1. Using the binomlal theorem expression, what is the expansion of (z+ 3y)°? O (z +3y) = + *y+a*y? + a*y³ + xy! + y° %3D O (a + 3y) = 25+ 5a y+ 102 y + 102?y +5+yo %3D O (a +3y) y+15yf+90y a2+ 270yP3+405ya + 243 %3D O (2 + 3y) = 25 + 15*y + 90a°y + 270a²y +405zy + 243y

Q: 3. Simplify the following Boolean expression: а. (х + у) z' + y(x'+2') b. x'z (xy + y'z' + yz) с. у…

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

Q: HW 2: If Z - N(0,1), find a) p(Z > 1.2) b) p(-2 <Z< 2) c) p(-2 <Z < 1)

A: If Z~ N(0,1)   which means clearly it is standardized normal distribution table.

Q: What is the cocfficient of x" in the power series expansion of v1 – 5x?

A: Given,

Q: 3. Prove that ox + 6x -4X12 is irreducible over Q.

A:

Q: Find the first piece S1 (x) of a natural cubic spline that interpolates the set of points (0,1),…

A: Formula for cubic spline interpolation is…

Q: 3. Determine a and b for Y X1 and Y2aX bX2 such that EX1 EX2}= 0, Var(X) Var(X2) Var(Yi) Var(2) 1,…

A: The provided information is:

Q: ○A. T(A) = 3A from R6×4 to R6×4 -9 9 B.T(A) = A [72] [173] 4 5 ASA-¹ from R2×2 to R²×2, where S A…

A:

Q: Is 6 a factor of 54y + 42z? yes no

A:

Q: 1) A (2, 5) and B (4, 3) V (x2 – x1) ^2 + (y2 – 1) ^2 V 2) F (1, 7) and G (6, 0) V (x2 – x1) ^2 +…

A: If we have given the coordinates of two points then we can easily find the distance between them…

Q: Find real numbers x, y and z such that (x + 4)i + (y – 5)j + (z – 1)k = 0

A: To Determine :-  The real numbers x , y and z  such that   x + 4  i +  y -5  j +  z - 1  k =0

Q: (d) (27+5)(2- i)|=/3 12z +5|. %3D

A: Solution D: We have to prove (2z¯+5)(2-i)=3(2z+5) L.H.S. Let z=x+iy So z¯=x-iy therefore…

Q: 7. Evaluate * (D5 - 3D4 + 8D³ + 16D² - 9D - 13)y = 0 y = (C₁ + C₂x)e¯x + С3ex +C4e²x cos3x + C5e²x…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: (8) In the ring (Z,, +6,•6 ), we get n {(a): a prime element in Zg} ...... (а) ф (b) ((0), +6, ·6 )…

A:

Q: n² – 1 E(A) Given that Var(R;) = Var(R,) : 12 12n n +1 + 12 E(A) and Cov(R¡, R¡) 12n(n – 1) for i #…

A: By definition, CovaX,bY=abCovX,YCovX+a,Y+b=CovX,Y

Q: 3. Evaluate the integral / Vr+3 (x- 1 4 4 (a) 극(z +3)72-(r + 3)52 + 국(2 +3)%2 +C 1 4 (b) (r + 3)"…

A: This question is related to Indefinite integration, we will solve it using given information.

Q: (7.8) Lemma. Let K, L be simplicial complexes which intersect in a common subcomplex, then z(K U L)…

A:

Q: 6/30° + j5 – 3 (а) -1+j+2ej45° (15 – j7)(3+ j2)* (b) - (4 + j6)*(3/70°) means you need to conjugate…

A:

Q: Q.4) Find the value of Sigma (d=sum of student id + 22, and c=12) 4c(d + x)(7c* +2cz +9z*) ((d +x)*…

A: As the student ID is not provided, I assume the sum of the digits are 10 (say). Then d=10+22=32 and…

Q: 2a In R^ show that : 2 as 211x11² + 211|4|1²³ = || Xx+y|11² + 11x-y₁1² ( This is known a the…

A:

Q: If gcd( m,91) = gcd(n, 91) = 1 %3D %3D

A: Given, if gcd(m, 91)=gcd(n, 91)=1,  To prove that                     91|m37-n37

Q: Using chain rule, what is the (2x-¹-3x)³ ? da O 24+108x²+54xª+81x6 x4 -24+36x²+54x4 -81x6 x4 O…

A: The objective of the question is find the derivative .

Q: 5x2 + 13x -dp x³ + 2x² – x – 2 Evaluate: (x + 1)ª(x – 1)³' + C (x+2)² (B None of the choices given…

A:

Q: 1: Find Z by convolution theorem. (z- 2)

A: convolution theorem

Q: 3. Differentiate. a) M(u) (1- 4u²)(u+2) b) g(x) = (-x+ 3)(x-10)

A:

Q: 5. Let h (z) = (z+1)(z+6)(z+10) z(z+2)(z+3) (z+3)(z–2)°, (z+2)(z+6) What is the residue of h (z)at z…

A: Given a function on complex plane as hz=z+1z+6z+10zz+2z+3+z+3z-22z+2z+6 Residue at z=-2 is given by…

Q: Draw the bifurcation diagram for i = (x – 3)(c + x)

A:

Q: Creani Cet G4)= ti t2+34)j +4k HICH) = 2JF L+3tj + find a) H4) XG4) (1+24)k こ b) G4). HGE)

A:

Q: 27x dx= |4-9x² 3x -1 3 xV4-9x² +C 2 a) 4 sin 2 3x b) sin 2 1 4-x² +C 2 3x с) 2sin -1 2 3 xV4-9x? +C…

A: The solution as follows :-