Let E = Q(V3, i). Then, Gal(E/Q) is cyclic. %3D False True O O

Q: KLM is a kite. If mZJKN = 28° and mZKLM = 103°, find mZ JML. * %3D %3D K J M

A:

Q: 4. Consider the following figure and proof. E R T Given: GA || TE Prove: AGRA~ATRE

A: Given: GRA and TRE are triangles. GA∥TE The objective is to prove ∆GRA~∆TRE

Q: The linearization a at a = 0 to √8+7x is A + Br. Compute A and B. A B=

A: To Find: Linearization for fx=8+7x at a=0

Q: H.W. Classify the following eq.,and reduceit to the canonical form: (3)U+Uyy = 0

A: As per company norms, we are supposed to answer only first question in case of multiple questions.…

Q: b) Prove Y)- min (t, Ye, Kg) is a UMVUE of o non

A:

Q: If AB = B for some B # 0, then A is inertible.

A:

Q: Let fr)-ll for x0, then/(x) is Selact one A-1 * CNone of these DNot defined E1 a.

A:

Q: 2 write Dirac Delta beinction and it's laplace trans forms.

A:

Q: 0 <m < n such that am = e. (Hin

A: Subgroup generated by any element in a finite group will have at most n element where n is order of…

Q: 6. If Z is the ocentroid of AWXY, WR = 87, SY = 39, and YT 48, find each missing measure. W a) WS =…

A:

Q: B. Let H « G and K - G, and assume that HNK = {e}. Show that if x E H and y E K, then xy = yx

A: We can prove given result by definition of normal subgroup:

Q: Ti Ik'→ IR? be a linear transtormation 3). let defined by -E: Co all ER T C3 x2 + Show that T is…

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Q: The ODE M(z. v) dz + N(z. v) du = 0 is exact if and only if

A:

Q: Form a DE with respect to t: x = Acos (In t) + Bsin(In t).

A: Sol

Q: Let o e C (RN), heRN - {0}. For te IR', we set (x + th) – (x) (x) = 1- Show that E C (IRN).

A: Since, you have post multiple question. I am answering first one. Please post again for the rest…

Q: * Let A E R"Xn, ĩ E R" \ {0} and A = 0. Prove that if the origin is stable if and only if ī is…

A: Given A∈ℝn×n,x¯∈ℝn\0 and Ax¯=0 To prove that the origin is stable if and only if x¯ is stable.  If…

Q: If f = xi+ yj+ zk,1Fl =r,and n =, then show that grad (E) == %3D

A:

Q: Show that the following relationships hold. a) (1+i)™sn[ = Sn+m[ ¯ Sm| b) än+1] = 1+ an] (m) (m), c)…

A: Considering the LHS (Left hand Side) : LHS=(1+i)mSn|¯ RHS=Sn+m|¯-Sm|¯ ( Right Hand Side)…

Q: If E, and E2 are measurable then (E,UE) is not measurable .

A:

Q: Sw 1. Given w = xysin( z?), x =s-t, y = s2, z = t2. Use the Chain Rule to find St

A:

Q: Suppose T: R + P, has an action on a

A: Given, And

Q: Compute the Jacobian of the mapping. G(r, s) = (8rs, 4r + 6s)

A: G(r,s)=(8rs,4r+6s). We need to find the jacobian.

Q: Prove that on average, permutations of length n have H, cycles, where Σ Hn i=1

A: We will take an arbitrary set containing n elements and observe the required permutations.

Q: m!n! If m, n e N, then prove that ,, dx = m.n (m+n+1)!

A: A detailed solution is given below.

Q: If e'z = /3 -i.Then Im (z) is %3D O a. e2 b. 0 С. 1 d. -In(2)

A: eiz=3-i Now let z=x+iy. Then, ⇒eix+iy=3-i⇒eix+i2y=3-i⇒eix-y=3-i…

Q: Find z when In z = e – nj

A: Complex number

Q: al HL b7 SAS C) NOt Co ng ruent

A: We will prove what relationship these two triangles have.

Q: Show that for every e>0 ther e exists P suuch that U (P, f) < U (f) + e

A: We will ise definition of U(f) and Infimum.

Q: Let I = , e2*dx. The approximation of I using the two-point Gaussian quadrature formula is: O…

A: Solution

Q: A) B) A P E в ATSB = A by ABDA = A by.

A: A). In

Q: Which of these best describes T?

A:

Q: Let w = z. In(xy² z®), then which of the following is- O a. O b. O d. O e. 0

A: While finding the partial derivative of a multivariable function, if we have to find the partial…

Q: N is the centroid of triangle HIJ. If KN=9, IM=15 and LN=5. Find KJ K. N/

A:

Q: If g(a) = a°(exin²a+eoa²a), then gʻ(a) is: atcos.

A:

Q: Let C: z-il=3 and I = $. e 3z dz. Then |=0 O I= 6ni None of these |= 4ti

A: Given that:     C:|z-i|=3 and I=∮ce3zz2dz   Note: As per our answering guidelines, we can only…

Q: 3) Show that the following graphs Hamiltonian are hot a a) d d 137 c) d) ol

A:

Q: The linearization at a = 0 to √8+7e is A + Ba. Compute A and B. A B= || ||

A:

Q: given funchion is Re(z) The Tf z to frey =S if z=0

A: Given function , f(x)=Re(Ζ)1-|Ζ|    Ζ≠0 0               Ζ=0 So given function is continuous at Z=0…

Q: Is ZXZ cyclic? [Here Z means (Z, +).]

A:

Q: Find e^z in the for u + iv if z = 11πi/2. (use 3 decimals)

A: Given z=i11π2 We have to find ez in the form u+iv

Q: Question 9. Let A E Mn,n. Prove that A is symmetric if and only if Ax · y = A"x · y for all x, y E…

A: See the solution it is done step by step.

Q: A. B● A B D E g с D

A: Check among the given graph, which is the Eulerian. Degree: Number of edges incident with a vertex…

Q: Find the of the GS that satisfies the given Cond hb Sum a n=4 b. h=6

A: Sum of Geometric series.

Q: R Given: RO = SE, RO || SE Prove: ZR LE E

A: First, we will show two triangles congruent .

Q: Find the inverse Z-transtorm of he follows housing de X(Z)= tanh (z

A:

Q: Show that Oa = {a} if and only if a e Z(G).

A: For a∈G, Oa denote the orbit of 'a' under the conjuction action.The orbits under the conjucation…

Q: Let w = r. In(xyz), then which of the following is 2 O a. O b.0 O d. O e.

A:

Q: If p(x, y, z) = x²z + ey/x, evaluate grad op at the point (1, 0, -1).

A: The function is φ(x, y, z)=x2z+ey/x