E A B >D Given: AE || FD, EC = BF and ZABF S ZECD. Prove: AB 2 CD. F

Q: We defined NCE) = ZE for ZE Z Ii]. Prove N (Zw) = NLZ) Ncw) for all Z,W E Z6] .

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Q: 13 Given: LA = LE, AB = BE, FB 1 AE, 22 = 23 F 23 4. В Prove: CB = DB A E

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Q: 3) Let PIASR ond Thi AxC ßeD. Then his a Anction. Te Ø # 4 B and ø 7b cD then that h'(Y x Y% ]=…

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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: If AB = B for some B # 0, then A is inertible.

A:

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: Given: DE = FG; GD = EF; ZHDE and Z KFG are rt.6. Prove: DH = FK D K G E

A: Given: In figure  DE≅FG; GD≅EF; ∠HDE and ∠KFG are right angles, To show: DH≅FK

Q: Given: AB = Dc and AC = DB. Prove: AABCE ADCB. A B C AB DC gven AC DB g ven BC CB A ABC ADCB…

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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 a, b, c in Q such that (1 + VA/(2 – V2) = a + bV7 + cVA. Note that such a, b, c exist, since…

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Q: f: [o,17 s R. )m =l,2,3, fcx) = 3. otherwise Prove that f t R[O,1]

A: The given function is f: 0,1→Rwhere f(x)=1 if x=1n,n=1,2,3,...0 otherwise

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

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Q: If f = xi+ yj+ zk,1Fl =r,and n =, then show that grad (E) == %3D

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

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Q: Let f(2)=³ and let C = {z € C : |z| = 1}, described in the positive sense. Determine the value of Ac…

A: Given that             fz=z4-5z2      and    C=z∈ℂ : z=1.

Q: How do I prove this?

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Q: 3. Show that the following ODE is homogeneous then solve it. 2xyy' = x2 + y?

A: 3). Given: 2xyy'=x2+y2 So, we can also write as: 2xydydx=x2+y2dydx=x2+y22xy....1 Let,…

Q: Exercise 4. sin(3z) Let f(z) : and C: |z| = 1. Then ſ. f(z)dz = z?(z-n) а. 0 b. Злі с. —6лі d. None…

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Q: The Hausdorff dimension of {z ER : |æ| = 4} is d. Answer: = P

A: Hausdorff dimension of the given set is d=5.

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

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Q: 2. Given: KM bisects ZJKL. Prove: m22 = m23 %3D K M 3.

A: Concept- Opposite angle are same

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

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

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Q: en Gx) show that GCxx) = to is a t Slution to x y" + Cy')a = c

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Q: Let H(x) be an antiderivative of 1sm z if H(5) = 7, then H(2) =

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Q: For which values of z is w =1/(z – i), defined? For these values obtain u and v and evaluate w when…

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Q: E Given: AC= BD D AE = DF ZA = ZD A Prove: ACAE= ABDF F

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Q: Prove that eie ei(0+2K) ,where k = 0,±1, +2,...., = D

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Q: 22. Given: 4I 2 Prove: a. AJIG AJZY JG GI b. JY YZ Y

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Q: (a) Let r = ri+ yj + zk and let r = ||r||. Prove that - (1) a

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Q: Exercise 3. sin(3z) Let f(z) and C: |z – n| = 1. Then S. f(z)dz = z²(z-n) а. О b. 2ni с. — 2пі d.…

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

A: Given expression is

Q: 2. Given: AB = DB 2. EB = CB Prove: ZA ZD E D STATEMENTS REASONS 1. AB DB; EB = CB 1. Given 2. Z1 2…

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Q: AB = DC 4. D Given: AC S DB, Prove: A ABC A C 1. AC = DB 1. 2. AB = DC 2. 3. 3. The Reflexive…

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Q: Consider the formula A = Vx Vy.p(x,y) ^ ¬q(x, y). (b) Show that A is falsifiable (i.e. not valid) by…

A: We are given a formula as : A≡∀x∀y.p(x,y)∧¬q(x,y) We need to show that A is falsifiable by giving an…

Q: F Given: ABCX is a O: DXFE is a C. Prove: ZB = LE X, D

A: Given that, ABCX is a parallelogram and DXFE is a parallelogram. We have to prove that, <B =…

Q: IF| = r r) = -i = 5xi + 2yj – 2zk so be it where div() , grad(f find all of

A: Solution:

Q: Evaluate cz dz, where c is |z| = 1 zG-2) Inz %3D

A: Let

Q: DG DH Given: DE ZDGH = LE DF Prove:

A: Consider the figure with given: DGDE=DHHF. Prove: ∠DGH≅∠E Consider △DEF. Apply theorem- If a line…

Q: Given the value of det(A) (above) what is true [select all] OA is invertible O ker(A) = R? O ker(A)…

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Q: Given: BC 1 AD; EF 1 AD; BC = EF; B LE 2. Prove: KA= D F A 1 C E %3D 2.

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

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Q: az az Q1/ a. Find and if z= (x² + y²) where x =r+ e*and ar as y=Ins

A: Solution: The objective is to find the partial derivatives of the given equation

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

A: Consider

Q: VneN 1+E, i i! = (n+ 1)! Vne N24 n!> 2" Let x€ R,-1. Prove that Vn eN (1+x)" > 1+ nx

A: 1. The statement, P(n) : 1+∑i=1ni·i! = (n+1)!  We have to show the statement, P(n) is true for n ∈N…

Q: 1 (aw C. Ifw=f(x.y) and x=1. coso, y=. sino. Prove that

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Q: DE DF EF 11. Given: GH Prove: ZE E LH GI HI DE 12. Given: GH EF ; LE = LH HI E H. EF Prove: HI DF…

A: Given: ∆DEF and ∆GHI DEGH=DFGI=EFHI

Q: 4. Given: AC DB, AB = DC Prove: < A E<D C 1. AC = DB 1. 2. 2. 3. 3. The Reflexive Property 4. A ABC…

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Q: (2х — Зу + 4)dx + 3(х — 1)dy %3D 0, у(3) %3D 2 -

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Q: D B. E C Given: AB XEB = CB × DB Prove: AABC- ADBE

A: To Determine: prove △ABC~△DBE Given: we have a figure in which we have triangles △ABC and △DBE also…