Let, a, = 3, a2 = 4 and for n2 3, a,= 2an-1+ an-2 + n + 1, express a, in terms of n. %3D %3D %3D

Q: We call  3√a the  ________ of a.

A: To fill: the blank in the statement. Given: The statement is " We call a3 the _____of a" . Concept…

Q: Q3- Find the numerical value of §. xdz, if c = c, + c2 + C3.defined in the given figure. (2,2) C2…

A: We will find out the required numerical value.

Q: Find the 73%, 82% and 94% response time for the following system given: ÿ + 2ỷ + 4y = U(t) %3D

A: Given y ..+2y.+4y=U(t)     where U(t) =Unit step function Taking Laplace Transform on both sides,…

Q: Let a, b e Z. If both a and b are odd, then 5a+b is even and a+4b is odd.

A: Proof:  Given that a and b are odd Let a=2k+1 and b = 2m+1 for some  integers k, m  ∈Z Now,…

Q: Show that if x > 9, then x³ – 8x? + 2x > 3. Show that for all n e N, if n > 10, then nª – 2n² > 3n³.

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Q: For all n ≥ 1, let an = (a) Find a1, a2, A3, A4. (b) Computea. i=1 (c) Computea. i=1 (n + 1)² n!…

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Q: Complete the table to show that ex eventually “overpowers” x5

A: Consider the given function below: Put different values of x and compute different values of y.

Q: Let a, b eR with a < b. Assume that a + <b - for all n E N. Show that b- = (a, b). %3D n n=1

A: We will show  two sets are equal.

Q: Q3- Find the numerical value of 6. xdz,if c = c, + c2 + C3.defined in the given figure. (2,2) (1,1)…

A: Given is∮c x dzalong C1equation of linex-12-1=y-11-1=tx=t+1   y=1dxdt=1   dydt=0∫c1f(x,y) ds=∫01…

Q: 4. Show that for all formulas p, p,0 E S(P), (a) (9 = 4) = ¬(4 ^ ¬ab).

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Q: for all integers n >1 E, i = n(n+1} %3D 2

A: To prove the sum of n natural numbers n≥1 is  ∑i=1ni=n(n+1)2

Q: Find the value of ‘v’ in v2 – 2v -15 = 0, if v is a natural number.

A: Given quadratic equation is,

Q: Suppose an = 4an – 1 + 6an – 2 a4 = 96, a5 = 430, and a6 = 2276. Find а1, а2, and аҙ. аз. a1 Preview…

A: Here, recurrence formula is, an=4an-1+6an-2-2an-3

Q: Let a, b eR with a < b. Assume that a + <b - for all n e N. Show that n n=1

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Q: Find A', B' and (AB)". Deduce that (AB) = B'A". %3D

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Q: Find the value of b for which 1+ eb + e2b + e3b + ... =9. b=3ln(2) – 2ln(3) b=2ln(2) + 3ln(3) b=…

A: Solve by infinite sum formula

Q: Determine whether the following is true: (a) (b) n+1 Σ₁2²= n · 2n+² + 2, i=1 n i-0 3¹ 1- 3n+1 13…

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Q: (9) Let X b(n,- and E(3x) = E(3-5x) find n.

A: It is an important part of statistics . It is widely used .

Q: Find a and b such that 2 1 = a -4 + b -4

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Q: . If an+1 = 2an + 3 and ao = 1, then a7 509 513 496 487

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Q: Given the explicit formula, find the first 5 terms. f(n) = 3"-1 %3D

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Q: Find conditions on a, b, c, and d such that AB = BA

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Q: Assume that n(U)=115n(U)=115, n(B′)=65n(B′)=65, n(A∩B′)=32n(A∩B′)=32, and n(A∩B)=19n(A∩B)=19 Find…

A: Now consider,

Q: 4. For each positive integer i, let A, = {x € R| -<x < } = (-;;4) a. Find U-, A;. i=1 b. Find N 4:-…

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Q: Let ab be a two-digit number where a is the tens digit and b is the ones digit. Find the number of…

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Q: (51) Let X = b(6, p) and E(3x) = E(2-6x) find p.

A: We have given that, The random variable X that follows Binomial distribution i.e. X~B(6,p). Here,…

Q: Let A= and B= then AB equa 2 2

A: Given A=1100 and B=1122

Q: If a_1=9a1​=9 and a_n=4a_{n-1}an​=4an−1​ then find the value of a_5a5

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Q: the value(s) of c such that 3c2n n=0

A: The given question is taken from the sequence and series in which we have to find the value of the c…

Q: If z̟ = 1 + jb , z2 = re¬j² , z1/z2 = -10, determine all possible values of b and r.

A: According to the given information, it is required to determine the possible values of b and r.

Q: Assume that n(U)=90n(U)=90, n(A)=41n(A)=41, n(B′)=50n(B′)=50, and n(A∪B)=63n(A∪B)=63. Find n(A∩B)

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Q: Let R = Z10 O Z100- (a) How many units does R have? (b) How many zero divisors does R have?

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Q: The value of Ax or h in Simpson's Rule is 0 b-a n 0 b-a 2n b-a 3n O (b - a) о

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Q: For each integer n > 2, let P(n) bè thế för n-1 Eili +2) = n(n-1)(2n + 5) 6. %3D i=1

A: Given                   P(n):   ∑i=1n-1i(i+2)=nn-12n+56,          n≥2

Q: HW/ O Find A. B , AXB For A= (+ 3j+2K

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

Q: Find the total number of in H.C.F. of n and 36 is 1.

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Q: Q3) Assume A = [4 16 3 11 7 21 [3 21 and B = 1 5 (3 14 3 show that (AB)' = B' A'

A: Given, A=431672B=321543

Q: Suppose X N(u=120, o = 3), determine the value of x such that P(X>x)-D0.05. %3D %3D

A: It is given that X follows N(mean =  120, SD = 3), then Z = (X - mean)/SD follows N(0,1)

Q: e Va € R, if 1 ≤ a, then ³n € N, 2a + n n+1 <a

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Q: Let x~ N( M, -) Ti- 5, Ź (xi-x)* 2 %3D %3D n -1 Ź(xi- 7)" 2 2. T2 = 2. 2. 2. Check the Consist of 6,…

A: We know that, Y=∑xi-x¯2σ2~χn-12 Then  EY=n-1⇒E∑xi-x¯2σ2=n-1⇒E∑xi-x¯2=n-1σ2---&gt;1…

Q: het A=" and let fce)= 20x²-4X+5. Find 3 4 -3 り 3 4 ) fCA)

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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…

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Q: Find all values of a, b, and c for which A is symmetric,

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Q: Find all m, n E N such that: n! + 2n + 49 = m²

A: This problem can be solved by graphical approach. Use a graphing utility to plot the graph of…

Q: (33) Let X = b(20, p) and E-x) = E(3–10x) find p. р.

A: Let X follows binomial distribution with parameters ( n =20, p) The mean of X is, Use the…

Q: Q3/ The value of k such that P2 (1) = 2.8, 2 4 of 1 2 Is

A: Lagrange interpolating polynomial for n=2 is:…

Q: If P(A) = 1 P(B) = 2 and P(A U B) 11 find (i) P(A/B), (ii) P(exactly one of A and B occurs), 12 4…

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Q: Find the explicit formula. 40, 50, 60, 70, .. А) а %3 30 + 11п В) а 3 31 + 10п С) а %3D53- 12n D) a…

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Q: Let 1 A = 1 3 2, Find A- in terms of c.

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Q: Evaluate if possible a) 2 ∞ Σα η=4 n2+4n+3

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