19. Given: PR || VO; RO || PV; PR = RO Prove: 1 and 22 are complementary. R V. E.

Q: Let S, := (1 - (-1)"/n :n e N). Find inf S, and sup S,.

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Q: 3). wh.ch of these condition ally Ca uvergent! Tuere may be more than 1 right answer. Odre arctan u…

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Q: QR MN ZN = ZR QS MP RS Given: NP Prove: R N

A: In △MNP and △QRS QRMN=RSNP=QSMP

Q: 00 fcos(x*) dx = ! Ex. 41. Prove that 2 V2 0.

A:

Q: 12. Given: RX ITTW Prove RS ST = WS SX I

A: Find the solution below

Q: Let x, y, z e Z Prove that if x – 2y + 3z is odd, then 4xy – 6z is even.

A:

Q: If I, = S e cos" xdx, where n > 2, prove that In 1+n(n-1)In-2 n² +1

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Q: Q.1 a- Verify Euler's theorem U= x"In(?)

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Q: Let x, y, z E R. Prove that if x – 2y + 3z is odd, then 4xy – 6z is even.

A:

Q: The solution of the IvP Elb+2)jl&+2)y=t", yL3)=o exists in the interval O 6, 00). noncof the giren…

A: given differential equation is t(t+2)y'+(t+2)y=t2,y(-3)=0

Q: 12, GIVEN: JKI KT, ET 1 KT, KV TL, IL EV. PROVE: AJKL AETV. T.

A:

Q: 6. Given: ZP=ZR; ZQ= ZS Prove: PO| RS P. 'R

A: ∠P≅∠R,∠Q≅∠S

Q: 7. Solve the following first-order linear DE's. y' + (cotx)y = xcscx, ) = 1

A: As per our guidelines we are allowed to do 1 question at a time. Please post other questions next…

Q: Let XN(3, 4) and let Y~ N(2, 3). Define S = X + 3Y, where 'X and Ya atistically independent RVs.…

A: Given that: X~N3,4Y~N2,3S=X+3Y, X and Y are…

Q: 2. Consider the following conditions. x, = 34.81 %3D x, = 36.78 n, = 12 n, = 15 si = 14 s = 10 %3D…

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Q: 2. Given: XW XY, HA I WY, KB 1 WY Prove: AHWA ~ AKYB. K Y.

A: Given data is : XW¯≅XY¯ Therefore ,  ∠XWY≅∠XYW∠XWY≅∠HWA∠XYW≅∠KYBTherefore,∠HWA≅∠KYB     .....1…

Q: 25. Which of the following is the answer for secx = V2 A. E + 2nk|k E Z}U {+ 2rnk|k € Z} 3 B. G+…

A: We will solve the problem

Q: O let X be fe VrV Finel ECX) ael E(x)

A: Note: As per guidelines we can answer only one question at a time. I request you to please repost…

Q: 6. Consider the following figure and proof. Given: RM || SN, RM 1 MS, SN 1 NT, Prove: ARSM~ASTN M T.

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Q: 3. Suppose AB=RS and mzB = mzS. What other information is needed to prove that AABC = ARST by SAS?…

A:

Q: Prove that i 224 s 2xP for xzO, y zo i and 1 t L-l with p>

A: Given that x,y≥0. And 1p+1q=1 with p>1. Consider gx=xpp+1q-x. Then g'x=xp-1-1 and g'x<0 when…

Q: (2) O show that you Y2,43, and Yu are solutians to NOTE : Geueral Solufion

A: Thanks for the question :)And your upvote will be really appreciable ;) Solution is provided below,…

Q: 4) Which of the following foumulas does not Kold for all x, we CZ O la wl= |2). Iw). (6) X W = ņ. W.…

A: We know that

Q: Let x, y E Z. Prove that if 3 ł x and 3 ł y, then 3|(2² – v²).

A:

Q: Let P = {p:p=6x-1, for some x EZ} and Q= {q:6y+5, for some y EZ). Prove that P= Q

A:

Q: Prove Va e Z, Vb e Z, 3|(a² + b² ) – 3|a ^ 3|b where xy means x divides y, i.e., there exists k e Z,…

A: In this question we use congruence modulo.The following  are useful in this question1) If  3 |…

Q: 6. Given: 21 and 22 are complementary Prove: SX 1 WX S. 2,

A:

Q: 2) Given: ZRAL E LYAL, ZRLA LYLA A Prove: AR = AY R.

A: Explained below

Q: 4 16 Define T: R? - R° by T(x) = Ax, where A = 1 3 -

A:

Q: H.W: if w=√x2 + y2 + z2, x= erCose, yerSine, z=ee prove that aw/ar = e²r/w and aw/00 = e²0/w

A:

Q: 2. Given: XW = XY, HA I WY, KB 1 WY Prove: AHWA~AKYB. W.

A: Given that XW¯=XY¯ in ∆XWY. So, ∠XWY≅∠XYWor, ∠HWA≅∠KYBGiven that HA¯⊥WY¯, KB¯⊥WY¯So, ∠HAW≅∠KBY=90°

Q: Given: HT || SF, LH = LS and HT SF Prove: AHOT ASTF

A:

Q: 2. Let P:C0, 1] → C|0, 1] be given by Pp = " – e°. Compute dP(y). Be sure to justify your…

A: We have Pφ=φ''-eφ We need to find dPφ If we have  y=fx⇒dydx=f'x⇒dy=f'x dx Similarly, we find dPφ for…

Q: 10.B.4: Suppose TE£(V) andcEF. Prove that det (cT) = cdim V det T.

A: Here given that T∈L(V),is the set of linear maps from V to V.

Q: 1. Prove with the usual notations that: (b) A + V =- (a) EV = VE = A (c) A= SEZ

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

Q: let X~~ Per(P) Prove ô is unbiare if ô-X let x exp(0) Prave e is unbiar

A: Introduction: One random variable follows Bernoulli with parameter p and other random variable…

Q: Given: QR = SR = WR = VR Prove: QT WU T. レ W

A: Answer

Q: if w= /x2 + y2 + z2, x= erCos0, y=erSin0, z=ee prove that aw/ar= e?r/w and aw/ae = e20/w

A:

Q: (b) Let z = x + iy = re?". Find |z| and z² first in terms of x and y and then in terms of r and 0.…

A: Given:

Q: Q. By e/2silon definition, check the con vergenie of Suquenies 2n+ フ the following く Sn> = ( =…

A: Find the attachment

Q: b. Let x, y,p E Z, where p is prime. Prove that x2 - p²y - p + 0. (Hint: you may use without proof…

A:

Q: 2) Suppose S,T E L(V) are such that ST = TS. Prove that null S is invariant under T.

A:

Q: 3 Prove Prive that d tin'u e I du

A: As we now the identity tan2(x) +1=sec2(x)

Q: B. Prove by direct proof general. P: Vn e ZE, (n – 1) (n+ 1) e Z,

A: I have solved B; you just need to expand (n-1)(n+1) and then use the fact that square is always…

Q: 2. Give the condition which ensure that |ez| < 1 where z in C.

A:

Q: 2. Prove that the solution of the following IVP is unique (Hint: by contradiction) du du + u = 3D0…

A: Given partial differential equation is, ∂u∂t+∂u∂x+u=0 ; u0,x0=u0x. Lagrange Method : Partial…

Q: Ex 6 Show that X -Ca,i) is HOM with y- (1,00) if X and y have the euraal Seibsipace op. af R Hint:…

A: Homeomorphism: Two topological spaces and are said to be homeomorphic if there exists a function…

Q: 4) Let x, y, z E Zg. Prove or disprove the following: Ifxy = xz, then y = z.

A:

Q: 1.) Given: T and R trisect SW XS = XW ZS = ZW Prove: XT = XR S T

A: Given that: T and R trisect SW.XS=XW∠S=∠W

Q: Let P= (p:p=6x-1, for some x EZ) and Q = {q:q=6y+5, for some y EZ}. Prove that P=Q

A: