Why are there different Fourier series equations? I don't quite understand what the difference between them all are

Q: S7. By making use of the relation 2 sin a sin 3 = cos(a - b) cos(a + B), prove that 0 S sin (nπx)…

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Q: 8. It is thought that the period T of a planet's year is related to r, its mean distance from the…

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Q: Exercise 3: Bijections Let X := {(x1, x₂) = R² : x² + x² = 1}. Find a bijection between X\ {(0, 1)}…

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Q: 7. Suppose there is a game where you spend $1.50 to flip N fair coins. If this results in exactly i…

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Q: Solve the initial value problem below using the method of Laplace transforms. y" +6y' +5y=32e³y(0) =…

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Q: S L-₁ ((5 + 1)²) = eat + aebt (s Find a + b.

A: Inverse laplace transformation

Q: Find the center of mass of the half of the solid sphere x² + y² + z² ≤ R² where y ≥ 0, with constant…

A: Here, the given function is x2+y2+z2≤R2 Since y≥0,the upper portion of the half sphere can be…

Q: Given the function f(x, y, z) = (x + y)2(x + y² +z): Is the function satisfiable, and if so, which…

A: A function f(x, y, z) is satisfiable if there exist atleast one particular set of values of x, y,…

Q: A manufacturer of bicycles builds racing, touring, and mountain models. The  bicycles are made of…

A: Let x1 be the number of racing bikes, x2 be the number touring bikes, and x3 be the number of…

Q: True or False? Upload your reasoning. If the statement is true give a proof or detailed reason why…

A: We know that If W is a non-empty subset of a vector space  (linear space) V , then W is a subspace…

Q: 1. Derive the law of sines using the triangle shown below. Suggestion: Try writing the length of the…

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Q: 6. What is the order of each of the following permutations? [1 2 3 4 5 6 [1 2 3 4 5 6 7 7 6 1 2 3 4…

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Q: 8. Suppose f € C[0, 1] and suppose 0 ≤ f(x) ≤ 1 for all x € [0, 1]. True or False: there exists ce…

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Q: Given three data points (1, 6), (3, 28), and (10, 231), it is found that the function y=2x2 +3x+1…

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Q: Solve the given initial value problem using the method of Laplace transforms. Sketch the graph of…

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Q: Q11: The symmetric difference of A and B is denoted by A + B which is defined by A + B = (A - B) U…

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Q: Exercise 2: Induction Prove by induction that for all n E N 2²-(₂) = Σ k= k=1 2 k .

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Q: ercise 108. Determine all maximizers and minimizers of the function f(11, 12, 1₂): ect to = 1…

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Q: Find all local constrained extrema of f(x, y) = x² + 2y - z² + z under cionstraints 2x - y = 0, x +…

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Q: 0²u ди อน 3. Consider the PDE 0x² ox ot 0. Use the method of separating variables to decompose the…

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Q: Find a public key for RSA cryptography based on the prime numbers p = 13 and q = 7. Write down the…

A: We are to find a public key for RSA cryptography based on the prime numbers p = 13 and q = 7 Write…

Q: If there are 64 grams of Np-240 present, how much Np-240 will remain after 4 hours? (Np-240 has a…

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Q: A weight of 900 pounds is suspended from two cables as shown in the figure. What is the tension in…

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Q: Finding the Least Squares Solution In Exercises 25-28, find the least squares solution of the system…

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Q: Problem 2 M, A, T, H are four positive integers in the following vertical addition. MA T H A T H T H…

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Q: Question 2. Find the maximum and minimum values of the function f(x, y) = rev² on the curve C, where…

A: The given problem is to find the maximum value and minimum values of the given function f(x,y) over…

Q: k(x) = - Step 2 of 2: Find two points on the graph of this function, other than the origin, that fit…

A: The given function is f(x)=-107x. To Sketch: The graph of this function with two coordinate points.

Q: Let D = (d₁d2₂ d3) and F = {f₁.f2.13) be bases for a vector space V, and suppose f₁ =3d₁-d₂ +5d3, f₂…

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Q: At which of the following points is the function f(x) = \cos x|+|sin (2 − x)| not differentiable? a)…

A: The given function is f(x)=cosx+sin2-x. To Find: The set of points where this function is…

Q: A boat on the ocean is 4 mi from the nearest point on a straight shoreline; that point is 9 mi from…

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Q: Consider a set of vectors S = {V₁, V2, V3} following statements is true? = {··]} Which one of the

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Q: (a) Differentiate the Maclaurin polynomial of degree 7 for f(x) = sin(x) and compare the result with…

A: We know, the Macluarin series expansion of sin x and cos x are given as follows.       sin x = x…

Q: A bag contains 7 coins, 2 of which have a head on both sides while the other 5 coins are normal. A…

A: P( X =0 |E1)=P(no head when biased coin tossed twice) =0/1=0 P( X =1 |E1)=P(Only one head when…

Q: Problems 1. Let A = {0, 2, 4, 6, 8, 10}, B = {0, 1, 2, 3, 4, 5, 6), and C = {4, 5, 6, 7, 8, 9, 10}…

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Q: (2+3i)x1+(4+2i)x2=1+i Find x2 in polar form.

A: The given problem is to find the value of x2 in the polar form for the given complex equation. Given…

Q: 2. Find the linear approximation of f(x) = x² - 2x + 4 at x = 3.

A: I have explained everything with in the solution. Please go through that.

Q: Let A, B be statements. Are (A V B) V ¬(A ^¬B) and AV B logically equivalent?

A: As you have asked more than one different questions, we shall answer first Que only as per the…

Q: 8.12 Consider the system represented in state variable form 01 -4 -5 y(t) = [ 10 ]x(t) + [0]u(t).…

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Q: Finding the Length of a Vector In Exercises 5-8, find (a) ||u||, (b) ||v||, and (c) ||u + v||.…

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Q: Find two negative numbers, x and y, whose product is 728and whose sum is a maximum. Number y =…

A: We have to find two negative numbers x and y whose product is 728 and its sum is maximum.

Q: f. Use a graphing utility (Desmos is recommended) to graph V. Find the x-value that maximizes the…

A: f) We have used DESMOS as the graphing utility to plot V=x2(61-4x) in [0,15.25]. The value of x…

Q: Find the rank and nullity of the T(ƒ(t)) = t(ƒ'(t)) from P₂ to P₂ transformation T.

A: Given the transformation  T  from  P2 to P2 i.e.   T : P2 → P2 given by ,            T(f(t)) =…

Q: 4. The graph of y = −3x + 5 is translated 6 units to the left. State the defining equation of the…

A: We have to find equation of new graph using given information. Graph of f(x+a) is obtained by…

Q: Evaluate (5856592 * 888747 * 76334) mod 10. Box in your final answer. Remember to show all work.

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Q: Let p be a prime and g be a primitive element of the finite field Fp. This means that g, g², g³,...,…

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Q: 3) Give an example of a function f(z) which has the following properties. Justify your answer. with…

A: Let us consider the given data, (b) A simple pole at z0=i-3 with residue 8i-3 and an essential…

Q: Consider the infinite series. 2 Σ(-1-3 n=1 Determine whether the series converges absolutely,…

A: Introduction: The convergence of series is given by using the alternating series test. Given: ∑n=1∞…

Q: d₁: [x,y,z]= [0,2,1]+t[3,1,1] And d₂: [x,y,z]= [1,-3,0]+[2,-1,1]

A: If we have two points A(x1,y1,z1) and B(x2,y2,z2) then distance between A and B is…

Q: Let A be the set A = {1, 2, 3, 4) and let B be the set B = {5, 6, 7, 8). What is an element in B x…

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Q: 12. True or Give a Counterexample: If fe R[a, b] then there exists € [a, b] such that f f(x) dx =…

A: The given statement is FALSE. Consider the function f:[0,5]→ℝ defined by f(x)=x+2  if 0≤x≤20…