Determine the definite integral that describes the shaded region above. 5 (6v² - 6v+6) dw 5 [² (6v² - 60+ -5 ○f (6v²- of 6) (6v² – 6v + 6) dv - 5 (6₂² - Gv + 6)df 5 -5 (6v² - 6v+6) dv (6v² – 6v + 6) dv

Q: Why must nCr always be less than or equal to nPr for any given n and r

A: Permutations and combinations are given.

Q: a a +1 2² (² + ¹ + x² = 1 [(¹-x)² + (1 + x)² ] F1 2 2 2

A:

Q: 50 50 51 7. + 40 39 40 • () - €) (") - () () - () () 7 8. 4 10 9. 2 10 8 8. 8 8. 10. + 2 3 6.

A: We can solve the given problem using concept of fractions.

Q: 2. Let A = 201-18 and /= 2 1 1 2 01 Find A(A+1).

A: A=[2 1      1 2]I=[1 0      0 1]

Q: a Prove that < 16 – a| for each a, b e R. - V62 + 1 Va? + 1

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Q: れ+5

A:

Q: Example 7.4.1. If a = (2, -1, 3) and b (1,2, 1), find a x b.

A:

Q: NCx) = x² - 2x - 5 MQx) = 2x+3 N of M

A:

Q: 2 solve the following set of three equations by Gramer and by A XI-X22X3 = 1 2X1 - X3 = 2 X₁ + X₂ +…

A: Given the system of equations: x1-x2-2x3=12x1-x3=2x1+x2+x3=3 Solve using Cramer's rule.

Q: 6. If z> 1, then N 1 - T || 1 H H + ....

A:

Q: 2-j5) Show that JA -25 (1+j2 \3+j4 = 57 + j24 - 2

A: the given equation is -2521+j23+j4-2-j5-j=57+j24 consider Left hand side…

Q: Find a closed form expression for k³ – 1 П k³ +1 k=1

A:

Q: H.W 1.: Use Cayley-Hamilton to find 4 -1 A' and A Where A = [2 1 1 0 1 0 11 2 ]

A: Find characteristics polynomial and use caylay hamilton theorem

Q: I. True or False. 1. N is closed under subtraction. 2. Z is closed under division. 3. Vx2 = -x if x…

A: A detailed solution is given below.     (As per our guidelines, We are supposed to answer only 3…

Q: Find the rank- 1 approximation of

A:

Q: 7 1 Let A = and D = -7 -3 -3 -7 Find A-D. A - D = |||

A:

Q: 5. Show that 1.2+2·3+3.4+...+ (n − 1)(n) = (n³ − n)

A:

Q: 11! 1.) 5!x4!x3! 2.) Р(8, 5) 3.) Р(12, 4)

A: Our aim is to solve the following :  1) 11!/(5!*4!*3!) 2) 10!/7! 3) P(8,5) As per our guidelines, we…

Q: 1. (a) 2 Let = (1, 0, -2) and = (-4, 2, 3). Find a real number x such that (ট' –æè) ⊥ à. (b)-1 (c) 3…

A: Let .To find a real number  such that .

Q: Prove that gcd(a + b, a − b) = ged(2a, a − b) = ged(a + b, 2b).

A:

Q: What conditions, if any, must be set forth in order for a + b to be equal to n(A U B)?

A:

Q: Q. 5. Show that "-C, 1+"C, =" C, . n-1

A:

Q: 5.1. Show that y2 , V2 , and v3 + V2 algebraic. are

A: We will use definition of algebraic numbers

Q: 6. The value of f A. + C B. C. D. (4-x² +C 4√4-x² 4√4-x² dx (4-x²) 1.5 +C +C

A:

Q: 1. D. 1. D. 10 matrix by 1Row methid. Solve

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Q: (1+a-c), (c) ₂F, (_n,‚a+n;c;1)=(-1)" !

A:

Q: Compute. 13 2) Σ k

A: Given, ∑k=113k2

Q: Hew.2 Exfress the Summ ef the Vecturs AB and if ACl,-1)_, B (2,022C(-l,3) and D(-2,2).

A:

Q: DIVISION BYt (:) - {}> 81. Show that In %3D

A:

Q: 3.20) what is the remainder when 1s+85+...t100s is divided by4?

A: Given 15+25+....+1005 is divided by 4

Q: A 21 2 B 22 스 23 C Z1 = 23 41+43 = 180° E 42+43 = 180°

A: We have to find the angle

Q: -4; -7; -10; -13; 1.2.1. Write down the next two terms 1.2.2. Describe the pattern you notice 1.2.3.…

A: the given sequence is  -4,-7,-10,-13,... 1. the next two terms will be -16,-19 2. Each term is…