If u, – 4u – u =0 u(x,0) = 10e Then u(z,t) = O 10e z14t O 10e z dt O 10e 21 O 10e zit 10e O 10e O 10e z2 O 10e t

Q: f(In x)2 dx O-r(Inz)² - zlnz+z+C -z(lnx)² + zlnz+ 2z+C O-r(Inz)² - zlnz+z O None of the choices…

A: The objective is to integrate the given function Use integration by parts, which states that…

Q: Let fxy (x, y) = 6 (x – y) , 0 < y < x < 1. If E (X) = , E (Y) = Cov (X, Y) = then %3D

A: Given,fXY(x,y)=6(x-y) ; 0&lt;y&lt;x&lt;1E(X)=34E(Y)=14

Q: Letr(t) = (t2, 1- t,4t).Calculatethederivativeofr(t) • a(t)att = 2, assumingthata(2) = (1,3,3)…

A: Given that, rt=t2, 1-t, 4t a2=1, 3, 3a'2=-1, 4, 1 Need to evaluate derivative of rt.at

Q: 6. Consider the PDE u; +u ux - u Uy = 0 for - ∞<x< ∞, - ∞<y< ∞, and 0 <t< ∞ with u (0, x, y) = (x -…

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Q: 1. Let f(x, y) = In(x - y) then at the point (4,1), fryis equal to: %3D -1/9 O 1/7 1/9

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 1) Let f(z,y)- . Compute DS(z,y) where u- (4-9)

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Q: 34. Solve Ut = KULT, 0 0, %3D u (x, 0) = 0, 0 0.

A: Given that ut=kuxx ---(1)  0&lt;x&lt;∞, t&gt;0ux, 0=0,  0&lt;x&lt;∞u0, t=f0,    ux, t→0  uniformly…

Q: Suppose that w = f(r, s, t), where r = r(x, y), s = s(r, y), and t = t(x, y). Which of the following…

A: Solution is given below:

Q: 22. Solve 0 0, x > 0, Urr + Uyy = 0, u (x, 0) = f (x), u (x, 1) = 0, u (0, y) = 0, и (х, у). O…

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Q: 15. Solve Orx + Pyy 0, -a < x < a, 0 < y < ∞, 8o, 0 < |x| < a, Oy (x, 0) = 0, || а. $ (x, y) → 0…

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Q: a) h(x, y, z) = In(z³ – 5x – 3y – 1) | 1 b) h(x,y,z) = z³ – Jx + y

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Q: Consider thế iñifial a. 2y"- 30y" + 150y' – 234y = 0, b. y"+ 6ay' + (9a² + 1)y = 0, y(0) = -3, y(0)…

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Q: Let X₁, X₂,..., X be a r.s. from N(,0) and Y₁, Y₂...., be another independent r.s. from m…

A: Solution

Q: If Z; is i.i.d N(0,y²) and X1~ N(0,o²) be independent of all Z's. Let Xi+1 = pX;+Z; for all i = 1,2,…

A: From the given information, The provided information are as follows: Zi~i.i.dN0,γ2X1~N0,σ2Zi and X1…

Q: solve: 3 (b) uloy) = ity ² "x = 0 w(x, 3x) = sin x = 0 Wyy u(x,0) = sin x wy (x,01 = cox { (c) in R²…

A: Solution

Q: 2) Find Ow/du and ow/ov for w=xy+ yz + xz, x=u +v, y=u-v, z = uv at the point (u, v)= (1/2,1). 3…

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Q: Find the value of dr/dt at t = 0 if r = (u2 + 7)^(1/3) and u^2t + u = 1.

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Q: (a) Let f(r, y) = -2r*y² – In(y²). Compute fyzz (b) Let g(r, y, 2) = 1(3y* – 52²). Compute

A: (a) Given function is fx,y=−2x5y2−lny2 We have to find the fyxx. First differentiate…

Q: iv) if zy = (x)- then zx + Zy = %3D %3D

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Q: 1. Let f(x,y, z) = vx + /y- Vz +In(49 – x² – y² – z²). Evaluate f(4, 4, 4).

A: Substitute the values

Q: Compute (S ,g) where f(t)=1– 3r² , g(1)=t-ť'onV = C[0,1]. %3D

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Q: 2) Let u(xy,2) = でさす。R。 () Find He(tいり, "g(1,0,り、 Uy(1,0,1). ニ0. (k) Show that oty a22

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Q: dz Let z-ay" – 4r, * = uv and y-v - 3u. Compute Ən (u,r)-(1,1) -

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Q: 4Ux+Uy=U² , U(x,0)=1/1+x²

A: In the given partial differential equation with the given initial condition. 4ux+uy=u2u(x,0)=11+x2

Q: = In z are two linearly indepen- of ry" + y' = 0, then the partic- - ry" + y' = f(x) can be written…

A: We have to choose the correct answer from the given options according to the given condition

Q: Suppose w = In(8x² + 2y² + 3z²), ¤= 9 cos(t) , y = 9 sin(t) , and z = 8Vt. Compute dw/dt in two…

A: The partial derivative of a multivariable function with respect to any of the variables can be…

Q: Please solve

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Q: 3. If (X(t)} is a WSS process and if 00 Y(t) = | h(u) X(t – u)du, then - 00 (i) Ry (t) = R(T)* h(-t)…

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Q: 2. Use Yule-Walker equations to determine the autocovariance function of a stationary ARMA(2,1)…

A: Yule-Walker Equations: The autoregressive models for the time series are used for their simplicity…

Q: 13. Let f(x, y, z) = xy+z², with x(s,t) = s², y(s, t) = 2st, and z(s, af/ds and df/dt %3D %3D

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Q: xy−5yz−7xz,x=st,y=e^(st),z=t^2 Compute ∂w/∂s(1,−2)=

A: The equation given as  w=-2xy-5yz-7xz , x=st , y=est ,z=t2. The partial derivative of the function…

Q: 8.1.33 Evaluate the integral belov 20 + y dy 20 - y - 20 20 +y dy = (Typ %3D 20 - y - 20

A: Solve the integration by substitution method and C is integration constand  and use reduction…

Q: E={(r,0,2) : 0< 0< n, 0s zs 1, vzs rs 1}. Compute y²e(x²+y²y³ dv•

A: Here, the given solid E is defined usimg the cylindrical coordinates as follows: E=r,θ,z:0≤θ≤π,…

Q: 3. Use Green's Theorem to evaluate (y-6y) dr + y + 10y) dy where Cis shown below y (-11) (1-2)

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Q: Suppose that w = f(x, y, z), x = h(s), y= g(s, t), z= k(s,t) and all the conditions required for the…

A: By using the chain rule for partial differentiation we will find the value of it.

Q: If Saz dy = In|ly +1- Inly +2| + c, then S- %3D y2+3y+2 dt = e2t +3et+2 In(e' + 1) + In(e + 2) + c…

A: The objective is to find the correct option

Q: 1- If z = 1+ y2, we can write: a) z = 1- (iy)?, b) z = 1- iy?, c) z = 1- iy, d) z 1 + (iy)? 2- If z,…

A: As you have posted multiple questions so according to our guidelines, I answered first three…

Q: If U(x,y)=In(x²-y) then Ux+Uyy= O (2x+2y)/ x^2+y^2 O (2x-2y)/ x^2+y^2 O (2x-xy)/ x^2+y^2

A: Uxx+ Uyy of the function U

Q: and further we require that u(r, z) is bounded as z - +oo. Find an expression for the steady state…

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Q: 1. Detanmne the rusutt OF a. Gradi ent f(x.y,z) ex sin cy) In (7) b. Divergenie =7? C Curl F=y2 t…

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Q: z+2 dz. J. Compute Jz-t|= 4 z(z-i)²

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Q: ☺ RB=R defuid by T☺)- matria "A" it. T@)- A:). つレ- TV4 Let T: -3v-Jw ). Füd

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Q: 18. (2) = t"(-t)" dt, show that F(m). m! +1, n+1 %3D m and n are positive integers.

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Q: Let f(x,y,z) = x² sin y + y e, where x = t +3,y = net-1 and z In 2t. %3D %3D at t 1 is: dt -2 O None…

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Q: Poblam cu (a) Compute Cm 2月-/ where xe [-,]. (1) 2n 2n-1 where ze C-1,1]. (b) Gompule Cm z nっ%

A: (a)

Q: 4) Let f(r, y, z) = In(r + 2y + 3z). Find Vf = . %3D

A: Given: f(x, y, z)=ln (x+2y+3z)

Q: Suppose z = f(x,y) where x = Puv and y=u+tv². Given that z,(4,3) = 4 and z,(4,3) = – 1. Compute z,…

A: Explanation of the answer is as follows

Q: u + 1, U2 + V2 1), (a) Compute u + vand ku for u = Solution: Ia + In) (1,2), v = (- 1,:

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: 16.1. Use an antiderivative to show that for every extending from a point 21 to a point 22 2" dz =…

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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.