5. Suppose we have an M/M/2/4 queue with average service time of 6 minutes, and we have found the following stationary probilities: 1 Po = P₁ = P2 = 1 P3 P4 6' Let W be the waiting time (in hour) given that a customer enters the waiting line. Find the pdf for W. == 4

Q: The product of2r - 3 and x +4 can be expressed as A) 2r2 +x - 12 C). 2r2- 12. D 2r2 + 5x - 12 B)…

A:

Q: Determine yu – 4uzy + a?uzz + 3u = 0 %3D the type of the PDE

A: We will check whether given PDE is hyperbolic, elliptic or parabolic.

Q: 2+3

A: Given,        2+3jyx-j=2j

Q: 1. (D² – D – 2) y = 30

A: Using auxiliary equation than pi  y=c.f + p.I   General solution

Q: 12 K M 16 J

A:

Q: Find a x b, and c* (a x b) a = 2i + 3j - k, b= -1 + 4j + 5k, c = 2i + 3j + 4k Show all steps

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Q: Let u (1, 0 -2) and v3,2. 4). Compute 2u + v. O (4. 2. 2) O (5.2.0) O (6.5. 0)

A:

Q: e par a cen Suppose (1) Determine P(X < 1/2). (2) Determine E(X) and V(X). is given on right. f(x)=…

A: f(x)=4x3   , 0&lt;x&lt;1         0        o/w

Q: 2j (5-j3) B) Given that (2a+ jb)+(b-j3a)=- Obtain the values of a and b. (2+j)(1+j4)

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Q: Q5 1 Find proj; (w) where w= and v = 2 -2 3

A: Solution:Given     w=10-2     and     v=123To find:projvwFormula:projvw=P wwhere P=v vTvT v

Q: None In|V3t ++ c 5+x2 In V5+x2 V5 5. In 5+x3 00 In 5+x

A: The solution is given below :

Q: Evaluate SA=_dx where A = x ² + 8x-3 and B=x²+3x²

A: To evaluate the following integral.

Q: O Determine rand s so that, 3.

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Q: Evaluate for: x = -2, y = 4, and z = 16 * J16 - (y +x)? |-2| 6. -14 O 2 18

A: To solve the given expression with  x =- 2, y = 4 And z = 16

Q: 8+t +6t -12t3 dt. 1. Evaluate 3t² +4)(+7

A:

Q: x³ + 27 dx . x+3 Evaluate x3 +9x + C 3 x3 3 +žx²+9x+C 3 x3 + x² – 9x + C 3 2 x3 3 x² + 9x+C 2 3

A: We know that, The sum rule: ∫fx±gxdx=∫fxdx±∫gxdx The Power rule: ∫ax+bndx=ax+bn+1an+1+C And…

Q: E[2A+ 3B + C – E + 2D] |

A:

Q: t- 2 dt t2+3t-18

A:

Q: 7b + 8b2​2​​ + 3 + y + 2b + 2y + 2 =   A 17b2​2​​ + 3y + 5 B 8b2​2​​ + 9bb + 5y C 8b2​2​​ + 9by +…

A: 7b + 8b2​2​​ + 3 + y + 2b + 2y + 2 = ?

Q: inn (Q4) = D4 OZ2 O Z2 Z4

A: we have to solve given problem:

Q: 2 d) ²₂t(t4 +3t)dt -2

A: We need to solve ∫-22t(t4+3t)dt

Q: 3 5 - Let C= 2 6 |. Find - 5C. - 1

A: The given matrix is                                C=-3   5  2   6  0-1 We have to find -5C.

Q: s'-4S+5)². ±+ S 9 - 2.

A:

Q: w+5 -dw w - 6w+10

A: A detailed solution is given below

Q: Perform the indicated operation. (2 – j) (-3+ j2) (5 – j4)

A: The product of a+b and c+d can be represented as:a+bc+d=ac+bc+ad+bd. We know that j2=-1 or j=-1.

Q: Find d²v dt² v=3t² +7t+9 d²v dt² कर U- -

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Q: 6. 3 3 Let A= -4 1 and C= -5 0 3 -2 -1 Find A+ C.

A:

Q: 12x +1 dx. (2x- 1)2 (3x+2)? Evaluate: 1 (A (2x- 1)2 (3x +2)² +C B (2x- 1)3 (3x + 2)3 3 + C ⓒ In…

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Q: dz (e2z – 1)2

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Q: Q3- If A = 4i + 2j – 3k , B = 5i + 2j – k Find |A X B|

A:

Q: 1 25. L-I s + 5s

A: Note : " As per our guidelines we will solve only first question . If you want any specific question…

Q: L-1 | 53 5 = 3s +1 3 – s2 + s - 1

A: Find the inverse Laplace transform of 3s+1s3-s2+s-1. Rewrite the denominator:…

Q: 2j(5-j3) (2+j)(1+j4) B) Given that (2a+jb)+(b-j3a)=- Obtain the values of a and b.

A: Given (2a+jb)+(b-j3a)=2j(5-j3)(2+j)(1+j4) Here we know  j2=-1 So we can write the above equation as…

Q: 42 x2 dx =. V(73 + 14) 42 / (x3 + 14)+ C V 28 V (x3 + 14) + C 14 (x3 + 14) + C 84 / (x3 + 14) + C

A: From the basic integration

Q: (Vx² + 4x – Vx² – 4x ) Find Lt

A: We know that: limx→∞ 1x=0limx→ac·fx=c·limx→afxlimx→afxgx=limx→afxlimx→agx

Q: 30° s V12 : 2/2

A: Right angled Triangle in which hypotenuse is √6 Adjacent edge is y with angle 30° Opposite side = x…

Q: v+ n² = 0 v-n² = 0

A:

Q: V3 E Q(V2). True False

A: