1. Parallelogram JKLM with vertices J(-1, 8), K(5, 6), L(7, -2), and M(1, 0); scale factor: k = ½, center of dilation: (-3, -2) JL. K'L L'(L_ M' (-

Q: Find the minimum distance from the point (5, 0, 0) to the paraboloid z = x2 + y2. (Give your answer…

A: Given:    z = x2 + y2  Point: ( 5, 0, 0 )

Q: Find the value of So(4x + y)dy- xydy where C is the path around the triangle in the counterclockwise…

A: The objective is to find the value of the given integral where c is the path around the triangle in…

Q: Find the distance from the origin to the plane 2 = z - x.

A: Given point is (0,0,0) Given plane is 2=z-x or x-z+2=0

Q: 21 コミメ-2 of the with the Parabola y=z Find the hく line area region bet ween the

A: Let us consider the double integration I=∫D∫f(x,y) dxdy where  D=(x,y)|a<x<b,…

Q: Find a parameterization for the line segment joining points (0,3) and (12,0) using the angle 0 in…

A:

Q: 13) Find the points of intersecti on of the parabola and the line. y=2x^2-3x-1 and y=x+5

A: Equate the equations with each other and solve for x to find the point of intersection .

Q: Find the distance from point P(1,1,1) to the pl r +y +z = 1

A: We have to solve

Q: 5. Use traces to sketch and identify the surface x2- y? - z2 = 4.

A:

Q: B) Use Lagrange multipliers to find the points on the ellipse 2x2+y? = 1, where f (r, y) = ry has…

A:

Q: 5. Find the area and centroidal distances of the curve that lies between he equations y%3D4-x^2 and…

A: The region bounded by curves y=4-x2andy=x+2 To find the area and centroidal distances.

Q: 5) Find the distances: a. Between l, = (2 + 2t, –1+ t,–3t) and l, = (4,–5 – 3t, 1+ 4t). %3D b.…

A: Given: (a). two lines l1 and l2 (b). Two Planes (c). A point (1,2,3) and a line  To Find: (a).…

Q: 4 and Consider the region in the second and third quadrants between the circles x² + y² = x² + y² =…

A: Concept: cartesian coordinates can be converted into polar coordinates using trigonometric functions…

Q: 4. Graph the surface 1 = y² + z² – by first sketching at least three cross sections in each of the…

A: Graph the surface by using a 3D graphing calculator like desmos. Three cross sections in xy plane…

Q: Which of the given points are the points on the hyperboloid x2-y?+4z2 = 4 where the normal line is…

A: Solution is in step 2

Q: Find the distance from the point (-4, 5, 1) to the plane – kr – ly – 2 = 5.

A:

Q: By differentiating implicitly, find the slope of the hyperboloid x +y? - z = 1 in the r-direction at…

A:

Q: 5. Among all the points on the graph of z = 10 – x² – y² that lie above the plane r+2y +3z = 0, find…

A:

Q: 9. Find the point (x, y) on the line y = 2x + 3 such that the distance from (x, y) to (1, 1) is as…

A:

Q: 4. Graph the surface 1 = y² + z² by first sketching at least three cross sections in each of the 4…

A: We have to graph the surface 1=y2+z2-x24 by sketching at least three cross-sections in each of the…

Q: 3. Calculate the centroid of the given illustration below. y-axis 7.5ft- 4ft 2ft 5ft- х-ахis 2ft

A:

Q: 5. What is the maximum vertical distance between the line v1+2 and the parabolh v for

A:

Q: Part (a) Evaluate 4e*dz, where C is the polygonal path consisting of the line segments from z = 0 to…

A:

Q: Find the minimum distance from the point (2, –6, 6) to the plane 2x - y + z = 0.

A: NOTE:- the distance between a plane say px+qy+r z +s=0 and a point say u, v, w is d= p u+q v+r…

Q: - )and (,- The points of intersection between the Curves r= 3cose and r= 2- cose are: A))and (…

A: Let's find intersections points.

Q: 3 Find the Minimum distance from the origin to the plane X+2y-z=5

A:

Q: -axis. 5. Evaluate dV, where E is the solid tetrahedron with vertices at (0,0, 0), (2, 0, 0),…

A:

Q: 24) By using Lagrange multiplier find a point in the plane x+2y+3z=13 nearest to the point (1,1,1)

A: We have to find a point in the plane x+2y+3z=13 nearest to the point 1,1,1 by using Lagrange…

Q: The area bounded by the curve y= 4x and the lines r = 7,1 = 10 and x - aris is O 4900 square units O…

A: From the given curve bounded region is shown below:       So,   I=∫x=7x=10∫y=0y=4xdydx

Q: 3. Use LaGrange multipliers to find the point on the plane 2r - y+4z = 10 that is closest to the…

A: Use Lagrange method to find point

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

A:

Q: 1. Find the shortest distance from the point (1,0, –2) to the plane x+2y+z = 4.

A: We have to find shortest distance

Q: 4. Use the method of Lagrange Multipliers to find the point on the plane r+y- 2 = 5 that is closest…

A: Given: The plane equation is x+y-z=5 and the point is -3, 5, 4.

Q: | the parametric equatioin for e line segment between a7) and (3,3)

A:

Q: find the line of intersection of th e given planes. 4x+ y + z = 0 and 2x - y + 3z = 2

A:

Q: 7. C is the hexagon in the xy-plane with vertices (5, –5), (5,5), (0, 10), (–5, 5), (-5, –5), and…

A:

Q: 1) Find the distance from the point (1, 2, 3) (a) XZ plane to the (b) Z axis

A: In this question we will use basic of geometry i.e concept of 3D geometry. We will first plot the…

Q: Find the minimum distance from the point (0,0,0) to the plane 9x+4y+z=5.

A:

Q: 2. Find the area of the smaller loop of the curve r = = 3( 1- 2cose)

A: We will solve the following

Q: Part (a) Evaluate 100e dz, where C is the polygonal path consisting of the line segments from z =…

A:

Q: Find Ja xydx + sin(x)ydy, where C is the boundary of the triangle with vertices (0,0), (0, 1) and…

A: Let I is the value of given Line Integral.

Q: Use Green's Theorem to evaluate 5x*dx +xydy where C is the triangle with vertices (0,0), (1,0),…

A:

Q: Find the area of on of the triangle that can drawn between the planes Зх — бу- 2г 15 and 2x + y - 2z…

A:

Q: Find the families of characteristics of the PDE (1-x²)w„ - u,, = 0 in the elliptic and hyperbolic…

A: Pde

Q: 1. Trapezoid JKLM with vertices J(-6, 6). K(-3,7), L(-1.3), and M-8, 0): (x, y) (x+7, y-3) J'() K'…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: 6. Find the area and centroidal distances of the curve that lies between the equations y-4-x^2 and…

A:

Q: Find the minimum distance from the point (1, 1, 11) to the paraboloid given by the equation z = x² +…

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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: Consider the region in the fourth quadrant between the circles x² + y² = 4 and x² + y² = 25 and…

A: answer is in next step. please give a like !!

Q: 9. f(z) = e'n/4z %3D

A:

Q: 1 Find the points have minimum distance From the origih to the Surface xyz =1.

A: Using the lagrangian ultiplies Let For critical points,