25) Which notation describes the translation of the sailboat B(70, 20) to the lighthouse B'(10, 80) as a change in (x, y)?   a.) (x, y) ==> (x + 60, y – 60) b.) (x, y) ==> (x – 60, y + 60) c.) (x, y) ==> (x – 60, y – 60) d.) (x, y) ==> (x + 60, y + 60)

Q: vdor (2,1,3) be the {1,)1), (1, 2, >).(O, 1, 0)1 be the {ll,),l), (1, 2,3).CO,1, 0)) linear…

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Q: Grplain why Ž diverges, 27 41 even though has a finite liniit 2 t 2

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Q: 1. Find a non zero unit vecor ôî that is orthogonal to u= (1,2,1) and Uz= (2,5,4) in R³.

A: Let's find non zero unit vector.

Q: find An eignuector of the matix 12 17 2 VZ V3 19 2 J3 -VIT -2 Ji

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Q: Q: Show that the functi on f:R →R given by f (x) = ax +b, where ab e R, a #0 is a bijection.

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

A: Find the image of (5,-1) and preimage of (-6,7)

Q: 8. The distance between the planes 2r-y-2z 5 and 2r – y - 2z = 7 is A C 2 9 dn 24

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Q: 8z Find at (2, -2, 1) if By z' +y +z2 = 6xz +6yz +21 eej49 1.

A: Given x2+y2+z2=6xz+6yz+21

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: 4. If A = 3xyz²i + 2xy³j- x²yzk and p = 3x² - yz, find (a) V-A, (b) A-V4, (c) V-(Vo) at point (1,-1,…

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Q: DE : -t de dyx= 3et dt with indial conditins : xl0)=6 yl0)=1

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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: followinp serves Dedermine is he conditionelly , I converye your work ond justify your absdlutely…

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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: Find the Avorare valne of Hhe famdtiun en the interal [ 0,4J VI+ 2x

A: Average value of the function on a given interval is 1/(b-a) integration of a given funtion…

Q: Let w = -4xy – 5yz – 4xz, x = st, y = et, z = t Compute (3,4) = as (3,4)%3D at

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Q: Find the value of X and Y in given that; 1 - 2y 4 7 2 2 - 2x 4 - 5 I3D 3. 2.

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Q: If x,y,z are real numbers satisfying the equation 25 (9x* +y° )+9z²-15(5xy+yz+ 3zx )=0 then prove…

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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 bottom face: o (r, 0) = (r1(r, 0), y1 (r,0), z1 (r, 0) where 0 <0< 27, 0 <r< 3 and 1(r, 0) = y1…

A: Given  Fx,y,z=5xi+5yj+4zkr=3height z=−2upper edge z=3 Explanation dimension for bottom face…

Q: Q3: A. Find Wer if W = f(x, y) {x = reost, y = rsint W₁,

A: From chain rule we know if w=f(x,y) and x=g(r,t) and y=h(r,t) then, ∂w∂r=∂w∂x∂x∂r+∂w∂y∂y∂r

Q: Compute the discriminant D(x, y) of the function. f(x, y) = x' + yt – 6x – 2y² + 1 (Express numbers…

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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: B/ If Ø = (x³y²z) and A = 2xzi - 3y2j+ 3xy²k Find a(A) at ду дх the point (2, -1, 3)?

A: When partial derivative is done with respect a specific variable, then other variables are treated…

Q: Fiven with z1 = (-3,1) and z2 = (1, 4). Show that |21 2| = |21||2|- %3D

A: Complex number and it's modulus

Q: 3. Assume that z= 2(r.y) and ee = ryz Find and

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Q: 4) Lett =,u = x? - y² ,v = 4xy³. Find %3D ax ду

A: t=uv

Q: Prove if X,Z, y > 0 xy (3x +2y – 4z)+ yz(y+3z – 4x)+ xz(x+2z –- 4y)>0 then

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Q: 2- Find x, y, z, u, t, v such that 2 3 8. 3 5 +2 9 8 14 a) X =-6, y = -1,Z = -1, u = 1,t=2,v= 2 %3D…

A: xyzutv+2123456=8359814   To find : the value of x, y, z, u, t

Q: Compute the discriminant D(x, y) of the function. f(x, y) = x³ + y4 - 6x-2y² + 2 (Express numbers in…

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Q: What is the midpoint between z1 = 9i and z2 = 4? (2, 4.5) (-4,-9) (-2,-4.5) (4, 9)

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Q: 2.) Use the chain cule to find dz and d ond guen the fllowng: Yoy must show in work that your the…

A: We have to find partial derivatives.  Concept:

Q: Find the condition for the two lines to be coplanar. a1 + bjx + C7x + d, =0 = az + b2x + C2x + d2 az…

A: The given lines are    a1 +b1x+c1x+d1=0a2+b2x+c2x+d2=0a3+b3x+c3x+d3=0a4+b4x+c4x+d4=0  To examine…

Q: 4. Now, determine the value of c in (0,1) such that f'(c) = 2 %3D fx) =4x

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Q: AXYZ ANPQ. Identify the congruent corresponding parts. AN 1. ZZ = 2. YZ = 3. ZP = 4. ZX = 5. NQ = 6.…

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Q: Calculate and at the points (7,41, 1) and (7,41, –1), where z is defined implicity by the equation…

A: Given the equation z4 + z2x2 - y - 9 = 0

Q: Find the cemplex fourth routs of Z: 2 J3-22

A: Given, z= 2√3-2i Therefore, r= √[(2√3)²+(2)²] r= √(12+4) r= 4 θ= tan-1(-2/2√3) θ= -30°

Q: (b) Note that v(t) = t² – t – 12 = (t – 4)(t + 3) and so O on the interval [2, 4] and v(t) > v %3|…

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Q: 6. 1 Let W = Span -1 4 and y = 1 What is the distance -4 1 10 from y to W ?

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Q: Compute Simits If they the eist 8+iz z²+4 hit Zマ-2 Re 2

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Q: (2, Prove that Ž (Pn+ Pn+1) hr 9=U (y+1) 27-²8 (14+ 2x=-1) y

A: What is Legendre Polynomial: Legendre polynomials are a set of complete and orthogonal polynomials…

Q: 2. Given z = , show that ху xy(zxx + Zyy) 2 y - x3 x²y? |

A: Function is the unique relation where each x is mapped to unique y. It can be of many type,…

Q: (1) What is the relationshi etween lines 11 and 12? wl Y = 2 y = 1+ 2t Z = 1+t

A: Given: L1:x=2        y=1+2t     z=1+tL2:x=4-t   y=1+t      z=2+t

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: Ihow do you bnd the imit of as x approaches 0?

A: The limit of x+1-1x as x approaches to 0

Q: 16. Find the points of intersection of x' = 4y and y= 4x. (as:(0,0,(16,64)

A: My Dear student according to the rules of Bartleby we can solve only one question post others as a…

Q: If Ø : R3 → R3 be defined as Ø (x,y,z) = (2x, 4x –y,2x+ 3yz) then show that Ø is invertible. %3D

A: Given that ϕ:R3→R3 is defined as ϕx,y,z=2x,4x-y,2x+3yz. Now, ϕ is invertible if ϕ is one-one and…

Q: Find the are length of f(r) = (r + 3)2 from r = 0 to x = c in terms of c. %3D 2/3

A: