 3z =√2xy. Find…

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Q: The region S = (x, y (x- 2) + y² < 4 is rotated about the line x = 5.

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Q: Find the points on the cone z^2=x^2+y^2 closest to the point (4, 2, 0).

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Q: Find the area of the surface when y = vx, from (4, 2) to (9, 3) is rotated about the x-axis.

A: Surface area formula for rotating about x-axis is S=∫2πydS where dS=1+dydx2dx

Q: A solld is obtained by rotating the shaded reglon about the specifled line. about the x-axis y y = V…

A: The given surface are y=x and y=20-x. The area between the two surfaces is obtained by ∬dx dy.

Q: Use Lagrange multipliers to find the points on the given surface that are closest to the origin. y2…

A: Given data:   The given expression is y2=36+xz.   The expression of the distance of a point from the…

Q: Let C be the curve of intersection of the parabolic cylinder x = 2y, and the surface 3z = xy. Find…

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Q: Find the points on the cone z = x² + y² that are closest to the point (-5,-2,0)

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Q: Given w = f(x, y, z) = 4x2 + y? + 422. Sketch the level surface of the function for w = 1. %3D 2.

A: Given that: w=f(x, y, z)=4x2+y2+4z2

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 points on the cone z = x° + y° that are closest to the point (1,-1,0) %3D +1

A: Given,

Q: ce cut from the first octant by the cylinder z = 12 – 3y, and the plane x + y = 2

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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: Determine the location of a point (x, y, z) that satisfies the condition(s). xy &gt; 0, z = −3

A: Here Our Aim is to determine the location of a point (x,y,z) that satisfiesthe condition(s):→…

Q: Let Q = 4x2 + 6xy+ 4y? . The points on the curve Q = 7 which are closest to the origin are: %3D %3D…

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Q: Verify Green's theorem for F =, where C is the part of the parabola y = x², and the line y = 4 for…

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Q: (c) Evaluate . 2y2 + 4z2 ds, where o is the first octant portion of a cone z = /x? + y? with height…

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Q: Find the points on the cone z2 = x² + y2 that are closest to the point (8, 2, 0).

A: we have given the equation of cone z2=x2+y2 and the point (8,2,0)to…

Q: Given w = f(x, y, z) = 4r + y + 4z². Sketch the level surface of the function for w = 1.

A: For the function of the form: w=fx, y, z, the level surfaces are defined using the equation, f(x, y,…

Q: Let B be the ball with center at the origin and radius 1 SS $3(x² +y? + z²)dV = 16 12m 24m :5

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