Q3: Prove that ,X; = y %3D %3D are symmetries of 31'4 12 113

Q: Given: WZ 1 bis. XY Prove: AWXY is isosceles. (Hint: This proof can be written in three steps by…

A: 2. given  WZ↔ ⊥bis XY¯ as WZ is bisector of XY XZ=ZY......(1)

Q: Given the bases B= (u1,u2} and B' = {u'1, u'2} for R, where and u'1= The transition mat rix PB-B'…

A: In this question we have to find the transition matrix from B to B'

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

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Q: Let X N(u, 1) of size n. Obtain UMVUE for u.

A: Given that  Let X  N(μ,1) of size n. Obtain UMVUE for μ

Q: het c denate the tine segment nd z=1. Show that zp

A:

Q: If A = x a, – zy a,, evaluate § A · dī around the path L defined by 0 < x < 2,0 < y < 1 as shown in…

A: Stroke's theorem:         It is also known as Generalized stroke's theorem. It states that the…

Q: 6. Show that the sets S = (1,5) and T = (0, 00) are equinumerous by finding a bijection from S to T.…

A:

Q: E valugte the cube raot of z when 2=27 Cis(210) ( Let 0s GS360°) Smallost ☺ ualus) targonst ualue).

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: Find –3xyd A over the D triangular region D with vertices (0, 0) (2, 0), (0, 4)

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Q: In the figure, ABCD is a cyclic quadrilateral. AB // DC in circle with centre O. BC and AD produced…

A:

Q: Given the bases B={u , u2} and B'={u'1, u'z} for R2, where , U2 and u'2 = The transition mat rix…

A:

Q: 25 If A E M, is symmetric, prove that AT is symmetric.

A: Symmetric matrix

Q: 4) Use Green's Theorem to evaluate f √1+x³dx + 2xydy. C is the triangle with vertices (0,0), (1,0),…

A:

Q: Suppose N E L(C) is nilpotent and has a Jordan form with only one Jordan block. Describe a Jordan…

A: According to the given information,

Q: Given z = 3 cis 120°, find z3 using De Moivre's Theorem.

A: We have to simplify

Q: 15) o veclovs ú = Givetw and Tñ=211 deternine the projection d on 2.

A: This question can be solved using the projection formula.

Q: Consider the region D in t

A: Given, the curves                 y=2x, y=4x, y2=x, and y2=3x To find ∬Dx2x4dA

Q: Given that th And AB is u shaded region A B

A: Solution of the problem as follows

Q: Given: H bisects LKHL KH = LH Prove: 可=正 K J 7,

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Q: Find to the the equation du green funclion corresponding pula)=fex) conditions U(o) =0 with and…

A:

Q: .Use the De Moivre's Formula to show that if z = (cose + isine), then z" + ; ÷= 2cos (n8) and (금) 3…

A:

Q: Solve the loieal Vahue Pr blem by the characteristic Hethod Using For a) flx)> 1 and A fx)- K.

A: Solve intial value problem Solving by characteristics equation

Q: Show that every positive sol fron of Ay + B, k=osl,2- & bosunded, %3D JK is i-e, ogy sB-if A<1. 1-A

A: Given yk+1=Ayk+B, k=0,1,2,... Then the objective is to find the solution at which the sequence is…

Q: A natural cubic spline S on [0,2] is defined by |So(x) = 1 + 2x – x³, S(x) = if 0<x< 1, |Si(x) = 2 +…

A: Given Sx=S0x=1+2x-x3if 0≤x&lt;1S1x=2+bx-1+cx-12+dx-13if 1≤x≤2

Q: Given the bases B= {u,,u2} and B'= {u'1, u'2} for R, where U2 and The transition mat rix Pg-g from B…

A: We first find the coordinate vectors of u_1 and u_2 relative to basis B' ,then we will form the…

Q: The following figure can make a regular tessellation. O True O False

A: We have to check the given figure is a regular tessellation.

Q: c If in is an involution of X, show that (x, y)in = (yin, xin) is an involution of X2). %3D

A: Let X be a lattice We have to show that (x, y)in=(yin, xin) is an X[2] X[2] is a 2 x 2 matrix We…

Q: 1. Given: DE DF DH bisects EF Prove: 4 DHE ADHF Diagram: E.

A: Given- DE≅DF  and consider the given triangle, To prove- ∆DHE≅∆DHF

Q: Given the bases B = {u,u2} and B'= {u', u'2} for R?, where and u'= The transition mat rix Pg-g' from…

A: Linear transformation problem.....

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

A:

Q: 5-The Center of aringR dented by cent CR)is the set Cent CR) - [CERIC.X = X-C,V XER? %3D Prove that…

A: solution You just need to prove that the centre is a ring within itself. Associativity of both…

Q: 4. What is the image of the half strips as shown on the figure, under the mapping z iz? Under the…

A:

Q: Os Find the Taylor seaies af the gien funkon Point as conter and deteamina the with the vadius af…

A:

Q: 3. DETERMINE THE UOLUME OF THE REGION BOUN DED ABOUE BY THE PARABOLOID Z=2-x²-y BY THE CON E

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Q: Consider IR and define Tę and E where I is the tepolagy cofinite topology and Ic is countable then…

A: Consider τp is co-finite topology and τc is countable topology. Assume, τp to be, a,b|a&lt;b And τc…

Q: Qsit Prove that the Centre of a gp îs noymal. of

A:

Q: Given: JKLM is a kite with JK 2 JM and KL = ML. K Prove: ZK M %3

A: in △JKL and △JMLJK ≅JM         (given)KL ≅ML         (given)JL ≅JL           (common)   △JKL ≅…

Q: Draw the region of z that satisfies the following cases. a) z-2i| 2

A: We need to find the equation of curve for the given problems in two-dimensional real plane and then…

Q: let Z be aranelom vanimble with Pelf (Z~Nco) Show that , the psf of Z² (Y=Z) is. chi-square

A: # Given : z be the standard normal variate  let y=z^2  then to show that y follow chisquare…

Q: 9) suppose that horx)=1, f,(x)=x ond dz(X) Prove that Ba(f, - where Ba is a Bernyterh Polymomial.

A: Given functions are f0(x)=1, f1(x)=x and f2(x)=x2 Since Bernstein polynomial is…

Q: 7. Use Green's Theorem (and no other method) to show that the area of the triangle with vertices…

A: Greens theorem

Q: => For The Wbech Ualuo of E doas the Martrix イK %3D have one roal eaomalue of Mutiplicty?? k =

A:

Q: 3. Show that a reflection a in the x-axis defined by o(x, y) = (x, -y) is an isometry.

A: The solution of given problem is followed by

Q: Suppose n is any integer. Compute / (2 – z0)"dz over the counterclockwise circle with radius r…

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Q: 2

A:

Q: Question 2: Show that the set S = {rVT + V2:rE Q) is dense in IR. Explain and show your work.

A:

Q: 5. If 4=2xy į +3x°y -3pyzk is solenoidal at(1,1.1). Find p.

A: DivA=0

Q: a. Let z1 = 2 – 3i, z2 = 3 + 4i and z3 = 1– V3i. Find z1z2 + z3 then sketch it on Argand diagram.

A: Simplify Z1Z2 + Z3 in simplest form and convert it into polar co-ordinates.

Q: 3.1 Show that upper bound of fe dz, where C is the circle |z + 4 – il = 7. z+5i-1

A: The given problem is to find the upper bound of the given complex integral over the region of circle

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.