Ys not a Dofme then there exist abz I+nk some a bEZ sech that kEZ even to prime When odd but rot is prine show that Abelian an 9ooup"

Q: SEr up AN INTEGNAL KEPRESENTAT7 ON OF THE ARGA OFTHE REFGrON BOUNDEO BY y =x3,y=0, x=-l, X= 2 ド

A:

Q: 15. Verify the SSS Postulate for triangle congruence by using congruence transformations. Given: XY…

A: Given: XY¯≅RS¯,YZ¯≅ST¯,ZX¯≅TR¯ To prove: ∆XYZ≅∆RST

Q: Compute the orthaganal piojectian of ? onto the lina L through -6 and the origin

A:

Q: () = 2 sec(a O conon1 O pton 2

A:

Q: Qy:s Evey Subop of an abelian is normal. Prove that the Con verse is mat, true (Consider Quaternion…

A:

Q: shor w that To- {0} abelian 7oup. where p an is prime.

A:

Q: Expand using Taylor upto four termns f((ntaih Ynt a k) senes

A: We will use some basic knowledge of Taylor series expansion of functions of 2 variables. Recall that…

Q: 2) Prove that the foll owing func tion is not differen tiable at (0,0). 2. 2. f(x.y) = (X.y) = (0,0)…

A:

Q: 6. a) Prove that S, is not abelian for all n23. b) Prove that A, is not abelian for all n24. Ay…

A:

Q: A Hessenberg matrex Hn is n Xn madicix that has 2 on the marn diaonal above zerros evermadherle.…

A:

Q: Use Catley dingrepls to Shaw that for n713, there exies a is generatet bt two edements of srder z,…

A:

Q: Compute 4n — бп? lim Vlan| for a,n %3D 3n2 +7 n-00

A:

Q: Show that if det A1:k,1:k > 0 for all k = 1, 2,... , m, then A is positive definite. Hint: Show A…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: Suppose TEL(V) has singular value decomposition given by Tv = $₁(v. e₁) f₁ +...+ Sn(v.en) fn for…

A: The problem is solved using the concept of singular value decomposition.

Q: (W/) Express In x in terms of In x, In y, and In z. - In y + 1. In z 2 2 In x + 1 2 In x- In y + In…

A:

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

A:

Q: QuestibaNo1e 4k R 18 an unit element, then. întegral doman with every unit n R is a unit in Rf9 and.…

A: Just use definition of unit and result will follow.

Q: 32. Prove statement d of Theorem 3.9: If G is abelian, (xy)" = x"y" for all integers n. bns liD to…

A: I have proved using mathematical induction

Q: What does Peano's Theorem 6.1 guarantee for the IVP dy = y cos(t2), y(to) = Yo dt O only one…

A: At least one solution exists for every (t0, y0).

Q: SHOW by Induction that : Alx)" /1-(1-2x)" A For all n e IN" from A (aS is a matix) obseivation Where…

A:

Q: 2 / The eanation rasine itis an e quation of acircle passing through the origin and center onthe X.…

A: Polar to cartesian conversion:

Q: Define injections f : N → N and g : N → N by f(n) = 2n and g(n) = 2n. From f and g, the…

A: Given  f:N→N and g:N→N are two injective function defined by f(n)=2n and g(n)=2n Let 2n = k then…

Q: that y? etcos 2t and Gecos 2t knowing are solühions of. yo _uys +luy'- 20y'+ 25y=0 what is the…

A: For the solution follow the next step.

Q: Homo: )g + 2) if the initiel cond. Sor yro)=1 number 1) 1s and yC") =5, 15 the ODE solvasle ? why!

A:

Q: Using the 2-transform solve Untz + 4unti 734n=3" with u-0,, =1 %3D

A:

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

A:

Q: Prove that Sn is not abelian for all n > 3.

A:

Q: (5) rs = sr. [First work out what permutation s effects on {1,2, ... ,n} and then work out…

A: Step:- 1 Given that D2n "1" is identity element of D2n. According to the properties of D2n, D2n has…

Q: 2) Find the third Taybr polynomi al B,(x) f fal= cos X at X = m. 3) Using ?, (x), eshimate cas…

A: As per bartleby guideline for more than one question asked only first is to be answered please…

Q: 6) let fl2) = CosCitaiy) 22atey Express flz) that f satisfies in the form and fornd z So the Canchy-…

A:

Q: 6. What is the coefficient of x'y" in the expansion (4x + 5y) s. Show your work here:

A: We find coefficient of x7y8 in the expansion (4x+5y)15

Q: 4. Evaluate det 210 TONO -4 0 2 5406 -2 by cofactor expansion about a row/column of your choice.

A:

Q: Find the Taylor expansion of 1/z² for points inside the circle |z – 2| < 2.

A:

Q: Find a defineton ofa duiabailidy kbation I on Zo by Fris rule : for eluments A nd B gf Im. ALB if…

A: Given: Divisibility relation "|" on Zm ,for  some A,B,C∈Zm A|B if and only if AC=B

Q: 1 find func- 88. Finding a Composition If T(x) = %3D Vi + Vx tions f. g, andh such that fo goh = T.

A: Given: T(x)=11+x To find f, g, and h such that f∘g∘h=T

Q: The polyromial X+X+1 is ireducilole aver Z2. Use it to Canstruct additlon and multiplcotion table of…

A: Let F8 be a finite field with 8 elements. Since the polynomial x3+x+1 is irreducible in ℤ2x,…

Q: Of length I1, tien 50) Show that S is generated by ((1, 2), (1, 2, 3, - · , n)}. [Hint: Show that as…

A:

Q: - Pcosø prove that dw xy is Cont s Lony) - the fun ction (-1, 2) = x*y+z and x = PSinf cse y=pSi- -…

A:

Q: O8.D. If w, and w, are stri (x, X2) -(y Ya) = x,y,W,+Xay,W, uinlde an inner product on R'.…

A: 8.D  Let w1 and w2 are strictly positive i.e. w1,w2&gt;0.(x1,x2),(y1,y2)∈ℝ2Define the product…

Q: Ques#3. Show that the units n a Commutabive ng with unit element kroms an abelian graup Aat…

A:

Q: If f: G,→ G, is Select one: а. сyclic b. not abelia C. empty sei

A: Given that, f : G1 to G2 is a group homomorphism. G1 is cyclic. Let e be the identity element of G1.…

Q: Find the Teylor expansion of 4(2): z" with center 1, where Nis a positive integer. Use the above to…

A:

Q: How does Abel's Identity allow us to conclude that if the Wronskian is 0 at a point t, then the…

A:

Q: Evaluate det(A) by a cofactor expansion along a row or column of your choice. 3 0 0 1 0] 4 4 4 1 0

A: Given that

Q: Qu:- Prove that funcdiod u = 3y - 2x -2xy-j+x* is har monic . Final funclion v such thut fc) = U+iV…

A: The general form of a complex number is given by z=x+iy, where x,y are two real numbers and i=-1.…

Q: 5. Let A z 3 4 87 8- ーん Prore that find ite diogonel form. A it diaganalianllen and

A:

Q: Sfind the Taylor secies for (x)= Tx)(+ 3×) Centeredat x=0. Ck X*. That is, revwrite it as kso

A: Solution is as shown in step 2

Q: What is thie generalized union and interdection of %3D where 1-10,1)

A: As given,  λ is the index set for A.  Hence, there are two sets possible,  Aλ=0  =  [ -(1/0) ,  0]…

Q: 4) defin 4, = 1, a2 = 3 , and an = Cnmy + an-z (n7.3). Prove by indeution on in21 that an < (1.75)*.

A:

Q: if :z = cos 0+isin 0 2z² z²+1 prove that: 1+itan 0

A:

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.