(b) Verify that 17(s +1) (s² – 2s – 3)(s2+2s +2) s+5 (s – 3) (s2 +2s +2)

Q: 9) x² + y² + 12x + 22y + 108 = 0 CX+67² + y +117²=49 CX-47² \ Cy-151²=9 CX-107² + (y +1272²=9 CX-5)…

A:

Q: (b) Suppose 2 5 1 2 4 6 0 А 3D| -1 -1 0 B -3 4 5 and C =|0 1 4 3 3 2 0 0 -3 compute tr( B' A' +…

A:

Q: S 2dx (3× +12メ -15)3

A: Given,  ∫23x2+12x-1512dx  We have to evaluate it.

Q: )- ニ ZS+ト 32 |ニ2+

A: To solve the equation: x+y+z=12x-4y-3z=9-3x+2y+5z=-5

Q: An instructor of mathematics wishes to determine the relationship of grades on a final examination…

A:

Q: b 2x 1! + 5x 2! + .+ (nt + 1)п! %3D п(п + 1)! + 10 x 3! + .. 2 3 + .. 1 n 1 + + + = 1 - 2! 3! 4! (п…

A: (b) Case 1 : n=1 2×1!+5×2!+10×3!+...+(12+1)1! = 1(1+1)!2×1! = 1(2)!2 = 2 Therefore, the result is…

Q: 2. {x|x = -29° + n360°} = {x|x = 331° + n360°} where n is any interger.

A: (2) Given- x|x=-29°+n360°=x|x=331°+n360° To find- The above statement is correct or not.

Q: An instructor of mathematics wishes to determine the relationship of grades on a final examination…

A:

Q: 1. Find the 5roots of z1 = -V3+iv3. %3D

A: (As per bartleby guidelines, for multiple questions asked, only the first question will be solved.…

Q: #31

A: The given expression is

Q: * Q1 1 |1 2 31 -1 -1 0 21 3 -3 11 14 5 -71 -41 -7] -14] 2. -11 3. 5 -7 5] 5. 1 2 3 1. 4.

A:

Q: write down the first five terms of each sequence

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

Q: 4. (1+ 4x²)y" — 8y = 0. ANS. yao(1 + 4x²) + a₁ Σ k=0 (-1)*+¹2²kx2k+1 4k² - 1 valid for x <

A:

Q: * Q1 [X1 x2 If 3 [x3 X4] 2 X1 + x2 -1 4x4 [x3+ x4 1. x1 = -2, x2 = 2, x3 = -2, x4 = -3. = -3 2. X1 =…

A:

Q: 3. (a) Show that x2 1 1 1 (x² – 4)² 4 х — 2 x +2

A: We can solve this problem using partial fraction. According to the Bartleby guidelines I have to…

Q: Show that when |z +1| < 1,z² =1+£(n +1)(z+1)" n=1

A:

Q: -xx-9 and y=-x+3 у -9-8-7-6-5-4-3 1 y=x: POINT(S): IN 76 NWA -2 N3456789 -2 -3 -6 -7 -8 23456 -9 +2…

A: We have to find the graph

Q: 19.The expansion of 1- x) = X. 1- 4x + 7x2 C.1-4x- 7x² - .. B. 1+4x- 7x² + D. 1+4x + 7x² + ... ...…

A:

Q: * Q1 X1 x27 -图 If 3 2 4 X1 +x2 %3D 4x4. [x3 3 +x4 1. x1 = -2, x2 = 2, x3 = -2, x4 -3. 2. x1 = 2, x2…

A:

Q: solve each system of equations using matrices. If the system has no solution, say that it is…

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Find (2n – 3)(n + 4). * О Зn +1 О 2n^2 + 5n -12 О 2n^2- 12 О 2n^2 + 11п +1 Simplify: 2a^2(5а- 6) -…

A:

Q: Determine x[2] and x[3] given (a) 2x[n+2] – 5x[n+ 1] = 4n, x[1] = 2 (b) 6x[n] – x[n – 1]+ 2x[n – 2]…

A: Given:  a) b) c)

Q: 1. x2 + 2x- 15 = 0 2. p? – 7p – 18 = 0 3. -3a2 + 27a - 54 0 4. 3x(2x + 5) = 0 5. 12x2 - 4x = 0 6.…

A: (1).             x2 + 2x - 15 = 0                     ⇒  x2 - 3x + 5x - 15 = 0                     ⇒…

Q: Зп + 1, A) 2n 4 — 2п n=1 n1-3n В) 42n n=0 (-5)1+2n C) 25п-3 n=4

A: Here we apply different tests like comparison test and Leibniz test.

Q: Find the least squares solutio 1 3 2 2 x= 5 1 5 8 O A. (0,2) O B. (0,1) OC (1,1) O D. (2.1)

A: Here we have to find the least-squares solutions to,  132215x=058 compare with, Ax=B

Q: * Q1 X1 +x2] 3 X1 4 X2 If 3 [x3 X4] [x3 + X4 1. x1 = -2, x2 = 2, x3 = -2, x4 = -3. 2. x1 = 2, x2…

A: We will perform the addition and scalar multiplication of matrices on both the sides. Then we will…

Q: x(n) (0.8)" u(-n-1) -1 1-(0.8)# خيار 3 0 خيار 4 -1 1-(0.8)

A: Solution

Q: 22. 5n2 + 35 = 0 23. 2m2 + 10 = 0 24.4m2 + 76 = 0 25. -2m2 -6 = 0 raw-Hill Companies, Inc.

A:

Q: Employ a suitable c 2n² +3n diverge (a) V5+n² n=1

A: ∑n=1∞2n2+3n5+n5limn→∞an+1an= limn→∞2(n+1)2+3(n+1)5+(n+1)52n2+3n5+n5= limn→∞…

Q: [1 4 -1] ‚Y = |0 2 -5. Find det(XYX-1). Lo o 7 8 -1| -V2 2 If X = 5.5 4 %3D -1l

A:

Q: 6. Show that when 0 < |z – 1| < 2, Σ (z-1)(z-3) 00 --Σ n=0 = (z-1)" 2n+2 1 2(z - 1)*

A:

Q: 2. Σ--1)k , k%3D k+1

A: The given sequence is ∑k=0∞-1kkk+1

Q: Solve for n if nEN: (4+8+12+ ... +4(n-1)) + (2+4.5+7+. .. 4+5n -%3D126.5 2

A: Sum of n natural numbers is n(n+1)/2.

Q: 4. Use Cramer's rulc to solve the lincar systemn. r+ 3y 2 5.r +7y 3

A:

Q: Consider the following LP Min z= 3x, + 2.x, +7x, s.t - x, +x, =10 -2x, + x, - x, <-10 X,,X,,X, 2 0…

A: In the given LP problem when we solve it via simplex method, we use a series of tableaus.

Q: 2.3.1. (3a³b*)³ =Bab 10 3D59 049 ab 2.3.2. (-4a³b²)° -4ab3+2 (24 - 43+ 82)2 4 44 4 2.3.3. 4. 4.…

A: As per the guidelines we can solve 3 questions only.

Q: Evaluate * (1 – x²)3/2° 1 + c 3 1-x2 -1 + c /1 – x² O Option 4 Option 2 2 1 1 + c /1 – x² :+c 3 V1-…

A: ∫ xdx/(1-x2)3/2 here assume that  1-x2 = u -2x = du/dx xdx = -du/2 ∫ -du/2u3/2 ∫ -u-3/2du/2 2u-1/2/2…

Q: 71 Compute Σ (5k2 + k - 3) i=1

A: Solved below

Q: 2х — у %3D 4 11%3D у — 2х + 5 -

A:

Q: 4. Show that V2 ¢ Q(v3) and Q(V2, v3) = Q(/2+v3). Hence find the mmp of V2+ V3 over Q.

A: We know that ,  ℚ2 = a + b2  / a , b ∈ ℚ ℚ3 = a + b3  / a , b ∈ ℚ  We need to prove that , 2 ∉ ℚ3 On…

Q: (b) Z/n = (q) if and only if kq 0 for all 1 < k <n.

A:

Q: B. Use combinatorial proof to solve the following problems 1. (;) (:3) = (2) (3) п-2 \k-2,

A: The formula for combination is nCr = n! / [r! (n – r)!] = [n (n – 1) … (n – r + 1)]/r!. Explanation:…

Q: 2. Find |A-'ATBA-1| where -2 1 4 -1 -4 -1 1 3 1 3 В — 5 -1 1 -1 7 2 -1 -7 1 4 -3 7

A: Recall that, |A|=|AT|, |A|-1=|A-1| and |AB|=|A||B|.

Q: 4. Show that V2 ¢ Q(V3) and Q(/2, v3) = Q(/2+v3). Hence find the mmp of V2+ V3 over Q.

A:

Q: 4 -2 3 Compute A - 413 and (413 )A, where A=-3 3 -6 - 2 2

A: Here I3 is identity matrix with order 3X3

Q: 1. Σ n! n=0 (-1)"x²n+1 2. ) 2n + 1 n=0 (-1)"x2n 3.) (2n)! n=0 x2n+1 4. (-1)"

A:

Q: 2. 4s+32 s²-16

A: