4-IN THE ADJACENT FIGURE, IF AB = AC AND DB = EC, PROVE THAT ABEC = ACBD

Q: 18) (SAnn B anlogbro dtiv C AB = 12, BC = 3x + 6, and AC = 5x – 12 a) Find BC b) Find AC

A: Since you have asked  multiple questions in single request  so we  will be answering only first…

Q: 6. In AABC, ZB = 90° and BD I AC prove that BD' = AD.DC

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Q: Q1: Prové by induction nzZ! ☆ (1- 1 htI ( Here JJ (Pi") stande for froduct) means (I- I

A: A detailed solution is given below.

Q: 2. In the figure, 21 = 2, 23 = L 4 and BD = CF. Prove that AC = EF and AB = DE. E В F D C 2.

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Q: GA Given: AC FB TO BC Prove: AB GF

A: Given : GAAC=FBBC To prove : AB¯ ∥GF¯ Proof : If possible let AB is not parallel to GF. So let us…

Q: 3 Given that u = 4i+ GJ and Iv[ = 2, find vif u and V are or thugonal to each other.

A:

Q: now tha 4.31) and that cov(y-ΣΣ) Σ- as in 4.32). – E,. x) = ΣΣΣ as in (4.32). %3D

A: E(y-∑yx∑xxx) = E(y)-∑yx∑xxE(x) = μy-∑yx∑xx μx AS E(y) = μy E(x)=μx ∑yx is the covariance marix…

Q: Given: 23 = Z1 Prove: АВ АС 2 3/6 E

A: Given: The angle ∠3 is equal to ∠1. Concept used: If the two angle of a triangle is equal then side…

Q: Given: LA ZE and AB DE Prove: CB DC

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Q: 3. Prove that {12a + 4b |a, b e Z} = {4c\c € Z}.

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: Solve the Auxiliary DE 75. и"" + u" — 2и 3D 0

A: Note: - “Since you have asked multiple question, we will solve the first question for you. If you…

Q: A P AB=AC 2m(DPC)=m(BPD)=m(BAC) Prove: BD=2DC

A: We will use triangle property to find solution to the problem .

Q: 11. What theorem is used to prove that BD 1 AC? C В. D A

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Q: 1. • If r + 1| < o, prove that |r³ + 1| < 0.331.

A: Here we use the fact  | x |&lt; a implies  -a&lt; x &lt; a .

Q: Prove that Ek=0 C) 7n-k . 2k = 32n %3D

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Q: 1S prove that (a + b) = a² + b².

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Q: Suppose csc(4) =2 where A terminates in QIV, and sec(B) = -3 where B terminates in QII

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Q: 4) For A = ajax + azāy + azaz , B = b,ax + b2ay + bzaz, show that A.B cos 0 = A.AVB.B

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Q: 0/ the Valke of & that makes the Velteof the fumetion 2.

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Q: 2. The exact value of sec 57 is O2 2V3 -2 2V3 3

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Q: 3. Let A = {8k +7 : ke Z} and B = {4j+3 : j e Z}. Show that AC B. %3D

A: I am solving only Q3,as you mentioned.

Q: By using Residue fined S 2+3 sin z(z-1)² dz, C:|2|=2? (6 €13) (4

A: See the details solution in below

Q: Q. 8. In Fig. 8.7, PQ || AB and PR || AC. Prove that QR || BC. B

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Q: If A= B = verify that A(B + C) = AB+ AC. :) 1 If A = 2 and B show that (AB)" =B'AT 4 -1

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Q: 2) × if it was 2+4i and 2=3-1 3+1 2+i 2 prove that x² + 3xy + y² = 6 =

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Q: 1. If PR = 25, QR = 6 and NR = 10, find MR. %3D %3D 2. If MR = 12, NR = 9 and PR =3 QR, find PR. %3D

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Q: (a) Prove that de 2n a>b>0 Jo a+ bcose Ja? - b2

A: We will use basic knowledge of Integral Calculus and trigonometric identities to solve this…

Q: 11. Given: AB CD, EB FD AB TCD Prove: a. AAEG ACFG b. AG GC

A: Given:

Q: By using Caushy Riucman Prove that? e ae

A: We will use the following result :  Result : Let the function f (z) = u(x, y) + i v(x, y)  be…

Q: (-1+i/3)°, by using deMoivre 's theorem

A:

Q: Prove indirectly: "V n E Z, 4 ł (n² – 2)."|

A: Ans:Let us assume that 4/n2-2;∀n∈zthen we have there exist a positive integer k such…

Q: Q: Prove that : sin' ne -de = na for all n e N. sin' e

A: solution is given below

Q: Given: ZA = LC DC AB DA | СВ Prove: A B

A: Given that ∠A≅∠C, DC→∥AB→.

Q: a) Let Z = 7 – 13i, find: i) Im ) ii) (Re Z)?

A: Complex Numbers: The complex number is basically the combination of a real number and an imaginary…

Q: Let a = 8 and b = 9. Find m,n E Z such that am+bn =1.

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Q: (a) Given that x= In2 and y = In 5, (i) express In 50 in terms of x and y,

A: Simple logarithm problem.....

Q: Solve the following IBVP: Ut = Urr, 0 0, u(0, t) = 1, u(1, t) = t, t > 0, u(x, 0) = 1 + sin(x) - x,…

A: Given:  ut = uxx, 0 &lt; x &lt; 1, t &gt; 0,  u(0, t) = 1, u(1, t) = t, t &gt; 0,  u(x, 0) = 1 +…

Q: 5 Given: 1 = 2 AB = CB Show: AADB = ACDB 2

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Q: Given: AC BD and ZC AB ZDBA. Prove: AABC ABAD.

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Q: Q(x) = √3/2+² Ser fet de Prove that & QQ (-∞ ) = 1

A: Here we can use Gamma function formula Γn = ∫0∞ xn-1 e-x dx to evaluate the given improper integral.…

Q: リ この Shmo that e す。 are soluting of I

A: Note: Here, we will consider the differential equation y'''-6y''+11y'-6y=0....(1) instead of…

Q: 1. In the diagram below, BFCE, AB I BE DE 1 BE, and ZBFD = ZECA Prove that AABC ~ ADEF. B. CE A,

A: That's easy to follow, just a careful observation needed.

Q: ,32 Let C: z-il=3 and I = -dz. Then %3D z2 1=0 None of these O I= 4nti O I= 6ni O I= 8ni

A: The solution is given as

Q: Show that, by det by b2 92 •92 =TT (ai-bi) br b2 b3 an

A: We have to show that det111⋯1b1a1a1⋯a1b1b2a2a2⋮⋮⋮⋮b1b2b3⋯an=∏i=1nai−bi Let us consider the matrix…

Q: 1),Given: AB || CD; AC 1CD Find: x and y A, ax ay by 4,

A: Here given as Given  CD||AB Also given ∠ACD=90Then∠CAB=909x=90⇒x=10

Q: Compute for the value of tanh-(1 – i) In 5 my + 2.13i In /2 + 2.13i Inv - 4.25i 2 In /2 + 2.13i

A: Let, tanh-11-i=z. Thus, solve for z:…

Q: By using Caushy Rieman prove that (2) and (3) (2) 4ca) = e (3) .w prove Thot()-

A: (a)

Q: . Prove that, e²i = e²1=22. ez2

A: Let,z1=x1+iy1z2=x2+iy2z1-z2=x1+iy1-x2+iy2=x1+iy1-x2-iy2z1-z2=x1-x2+iy1-y2…

Q: what Reasow: Complete the proof that AHIK = AGJK. I HI I HJ GNew Givew Given K 26全CH Z GkJ Î CHKI ?…

A: angle G = angle H ( right angled angle) angle GKJ = angle HKI ( vertically opposite angle)…