Use a parameterization to find the flux SF •ndo of F= 3xy 1+3yzj +3xz k upward across the portion of the plane x+y+z=2a that lies above the square 0≤x≤a, 0≤ysa in the xy-plane. The flux is.

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Q: y"+y = tant, - < t <Hint: use variation of constants me

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Q: Problem 3. Let a, b and n be positive integers. Prove that (a) gcd(an, b″) = gcd(a, b)” and lcm(a”,…

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Q: 1. Let p be an odd prime and g be a primitive root mod p. Show that Z = {gik : k = 1,...,p-1} if and…

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Q: 9. Given: z = 4x2y3 - 2x3 + 7y2 find a. 6х2у2 J2z ?х у

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Q: h.x"+y'-y=0; x(0) = 0, x'(0) = 1, y(0) = 0, z(0) = 0 2x'x+z' -z = 0 x' + 3x + y' - 4y + 3z = 0

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Q: For example H = {he Z10 ne Z} = {02468 is the set of even numbers in modulo 10 includes addition and…

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Q: Consider the relation R = {(a, c), (a, d), (c, b), (c,d), (d, d)} on the set {a,b,c,d}. Find the…

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Q: (b) y(4)y=3t+cost

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Q: Question 3. (a) Let f: R→ R, f(x) = 2³+1. Is this function onto its indicated codomain? Prove your…

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Q: solve: y'' - 5y' + 4y = 20cos(2x) + 30sin(2x) y(0) = 1 y'(0) = 3

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Q: Find the inverse Laplace transform L¯¹{F(s)} of the given function. 2s+8 s² +8s + 25 F(s) = Your…

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Q: #3) Solve the given differential equation by variation parameters. 3x²y"+7xy'+y=x²-x

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Q: 3. Use this set of equations for Q3 and 04: 8x₁ + 2x₂ + 3x3 = 51 2x₁ +5x₂ + x3 = 23 - 3x₁ + x₂ + 6x3…

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Q: Prove that if K be a normal extension of a field F and L is an intermediate field so that F⊂L⊂K,…

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Q: Find the Laplace transform Y(s) = L{y} of the solution of the given initial value problem. y" + 16y…

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Q: 1. y" + 5y + 4y = 5e4x + 4, y(0) = 0, y'(0)|= 1

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Q: Exercise I.1. Consider F := B := {v € R" : ||v|| ≤ 1} and fix xo € R". (a) Suppose to, t₁> 0 and vo,…

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Q: For the function v= 12sin 40, calculate the: a) Mean b) Root mean square (RMS) Over a range of 0≤0≤…

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Q: Find the inverse Laplace transform L¯¹{F(s)} of the given function. 12s² - 10s +175 s(s² +25) F(s)…

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Q: 1. Let C denote the unit circle with positive orientation, Evaluate 1 S=+ = + + 100 2100 dz

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Q: 3. F(s) = = 3s+2 (s-4) (s+1)(s-3) 4. F(s) = 5s-2 s³+3s²+s

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Q: Find the general solution of the following differential equation. 1-4y² 8y X dy da =

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