4. Let V = span{(1,0,0), (0, 1, 0), (1, 1, 1), (0, 1, 1)} F³. CF°. Show that V = %3D

Q: 19. f(x, y) = x + y+y+ 1, constrained to the triangle with vertices (0, 1), (-1,–1) and (1, +1). %3D

A: As per bartleby guidelines i can answer only one question, kinldy upload rest questions separately.…

Q: B) Use Green's Theorem to evaluate F dr, where C is the triangle with vertices (0,0) (3,0) and (3,…

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Q: Find equations of the following. 2(x - 9)2 + (y - 2)2 + (z - 8)2 = 10, (10, 4, 10) %3D (a) the…

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Q: Find the coordinates of W. When point W lies on UV such that UV:VW is 5:2

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Q: Find a parameterization for the line segment joining points (0,3) and (12,0) using the angle 0 in…

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Q: Find the position function of a particle moving along a coordinate line that satisfies the given…

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Q: 6. Assume a joint pdf given as [λxy², 0≤x≤ y ≤1 fxx2,y)= (0, otherwise and let B = {Y≥ 2X and W=X+Y…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts.  In case…

Q: O A line passes through the point Po(xo, Yo) and has gradient m = tan a. Show that a general point…

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Q: Suppose that u = Va2 – y? and v = arcsin() where x-y 0 and- . Which of the following is/are true? A.…

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Q: Find equations of the following. 2(x − 5)2 + (y − 1)2 + (z − 9)2 = 10,    (6, 3, 11)   (a) the…

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Q: Sketch the triangle defined by A and compute LA fdA for A = {(x, y) E R²;0< x <a and y <x} and ƒ: A…

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Q: Find the solution for the damped motion. my'' + cy' + ky = 0 with m = 10, k = 90, y(0) = 0.16,…

A: The given ODE is homogeneous with constant coefficient. The characteristic equation is given as:…

Q: Exercise 4.3.8 Show that if A = E oiu;vf , then At = Ei=1 0,'v¿u

A: Given function is, A=∑σiuiviTi=1r As we know that, A+B+=A++B+ So, we can write the above equation…

Q: Find a parameterization, x = x(1), y = y(t), tE [0, 1], for the line segment from (2, -1) to (5, 5).

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Q: Find a normal vector to the level curve f(x, y) = c at P. f(x, у) - x² + y² .2 1 Р(3, 3) 6' C =

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Q: (b) Utt = t>0, u (r,0) = 3 sin r, u (r,0) = 0, 0 0.

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Q: If Y - Exp(2) and Z ~ Exp(3) are independent, what is pdf of W = Y + Z?

A: Concept Sum of independent exponential distribution is gamma variate. Suppose X1, X2...,Xn ~exp(@)…

Q: Evaluate yz dx +y dy +a dz, where C is the line segment from (2,0, –1) to (4, 1, 2).

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Q: Find equations of the following. y = x2 − z2,    (6, 11, 5) find the tangent plane and normal line.

A: According to the given information: Consider the given equation at the given point:

Q: find ow/ar if w = (x + y + z)², ar www w x = r – s, y = cos(r + s), z = sin(r + s) at the point (r,…

A: See the attachment

Q: Let W, be a standard Brownian Motion. (a) What is P(W? < 4)? (b) What is E(f" dW,\W3 = 5)?

A: Given Wt be a standard Brownian Motion. E∫06dWs/W3=5

Q: 2. Approximate f,(3,5) using the contour diagram of S(x, y) in Figure 14.9.

A: Given query is to find the value of fx(3,5).

Q: Q1: - Find Ow/Du and Əw/Əv if w- xy + yz + xz ,x-utv, yru-v,z-uv at the point (u,v)- (0.5,1) (30…

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

Q: 5. Let C be the curve parameterized by r(t) = (t,-t,t²) Evaluate y ds.

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Q: What is the angle between the lines M ww x-2 y+4 z-3 x-2 y-5 1 2 E-3 and 1 1 O a. /2 arccos(/3) OC.…

A: Given two lines: x-21=y+42=z-31 and x-22=y-51=z-32

Q: et y = [ 2   3   -1] and u = [ 2   -6   -6] compute the distance d from y to the line through u and…

A: first we shall find equation of line then find distance from line of that point

Q: Find the orthogonal trajectory of the given family of curves: 1. y = C (sec x + tan x) 2. x = C,es*…

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Q: The region S = (x, y (x- 2) + y² < 4 is rotated about the line x = 5.

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Q: Q.2 Find curlF at point (1,0,0) where f(x, y, z) = xe*y + y + 2

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Q: | the parametric equatioin for e line segment between a7) and (3,3)

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Q: Find the Jacobian a(x, y) / a(u, v) for the indicated ch x = e-u sin v, y = e-U cos v a(x, y). a(u,…

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Q: Show that cos(ωt − β), cos ωt, sin ωt are linearly dependent functions of t.

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Q: find the distance d(u, v) between u and v in the given exercise.

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Q: Find the equations of the normal line to the surface z 6z y at the point (1, -1,-6) t+ 6 Submit…

A: To find the equation of normal line to the surface at (1,-1,-6)

Q: Find ∂U/∂T and ∂T/∂U when ((TU −V )^2)ln(W−UV) = ln(2) at the point (T,U,V,W) = (1,1,2,4).

A: Given that: TU-V2 ln W-UV=ln 2  We have to find ∂U∂T and ∂T∂U at the point T, U, V, W=1, 1, 2, 4

Q: Fit a trigonometric function of the form f(t) = co +C sin(1) +cz cos(t) to the data points (0, 6),…

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Q: Find the orthogonal trajectory of the given family of curves: 1. y = C(sec x + tan x)

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Q: 1. Given the following lines: 3x D:: * = y – 1 Dz: x+ y-6 = 0 a-) Give a normal vector associated…

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Q: Determine the location of a point (x, y, z) that satisfies the condition(s). xy &gt; 0, z = −3

A: Here Our Aim is to determine the location of a point (x,y,z) that satisfiesthe condition(s):→…

Q: Evaluate (x-y+z-2)ds where C is the straight-line segment x=t, y= (1-t), z=1, from (0,1,1) to…

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Q: 3.8 If H = (x – y)a, + (x² + zy)a, + 5yz a, evaluate f H dl along the contour of Figure 3.28.

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Q: Show that cos(cot – B), coscot, sincot are linearly dependent functions of t.

A: We have to check

Q: A tangent vector to the curve Cat P corresponds to: A) 7 = (1,–1, –v2)

A: Given that                   C is an intersection curve in the first octant, between the surfaces S1…

Q: Evaluate | 9+x* dx+xy*dy along the positively oriented curve C where the C is the boundary of the…

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Q: (b) Given  = (x²y)î + (xz – z²)f – (xyz)k, determine the following at point (1, 1, 2): (i) V- Â.…

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Q: The domain of ƒ(x, y) = In xy is points .(x, y) in the first quadrant

A: We have to tell about given statement.

Q: (c) Determine the natural cubic spline that interpolates the data f(0) = 0, f(1) = 1, f(3) = 4 and…

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