Let p be an odd prime number. Prove that [(3)=1] → [p = 1 mod 6).

Q: Let C = C₁ U C2 U C3, where C₁ is the line segment from (-1, −1) to (0, 0), C₂ is the line segment…

A: a. Suppose,  F=∇fF=∂f∂x,∂f∂y So, ∂f∂x=12x+2+tan-1y∂f∂y=x1+y2+3y2 Now, ∂f∂x=12x+2+tan-1y Integrate…

Q: Let C = C₁ U C2 U C3, where C₁ is the line segment from (-1, −1) to (0, 0), C₂ is the line segment…

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Q: e following function: Find fyy. Points fyy = || f(x, y) = 5x4y6x4y5 - 21

A: The given function is f(x, y)=5x4y6-x4y5-21 . We have to find fyy .

Q: Given f''(x) = = (5) Find f = - - 16 sin(4x) and f'(0) = 6 and f(0) = = - 5.

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Q: Given that C = C₁ U C₂ U C3, where C₁ is the line segment from (−1, −1) to (0, 0), C₂ is the line…

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Q: (6) Let W be the region in R³ inside x² + y² = 1 that is below z = 3-²-² and above √² + y². More…

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Q: 4. a) Prove that I A i) V=I- I+A 1+A ii) fx+nh = Σx=0 (1) 4k fx. =

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Q: 1. Derive d'Alembert's formula u(x, t) = ½ (ƒ (x − ct) + f (x + ct)) + f + g(s)ds by determining the…

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Q: Question 6 Suppose that a particle moves along a straight line with velocity v(t): = 12 - 6t, where…

A: Solution :

Q: ¹ is not linearly homeomorphic to P if 1 < p ≤ 0.

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Q: A company makes cylindrical cans for packing a food item that is Tcm high and has a base radius of…

A: Given: The radius of the base of the cylinder is 10 cm and the height is 7 cm. To find: The volume's…

Q: If G (x, y, z) = curlF (x, y, z), where - F(x, y, z) = (y — z, z — x, x - y), then div(curlG (x, y,…

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Q: Derive Σ PIN) = 1 from equation 1 1. N=O eq] P(N) = N'`~ N! Hint Sex ≤ x² n₂D nl [nd e N

A: Please see the answer in next step

Q: Let G be the solid in the first octant bounded by the planes x = y, y = z, z = 0 and x = 1. Set up…

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Q: IV. Define f(x, y) 1. 2. 3y √1+x¹ Find the rate of change of f at the point (-1, 1) along the…

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Q: Set up an iterated triple integral equal to √√3 3-x² 1 = √ √ 3 S0² x²+y² 3 2-√4-x²-y² using: a.…

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Q: Find the Fourier series for the following functions: f(t)= |sin t], -π <t<n and The function is odd…

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Q: Which of the following is\are true? O (I) and (II). O (1) only. O (II) only. O None of the two.

A: In the event of bankruptcy, common stock investors receive any remaining funds after bondholders,…

Q: f (x₁,x2,... xn) with k numb 9 of constraints by the Lagrange Multiplier method will result to a…

A: This is a problem of optimization.

Q: Let C = C₁ U C₂ U C3, where C₁ is the line segment from (-1, -1) to (0, 0), C₂ is the line segment…

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Q: Suppose is the surface generated by revolving the curve y = 4(x² - 1) about the y-axis. 1. Determine…

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Q: 3y > » √+x4 Definc f(x,y) (a) Find the rate of change of f at the point (-1,1) along the direction…

A: Given: fx,y=3y1+x4 To find: (a) Rate of change of f at the point (-1, 1) along the direction &lt;1,…

Q: Σ 1+4+1 6 is equal to

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Q: Given a piecewise function f(x) = 2, 2x² + 2x X log₂ (x-1), x < -2 -2 < x < 2, x‡0 x ≥ 2. 1. Sketch…

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Q: True/False: Answer a) for True, b) for false and mark on the scantron. 24. The following is a…

A: INTRODUCTION: A map from a parameter interval R = [a, b] to the plane, r(t) = x(t),yt, represents a…

Q: 10. Using Theorem 6.4. (Gram-Schmidt process) obtain an orthonormal basis 3 v} for span(S). Then…

A: Since you post non interlinking three questions as per our guideline we can solve only first…

Q: Define the force field Ē (x, y, z) = . a. Find the divergence and curl of F. b. Let C be the…

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Q: 1. Find the coefficient of 2³6 in the expansion of 6 (1 +5x²5 + 12x50⁰) (x+x² + x³ + x¹ + x³ +rº +…

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Q: For any partial order there may be a number of linear orders that are consistent. For example, for…

A: This is a question from Relation.

Q: 16. Use one of the Green's Theorem area formulas, compute the area of the region enclosed by the…

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Q: Evaluate O 8 27 e (1) ² × (1) ² ³ ○ 32 243 ㅇㅎ ○ 1024 59049

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Q: Which of the following sequence is divergent? 32n² n² + 1 sinh n sin n ° {2 (+)} {-3-} None of the…

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Q: a. Find whether the following graph is bipartite or not. Explain your answer by your own. 7 187 1146…

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A: Disclaimer:  Since you have posted a question with multiple sub-parts, we will solve first three…

Q: Let f be a function of two variables such that and f(2,1)= 4. f(x, y) = af a. If, in addition, x =…

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Q: Find and sketch the domain of f(x, y) = √√₁ - (x + 1)² − y² + 2ln(x − y + 1)

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Q: Which of the following values is the directional derivative of f (x, y) = ln (x² + y² + z²) at the…

A: To Find: The Directional derivative of fx, y, z=lnx2+y2+z2 at the point 1, 3, 2 in the direction of…

Q: Define the force field ₹(x, y, z) =. Let S be the portion of the plane z = 2 - 2x in the first…

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Q: Let A E Cmxn and be Cm. Show that the following three statements are equivalent: . There exists a…

A: As per the question we are given 3 different statements about the matrix A ∈ Cm×n and the vector b ∈…

Q: x1 + x2 + x3 2x1 + 3x2 + 4x3 3x1 +4x2+2x3 6 20 = 17. = =

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Q: If L, CL₂ and L₂ CL4, then L₁ L3 C L₂ L4 Select one: O True O False

A: We know that for two sets A and B, we say A⊂B if and only if all the elements of the set A are…

Q: Using Part I of the Fundamental Theorem of Calculus, evaluate: d dx I 12 t² dt =

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Q: . Matrix A has the eigenvalue λ = -1. Find the corresponding eigenvector K. A = /2 0 0 045 4 3. 0

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Q: Solve the following initial-boundary-value problem by using the separation of variables technique:…

A: Given :             utt=uxx                0≤x≤1   ,   t&gt;0 u0 ,t =0  ,u1 ,t =0…

Q: m = ∞ Exercise 8.9. Let (91, 92, ..., 9m) € G₁. Prove that |(91, 92, ..., 9m)| = ∞ if and only if…

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Q: 4.1 Consider the sequence of functions {fn(2)} = {n²r(1 − 2)"} for z € R and n = 1,2,3.... 4.1.1…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three…

Q: John invested $4500.00 for 6 years at 5.4% simple interest. Determine the amount of interest John…

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Q: fxx = || f(x, y) = 5x4y6x4y5 - 21

A: For the given function f(x,y)=5x4y6-x4y5-21      has  fxx=12x2y5(5y-1)

Q: || 2)) D3. IS D3 1

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Q: 4. Solve the Cauchy problem Utt = 9uxx+cos x, (x, t) E Rx (0, ∞) u(x,0)=0, TER u(a,0)=0, x ER using…

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