3 a A- E Prove ZBED = ZABC + ZCDE. %3D

Q: 6. Suppose that {a,} satisfies the hypothesis of Leibniz's Theorem. Use the proof of Leibniz's…

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Q: 5. Show that if x,y∈Z and 3|x^2+y^2 then          3|x or 3|y 6. Show that if c=sa+tb where c=(a,b),…

A: Please check that x=1,y=3, then x^2+y^2=10 does not divide by 3. So  must 3|x and 3|y instead of 3|x…

Q: 3. Find two elements a and b in Z25 such that a and b are units, but a +b is not a unit. Justify…

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Q: ands 1. Let m*(A) = 0. Prove that for every B, m" (BUA) = m" (B). %3D %3D

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

Q: Let O 3i] A = %3D 3i 6] Find the Laurent expansion of the resolvent of A around the point z = 3.

A: Given: The given: A03i3i6 To find the Laurent expansion of the resolvent of A.

Q: 5. Use Taylor's theorem to write down an explicit formula for R, (1). Conclude that R, (1) + 0, and…

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Q: . Eualuati losh (12)d2 uhere. C di the Ciscube. lel=2

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Q: 14. Given that Z calculate /Z/ and arg Z. %3D 3+ i'

A: Argument and modules of complex number

Q: 7. In ABCD, AC and BD divide each other in half at E. (a) Prove that ZDBC ZBDA. (b) Prove that ADBC…

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Q: How do I find the value of X?

A: Triangle

Q: (1 mark) Let x, Y, A, µ E Z. Prove that if 1 = Ar+ µy then I, y are relatively prime.

A: Basic properties of gcd will be used to solve this problem. The typesetted solution in latex is…

Q: Prove that c = cn. i=1

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Q: 3) Given: MN||PO; LM = 20 Prove: MP||NO

A: Given that:  MN||PO and   ∠M=∠O

Q: 8. Work out a Gaussian quadrature formula of the form Ans. A; = 1, x; = Aif(x1) + Arf (x2). f(x) dr

A: The given problem is to prove the following integral, the proof is to show the 2 point gaussian…

Q: If B,>3, then a measure of kurtosis is Leptokurtic Mesokurtic Platykurtic None of the above

A: In question, We'll discuss about measure of kurtosis.

Q: ) 9f cp andeobea Semi diasmeter pairaf conjuegate 4-the llMipse 4L1 then the adeesof carvatere al P…

A: Given: The equation of the ellipse is x2a2+y2b2=1. We need to show that the radius of curvature at…

Q: 2, z) = 5 and the surfac e at (1,2,3). Evaluate = reasons).

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Q: A cubic spline S is defined by: So(x) = 3(x – 2) + (x – 2)² – 4(x – 2)ª 32 if 25x53 S(x) s,(+) =…

A: true

Q: Evaluate S, 5y²dV where E is the reqion below x + 3y + 6z = 9 in E the first octant.

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Q: If e'z = /3 -i.Then Im (z) is %3D O a. e2 b. 0 С. 1 d. -In(2)

A: eiz=3-i Now let z=x+iy. Then, ⇒eix+iy=3-i⇒eix+i2y=3-i⇒eix-y=3-i…

Q: Find the value(s) of k such that A is singular.

A: A matrix is singular if its determinant value is zero. So we find the determinant value of the given…

Q: 1. Condense and expand. a) Condense as a single quantity: 1 In(3)+- In(x? +1)-3 In(1+x) 3 b) Expand:…

A: Given, (a)  To condense ln3 + 13ln(x2+1) -3ln(1+x) (b) To expand lnx2+1x+2(1+x)5

Q: (a) /3yin In (g) dy

A: First remove the constant and then substitute the formula by integrating by parts and then simplify.

Q: 4. Let A %3D {a, b, c}, В %3D {x, у}, and C %3D {0, 1}. Find a) АхВх С b) СхВхА с) СхАх В d) ВxВxВ.

A: Given that: 4. A={a, b, c}, B={x, y}, C={0, 1}   NOTE: As per our answering guidelines, we can only…

Q: 34. Prove parts (a) and (c) of Theorem 3.2.3.

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Q: Example 8-13. If X ~ B (n , p), show that : E(X-r)* = " ; Cov (, X) =- pq n

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Q: 5. 9 ycotx %D CSC

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Q: Activity 1: Give the proof of theorem 42. Given: MZFBO > MZFOB and mZIBO = 1OB Prove: MZFOI < MZFBI…

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

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Q: 1. Find the area inside the inner loop of r 3-8cos 0.

A: according to our guidelines we can answer only  first question and rest can be reposted.

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

A: Given that ∠A≅∠C, DC→∥AB→.

Q: 1: Find Z by convolution theorem. (z- 2)

A: convolution theorem

Q: If g(a) = a°(exin²a+eoa²a), then gʻ(a) is: atcos.

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Q: dz and ду dz Find z = a° In (1+ cy) az dz ду ||

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Q: B E D Suppose AB= AE. Can you use the SSS Postulate or the SAS Postulate to prove AABC = AAED?

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Q: Find the value OF the Modulus oF Z in z=(2-1)(5+j12) 3.

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Q: 10. Which theorem can you prove, given that mzl=m2 in the figure above? Explain your answer.

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Q: 9. Let D have characteristic 2. Show that (a) (a+b)² = a² + b² (b) (a+b)“ = a“ + bª 4 153

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Q: enoitetimil torte stigasb = 4", where m, neN. 10. Prove the identity: 3 r=0 itong s

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Q: terms HK K . J 12 in

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Q: QUESTION 2 Ustng De Molure's Theorem, evaluate 12 3 -itl ard leave four angwer in the form Z=a+ ib

A: Topic:- complex number

Q: 15. YABCIa stnight Ine, ZCRO, and D Mbecta C+ ZCBG, then Zx y

A: Solution Given   From above the figure IfABC  ↔ is a stright line ,∠r=∠s BE→ bisects the ∠CBO . and…

Q: k and Ĉ = к апd rs along the a ICorteeion

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Q: 123 A=162 3 3 5 9 3 Let Calceelate Ā By Cayley- Hamil ton theorem.

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Q: QUESTION 3 Prove: ( N A = U A°. a EA Attach File Browse Local Files

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Q: a lal a. 01 : R³ → → M22(R) given by 0 where |2| is the modulus of x.

A: I am providing the solution of part(a) only and the detailed solution is as follows below:

Q: Section 3.1 Phblem H2 Compute the derivativo at the qiven value of a ha)=/3x-4 for aF 2

A: Given:…

Q: -- a) such that ab =1. Let p>1 be a prime number. Show that for each a + 0 in Zn there is b in Zp…

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Q: (a)] Show that 1+(1+z)/2 csch z In • [(b)] Use part (a) to find all the values of csch (-2i).

A: Let: