3. Determine the translation rule from the pre-image and image. a) A (3,5) A' (-1,3) T (x,y) ------------- > ( b) A (-4,11) A' (3,0) T (x,y) > L c) A (0,-8) A' (-1,-3) T (x,y) >(. d) A (8,3) A' (11,3) T (x,y)- ----- >

Q: Find the distance between the planes 5x − 3y + z = 2 and 5x − 3y + z = −3

A:

Q: 5. Write a rule for the translation of a point of the plane figure above. A. (x,y)→ (x-2,y+3) B.…

A: Translation of a point of the plane means moving all the points of that plane to a new coordinate.

Q: 2. An is a set of points (x, y) in a plane such that the sum of the distances between (x, y) and two…

A: We know that, The sum of distances to any point on the ellipse x,y from the two foci c,0 and -c,0 is…

Q: The figure below shows the expression for the x-centroid of line L. Suppose length L is 10 cm and…

A: Suppose L is the length of the line. Then, the x-coordinate of the centroid of the line is…

Q: (2) Evaluate S. 2 - xy ds where C is the upper half of the circle centered at the origin of radius 1…

A: Evaluate.

Q: 7. Sketch the surface 15zs9-x' - y² and x'+y' <1

A: To find:

Q: he transformation from Cartesian to plane coordinates in x-direction is given by x=rsine x=rcos20…

A:

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: 4. Prove that the midpoint of the line segment connect- ing the points (x 1, X 2, - . . , Xp) and…

A: The midpoint of a segment can be considered to be the average…

Q: Find the equation of the tangent plane to th surface 3x? + 5y? + 4z2 = 24 at the point (1, –1,2). 1.…

A:

Q: Determine the intersection of 3x – 4y – 5z = 0 with [x, y, z] = [3, 1, 1] + t [2, -1, 2].

A:

Q: An angle with its vertex at the origin of an xy-coordinate plane and with initial side on the…

A: We know, An angle with its vertex at the origin of an x-y-coordinate plane and with initial side on…

Q: Bounded by the coordinate planes and the plane 3x + 2y + z = 6

A:

Q: F - dr where F(x, y, z) = (4.25yz cos(xyz), 4.25xz cos(xyz), 4.25zy cos(ryz)) Evaluate п 1 and Cis…

A:

Q: This is for Calc 4, told me to post under advanced math though, please help me solve

A:

Q: Suppose ƒ(1, 2) = 4, ƒx(1, 2) = 5, and ƒy(1, 2) = -3. Find an equation of the plane tangent to the…

A: Equation of the plane tangent to the surface  z=f(x, y) at (a, b) is z=fa, b+fxa, b(x-a)+fya, b(y-b)

Q: 8) Find equations of (a) the tan gent plane and (b) the normal line to the given surface at the…

A: Tangent plane: It is defined as the plane which passes through the surface of the points or it can…

Q: The points on the surface x2−2y2−3z2 = 33 at which the tangent plane is parallel to the 8x+4y+6z=5…

A:

Q: Find the distance between the planes x + 3y – 2z = 3 and 2x - y - z = 4. %3D

A:

Q: 5. Evaluate f (x²zdx – yx²dy + 3dz) where C is the boundary of the triangle with vertices (0,0, 0),…

A:

Q: 22 Prove that the line Z=2+46 is perpendicular to thme plane X-2y+2=6

A: As per our guideline we are supposed to do 1 question at a time. Please post other questions next…

Q: A(n)________ is the collection of points in the plane the difference of whose distances from two…

A: The given statement is "A(n)________ is the collection of points in the plane the difference of…

Q: Find an equation for the tangent plane to z-x-y = 3 at the point (2, 1, 8) Z - ) %3D

A: given z-x2-y2=3 at point 2,1,8

Q: The point on the plane 2x+y+z=1 that is closest to the point (1, 2, 3) is (a, b, c). Then a+b-2c= O…

A:

Q: 1. A such that the difference in distances between (x, y) and two fixed points (called is the set of…

A: A___ is the set of points (x, y) in a plane such that the difference in distances between (x, y) and…

Q: Find the linearization L(z, y, z) of the f(x, y, z) = 2,/z° + y° + z° at the point (1, 2, 3). %3D…

A: Consider the provided function, fx,y,z=2x3+y3+z3 At the point 1,2,3 find the linearization. The…

Q: Find the distance between the given point and the given plane. Point: (−1, 4, −2) Plane: x+2y+z=3

A: We can use distance formula to calculate the distance.

Q: (2) The distance from the point (1, 2, -1) to the plane 3x - y + 2z = 6 is. (3) Consider the…

A:

Q: Let R = (c, 1,-1) where c denotes a real number. Let ä denote the plane x + y – z = 2. Find the…

A: Given Information -  The distance from the point R = (c,1,-1) to the plane x+y-z = 2 is 2. We have…

Q: ompute the line integral ∫C [2x3y2 dx + x4y dy] where C is the path that travels first from (1, 0)…

A: The line integral is given ∫C2x3y2dx+x4y dy Consider fx,y=x4y22. ddxx4y22=12·4x3y2+22x4y…

Q: Find the distance between the point (0, 0, 0) and the plane 2x + 3y + z = 12.

A:

Q: 5 – 4z Show that the reactiob w= transformation the circle z =1 4z -2 in to a circle of a radius…

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Q: (6) Suppose the closed curve C in R? starts at the point (-1, 1), goes along the parabola y = r? to…

A:

Q: Determine the location of a point (x, y, z) that satisfies the condition z = −5

A: The condition is z = −5

Q: 4. Find an equation for the plane in R³ spanned by the points (1,5, 1) and (1, 4, 2).

A: The two vectors are given as v1 = 151v2 = 142 Let xyz∈span{v1 , v2} Then xyz = mv1+nv2= m151+n142=…

Q: The point (-2,0,8) is. A. In die xy-vlak O In the xy-plane B. In die yz-vlak O In the yz-plane C. In…

A:

Q: (10) Find the distance of (3,-1,2) from each of the following: a) line: x = 1+ 2t, y = -t, z = 1-t…

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Q: 1- -Н(y)-Н(yх) Prove that 2- H(x,y) = H(y) + H(x\y) 3- H(x,y) = H(x) + H(y}x) 4- Н(х., у) %3DН(х) +…

A:

Q: 1. 2. The area bounded by y = = -(x - 1)² + 4 , and the lines x =1, y = 2, and y = 4 rotated about…

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Q: Find the shortest distance from the point (0,2,3) to the plane x+2y+z=1

A:

Q: 2. Find the eanation of the plane Containing the point (2,3,3)'and the line Of intersÉCtion 'of the…

A: We have to find the equation of plane containing the point (2, 3, 3) and the line of intersection of…

Q: Find the shortest distance between (3,4,1 ) and the plane X+y +Z = -2

A: Using distance between plane and point formula we can calculate.

Q: 4. y=4-x² , y=3x and the x-y plane is given by the fol expresions.

A: We have to choose the correct option according to the given information

Q: -6 3 Let y = -5 and u = -4 -2 Compute the distance d from 3y to the line through u and the origin.

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Q: parametrization for the line segment beginning at P1 and ending at P2. P 1(-4, 0, 3) and P 2(0, 5,…

A:

Q: Find the general equation of the plane passing through P(−1, 3, −2) and having n = (−2, 1, −1) as a…

A:

Q: 5. Are there any points on the graph of x2 – y² – 22 = 1 where the tangent plane is parallel to the…

A:

Q: The pyramid is bounded below by the xy plane above by the plane x+y+z=3 and on the sides by the xz-…

A: According to the given information it is required to set the double integral to find the volume of…

Q: 10. Find a tangent plane to z² – x² +y² = 1 at (7, –5, 5).

A: To find a tangent plane to the given curve at the point (7,-5,5)

Q: Find the distance from the point to the plane. (3, 0, 10), 2.x + 3y + z = 2

A: