Qt Let T= {carb) a,b ER\fopp and of defined onI by Carb)*(c,d)= (ac, bd) for all (a,b), (c,d ET, show that (T, *) is a Sroup or Hot?

Q: 3. For f(x, y, z) where x = u – v, y = v – w, and z = w – u: - Compute - Show that of - af af and af…

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Q: Let G = Z31, S = {1,5, 6, 25, 26, 30}. %3D %3D Prove that Cay(G, S') is normal.

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Q: Let, T: R' → R';T(x, y,z)= (x+y + z,2y + z,2y + 3z Tost uhothor the troncfCormotion T is linoer

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Q: 3. Let SP(la, b, c,d.e) and define W:SXSS as the union function: (A, B)AUB. for ill (A. B) ESXS. (a)…

A: Given: S=P({a, b, c, d, e})Define A:S×S→Ssuch thatA(A, B)=A∪Bfor all (A, B)∈S×S We see that S is a…

Q: Let f = 12r + kry + Jryz re-express f O f(r,y,z) = (x, ry, Tyz+) O {r,y) = (x, ry, ryz*) O f(x,y) =…

A: GIVEN f= ix+kxy+jxyz4     ....(1)

Q: det (NT) is sPace Toflogecu! and T=0U{un}such that 7Show that (N, Cl is compact slase

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Q: Glven: XY and ZW Intersect at polnt A. Which conJecture Is always true about the glven statement?

A: as given that XY ↔ and ZW↔ intersect at point A. so, here we understand few terms which is given in…

Q: KB is ∀xy F(x, y). Prove using resolution-refutation that ∀xy F(y, x).

A: Solution: First, we convert clauses to CNF : (1) ∀xy Fx,y from KB (2) ∀x Fx,Ax (3) Fx,Ax CNF

Q: matoix Such that show that Let is Then detx = tt mxn

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Q: Let E=RandT:R R be a Linear tiansformation I(,)=(2,3)and Tls0)=(3,2) Check whether T exists or noti2…

A: Given T:ℝ2→ℝ2 is a linear transformation such that T1,1=2,3 and T1,0=3,2. Now find the matrix of the…

Q: Prove: If f1, f2 € R(a) on [a, b] with fi < f2, then ' fi da < s' fz da

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

A: Sol

Q: 6. If F = Pi + Qj + Rk, prove that div (curl F) = 0

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Q: Let g) be a on .R Such thiat derivable ction g4)=5,914) = 2, t fin)=g(w) Coscn) egc) and f'ce).

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Q: Let X; ~ X"(1) i= 1,2, . - ·, n and assume they all uidependent are Y = Ź Xi %3D しニ」 ان منتتفينتمنل…

A: Given, Xi~χ12 ,i=1,2,...,n a. Y=∑Xii=1n Therefore, X1+X2+.....+Xn~χn2 above is possible using…

Q: OVESTON Prove that A is inveitine if at0 and at b l Gind The pivos 9 A %3D a a

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Q: of at (x, y, z) = (2, 3, 4). ay Let f(x, y, z) = (x + y)z. Evaluate

A: Given :fx,y,z = x+yz

Q: Compute F. Oszs V1-x2 –y? Let E be the hemisphere described by and F=Vz2 + x² +y² i + Vz² + x² + y²…

A: By Gauss divergence theorem:∬∂EF·nds=∭Ediv(F)dvhere givenF=x2+y2+z2( i^+j^ +k^…

Q: Let po) - X In (x) , using the following approx im for the secoud denvative fcxo) = FOXO -h)-ZR…

A: Introduction: Apart from differentiating a function analytically, the derivative of a function can…

Q: 10) Prove the following. Use a 2-column proof, a paragraph proof or a flowchart proof. Given: V is…

A: Given V is the mid point of YWUY || XWwe have to prove that ∆UVY ≅∆XVW

Q: Home uork: Let abeQ such that acb. Prove that HxE OK cbx

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Q: F(X)=JX F: [o,2]-> show i fis lipschit z funcla or not find k to

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Q: 1) Prove that Ym,n EN such thert m¢ nt = n<m using the princdple of in duction!

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Q: Let (An) and (Bn) be (Fn)-martingales on (2, F, P) and let Cn = A - Bn. Show that E [(Am - An) |Fn]…

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Q: (a) Assume that f(x, y, z) and F (x, y, z) are arbitrary differentiable functions such that f(x, y,…

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

Q: LET T be the function  from R2 into R2 such that T(u)= projvu, where v= (1,1). find T(x,y) find…

A: Recall: projvu =u.vv2v

Q: Let A: C [0,1]→C [0,1]. Prove that operator continuous reversible, find A. 2.11. Ax(t)= x(1)- -…

A: The given operator A such that A:C0,1→C0,1. We use the inverse operator method for solving linear…

Q: If u(z,0) = f(z) ue(z,0) = 0 u(z, t), u(z,t) → 0 as |z| → 0 Show that f(z+at) + f(z- at) u(z,t) =…

A: If we have a D'Alembret wave equation given by utt=α2uxx       , -∞&lt;x&lt;∞,   t&gt;0, α is fixed…

Q: Let r, y EN such that y # 0, then y+r#0.

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Q: Q1:- Let T =- where W-N(0, 1) and V~xShow that T2-F(1,r).

A: We know that  The ratio of chi-square divided by its degrees of freedom is called the…

Q: Q2/ Show that {1,cosx, sinx,cos2x, sinx,...} Form an orthogonal set on [-Tt,t] *

A: A set of vector B is orthogonal if every vector in the set is orthogonal. Therefore, the dot product…

Q: Let A = Z. Let R be defined on A x A where a Ry if 4 (x- y). Prove that R is transitive.

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Q: Determine if the veetor is in Spanis} where S-3,01,2,0L3,4,2, 183 Ifit is, write T as a linear…

A: The solution is given as

Q: 8. Let S= I+T*T: H- H, where T is linear and bounded. Show that s1: S(H)– → H exists.

A: Let S=I+T*T : H→H where T is linear and bounded. Since T is a bounded linear operator and…

Q: Let F I2). Evaluate JJaw as z² + y? 0

A: In the given question, the concept of the Divergence Theorem is applied. Divergence Theorem Assume S…

Q: Let W(t) be Brownian motion. Using Ito's lemma evaluate | (4w (t) – 124W (t))dW(t)

A: Note: Hi there! Thank you for posting the question. As you have posted multiple questions, as per…

Q: Q) let P aprobabiity funckion on S: La,a,a) Find plai) If:- i) pcaz) = and plas) = ii) pc{ãa, az} ,…

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Q: 2. Let T: R4 → R4 be given by -). Set z = T(v) = 000 -4 1 0 0 0 01 0-5 0 0 1 0 I Prove that R4 = (T,…

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Q: Use Green's Theorem to evaluate F dr, where F(2, y) = (9xy, y" - 8) and C is the rectangle with…

A: That's easy. Have a great day!!!

Q: prove tらット IF Sequeree divergent to is THEN is boumdad below. the thif every conveng ent Sequenca…

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Q: If F G) and g(x) are conbinuous on [anb] andit =Sprove thab. SF= 58 prove thab Icefanb] Such that…

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Q: The function u, takes on the following values : 1 1 1 1 1 u, = , u. + .....u, 10 1 + 3+1 + 32 +…

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Q: Let fun chan defined by g(2) = V Z+8' –-8, ts devivalie z+h+8- Vz+ 8 is equal to the expressian. A)…

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Q: dv 4.)Prove that f -Incosv + Insinv + C sinvcosv

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Q: #04 Check thet the funetions 7,g and h are linearly dypendint oY independent 7 f(1)- é, g)=ë, kp-t…

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Q: Use Hölder inequality to prove |lulla < ||u||3||u||;-1 for u e L" (N) 1-2 Where p <q <r and p r

A: It is given that u∈LrΩ where, p≤q≤r and 1q=λp+1-λr.

Q: Use Stokes's Theorem to evaluate F dr, where F(x, y, z) = x²i+z²j-xyzk and S is z = /169-x² -y² .…

A: As per our guideline we can't use any computer algebra. I calculate both line integral and surface…

Q: Q3. Let z, y be real numbers such that ry 1 and z #y. Prove that

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Q: Prove that if w = f(x,y,z), x=r-s, y=s-t, and z =t-r then ôw ôw ôw + âr' as = 0. ôt

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Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.