Show that if a is a quadratic residue (mod p) and ab = 1 (mod p) then b is a quadratic residue (mod p).

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Q: 14. Suppose that the complex number z has modulus one, and that 0 < Arg z < . Prove that 2 Arg(z +…

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Q: by For a set of functions S= {v₁(t), y2(t), ..., yn(t)}. The Wronskian is defined y (t) y' (t) : :…

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Q: 9. (D²+1)y = cotx 10. y" - 2y' + y == ex x²+1

A: By the method of variation of parameters

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Q: The cost of producing x bags of dog food is given by C(x) = 400+ √200+ 15x² The marginal-cost…

A: Given Cx=400+200+15x2-x. Now, the marginal cost function is the derivative of the cost function. So,…

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Q: 1. The Folium of Descartes is an implicitly-defined curve, significant in the history of…

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Q: Find the general solution of the given of DE: y"+y = 0. (Use Maple to find m₁,m₂,m,,m₁)

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Q: (xi. Yi) i = 1, ...., ax y - Bx Linearize the equation. Find least square solution to the equation |

A: First we write the least square loss function. Then for optimal solution we make derivative equals…

Q: If a rotation quaternion is [0.866, 0.162, 0.382, 0.279], which of the following quaternions is…

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Q: 3. We discussed in class that En-o(-1)"x"=1-x+x²-x³+...; if |x| < 1 Use that result to find the…

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Q: y"" 1 x² ln x

A: As per our guideline, we are supposed to solve only one question. Kindly repost other question as…

Q: Prove Akv2v. Where is an eigenvalue of the matrix A. (Hint: use induction with k-1

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Q: A woman's clothing store has designs for 7 shirts, 3 pairs of pants, and 4 jackets. How many…

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Q: Two very large tanks A and B are each partially filled with 100 gallons of brine. Initially, 105…

A: Given: Two tanks are partially filled with 100 gallons of brine. 105 pounds and 45 pounds of salt…

Q: Evaluate the triple integral = 2. B = {(x, y, z) | x² + y² ≤ 7², x ≥ 0, y ≥ 0, 0 ≤ z ≤ 10} and g(x,…

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Q: Solve the tridiagonal system: J C - 2x1 + x2 = -x1 + 2x2 + x3 = 2 -x2 + 2x3 + x4 = 2 -x3 +2x4+x5 = 2…

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

Q: Show that the cross product is not in general associative. That is, find an example using unit…

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Q: given function, F(t) = AF (H) 1 M. 3 -3 3 3; oct 23 -3; -3<+ ²0 9 15 Q1- Find Fourier series…

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Q: Given the generator matrix [101 1 0 1 0 1 1 B 9 G = · G for w€ (Z/2)ײ. for the (5,2) block code…

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Q: a sequence has a first term of a(n) = 12 and a common difference d = -7. Write the formula that…

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Q: Consider the function f(x) = 2x + 5x-¹. For this function there are four important intervals: (-∞,…

A: The given function is fx=2x+5x-1. We have to find the critical points, increasing and decreasing…

Q: c) Find the radius of curvature of the graph of R(t) at the point where t = FI'm

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Q: List all equilibrium solutions of the differential equation, and classify the stability of each…

A: Since you have asked for multiple questions (e) or (d). According to our guidelines, we will solve…

Q: 1) When and why should a utility approach be applied?

A: Answer:

Q: - 4 4 2.5² 3.5³ + 4 4.54 +

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Q: Practice Identify y-int, x-intis), axis of symmetry, vertex from the following equations. Then graph…

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Q: Let f: X → Y be a continuous map from a compact space X to a Hausdorff space Y. Let C be a closed…

A: Kindly refer to Step 2 for the solution.

Q: Given the vectors A=-a,+Sa-3a Ã= 5ª B=11a -0.5a +2.5a Evaluate the following |₁|(2a + B) O 54.1473a…

A: Given Data: Let us consider the given vectors, A→=-ar++5aθ-3aϕB→=11ar-0.5aθ+2.5aϕ To evaluate:…

Q: [(xy)ds_C: r(t) = (2cos(t), 2sin(t)), 0≤t≤π/2 C

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Q: Let u € R³ and W = span ((1, 1, 0)", (1, -1,0)). With respect to the standard inner product, which…

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Q: The volume is incorrect

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Q: dy Write down a differential equation of the form =ay + b whose dt 11 10 solutions all approach y =…

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Q: Determine the order of the given differential equation and state whether the equation is linear or…

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Q: 1. Let F be a field and F be a subfield of E. The mapping : a(f)=f(a) is called the evaluation Given…

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Q: A gender-selection technique is designed to increase the likelihood that a baby will be a girl. In…

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Q: Find the saddle points and values of the payoff matrices. (To enter the saddle points, order your…

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Q: Write .565656.. as a fraction. (Use the sum of a geometric series)

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Q: 18. Deductive Reasoning is the process of reaching a general conclusion by examining specific…

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Q: What is the linearized form of the function y = A ln x + B. Write the transformations that should be…

A: Linearized form of the given transformation

Q: Suppose f(x) is a function with the following properties: · ƒ"(−1) = ƒ"(0) = ƒ”(1) = 0, › ƒ"(x) > 0…

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Q: Use the change of variables x = u/v, y = v to compute the provided integral, where R is the region…

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Q: 3. Suppose that a store offers gift certificates in denominations of 25 dollars and 40 dollars.…

A: We need to determine which amounts can be made from 25 dollars and 40 dollars. Since 25 and 40 are…

Q: Solve for x, where x is a real number. 9 4x = 8 27

A: The answer is x=1/6 (No option is correct)

Q: Consider the solid obtained by rotating the region bounded by the given curves about the line y = 6.…

A: V=π∫outer radius2-Inner radius2dx   =π∫026-3e-x2-6-32dx   =π∫0236-36e-x+9e-2x-9dx…

Q: 3.7 Nikita creates an RSA cryptosystem with public key (n, e) = (1433811615146881, 329222149569169).…

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Q: 3. Give a generating function appropriate to counting the non- negative integer solutions to…

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Q: Identify y-int, x-intis), axis of symmetry, vertex from the following equations. Then graph and…

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