Let w = (2, −2, 1) and v = (4, 5, −4). Solve for u if v + 5u =3w − u.

Q: Find R(t) if R′(t)=⟨1+2t,2e2t⟩ and R(0)=⟨1,3⟩.

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Q: Find V · (V × F), if F(x, y, z) = 7e**i+9xe³j – eu=k. V·(V × F) =

A: Given thatF→=7exzi+9xeyj-eyzkto find ∇.∇×F

Q: ) Use the d'Alembert solution to solve = 2 -00 0, 1 u(x, 0) = e, u(x, 0) : 1+ x2*

A: As per our company guidline we are supposed to answer only first question. Kindly repost other…

Q: Express ∂w/∂r and ∂w/∂s in terms of r and s if w = x2 + y2, x = r - s, y = r + s.

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Q: F= [y°, 2², x²], C : r= [3cost, 3sint. 2t], 0 < t < 4n

A: Given that F=y2, z2, x2 and the curve, C, such that, r=3cost, 3sint, 2t for, 0≤t≤4π. Differentiating…

Q: Use the equations to find dz/ðx and əz/ðy. x2 + 8y? + 9z2 = 1 Əz ax az ду II II

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Q: Find (a) u x v, (b) v x u, and (c) v x v.

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Q: Find (a) u × v, (b) v × u, and (c) v × v. u = i + 2j − k, v = i + j + 2k

A: Given vectors are (a)

Q: (x² + 4xy + 2y²)dy + xydx = 0

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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: Given F(r, s, t) = r(3s4 – 6t°), compute: Frst

A: This is a partial differential problem

Q: Complete the proof that ZYXZ SUT. P Q R. U W Y

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Q: Find the values of the constants a, b, c so that F = (axy + bz*)i+ (3x² – cz)j + (3xz? – y)k Is…

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Q: Find (a) u × v, (b) v × u, and (c) v × v. u = i − j, v = j + k

A: Given: Two vectors are . In part (a) Find the vector product of two vector u and v. therefore the…

Q: Let u(x, t) be the solution of n. и = xt, -00 0, .2 ди (x, 0) = 0, –00 < x < ∞. u (х, 0) - %3| -…

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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: Use the separation of variables method to solve 4urz = Utt, H 00 ur (2, t) = 0 ur (0, t) = u(x,0) =…

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Q: If u=2i + j -3k and v=i + 4j +k, find u x v.

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Q: snip

A: v=2i-3j+6k and w=5i+3j-k

Q: Let y1, Y2 be two independent solutions of t?y" – 2y' + (t + 3)y = 0. %3D If w(y1, y2)(2) = 3, then…

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Q: Find two values of r such that y =x" is a solution of x*y" + 4xy' - 18y = 0 , x> 0. O A. r= -9, 2 O…

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Q: Given F(r, s, t) =r(3s² + 9t°), compute: Frst

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Q: Let a ∈ R and find the solution to y'(t) - a y(t) = 0.

A: The given differential equation is dydt-ay=0 , a∈R.we will slove this by the method of  separartion…

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

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Q: Find the values of the constants a, b, c so that F = (axy + bz3)i+ (3x² – cz)j + (3xz? – y)k Is…

A: A vector F→ is said to be irrational if and only if cure F→ =0 i.e∆ x F→ = 0Given F→ = (axy+bz3) i^…

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

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Q: Find the value of zo so that dz = -2ri Izl=13 (z – z0) (z – 14i)

A: Given integral is ∫|z|=13z(z-z0)(z-14i)dz = -2πi   ---(1)

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

A: Given u = (1, −1, 2), v = (0, 2, 3), and w = (0, 1, 1). And 2x-u+3v+w=0 Plugging the values,…

Q: If A = x° yz? î – 3x² z³ j + yz? k , then a² A at the point (1,0, 1) will be дхду 3 î -3) -3 î

A: The vector A is A=x3yz2i-3x2z3j+yz2k find ∂A∂y=x3z2i+z2k ∂2A∂x∂y=3x2z3i the point 1,0,1…

Q: Find u x v, v × u, and v × v. u = 6i + 8k v = 3i + 8j – 4k. (a) u x V (b) (c)

A: This question is based on cross product.

Q: If y,, Yz are two independent solutions of y"+ p(t)y+ q(t)y=0 then Select one: a. V2 w(V1.V2) b. V2…

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Q: If u = x²zî + yz?j – xyk and 0 = x²yz then find the value of u. (To)

A: Consider a function fx,y,z. The gradient of the function can be defined as, ∇→f=∂f∂xi^+∂f∂yj^+∂f∂zk^…

Q: solve for w where u = (0,-1,1,1) and v = (3,0,-1,2) 5w = u-3v w=?

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

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Q: Solve for w where u = (1, -1, 1, 0) and v (2, 0, –1, 3). 3w = u - 2v w =

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Q: dt Determine dw if t = (6r* +3r*) -(*+2r-5)'. -s)'. and w =

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

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Q: : Solve by using Separation of variables method? E= k a²u for 0 0 u(0,t) = u(L,t) = 0 for t > 0,…

A: According to the given information, it is required to use separation of variable to solve the given…

Q: Find two values of r such that y =x' is a solution of x*y" + 4xy' - 18y = 0, x> 0. O A. r= -6, -3 O…

A: Given differential equation is a linear, homogenous differential equation with variable…

Q: Find dw/dr and dw/dΘ for w=2z/y-3x if x=3Θ+2r, y=3r^2 + Θ, and z =4r-Θ, where Θ = 2 and r = 5.

A: w=2zy-3xx=3θ+2r,y=3r2+θ, z =4r-θTo find ∂w∂r and ∂w∂θ for θ=2 and r=5

Q: If y1, V2 are two independent solutions of y" + p(t)y' + q(t)y = 0 then Select one: а. w(V1.V2) v?…

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Q: S g find Ju u and av Write the anuser in terms of U ty D Using the chain rele and V 2 to

A: Answer

Q: (x, v) = (2ry) i + (r – 2rv) j ,2]. -

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Q: Determine the real number \( \alpha \) u x v and î áre orthogonal, where u = 3î + ĵ – 5k and v = 4î…

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

A: The given vectors are Let the vector x be

Q: Given that i = and i = and that i • v = 188 determine the value of the constant A.

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Q: In the diagram below we have that ST B = 69° and CDU = 62°. %3D %3D E A S -V U Find: 1. ВСТ 2. ABT =…

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Q: Solve for v in terms of r, s, t, and u. ru = tsv %3D V =

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Q: Use the separation of variables method to solve 4urz = Utt, H 00 ur (0, t) = ur (2, t) = 0 u(x,0) =…

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