Use a direct proof: p is a prime # and x ∈ Z. If x2≡x (mod p) then x ≡ 0 (mod p) or x ≡ 1 (mod p). Show all work clearly and neatly. Do not skip steps.

Q: Evaluate the Legendre symbol () (a) using the reciprocity law 1873 8389 only for the Legendre symbol...

A: As per the question we have to evaluate the Legendre symbol (1873/8389) using : Reciprocity law of ...

Q: +0+ 2n in Σ n = 1le" 3.

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Q: Write down the characteristics of cosine function and draw its graph

A:  To write characteristics of the cosine function, and to draw it's graph.  

Q: The following table shows the amount spent by four U.S. airlines to fly one available seat 1 mile in...

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Q: Consider the matrix 7 7 -3 A = 4 -5 -3 4 -7 (a) Given that the matrix A has an eigenvector calculate...

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Q: Give a recursive definition for each of the following. (You don’t need to prove your definitions are...

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Q: Python Program to find Volume & Surface Area of a Cylinder?

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Q: Solve a, = 2an-1+ 3an-2 with ao= 1, a,= 6. %3D

A: Given an=2an-1+3an-2 with a0=1, a1=6 We will solve the given recurrence relation. 

Q: 2.. Evaluate. tha.fallowing.integvals.after.reveniag.the erderaf.integratiRm. sing dy.dx. TT Ans..2 ...

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Q: 8. O Solve and state restrictions X-2 %D x+2 x2-4

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Q: 4. Riley was a spectator at his town's air guitar competition. Contestants were allowed to play eith...

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Q: Theo Corp finds that their profit (in thousands of dollars) when producing and selling x hundred des...

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Q: 3. Evalnate. the. fallowing.deuble.integrals.by.conver.king.b. polar.Cto.r.dinates. Ans: 3.6. C.... ...

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Q: Given the graph of the function below. Find the limit of the function as x approaches -1.* (3, 4) (0...

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Q: 6s² +26s + 26 r Example: Given F(s)= determine f(t). (s+1)(s+2)(s+3)

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Q: Find the average value of f on [0, 32]. 16 24

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Q: An instructor wants to create a test that has true-false questions, multiple choice question and ess...

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Q: Decide whether the pair of graphs are isomorphic or not. If they are isomorphic find an isomorphic m...

A: To find- Decide whether the pair of graphs is isomorphic or not. If they are isomorphic find an isom...

Q: 1. Answer the following question? A. 2r* + 5x² + 3x² + 2x - 50 x' +3 direction does flx) approach th...

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Q: Find the area of the triangle with vertices (4, -1), (13, 1), and (6, 8). Area =

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Q: 7- Sketch the graph of y= cot x over the domain 0< x <2n 4

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Q: [8] (a) Write in words how to read the following out loud: {n EZ | n is a factor of 9}. (b) Use the ...

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Q: 1: What would the coordinates of triangle DEF be after a translation of 3 units right and 2 units do...

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Q: Prove that a group of order 7is cyclic.

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Q: The grade point averages (GPAs) of a large population of college students are approximately normally...

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Q: 3 A square matrix M is said to be nilpotent provided Mk = 0 for some positive integer k. [1 1 17 If ...

A: Given A = 111011001

Q: Values of function y(x) at discrete values of x for 0 <x < 10 are given in table. Using trapezoidal ...

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Q: The distance d of a point P to the line through points A and B is the length of the component of AP ...

A: Solution:-

Q: For each of the following series, determine if they converge or diverge (justify your claim). n (a) ...

A: Use the following tests to evaluate the converge; i) Series divergence test ii) Integral test iii) C...

Q: Find the surface area of the part of the paraboloid z = 9 – 2.x - 2y that lies above the %3D

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Q: Convert ff Incxag) dA.aver. the.regian.cx.<e. segian.e.x+y.c.e. -.to.polar.form. and. then..evaluate...

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Q: Use the discrete logarithm with base g = 3 to find the square roots of 5 in F19.

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Q: The table shows the seasons when 7 different students play a sport. Fall Sport Winter Sport Spring S...

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Q: Q1 1 u2 uj 2 Given are the vectors and Span{v1, v2} a) Determine if these vectors are in the linear ...

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Q: 10- A cosine function has a maximum value of 1, a minimum value of -5, a phase shift of t/4 to the r...

A: Let equation of function  f(x)=aCOS(2x+π/4)+b

Q: E Valua te :- when

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Q: Consider the function f(r, y) = 21? + ry – 6zy + 5x +2. (a) Show that (1,3) is a stationary point of...

A: Find the maximum and minimum, using send derivative test.

Q: Let w = (-5, -7, -2), v1 = (2, 1, 1), ö2= (-2, -2, -1), 03 = (-5, –3, -2). If possible, express w as...

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Q: find dy,if y= x²+2)Cx*+3x+) %3D

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Q: Express the following expression trigonometric ratio and the evaluate to an exact value.(: 5- as a s...

A: Given expression is f(x)=8cos2π6-4 Now, We cab write it  as f(x)=8cosπ3-4              (1)

Q: WITHOUT a calculator, identify VERTEX form, STANDARD form, AND FACTORED FORM. Then use the three for...

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Q: Question 7 Find all distinct (real or complex) eigenvalues of A. Then find the basic eigenvectors of...

A: Finding eigenvalues and eigenvectors of A

Q: Show that the equation dy + 2k possesses solutions of the form 00 Σ C,e -kt cos (a, x + E) cos (w,t+...

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Q: (x+7)" X if the given power series is convergent n=2 2" n – 1 at x = - 9, is it conditional or absol...

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Q: By using the substitution u = x3", find nx3n-le*" (e*™ + 8) dx where n is a constant. Hence, evaluat...

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Q: Determine whether each statement is true or false. You have one submission for each statement. 9000 ...

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Q: hit vectors orthogonal to a = (3, 3, 0) and b = (- answer so that the first vector has a positive fi...

A: INTRODUCTION: The formula for the units vectors orthogonal to vectors A and B is given by, v1 and v2...

Q: 3. For the ry-plane, consider the new variables u = 2? - y°, v = and the region R = {(x, y) | x > ly...

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Q: Home work : f ind the a ppro ximate value af the following! 2 ( 8.02) (3.96) + (3.03) 2 - I (5.07) +...

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Q: n (-1)³n n4 + 1 n=1

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