Let and ond let F:Co, a) -R be a quactien that is and q =3 dipperenhable on Coja), and such Hhat Fle) =q; all IE Co, 0), F' = -9x°, Compute Fc3) 2. For

Q: Verify that cos kx is a rolulion Also, stafe what kind of DE is the DE above :

A: This question is about solving differential equations.

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: B) Use Green's Theorem to evaluate F dr, where C is the triangle with vertices (0,0) (3,0) and (3,…

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Q: - Show that the norm tion t= aT+B. Use [a, b] onto [0, 1] (7) = 1, ý(7)= T, V т,

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Q: Ex: © Suppise that the fiowing Aransferuntin Conneclğs the lei) and (ti) coordnate Syshems; a4ス?) 2…

A: Given that, ζ=x¯1=ex1+x2x¯2=ex1-x2 To find: a) Jacobian matrix J and J-1 b) Compute J¯

Q: Let r(t) = (t, 3 cos(t), 3sin(t))

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Q: let theorem a, bor about a) Find such that acb. Use the axioms and that : prove R to b) Find CEIN:…

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Q: Find the family of orthogonal trageclarnes fo he for

A: Given that            y3 = k x5 Here we have to find the family of orthogonal trajectories to the…

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

A: We have to simplify

Q: A) Show that the surtace x-2yz ty' =4 is orthogon al to any of the sm tamily of sur faces…

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Q: Can there exist a AROS in which the trisectors of 20 intersect RS at D and E, with RD = 1, DE = 2.…

A: Given: ∠O intersect RS  at D and E in a △ROSwith the data  RD=1;   DE=2;…

Q: Drag the postulate or theorem that proves the trieng AZWX AY XW a. ATSU AXVW # SSS E SAS

A: which criteria follow to congruent triangle

Q: Find all isometries on C which map 1 to 2 and 1+ i to 1.

A: Answer is provided below  If you have any doubts,feel free to post the same again

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: Find a relating ab and c Sothat the linear Systen X +2y- 2X +3 y +3Z = 6 5X +9y - 6Z = c eojarrar A…

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Q: a) Show that fi (x) = x, f2(x) = cos 2x are orthogonal on

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Q: Given: 2J and ZL are rig of JL and MN. Prove: AJKN E ALKM Statem 1. ZJand ZL are right a 2. Kis the…

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Q: defined BCX,x). a norm Dn

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Q: 4) Osig the inteecal de finiton, find the convo wto a gis diaM fug a of f(+)= cs 2+ 9C-) = e b)…

A: Given:

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

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Q: If f has a simple pole at zo and g is analytic at zo, show that Res (fg, z = 20) = g(zo) Res (f, z =…

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Q: -Let e bodefined on Z by afb if 3 (29+75) a) Prove tect R 5 an eaulualerce Pebatiors…

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Q: (o, 1,) 1. find th directional denivatve in the dire chons of at 2 Gve inter pretahon of amp uted…

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Q: ) Let z be a c complese number then cos ( 58+2) is bounded in C2

A: Since, sinz and cosz are unbounded on C. These are unbounded along horizontal axis .

Q: Csc? %3D 2cotx

A: csc2x2cotx=csc2x

Q: F/ prove JhaT cosh(z1+2=)=Coshz.coshaa + Sinh2,Snhze

A: Note: You have not mentioned which question to be solved. Here we are providing answer for 1…

Q: Determine the set of all z where h(z)=cos(z)/e^z is analytic.

A: Analytic function A function fz is said to analytic in the region R if the derivative of fz exists…

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 C:z-1 in the counterclockwise direction and / = . Lnzdz, J = , zdz, and K = $. cotzdz. For which…

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Q: Complete the two-column proof. Given: ZB = ZR, ZBPC = ZRCP Prove: ABPC =ARCP R Statements Reasons I

A: Answer and explanation is given below...

Q: Classify the following eq.,and reduceit to the canonical form: (1 (2) u -a²u (3)uxx +4 y = 0 = 0 (a…

A: The general linear second-order partial differential equation in the dependent variable u and…

Q: Use the diagram to prove that ACAS ATAS. A T. Given: CS = ST and mzCAS mzTAS= 90 Prove: ACAS= ATAS

A: Given : CS ≅ STm∠CAS = m∠TAS = 90°

Q: prove that the Lollowing examples satisly Laplace eqadion are -2y Cos 2X

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Q: Let z, w E C. Show that zw = 0 implies z = 0 or w = 0. %3D

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Q: (a) Let r(t) = ti+tej+fk. Find ((1),4 × (?),1) - (1)a tuj

A: First we find out first derivative of r(t) with respect to 't' then find out 2nd derivative and then…

Q: a. Show that T: 1² → 1² defined by Tx = y = (n), n, = r, is compact where x = (5,) and where0 <r< 1.

A: Show that T: l2→l2 defined by Tx=y=ηj, ηj=rjξj is compact where x=ξj and 0&lt;r&lt;1. Definition:…

Q: Let 1 an(r) : u(reie)e ino de %3D Prove that:

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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: Let r(t) = (3 cost, 5 sin t, 4 cost) . Show that llr(t) II is constant and conclude, using Example…

A: Consider rt=3 cos t, 5 sin t, 4 cos t. rt is always non negative.  Calculate rt rt=3 cos t2+5 sin…

Q: Show that fi (x) = x, f2(x) = cos 2x are orthogonal on

A: Given that, f1(x)= x, f2(x) =cos2x and interval is [0, 90o] Wehave to find that the functions are…

Q: of the following conditions imply that B = se, either prove or give a counterexample. B] AUB = AUC…

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Q: b) Show that the following wo matricegane orthogonal tker A =-V3 -2VTO 3/T15 15 E/NTS

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Q: Consider the following coordinates. W(1,8), X (7,8), Y(4, 5), and Z(1,2) Select all methods you…

A: Given : W(1,8), X(7,8), Y(4,5) and Z(1,2) To find : All methods to prove triangle WYZ  is congruent…

Q: Suppose that for every r E R, pqr 0. Show that R is isomorphic to R/I, × R/Iq.

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Q: QR I RS and UV 1 TÚ. Construct a proof that ZQRS = ZTUV.

A: First, we sketch the situation roughly  We have to prove:

Q: + Let U= -Zit V=a Deteronine sich Shat cthogonal paralle! a) u v ae

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: (f) Find the length of the projection of i onto ū.

A: Given

Counting Principles

In statistics, the counting principle can be said to be the concept in which the quantity of an item is determined. There can be a single item, or a group of items, or items that are related to each other. In every possible set of items, the quantity of the possible item groups or their sorting measures can be determined with counting principles.