A rain gutter is to be constructed from a metal sheet of width 30 cm by bending up one third of the sheet on each side through an angle θ. How should θ be chosen so that the gutter will carry the maximum amount of water?

Q: a. f(t) = cos(2t). Find F(s) b. g(t) = e²t sin(3t). Find G(s) c. H(s) = 3s +1 s² - 2s + 5* Find h(t)

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Q: αι = Ω_(7q+6) @ = 0 = ΠΩ(+1)t-qΩ-11+4 Ω_(q+1)t-q ΠΩq+1)t-q + 1 Πιο Ω-(n+1)t-q Ο Th ΣΠ +1 h=0 k=1 6 1…

A: Given: The Information that leads to the required proof.We need to prove the equations marked in…

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Q: 2. Complete each of the following. a) Let [x] € Z/nZ. What is the additive inverse of [x]? b) Show…

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Q: Suppose that U₁,...,Uk are subspaces of V. Prove that V = U₁ ☺ · · · ÐUk if and only if the…

A: Please find the attached solution

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Q: Q1. Evaluate the series S = -|2 + N|T + -12 + 1 + 211 :

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Q: if sis a group of order p", then its center 24, peing a primes

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Q: ]i+ 5x sec² (xy) —- 3] + [6 y j+(6xz+2) e³x² –3]k, For F(x, y, z)=[5ysec²(xy)+6z²e³² find the curl…

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Q: Consider the recursive definition of the function f(n) f(0) = 0 f(n) = 1+ f(n-1) Find ƒ(1), ƒ(2),…

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Q: 2.22 Verify the Vizing's Conjecture for G=K, K, and T = P₁

A: Please find the attached solution

Q: Prove that every minimal dominating set in a graph G is a maximal irredundant set of G.

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Q: Determine whether the given function is a solution of the differential equation. y = √√√x; xy' - y =…

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Q: Suppose n ∈ N. Let S be the following statement: If n is prime, then 2n + 1 is prime. (a) Write down…

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Q: C. Write down a sequence for the number of shapes/dots in each pattern. Explain how to obtain the…

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Q: Question 2 Consider the initial-value problem dy dz = 1+ 2z-y, y(0) = 1. (a) Use the Euler's method…

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Q: The following Lewis diagram represents the valence electron configuration of a main- group element.

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Q: 8. Show how the Gaussian quadrature rule can be used for a [₁1(a), 5 dr-f - V ( -√² ) + ( + √(√² )…

A: Given : I=∫abf(x)dx To prove : ∫-11f(x)dx≈59f-35+89f0+59f35 To find : ∫0π2 x dx

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Q: Let A, B E Rnxn and let R[x] be the set of all polynomials in variable x with coefficients in R.…

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Q: 2. y+3y"+4y+2y=0; y(0) = 4; y'(0)=-4; y"(0)=1 a. y=e* (4+sin x) b. y=4e¹ cos x c. y=e*(1+3 cos x) d.…

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Q: ILLUSTRATION 4.60 The plane ax + by = 0 is rotated through an angle o about its line of intersection…

A: Given that the plane ax+by=0 is rotated through an angle α about its line of intersection with the…

Q: Low Output S: $200 million Y: $30 million S: $120 million High Output S: $100 million Y: $50 million…

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Q: Consider the u(x, y) = 2x - x³ + 3xy² function. Prove that it is a harmonic function and find its…

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Q: 7. The pair of equations dx dt dy dt -5x + 2xy -4y + 3xy models two coexisting species with…

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Q: Given a system of equation as: 2x-y+z=4 x+3y-2z=-4 -x-y+z=1 Solve this equation system by using…

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Q: In each of Problems 13 through 16, determine the critical point x = xº, and then classify its type…

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Q: Calculate the following limits, or explain why they diverge. (d) lim sin n→∞ (e) lim n→∞ n+ 1 n² + 1…

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Q: (x - y)y' - 2y + 3x + == 0 ; y(1) = 5 + X² = 0 X

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Q: 11.[2] Show that vectors A = 4ax - a₂, B = ax + 3ay + 4az, and C = -5ax 3a, 3az form the sides of a…

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Q: Question 1. Consider the integral e dx. (a) Approximate the integral by the Trapezoidal rule using n…

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Q: 2. Answer

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Q: Formula for rebate fraction

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Q: If G is a group and H is a subgroup of index 2 in how that H is a normal subgroup of G.

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