4. Let, a, = 1, az = 2, b, = 0, b2 = 1, for n 2 3, an = 2an-1+ bn-1 for n 22 bn = bn-1+ an-1 express a, in terms of n.

Q: 9. Show that exp(iz) = exp(iz) if and only if z = nл (n = 0, ±1, 2, ...). (Compare

A: To prove that exp(iz)¯=exp(iz¯) if and only if z=nπn=0, ±1, ±2, . . ..

Q: 23. Given that 4sinh - 2coshx = Ae*+ Be* then A and B are respectively А. 1,-3 C. -1,-3 В. -1,3 D.…

A: Topic- trigonometry

Q: 0 2 4 6 2 3 4 5 If A = Compute C1(A). 2589 3 2 1 7

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Q: then 7(1 - а)М? + 6(1 - а) Мт %3D ВM?, 7(1 - а)т? + 6(1 — а)Мт %3D Вт?, Subtracting we obtain Y(1 –…

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Q: Given 21 = Z3 Prove jk 13 2.

A: Given,  ∠1≅∠3 To prove  j∥k

Q: 37.) Show all step to evaluate: SN NS /3-y² /3-y² dzdxdy

A: We have to find the value

Q: D. Show that if a, = 3n³ - 17n² + 2n - 6, then an O(n³).

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Q: 4.1c. Show that the product of two integers that can be represented by x2 +dy?, is always another…

A: Prove that the product of two integers of the form x2+dy2 is always of the form x2+dy2. Consider two…

Q: From (2) we get: 7h 1 (7g+7)n+1 - 2-(7g+6) (2 - N-(79+6) II ig+1)k-(a+1)t-q +1 h=0 k=1 7h 1…

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Q: 2. Let, a, = 3, az = 4 and for n2 3, a, = 2a,-1 + an-2 + 5, express a, in terms of n.

A: Introduction: The disparities between every two successive terms in an arithmetic progression (AP)…

Q: {2, 3} CA implies that 2 E A and 3 e A. Select one: O True False

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Q: Show that the series 3. + + 4 To t (-1) Lonverges absolutely.

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Q: Prove that if |z| = 3, then %3D 5 2z – 1 7 - 13 4+ 22

A: The given is related to complex numbers. The solution is explained below.

Q: Compute Re if z₁ = 5√√2 + 2√3i, and z2 = 3√√√2-5√3i 2

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Q: Consider the following IVP: у зу -10у - 1, уo) --1, у(0) - 2 Find the general solution. A 13 St re…

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Q: Prove that in Q(/-5) we have (3,1+ 2v-5)(3, 1 – 2-5) = (3).

A: To show the equality, first we take an element of the product and show that it is in (3) and then we…

Q: 00 8tan-in Zn=1 n3D1 1+n2

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Q: If (n + 1)(n + 2)an+1x" - nan-1x" = 0, n=1 show that for k = 1, 2, 3, ..., we have 1.3.5... (2k - 1)…

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Q: 6. Compute 1,= de for p= 0,1 10

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Q: Min. z = 4x1+3x2 s.t. 5x1 + 3x2 2 15 4x1 + 2x2 < 16 X1 20,x2 2 1

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Q: to: explicitly state the te- Σ2/ n=1

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Q: et, a1 = 3, a2 = 4 and for n > 3,an = 2an-1 + an-2 +n², express an in terms of n. %3D

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Q: 2. We can expect 15 x % of the batteries to last less than 30 months. 3. We can expect 16 v % of the…

A: The empirical rule for Normal distribution can be described as Here mean μ = 39, and SD σ = 3

Q: (16) Show that AB=BA for 0 0 0 3 0 0 0 1 A = and B = 0 3 1 2

A: A=-100030001 and B=500030002

Q: Suppose that Z~N(0,1). Then find Pr(2.78 < Z < 2.84)

A: Given data, Z~N(0,1) That is Mean=0 Standard deviation=1 P(2.78 &lt; Z &lt; 2.84)=?

Q: 27) Calculate AC, BC and (A + B)C. Also, verify that (A + B)C = AC + BC 0 6 71 ΓΟ 1 1] 2 If A = -6 0…

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Q: Consider that: 1 + 2 + ... + n = An^2 + Bn + C  For all n and for some constant A, B and C.…

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Q: If in a AP the sum of m tern=ms is equal to n and the sum of n terms is equal to n ,then prove that…

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Q: Compute [rN (1- ) ]- d. K

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Q: 2-Prove that: B (m, n)-ß (a,m) 3- Simplify to the simplest: (2+0(1-0) (1+0)(3-2)

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Q: If E (ar + br) 2n and n+1 k=1 Σ (ακ-bk) -- 1, then Σa- n+2 k=1 k-1 O 2 3 2 O 1 5. 2 Ο None

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Q: Show that 3n2+8nlogn is big-Oh (n²)

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Consider the following LP Min z = 3x, + 2x, +7x, s.t - x, + x, = 10 -2x, + x, – x, <-10 1 Solve the…

A: Given, Min Z=3x1+2x2+7x3s.t,                    -x1+x2           =10              -2x1+x2-x3≤-10 The…

Q: If x1=3, ,x2=3, xn=−6xn−1−5xn−2, ∀n≥3x1=3, ,x2=3, xn=−6xn−1−5xn−2, ∀n≥3. Find the general tem xn

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Q: If (ar + bx) = 4n and n+1 k-1 (ak-br) = then ar = n+2 k=1 k-1

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Q: For xn = 5n² + 9n³ + 1, an = en = n², prove or disprove: an = O(an) (n → 0)?

A:

Q: Suppose X~N(125,16), and Z~N(0,1). Then x = 141, is equivalent to z = ______. (Round your answer to…

A: For large sample n&gt;30 so, it is a z test. x~N(125,16) =125+16 = 141= x.

Q: Let, a1 = 1, az = 2, b1 = 0, b2 = 1, for n 2 3, 2ап-1 + bn-1 for n 22 b, = bn–1+ an-1 an express an…

A:

Q: Show that  1/3 Tn + 2/3Mn ) = S2n.

A: By definition, Tn=12∆xfx0+2fx1+....+2fxn-1+fxnMn=∆xfx1+fx2+.....+fxn-1+fxn…

Q: 3. Let, a1 = 3,az = 4 and for n > 3, an = 2an-1+ an-2 – 5, express a, in terms of n. %3D %3D

A: An arithmetic progression is a sequence of numbers such that the difference d between each…

Q: D. Let Find 2,-

A: We will find out the required value.

Q: Suppose X~N(163,7), and Z~N(0,1). Then x = 152, is equivalent to z = ______. (Round your answer to 2…

A: Z-score: The z-score value is a numerical measurement that describes a value of the relationship to…

Q: . Let, a, = 1, az = 2, b; = 0, b2 = 1, for n2 3, a, = 2an-1 + bn-1 for n22 b, = br-1+ an-1 express…

A:

Q: 8 Show that 1+2++ In S 1|+ |r2|++|rn| for any numbers r1, 22, ....

A: To show,    x1+x2+.....+xn≤x1+x2+.....xn   for any numbers  x1, x2,....., xn . Which is generalized…

Q: If p,q,r are prime number but p is not equal to q, then what is gcd(p,q)? What is the smallest…

A: It is given that p and q are prime numbers. Assume that gcdp, q=d. Then, d is the greatest common…

Q: 3. Show that if (AB)₁, (αB)₁, (Aß)₁, (αß)., and (AB)2, (αB)2, (AB)2, (aß)2, be two aggregates…

A:

Q: (16) Show that AB=BA for 1 5 0 0 A = 0 3 0 0 0 and B = 3 1 2

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Q: 20. a. If AB = 5.378" and ÁC = 3.782", find (1) DB and (2) ACB. (1) (2) B b. If DB = 3.017" and ĀCB…

A: Consider the given information and figure. AB=5.378'' and AC⏜=3.782'' In the given figure, the…

Q: 6n_ and If (ar + bx) = n+1 k-1 , then 1 (ak – br) = 712 n+2 k-1 k-1

A: If ∑k=1nak+bk=6nn+1 .......................(1)  and  ∑k=1nak-bk=nn+2-1n ......................(2) we…