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

Q: Question 1 -x2 1 4a?t prove that VE If v = dv ôt

A:

Q: In the figure, ZY = ZX and YZ is produced to T. Prove that YT> XT. Y

A:

Q: Prove by mathematical induction: For Vn E Z*,7|(232 – 1)

A:

Q: H) 9f zyzec then prove thal nl x=4=Z, (alogen) %3D

A:

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

A:

Q: Z1 is complementary to ZM 22 is complementary to ZM Z1 = 2 Given: Prove: M R 2

A: Given: ∠1 is complimentary to ∠M. ∠2 is complimentary to ∠M. To prove: ∠1≅∠2 According to the…

Q: W 29) What additional information can be used to prove AVUW E AYXZ by ASA? A) Zv = Zz B) 스w Zz D)…

A: We have to find extra condition for congruence of the triangles VUW and YXZ by ASA. Given △VUW≅△YXZ…

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

A: ∠P≅∠R,∠Q≅∠S

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

A: We have to simplify

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: Exercise 4 Show that for cach k EN it holds that kn-k < n! S n", Vn E N, n2 k. Deduce from this that…

A:

Q: Prove that if 0 < a < y, then ỹ – VI < Vy– a.

A:

Q: Given that n ≥ 2 , x ∈ Rn  Prove that there exists a y ∈ Rn in where y ≠ 0, and xy = 0

A:

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

A:

Q: 1. Prove each of the following results: (a) |zw|=|w-z, Vw, z EC (b) ||zw|≤|zw, w z (c) |z| ≤ Re(z) ≤…

A:

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

A:

Q: J prove that for 0 <r<R

A:

Q: IS T-dist prove o E(T)=0 QvarしT)=て %3D V-2

A:

Q: Given: ZG = ZI, FH bisects ZGFI Prove: GF = IF H

A: Given that ∠G≅∠I FH bisects ∠GFI To prove that GF≅IF

Q: Suppose that C> 1. Prove that if t > Vm ln C+In C, then ()/F) >C.

A: We will use the following Strining's approximation :  n! ≈ √(2πn) e-n nn To prove the given…

Q: Given: ZABD = LAED Prove: ZC = LF C B A E F

A: Given: ∠ABD≅∠AED if ∠ABD≅∠AED then  180∘-∠ABD=180∘-∠AED                                         ∵…

Q: Suppose AE R, v#0, and (A- A)v#0. Use the fact that A is symmetric show that it is impossible to…

A:

Q: if x, y>o such that x Sy then Vã svy Prove by direct method

A:

Q: In AABC andAXYZ, AB = AC = XY, BC =Y Z and mZZ = 90. Prove: mZX > mZA %3D

A: We have given two triangles , ∆ABC,∆XYZ and AB=AC=XY and ∠Z=90∘ . and BC=YZ We have to prove that…

Q: nd C such that AC=E

A:

Q: Let a,b E R with a # 0, b # 0. Prove that (ab)¯1 = a°1b´1. %3D

A:

Q: Use the accompanying diagram to solve Exercises 10 and 11. JKI KT, ET I KT, KV = TL, JL = EV. 10.…

A: topic - congruent triangles

Q: In the given figure, X > K. Prove that WY> JL. K X Y W

A: Here , we have ∠X&gt;∠K we have to prove that WY&gt;JL

Q: MN 1 NP, QR 1 RP ΔΟRP Given: Prove: ΔΜΝΡ ~ N R P Exercises 17, 18

A: A triangle with two perpendicular lines

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: If u=l0g Cx +ytz- 3>yz) prove that Ce+y+z) he

A: Given that u=logx3+y3+z3-3xyz Then  ∂u∂x=3x2-3yzx3+y3+z3-3xyz ∂u∂y=3y2-3xzx3+y3+z3-3xyz…

Q: 6. Use Green's Theorem to evaluate O (y* – xy?) dæ + (2 – a*) dy where C is shown below. y -2 ² +y²…

A: Green's theorem

Q: Let BE Cnxn. If z" Bz = 0 for all z E C, then show that B = 0.

A: Given expression is

Q: 1. If x, y, z E R, prove that (a) \x+y\ < \x| + \yl- (b) |x– y| < |x – z|+|z– y|, and (c) ||지| -…

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Q: Consider f : N → N, g : N → N and          h : N → R defined as f(x) = 2x,g (y) = 3y + 4 and h (z) =…

A: Given, Consider f : N → N, g : N → N and          h : N → R defined as f(x) = 2x, g (y) = 3y + 4 and…

Q: Express the following tunctrons in the form u+iv f(2)=In (I+z)

A: Solve the given problem.

Q: 19. Given: OABCD; BE | MD: M is the midpoint of AB. Prove: DE = BC %3D E D. A M В

A: We have the given figure as, Here, □ABCD is a parallelogram and in figure BE∥MD. M is the mid point…

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: Proue that || A|1maπi <j <n 1 Σajl . m

A: In the given question we have to prove that   A1 = max1≤j≤n{∑i=1maij}                         (1)the…

Q: Solve the glven differentlal equation by using an appropriate substitution. The DE Is of the form Y…

A:

Q: 1. Compute e? and In (z) in the form a + jb, where z equals to. i. 3+ jn ii. V2-j ji. j TT 1

A: It is required to find ez &amp; lnz for the given complex numbers. A complex number z=a+jb can be…

Q: 10. Given: YT = YP, LC = LR, Proof ZT= LP Prove: CT = RP R

A: Consider

Q: Let M, = Z, – Z;-1, Zo = 0, where {Zn, n21} is a martingale. Show that E(M,„Z„-1] = 0

A:

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

A:

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

A:

Q: B a. In the figure, if AX = (3x + 1) cm, BX = 4x - 1 cm, AY = 4x + cm, YC= 5x-1 cm and x = 2, prove…

A: SOLUTION-

Q: Given: MN and PQ intersect at K; ZM = LQ Prove: ZP = ZN K N

A: Solution: Consider the given and MN and PQ intersecting at K therefore  ∠MKP = ∠QKN    ...(1) Also,…

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:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.