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 elements are in X′∪YX′∪Y if n(U)=50n(U)=50?

Q: 7. In A ABC,X is the centroid. A A. If CW = 15, find CX and XW. W B B. If BX = 8, find BY and XY. C.…

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Q: Given that the system zy² + zu + v 2r+ 2y-uv 2 zu + yu – ryz = 1 at (u, v) = (1,1)? can be solved…

A: Given system of equations as follows, xy2+zu+v2=3x3z+2y-uv=2xu+yv-xyz=1

Q: If W(-10, 4), X(-3, -1), and Y(-5, 11) dassify AWXY by its sides. Show all work to justify your…

A: Given,           If W-10, 4, X-3, -1, and Y-5, 11 of ∆WXY.

Q: Evaluate / (x - 2y + z) ds. S: z = 3 - x, 0sxs 3, 0sys 2

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Q: Use the method of separation of variables to solve: (ôu ôu - = 0 in (0,1) × (0,+∞), (2) u(0,t) =…

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Q: . Finish showing the Complementary Slackness Theorem by establishing that under the hypothesis of…

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Q: Ex: O calkulake th gui for the disanse formula in a barred cordihute system defined by R = Ax, whene…

A: Here, one matrix function, A=1-223 is given Let the X=a1b1a2b2 So, X¯=AX=a1b1a2b2.1-223…

Q: 5. Evaluate Fale JJJ (²+ + ² dv, where a, b, c > 0, and & is the region given by E 22 + y² 2² 6² +2…

A: Given triple integral is ∫∫∫Ex2a2+y2b2+z2c22dVa,b,c>0x2a2+y2b2+z2c2≤1 in the first octant. Now,…

Q: Find the Wronskian of a given set {yı, y2} of solutions of 7. (1 x2)y"-2xy' (a 1)y0, _

A: Consider the given equation.

Q: Let, T:R' → R³;T(x,y,z)=(2x+ y, y- z,2y+4z) 2. Find the rank and nullity of T.

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Q: Let X₁, X₂,..., X be a r.s. from N(,0) and Y₁, Y₂...., be another independent r.s. from m…

A: Solution

Q: If the Wronskian of the DE : x'y" + xp(x)y' + 3y 0 is et Then p(x) %3D -2x O

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Q: If xly then gcd(x,y) = y. إختر واحدا:

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Q: Prove that if 0 < a < y, then ỹ – VI < Vy– a.

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Q: Given that vec F =x^ 2 y hat i -(z^ 3 -3x) hat j +4y^ 2 hat k find the k- component of ( nabla* vec…

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Q: AXYZ is isosceles with base YZ and M is any point on YZ. Prove that a. ZXMY > ZY Z. b. XM < XY M

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Q: find the Lineartransfromation T:Manz (R)R whose matrit Mp --

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Q: Show that the opelator Tilol defined by Y=19;)=Tx.-E] *=(h:)is Linear and bounded

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Q: Given that the system xy² + zu + v² = 3 x³z + 2y – uv = 2 xu + yv – xyz =1 can be solved for x, y,…

A: Given that,

Q: b) Show that the implicit Trapezoidal method h Wi+1 = Wi +5 f (ti+1, Wi+1) + f(ti, w;), is…

A: The solution is given below in the next step:

Q: dz Let z-ay" – 4r, * = uv and y-v - 3u. Compute Ən (u,r)-(1,1) -

A:

Q: If z = f(u) + g(u), where u = = and v = x · y. Prove that x · Zx – y · Zy = y² ·Zyy – x².Zxx using…

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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: Verify, if u = x + y+ z, v = x° + y° + z³ – 3ryz, w = x²+y² + z? – xy – yz – za are functionally…

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Q: Show that if AT Ay = y for all y in Rn , then ATA = In .

A: Given that     ATAy=y  ∀y∈Rn. To prove ATA=In

Q: Suppose that w = f(z,y, z), z = h(s), y = g(s, t), z= k(s,t) and all the conditions required for the…

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Q: A function f(x,y) is homogeneous of degree 7 in x and y if and only if, __________.

A: Given problem is solved below.

Q: Find the value of x, y, & z using Gauss Jordan Method x+ 2y + 6z = 15 3x + 4y + z = 16 6x - y - z =…

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Q: Compute the discriminant D(x, y) of ƒ(x, y) = x2y2.

A: fx, y=x2y2 Partially differentiating with respect to x, we get ∂f∂x=2xy2 Partially differentiating…

Q: 0, 2 is defined by A natural cubic spline S on 5. So()12x - 0 if 1 (1) S(r)2b(x1)c(x - 1)2d(x - 1)…

A: 5.Note that, the natural cubic spline must satisfy the conditions

Q: ; Let x, y ER" be given. (a) lf ||x|| = ||y|| = 1 and x - y = 1, show that x = y. (b) If ||x|| ≤ 1…

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Q: xy−5yz−7xz,x=st,y=e^(st),z=t^2 Compute ∂w/∂s(1,−2)=

A: The equation given as  w=-2xy-5yz-7xz , x=st , y=est ,z=t2. The partial derivative of the function…

Q: A natural cubic spline S on [0,2] is defined by (So(x) = 1+ 2x – x³ S(x) = Is, (x) = a + b(x – 1) +…

A: Given: Natural cubic spline S on [0,2] is defined as: Sx=S0x=1+2x−x3 if 0≤x≤1S1x=a+bx−1+cx−12+dx−13…

Q: Compute the indicated 3 X 3 determi­nant using cofactor expansion along any row or column that seems…

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Q: Show that if f(x, y) is homogeneous of degree n, then                                     xfx(x, y)…

A: It is given that fx,y is homogeneous of degree n,

Q: Find the bounded อน əx solution of อน 2 + U if U(x, 0) = 6e-3x. at

A: We have ∂u∂x=2∂u∂t+u  The initial condition is ux,0=6e-3x Now, ∂u∂x=2∂u∂t+u can be written as…

Q: Find (x ,y, z) by using Jacobi or Gauss of Gauss Jordan method 5z — Зу + х%3 -1 2y – z = 2 z - 4x =…

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Q: Let f(x,y,z) = zIn(x³ycos(z)), find Z 3x² O In(x3ycos(z)) - ztan(z) 0 2 Y о 3z X af ila

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Q: 1- If z = 1+ y2, we can write: a) z = 1- (iy)?, b) z = 1- iy?, c) z = 1- iy, d) z 1 + (iy)? 2- If z,…

A: As you have posted multiple questions so according to our guidelines, I answered first three…

Q: Let z, w E C. Show that zw = 0 implies z = 0 or w = 0. %3D

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Q: Let, T: R3 → R³;T(x, y, z) = (2x + y, y – z,2y + 4z) Find the rank and nullity of T.

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Q: b) Suppose to i that and V х-у Calculate the x and and y by and Jacobian ð (u, v) 2 (x, y) hence…

A: Suppose that x and y are related to u and v by…

Q: Show that e", sin x, cos a are linearly independent using Wronskian Method.

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Q: Suppose that T :C C is R-linear. Show that T is C-linear if and if T(iz) = iTz for all z.

A: First we describe the definition of C-linear function:

Q: Uyy=4Uxx , U(0,y)=U(5,y)=U(x,0)=0 Uy(x,0)=3sin(2pi x)x)-2sin(5pi x), y>0

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Q: 4) Let f(r, y, z) = In(r + 2y + 3z). Find Vf = . %3D

A: Given: f(x, y, z)=ln (x+2y+3z)

Q: (R, d), where d(r, y) = |r – y|, is separable. %3D

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Q: Show that Z/mnZ is isomphoric to (Z/mZ)×(Z/nZ) where gcd(m,n) = 1

A: Concept Used:( The First Isomorphism Theorem) If ϕ be the  ring homomorphism from G to G then…

Q: Let z = F(x , y) = xy2 + - , where x = u2 + v2 - 4 and y = uv . az Use the chain rule to find at (u…

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Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.