Integrate: Show that B(p+1,q)+B(p,q+1)=B(p,q).

Q: Solve for x, where u = (1, -1, 2), v = (0, 4, 1), and w: %3D 5u – 2x = 3v + w X =

A: It is vector problem.

Q: press your as a action. y = Vx, y = x², x = 0, x = 4 %3D

A: In this question, the concept of the definite integral is applied. Integration Integration is a…

Q: What must be value of X so that B is diagonalizable?

A: A matrix A can be diagonalized if there exists an invertible matrix P and diagonal matrix D such…

Q: AB is orthogonal

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Q: f(x, y, z) = z(x² + y² + z²)-3/2 over the part of the ball x² + y² + z² 2.5

A: Here we will use cylindrical co ordinate system to find value of integral  By using above figure…

Q: What is the cross product of the vectors 214 3k and 6.9- 3k ? Explain why your answer is conne ar…

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Q: Show: Cov (X,Y) = E[X(Y – μY)]

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Q: How do you compute the magnitude of v = (V1, V2)?

A: Magnitude of v = < v1, v2 > Magnitude of vector v is represented as || v ||.

Q: Solve for x, where u = (1, −1, 2), v = (0, 2, 3), and w = (0, 1, 1). 3u + 2x = w − v

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Q: SI. 1dV, where B = {(x,Y, z): 1 < x² + y² + z² < 4, y 2 0}.

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Q: solve this linear equation using cramers rule x+ y−z=0 2 x−3 y+z=1 2 x+ y+2 z=7

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Q: Use Cramer's rule to solve for r' and y in terms of x and y: y = 31' – 2y

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Q: Determine whether X and Y are independent: 2e--2y x, y > 0 a. fxy(x, y) =

A: Hello! As you have posted 2 different questions, we are answering the first question (4-2). In case…

Q: Evaluate by separation of variables. dB u(1 – u?) sec² ß | du

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Q: Find r, y, z and t where 6. + 2t 4 r+y 3 %3D -1 2 +t

A: Given  3 xyzt = x6-12t + 4x+yz+t3 We have to find x, y, z and t.

Q: af Given f(x, y) = In(6x² + 8y²) then %3D

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Q: Suppose that f(z, y) = 10z²y² + 8z? + 2y? then find the discriminant of f.

A: We have to find the discriminant of the function of two variables fx, y. It is given that the…

Q: Show that Plx-1,y) = A(x, y) X+ y-1

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Q: Use Cramer's rule to solve for y without solving for x, z, and w. 4x + y w = 3 5x + 2y 4 4x 2 y 5z +…

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Q: mTQ = %3D mQR = %3D U 44 mTS %3D T. R 25 MSQR %3D MRQT %3D

A: Problem 1   Problem 2

Q: P is the midpoint of GH implies that GH = 2PG.

A: We have to prove that GH=2 PG if P is the midpoint of GH. Drawing the figure of given condition, we…

Q: Let X and Y be iid N(1,3). Let U = 4X + Y and V V_dependent or independent? Justify your answer. 2X…

A: Given X  and Y be iid with N(1,3). Mean, μ=1 Standard deviation, σ=3  U = 4X + Y and V = 2X — 3Y

Q: (B) Show that the area of triangle is - ÁxB (Using Vector method)

A: Let, a parallelogram be:

Q: Use the Chain Rule to find dw/dt. w = xevlz, x = t, y = 4 -t, z= 9 + 2t 4xv dw 7,6 dt

A: Given that      w = xey/z , x = t7 , y = 4-t , z= 9+2t Here we have to find  dw/dt

Q: Use Cramer's rule to solve for y without solving for x, z, and w. 4x + y + z + = 7 5x + 3y z + 8 W…

A: Let's find.

Q: af (2,0) ay f(x, y) 3D хетУ + 5у%; af (2, 0) = Əy

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Q: Let f(x ,y, z) = x²yª + z³ and x = 4s?, y = 2st?, and z = 3s?t. %3D %3D

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Q: What is the dimension of {(x, y, z) E R³ : x +y+z = 0}?

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Q: %3D then przove that .cūxR=0 and vxcãuFR)= 2Ù

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Q: If S(x, y)= x² +y , find f, and f, . %3D Vr

A: Fx is partial differentiation of F with respect to x.

Q: Defined byT (x, y, z) = (y+2z, –2x+y+2z, –3x– y+52), is diagonalizable.

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Q: Find mZB. 141° 72° B 47° mZB %3D Submit

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Q: Use Cramer's rule to solve for x, y and Z 2х + у — 3z %3D 0 | 4х + 5y + Z %3D 4 %3D

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Q: im(z,v) →(0,0) F(x, y).

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Q: Repeat Exercise 27 for the forces KX = (2, – 3) and KY = (- 2, 3).

A: The given two force vectors are, KX→=2,-3KY→=-2,3 When we find the addition of two vectors, then the…

Q: a) If W =(x,y), where x v²-g' and y 2vg calculate W+ %3D

A: We’ll answer the first part of this question since due to complexity. Please submit the question…

Q: Differentiate the follo ear and non-linear. w +z =2 1. x +y- z= G X +v-

A: (i) First we differentiate the given equation with respect to x: xy+z=2⇒ddxxy+z=ddx2⇒y+xdydx+dzdx=0…

Q: Find 2 (v x u), given u x v = (-, 5, 8). %3D

A: u×v=-83, 5, 8

Q: EXERCISE 4.11.2 ONLY DO (D-F)****

A: For part d: According to the given information it is required to prove that for any positive integer…

Q: Given f(x, y, z) = /2x – y – 5z, find - - f-(x, Y, z) = %3D f,(x, Y, 2) = %3D f-(x, Y, z) =

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Q: Find V · (V × F), if F(x, y, z) = 6e²*i+ 5xe"j – 2ev³k. %3D -

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Q: 26 + 4z4 – 2z2 +1 dz (z – 2i)6

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Q: Dketch a 3-dhensranal grapn of the equetey 1巻)Z-6-2ーy2 ×Z0 42O 2) 0-

A: 1) given equation to draw the graph is z=16-x2-y2 ,x≥0,y≥0 since x,y are positive the graph will be…

Q: Solve Utt currrx = 0, -0 0, %3D u (x,0) = f (x), Ut (x,0) = 0, -0 < x < ∞ ||

A: Given that,utt+c2uxxxx=0-∞&lt;x&lt;∞t&gt;0ux, 0=fxutx, 0=0The pde is solved as shown below

Q: Given f(z, y, z) = /1z2 + 3y? + 222, find %3D f-(z, y, 2) =| f,(z, y, 2) = f.(z, y, z) =

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Q: Find those constants a, b, c, d such that f(z) = ax² + bxy + y² + i(x² + cxy + dy?)

A: The given function is : fz=ax2+bxy+y2+i(x2+cxy+dy2)

Q: Use Cramer's rule to solve the set of linear equations x-2y- 3z =-1 3x + y-z =9 - 4x + 2y +z = 2

A: Here we have to use Cramer's rule to solve the set of linear equations.…

Q: Solve the IVP y" + 4y/ + 5y = 38,(t), y(0) = 0, y'(0) = 1. %3D %3D

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Q: Find Cov(X, Y)

A: Covariance: It is a statistical measure used to establish a relationship between two random…

Q: Find 2 by using the Chain Rule with y as a composite of dx y = csc(u), u = x3 + 2. %3D

A: Given: y=csc( u) , u=x3+2  To find dydx