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Q: 37.) Show all step to evaluate: SN NS /3-y² /3-y² dzdxdy

A: We have to find the value

Q: EX: Let S.[22] be asubset of IR Si-[-2-4J; S₂ = (-1,0]; S3 - (04]; S4= (1>2] {Si}, is a…

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Q: found z already what is w?

A: Definition: A set x1, x2, …, xn of a vector space is linearly independent if there are scalars α1,…

Q: let X1, X2, ..... XN Find UMVUE for 0² N(0,1) 0 € (-∞0,00)

A: Dear student, If you find this solution helpful please upvote ? it.

Q: Part 1 of 5 (a) When a = 0.10 and n= 22, Xieft 11.591 = 32.671 Kright Part: 1/5 Part 2 of 5 (b) When…

A: a)GIvenα=0.10n=22

Q: 9. Prove L'S 25+1 Cs+2)?(S-1)2. %3D

A: Consider F(s) = 2s+1(s+2)2(s-1)2                            (1) Let 2s+1(s+2)2(s-1)2 =…

Q: 4. (a) Use Gauss's lemma to evaluate (), showing all working.

A: The given term is, 1119

Q: 7. If [G: H] = 2, prove that gH = Hg (18 from 6.5)

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Q: In a class of 40 students 25 speaks hindi and 15 speaks both english and hindi. All students speak…

A: Given Number of students speaking Hindi ,n(H)=25 Number of student speaking both English and Hindi…

Q: 2.If alb and alc then al Cbx tcy) for all X>YEZ.

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Q: 3. Prove the Archimedean Property, if x ER. then there exists K E N such that r SK.

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Q: Q5 Show that EL >². n n =1

A: Consider that x is a random variable. From the formula of population variance;

Q: 3 E in (1 -) -in2 , . =-In2 =1 k2 –1 k=2

A: We will  use the limit of partial sum

Q: If (n + 1)(n + 2)an+1x" - nan-1x" = 0, n=1 show that for k = 1, 2, 3, ..., we have 1.3.5... (2k - 1)…

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Q: Min. z = 4x1+3x2 s.t. 5x1 + 3x2 2 15 4x1 + 2x2 < 16 X1 20,x2 2 1

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Q: 1. Let, a1 = 7 and for n 2, an An-1 express an in terms ofn. %3D ". **

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Q: Σ 9n n = 1 Identify an-

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Q: for n>2, 5 . Deermine for whpch n, n2-2 let |anlく,

A: Given  an = 5nn2-2

Q: 3. For all æ E Z[i], there are N (x) elements in Z[i]z.

A: The set of Gaussian integers is a subset of the set of complex numbers containing the elements with…

Q: 2, z) = 5 and the surfac e at (1,2,3). Evaluate = reasons).

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Q: — (i) For any {(xi, Yi)}=1, Sxy = = n n i=1 (xi — x)Yi n 1 ii) For any {(xi, Yi)}_1, Sxy = = ΣXi Yi…

A: Answer: i)

Q: 15. Let z = 2cos0 + i(1 – 2sin0) where -n < 0 < n Show that Iz – il = 2

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Q: (-1)"+ (2n)! Let an = an+l ant1 Compute an

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Q: 28 + 58 lim z-5i z7 – 54iz3

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Q: see the equation as attached here

A: Solution:Given    0&lt;an≤bn and∑n=1∞an divergesTo prove:∑n=1∞bn diverges

Q: Suppose that Z~N(0,1). Then find Pr(2.78 < Z < 2.84)

A: Given data, Z~N(0,1) That is Mean=0 Standard deviation=1 P(2.78 &lt; Z &lt; 2.84)=?

Q: (27) Let X = P(2) and )E(5-5x) finc

A: Given X≈Pλ That is, EX=λ

Q: 1The land of Zoo Nearland consists of two islands, the Each year 35% of the populatiou of the East…

A: (a) given let ek and wk be the population of the east and west islands respectively to find  a…

Q: Theorem = 7 K 51 M 25

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Q: Show that for all n E Z, n² 5.

A: Consider the given condition: This shows that whatever will be the values of n, it will always be…

Q: 6.Use.chain.Rule.to.frind.E GV. ... 2Sin.x.Eoguy Xロサ.……4こ… ...... .......

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Q: two positive iontages and bare by 2, them prove that. (2° +1) is most divisible by (2²-1) let a with

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Q: Let n e Z. n#-1,3,

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Q: O If z-frxy) show that つる

A: As per our guidelines we are supposed to answer only one question. For the solution of the problem…

Q: S. ADEF with N-2,-1), -1, 3). 6ARCD with A(I, 4), R3, 2), CO, -2). FO. -1) in the sasis D-3, 1) in…

A: #5  Reflect the triangle DEF in x axis  For reflection over x axis , the rule is  (x,y) -----&gt;…

Q: Suppose gcd(a, n) = 1. Then a(") = 1 (n

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Q: (*) 3. Let 2 = {A, |n = 1, 2, 3, ...}, where A, Find UN and N2, then !! %3D prove your conjecture.

A: We solve this problem using the basic properties of union and intersection. Also some basic steps of…

Q: Show a Check for each. In othe 4) Find a. / (z + 4) dz

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Question 11 of 20 There are 17 players on a Calvinball team At the start of the game, the 13 players…

A: There are 17 players on a Calvinaball team. At the start of the game, the 13 players on the field…

Q: 3. Let, a1 = 3,az = 4 and for n > 3, an = 2an-1+ an-2 – 5, express a, in terms of n. %3D %3D

A: An arithmetic progression is a sequence of numbers such that the difference d between each…

Q: 10/Find all ValuSofZ Suck thet E=-Z 20/Pronf that le"+

A: The given problem is to find the values of z for given complex equation and to the prove the given…

Q: (c) Show that 1 and –1 are the only units that have finite order in R*.

A: Units in R*

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Q: Express 3x, xπ, and xsin x using the base e.

A: Our Aim is to express the following function using the base e given below:-(i) 3x(ii) xπ(iii) xsin x

Q: (35 Show that the following grephes are Hameltonian 8) e a) d c) a ol

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Q: #02:-Discuss all the cases of reducible to hamggenou D.E form.

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Q: Q3- Give an example of two denes not equal X subsets of (R,Te) and (z,ror ). ( Explain your answer…

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Q: (16) Show that AB=BA for 1 5 0 0 A = 0 3 0 0 0 and B = 3 1 2

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Family of Curves

A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.

XZ Plane

In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.  

Euclidean Geometry

Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.

Lines and Angles

In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.