4. Solve the following Binomial problems: a) Find the expansion of (a + b)² b) What is the coefficient of b⁹ in (2 − b)¹⁹? 101 c) What is the coefficient of a¹0¹6⁹⁹ in the expansion of (2a − 3b)2⁰⁰? -

Q: x y! =y+x²y, y(0) = -2 2. y! -

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Q: Date Jan 16 Feb 16 Mar 16 Apr 16 May 16 Jun 16 Hours light 8.95 10.18 11.62 13.27 14.65 15.40 Date…

A: Given:  Date Jan 16 Feb 16 Mar 16 Apr 16 May 16 Jun 16 Hours light 8.95 10.18 11.62 13.27 14.65…

Q: The general solution of the system of coupled equations =2a+ay, be + cy can be written as D 3 [8] =…

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Q: 21 Solve in terms of Besselis Function, 2 11 the ODE: x² + xy + (x³²+ =)=0 let Z=Lnx

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Q: Q1. Find the inverse of the following matrix by using Gauss-Jordan eliminations 1 -1 2 3 12+1 2 0…

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Q: 2. An emergency committee consisting of 12 health's officer staffs is chosen from 10 doctors and 12…

A: An emergency committee consists of 12 health officers that are to be chosen from 10 doctors and 12…

Q: Maximize: z=5x+y subject to: x-ys3 5x + 3y ≤ 75 x20, y20

A: Given,           Maximise: z=5x+y    subject to:                      x-y≤3…

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A: This is a problem of the Exact differential Equation.

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Q: Take the Laplace transform of the following initial value problem and solve for Y (s) = C{y(t)}: y"…

A: We have to solve the given problem by Laplace transform.

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Q: (iii) If (X,r) is topological space, A,BCX. Prove that (a) b(A)=AA (b) If ACB, then d(A) ≤d(B)

A: First part Is obvious from definition of boundary points of a set.

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Q: Prove that eie ei(0+2K) ,where k = 0,±1, +2,...., = D

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Q: 9. Wheelchair ramps must have an angle of elevation no more than 4.8°. The wheelchair ramp outside…

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Q: The simple expression of the True False 21 a³ b³ c 3 a³ b²c² is 7 b5 c 3 a5

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Q: Q4: Evaluate the surface area of the object obtained by rotating 1+ 1² dx x = √√√y +5, √5 ≤x≤ 3,…

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Q: We call g(x1, x₂) = ax² + 2bx1x2 + cx a quadratic form, a, b, c are constants. Suppose X1 X = try to…

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Q: answer to this question please

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Q: What is the domain?

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Q: a) Find the root of the equation f(x) = 2cosx-x² to 2 decimal places using the Newton-Raphson…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer only in type written…

Q: 1. Find the Fourier series of the function f(x) = |x| which is defined over the range - T<x< πT.

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Q: 9. F(x)= 4x¹-6x²+1 is even function True False оо

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Q: Evaluate the following: (Complex Numbers & Variables) 1.) √j√j

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Q: Exercise (7) 1.Find the roots of the equation f(x) = x³ - x - 1 using x₁ = 1 For 4 iteration by…

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Q: Your "friend" has shown you a "proof" he wrote to show that 1 = 3. Here is the proof: Proof. I claim…

A: Let the two statements are  M: 1=3N: 1=1

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A: We have to find dual of given problem by the dual simplex method and the optimal solution.

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Q: 4. Let f(z) = cosh z. (3) Show that f: S→ f(S) is ono-to-one.

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Q: 1. If Y= 4 In (In (In(sec(x)) then Ý -[4 (tan)/{ In ((In (sec)) In (sex)}] O True O False

A: We have to derive the given function.

Q: The cardinal number of ​{2​, 4​, 6​, 8​, ​..., 1002​} is enter your response here.

A: Given the set is  {2,4,6,8,....1002}

Q: Solve []=[ 'y' 3 - 17 ][] 2 -3, x(0) -4, y(0) = 1

A: Given: x'y'=32-17-3xy, x(0)=-4, y(0)=1 To find: Solution of given system of differential equations.

Q: Solve the given initial value problem. O x³y²y³ = -18 Oxy² - xy³ = 36 Oxy² + x³ = -18 O x³y² + x³ =…

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Q: 2. Q(-∞0) = 1 using the definition of error function.

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Q: 1. x₁ + 6x₂ - 8x3 = -6.6 10x₁3x₂ + 6x3 = 8.6 x₁ + 15x₂9x3 = 0.8

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Q: B/ If Ø = (x³y²z) and A = 2xzi - 3y2j+ 3xy²k Find a(A) at ду дх the point (2, -1, 3)?

A: When partial derivative is done with respect a specific variable, then other variables are treated…

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A: Here I used counter example to show that the statement one is false and give the proof for statement…

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Q: A/HM-012 is a matrix then find the M. M 3 4 5 8 ( :) 86 14 149 23 O 1 2 14 23 5 23 50 86 14 50 86 :)…

A: If A=abcd, then AT=acbd.

Q: Determine wo, R, and 8 so as to write the given expression in the form u R cos(wot - 8). = u= -5…

A: We simply convert the given equation in its general format.

Q: 2. Q(-∞0) = 1 using the definition of error function.

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Q: Exact Equations. In each of Problems 1 through 12: (a) Determine whether the equation is exact. If…

A: The given differential equation is 2x+3+2y-2y'=0 To find:(a) the given differential equation is…

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Q: where _13-4 mod 13

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