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 b) X =-6, y = 1, z = -1, u = 1, t=-2, V=2 %3D x-6, y =-1, z= -1, u = 1, t= 2, v= -2 d) X=6, y = -1, 2= 1, U = -1, t=-2, v = 2 e) X =6, y = -1, Z= -1, u = 1, t = -2, v = 2

Q: if x=u(1-v),y=(uv) then verify that a(u,v) a(x,y). =1 a(x,y)'a(u,v)

A: Given x=u1−v and y=uv We have to verify ∂u,v∂x,y⋅∂x,y∂u,v=1 Solve x=u1−v and y=uv for u and v, we…

Q: 4. Let U = {m,a,t,h,e,w,d,i,n} %3D X = { e,w,m,a,t} y = {e,w,d,i,n} %3D %3D Z= {h,e,w} Find Z' N (Y-…

A:

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: 5. Show that if x,y∈Z and 3|x^2+y^2 then          3|x or 3|y 6. Show that if c=sa+tb where c=(a,b),…

A: Please check that x=1,y=3, then x^2+y^2=10 does not divide by 3. So  must 3|x and 3|y instead of 3|x…

Q: 1. Show that S, has the presentation (x, y|x² = y = (xy)² = 1). %3D

A: The symmetric group S3 is given as S3=I, 1 2, 1 3, 2 3, 1 2 3 1 3 2 where  I=123123, 1 2=123213, 1…

Q: 5. By Chain Rule , evaluate a. y' for y = u? + 4u and u = 4x3

A: This question is related to Differentiation, We will solve it using given information.

Q: 3,4,s, then メ. rind PCX=5) , P(X==), P(x<2) P(XS2)

A: Given that  Let X denotes the random variable having values 1,2 ,3 ,4,5  We have to find P(X=5),…

Q: if x=u(1-v),y=(uv) then verify that a(u,v) a(x,y)-1 a(x,y)'a(u,v)

A: Given: x=u1-v,  y=uv To verify ∂u,v∂x,y×∂x,y∂u,v=1

Q: Tarkastellaan yhtälöä [5 y' у, У — -8 ominaisarvot ovat A = 3 ja X2 = 1 ja näitä vastaavat…

A:

Q: Let Z, = 2 cis 30° = 3elli %3D Z = In (1 + i) %3D If Z = Z,Z, + Z, Find Z].

A: From the given information. Write the complex numbers Z1, Z2 and Z3.

Q: Let Z, = 2 cis 30° Z2 = 3elli %3D Z = In (1 + i) If Z = Z,Z, +Z3 Find IZ.

A: First we convert all expression into a+ib form then make necessary calculation.

Q: 5. Determine mZU if mZR = 9x 10 and mZU = 3x + 4. %3D %3D R S T. mZU = 50.5° mZU = 35° %3D mZU = 75°…

A:

Q: if x=u(1-v),y=(uv) then verify that a(u,v) a(x,y)_1 a(x,y) a(u,v)

A:

Q: 4. If X and Y are independent RVs, then O2+ ,(@) = ¢,(@) × ¢,(@)

A:

Q: Hi,I am doing some practice questions and I was wondering how to go about doing the problem in the…

A: Probability of an event:The formula for probability of an event is as follows:

Q: if x=u(1-v),y=(uv) then verify that a(u,v) a(x,y). -=D1 a(x, y) a(u,v)

A:

Q: Compute ∇ƒ(-1, 2, 1), where ƒ(x, y, z) = xy/z.

A: Given,f(x,y,z)=xyz     As we know ∇f(x,y,z)=∂f∂x,∂f∂y,∂f∂z

Q: Find r, s, and t so that (a) z = 1 2 x, (b) z + u = x, (c) z − x = y.

A: Given  And z+u=x and z-x=y. We need to find the value of r , s and t.

Q: Then, we assume that Wn+1 - H Wn - l kn+1 kin 1 2 E Wn-p Wn-p p=0 p=1 (6) n+1 - € Zn - € Vn+1 = 1 Vn…

A:

Q: If x,+iy, =x,+ iy, then x =y, 1

A: Given there are two complex numbers. They are x1+iy1 and x2+iy2. And it is given that x1+iy1=x2+iy2.…

Q: 1. For U, iid uniform on (-0,0) show that - min, {U,} is sufficient for e > 0.

A: # given ui follow  uniform distribution (-theta,0) then to show that -min(ui) be the sufficient…

Q: 43 If uzzt+y+z , u?v =y+z,u³w=z, Show that a (x,4,z)

A: Q3. Here, u=x+y+zand,u2v=y+z⇒v=y+zu2=y+z(x+y+z)2and,u3w=z⇒w=zu3=z(x+y+z)3

Q: Find the angle (in DMS) between the line L1 through the points P1(2, 1, 4) and P2(–1, 4, 1) and the…

A:

Q: If x, +iy,=x,+ iv, then x =y,

A: Given x1 + iy1 = x2 + iy2

Q: Prove that MSE(Ô) = V (ô) + [Bias(Ô)]²

A:

Q: Show that if x,y∈Z and 3|x^2+y^2 then   3|x or 3|y

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

Q: 11. Given u %3D 2 + 3і, v %3D 1 — 2і, w - -3— бі, find lu +vi. и+2v, и — Зу + 2w, uv, uvw, lu/vl.…

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

Q: Calculate ff, f(x, Y, z) dS For y = 9 – 22, 0 < x, z < 9; f(x, y, z) = z Sls f(x, y, z) dS =

A:

Q: Suppose that X,Y⊆UX,Y⊆U. If Pr(X)=0.29Pr, Pr(Y)=0.23 and Pr(X∩Y)=0.08 what is Pr(X′∪Y)

A: consider the problem by Venn diagram Here Y is the subset of X And ABCD is the universal set  So…

Q: 15. In AXYZ, if ZX =ZZ, XY = 13x – 21, YZ = 8x – 6, and XZ = x + 4, find x and the measure of each…

A: given: in ∆XYZ, ∠X≅∠Z XY=13x-21YZ=8x-6XZ=x+4 we have to find x and the measure of each side. that is…

Q: Utu = c²uxx , u(0, t) = 0, u(1, t) = 0, u(x,0) = 0 U¿(x,0) = x² – 2x, 00 t> 0 t > 0 0sx<1.

A: Given P.D.E

Q: 4 1) B= |_1 matrisinin özdeğerlerini ve bu özdeğerlere karşılık gelen özvektörlerin bulunuz ve B…

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Q: 13. If T:(x, y)– (x – 1, y + 6), then T':(x, y) → (__, .

A: GivenT(x,y)=(x-1,y+6)To findT-1(x,y)

Q: The distance between u = (15, 7, 4, 6) and v = (3, 2, 1, 4) is 82 182 V182 O 48

A:

Q: Find the Duf of S(x,y,z) = 3xvy+4xz² from Po(2,1,1) to P(4,7,2) %3D

A:

Q: 14) Find mzYIJ if mZHIY = 28°, %3D MZYIJ = 139x + 1, and mZHIJ= 168x. %3D Y

A: Given : m∠HIY = 28°m ∠YIJ = 139x + 1m∠HIJ = 168x

Q: Compute ∮c (ydx+zdy+xdz) where C is the triangle with vertices (3,0,0), (0,0,2), and (0,6,0)…

A: The given points can be plotted as A(3,0,0) B(0,0,2) C(0,6,0)

Q: Determine whether (x-y)|(x-y"), Vn Z+ and x, y € Z, x #y.

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

Q: et §, ŋ, o be real numbers and consider ctors (1,5,§³); (1,ŋ,n³); (1,0,0²). Determine e conditions…

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Q: Find (a) u × v, (b) v × u, and (c) v × v. u = (3, −2, 4), v = (1, 5, −3)

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Q: G be H and Ki Then direct 7(H) and Let direct pradeuct 7(G) Yoduct z'(k). is

A:

Q: Find (a) u × v, (b) v × u, and (c) v × v. u = (3, −3, −3), v = (3, −3, 3)

A: Given: u=(3, −3, −3), v=(3, −3, 3)

Q: State the postulate or theorem that justifies the statement. 1/2 3/4 7. 23 = L7 8. 23 = L6 5/6 7/8…

A:

Q: Let u = (1, 2, 3), v = (2, 2, -1), and w = (4, 3, –4). Find z, where 2u + v – w + 3z = 0. Z =

A: u=1,2,3v=2,2,-1w=4,3,-42u+v-w+3z=0

Q: When u × v = 0 and u ∙ v = 0, what can you conclude about u and v?

A:

Q: Suppose z = f(x,y) where x = Puv and y=u+tv². Given that z,(4,3) = 4 and z,(4,3) = – 1. Compute z,…

A: Explanation of the answer is as follows

Q: Let X,Y⊆UX,Y⊆U. Suppose that n(X)=26n(X)=26, n(Y)=24n(Y)=24, and n(X∩Y)=20n(X∩Y)=20. How many…

A: To derive the number of elements in the set X' union with Y , from the given data

Q: a,b,x,y, are negative numbers a⁵ + b⁵<= 1 x⁵ + y⁵ <= 1 prove that a²x³ + b²y³ <= 1

A: Given information: The numbers a,b,x and y are negative numbers. The conditions are a5+b5≤1,…