For 3 and 4given the translation rule: T(x,y) (x+2,y-3)

Q: 5. What is the angke between the planes 4x – 5z = 11 and 16x – 20z = 13? (a) n () (b) (d) 0

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Q: Use the sub no spaces: T-2y = - %3D 3x + 2y

A: Given that: x-2y=-10           ........(1)3x+2y=-14      ..............(2)

Q: For planes 2x + y - z = 2 and 2x + 3y + 5z = 4. %3D

A: Angle between two planes is given by: cosθ = a1a2 + b1b2 + c1c2a12 + b12 + c12 a22 + b22 + c22

Q: 5) s how that the line af intersection f the Planes X+24-22= 5 and 5x-2y-73D0 is Parallel to theline…

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Q: Find the distance between these two planes x + .2y – 2z = 3 and 2x + 4y – 4z = 7 اخترأحد الخيارات а.…

A: Given: x+2y-2z=3                                                          ..12x+4y-4z=7…

Q: Use the chain rule to find where First the pieces: End result (in terms of just t): = 历 内 z = x²y +…

A: Here given that                       z=x2y+xy2,  x=3-t3,  y=3-t6 We have to find dzdt by using…

Q: Find ∇2f, given that f(x, y, z) = 1 / (x2 + y2 + z2)1/2.

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Q: Please solve this problem

A: Given integral is,

Q: 3. If f(r) VI-I, g(z)%= VI+1 find the domains of(Jgx) and %3D %3D (f9)(x) V-1?( 17(

A: Given ptoblem:- 3. If f(x)=√(x-1), g(x)=√(x+1) find the domains of (fg)(x) and (f/g)(x). Is (fg)(x)…

Q: Use Gramer's Rule to Find K,y and Z -y-2Z = -8 + 32 = 2 %3D 7X +y+Z = o

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 8. The distance between the planes 2r -y-2z 5 and 2r - y- 2z = 7 is A C 2 D 4

A: As the planes are parallel than for calculation distance between planes we use formula:…

Q: For planes 2x + y – z = 2 and 2x + 3y + 5z = 4,

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Q: T: R2 R2 is defined by х + 7х, [3x, – 4x2] X1 %3D and B = {u,,u,} and B' = {v,v,}, where %3D -- --…

A: Given transformation T:R2→R2, defined by Tx1x2=x1+7x23x1-4x2 and B=u1, u2 and B'=v1,v2 Here u1=22,…

Q: Let z = 2r - 3y and z = 4u – 5v, y = 4u + 5v. Find usig the chain rule.

A: Let z=2x2-3y2 and x=4u-5v, y=4u+5v

Q: The planes x - 2y + 32 - 3 =0 and 3x + y - z + 5 =0 are perpendicular. Select one: True False

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Q: find the point of intersection for the following 3 planes  x–2y+z+6=0 2x+y–z+2=0 2x+y+3z+2=0

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Q: Find the line of intersection between the two planes x+2y-z = 5 and x-4y+z=3

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Q: Use the Runge-Kutta 4th order method to find the values of y where x is given that y = 1 when x = 0…

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Q: 2. Find the images of the mapping W= z2 of the line y = 2.

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Q: If (x, y) > (x+3, y-7) maps TUVW to T'U'V'W', what is the algebraic description that will map…

A: x, y→x+3, y-7 maps TUVW to T'U'V'W'. That is, the x-coordinates of T, U, V and W are added by 3…

Q: Q1. Find the Jordan nomal form of T-2 A =|0 -2 -2

A: A Jordan normal form is an upper triangular matrix of a particular form called a Jordan matrix. Such…

Q: Let ƒ(x, y) = 4x2 - 9xy + 6y3. Find ƒx (x, y) and ƒy (x, y).

A: To find the derivatives.

Q: For planes 2x + y - z = 2 and 2x + 3y + 5z = 4

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Q: Find f, and f, for f(x, y) = 12(6x-3y +8)°. %3D 1,(x.y) = %3D

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Q: Please help me prove this: Suppose x, y ∈ R. Prove that if 3x^3 + 21y = 3y^3+ 21x, then x = y or…

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Q: Verify that wxy = wyx for w= In (4x + 5y). W. ху Wyx Compare wxy and wyx. Choose the correct answer…

A: Given query is to find the correct option for partial derivatives.

Q: For 16 - 19 consider the translation defined by the coordinate notation T(x,y) (x+4,y-6)

A: Explanation of the answer is as follows

Q: Find the real numbers x,y,z,t if -3x +y+ zt = 0 3x + y(t – 1) – z(t+ 1) = 0 3x +y+ zt =t+2 - 3x +…

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Q: 5. By Chain Rule , evaluate b. y' for y = u² + 2u and u = x² + 2 %3D

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Q: ) s how that the line af intersection f the Planes X+2y-22%= 5 and 5x-2y-Z=0 is Paraliel to theline…

A: Solution is written in below steps.

Q: The linear operator T: R2 --> R2  defined by T (x; y) = (4x + 5y; 2x + y) is it diagonalizable?

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Q: a. R1 is defined on R by x R1 y if x² + y? = 1. b. R2 is defined on R by x R2 y if 4x² + 3y² = 1. c.…

A: (a) Given relation is xRy⇔x2+y2=1 The relation is not a function because Take x=1/2,…

Q: 1. Let T1,T2 : R3 → R² be given by: T1((x, y, z)) = (3x – 2y + 5z, x + 4y – 7z), and T2((x, y, z)) =…

A: Solution is given by using the matrix representation of given transformation as

Q: Give equations for two distinct planes whose trace in the xy-plane hasequation 4x + 3y = 8.

A: Given information: The xy-plane has equation 4x + 3y = 8. Calculation: The equation of the plane is…

Q: Consider the fiunction f(x,y) = x² + xy – 5x - y +1. Then:

A: f(x,y)=x2+xy-5x-y+1

Q: 2. Let C be the closed path constructed by joining the segment [-2, 2] on the real axis with y(t) =…

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Q: If z = x + y, x = 2t, y = 3t, then %3D %3D 1 5 II

A: Recall:    If f(t) and g(t) are two function of 't' and h(t)=f(t)+g(t) then…

Q: QY Use Gramer's Rule to Find K,y and Z -y-22 =-8 %3D 1 + 32 = 2 %3D 7X +y+Z = o

A: Craners rule used

Q: B. If the two planes ax-4y - 9z = 4 and perpendicular. Find the value of a. x-2xy + 3z = 1 are

A: Topic = Geometry

Q: Determine whether the following planes below are parallel, perpendicular, or neither. choose one O…

A: Solution: Given: 1. x+2y-6z=0    -6x -12y +36z = -3

Q: Find real numbers x, y and z such that (а) (b) 7xi + (y – 3)j + 6k = 10i + 8j – 3zk (x + 4)i + (y–…

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Q: z=f(x,y)=x^4-3xy+1 and x=2t, y=t^3 find dzdt using the chain rule

A: Given query is to find the derivative using chain rule.

Q: 11 f(x,y) 3x-7y+2, R is the rectangle with opposite car- ners (-1,0) and (1,3).

A: 12. Given: fx,y=2x+2y+2 and triangle with corner 0,0 To find the area of the triangle. The formula…

Q: Ye = C1 + C2x + Cze3x + C4xe3x Yp = Ax² + Bx + c Since Czx & Bx and C, & C are similar how do I use…

A: Complementary solution is: yc=C1+C2x+C3e3x+C4xe3xParticular solution is:yp=Ax2+Bx+C

Q: %3D If MZJKL = (8x- 6)° and mJML = (25x- 13), find mJML. %3D K J M

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Q: For planes 2x + y - z = 2 and 2x + 3y + 5z = 4.

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Q: Suppose that r, y, z satisfy the equations x+y+z = 5-a %3D 2x +y = 7 – a %3D x - y – 2z = 0, %3D…

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Q: Use the chain rule to find where First the pieces: End result (in terms of just t): d = 江 西 血麵| 2 =…

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Q: Use Gramer's Rule to Find K,y and Z -y-22 = -8 %3D + 32 = 2 %3D 7X +y+Z = 0

A: As per our guidelines we are supposed to answer only one question at a time. So submit the other…

Q: Is AX'Y'Z' a reflection of AXYZ across line g? g X. Z' Y X'

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