aegα, F). 9. a = i, F = Q 11. α-νπ, F-Ο 10. a = 1+i, F = R 12. a = JT, F = R

Q: Under what conditions on A and B does the B.V.P x'y" - 3xy' +3y = cos x, solution, no solution ,…

A: Given equation is, x2y''-3xy'+3y=cosx Take the homogeneous term, x2y''-3xy'+3y=0 Take y=xn,…

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A: Given that,   U(x,y) = x2+2y   and x(r,t) = rsint,     y(r,t) =sin2t we have to find ∂u∂r,    ∂u∂t…

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A: Given: The expression 2cosϕsinϕ+cos2ϕcscϕ, To simplify: The given expression in term of one…

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Q: 2. If z y where z= s cos t and y=s sin t, find az/ôs and az/at.

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A: In this question we are given with a equation which is a differential equation and we have to find…

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A: Assume the truss members only bear axial loads, the following set of 10 equations can be determined:…

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Q: 3- if you know that the wavefunction for a particle is given by Y = Aei(kxx-wt) Prove that the…

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Q: 4. Calculate leme/) at (z,y) = (a, 4). sin(z/g) ey2/2 A ev2/2 B 4

A: Here we have to calculate ∂∂xesin(x/y)=? at (x,y)=(π,4)

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A: Given equations are x32=x1 →(1)x22=1-x1 →(2) Let us represent in figure,

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Q: 2. It Z = e tanly) , wnere x = S"+ t and y=St, find 22 when S=1 and t =0 2t

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Q: 2- find Ow/ar if w = (x + y + z)?, z = sin(r + s) y = cos(r + s), at the point (r, s)=(1, -1) X = r…

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Q: Fird the Aren of the Reyion c2-9 cos In teriur of (2€)

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Q: 1) Let c. 12i| =3 and I = e dz. then %3D I= 1o TTi? %3D

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Q: Solve 2cos? (x) +3 cos (x)+1=0 for all solutíons osx<2 TT

A: Given 2cos2x+3cosx+1=00≤x≤2π

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A: Answer and explanation is given below

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Q: Only correct explanation accepted. LetZN(0,1)FindE(Z).

A: Given  Z~N(μ=0, σ2=1)

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A: Let y be a function of x and if a is a constant, then we know that ddx(a-x)2= -2(a-x). Here, we need…

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Q: a. Show that If z=x+ iy where y 1 b. Evaluate: cosh (iz) + sin (2)

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Q: 1. If Z = sin r+ 2 I+1 6. - ", find dZ/dr.

A: differentiate with respect to x

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Q: Evaluate the integral. 1/2 |[cos 9t i- 3 sin tj + sin? 3t k] dt T/2 | (cos 9t i- 3 sin tj+ sin 3t k]…

A: We have function ∫0π2r(t) =∫0π2[cos9t i -3sint j + sin23t k ]dt

Q: %3D 20 24 tan 24 through solve this egni: Hint :oU=KL +2 =0 மு 3K²=Par ET %3D 2.

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Q: Use Green's Theorem to evaluate >[2²y² dz + (yz²³ + y²) dy where Cis shown below. 90 O-384 O-48…

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Q: If u =x² cos y +ye», where x =s+2t and y= st, prove that ди 2- Əs ди 3 (s— 21) (х' siny — хуе" —…

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Q: Compute the length of the cardioid r = 9 – 9 cos(0).

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Q: L[t cos 2t

A: Please find the detailed solution in below images

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Q: 2n 1 (cos=0 0 +i sin e) + 10 2cosno eine

A: The general form of a complex number is given by z=a+ib, where a,b are two real numbers and i=-1.…

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Q: If z = exy where x = In(u + v) and y = sin(u-v), find az and az du

A: We use the partial derivatives and chain rule of differentiation to answer the given question.

Q: + 8z7 – 5 sin z)dz O 4e -z +5cos z +e O 4e +z" +5sin z +e O 4e +z* - 5sin z +e O 4e +z – 5 cos z +e…

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Q: .2π π 1 -εrocos? θ r dr sinθdθ φdφ x 32 πο X = ?

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Q: a. Show that W[5, sin2 t, cos(2t)] = 0 for all t by directly evaluating the Wrosnkian.

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Q: The auxiliary roots of the auxiliary equation associated with a certain HLDE are m=±3, ±3i, ± 3i.…

A: Solution is given as below:

Q: (4) If z = f(r, y) where, a = e" cos v and y = e" sin v, show that (i) dz az e2u. (ii) az 2 2 dz -2u…

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Q: What is the general solution of (r + sin 0 cos 8) dr + r (sin 0 + cos 0) d0 = 0 ? %3D rsind rcose =…

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Q: 22-j is 1. -1+jZ If Z = cos 0 + j(1+ sin 0), show that the magnitude of

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Q: 8. dr Cos dr |I+ sinr 9. 13 10. VH + 16 dt

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.