Solve the congruences: 52x + 4 = 8(mod 22) 17x = 19(mod 100) 3x = 9(mod 12)

Q: 8. d²y dy Solve the Cauchy-Euler equation x²- +8x +6y=0. dx² dx

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Q: 7. all integers. a) \n (n²+1>n) b) n (4n = 3n) c) 3n (n = n³) d) Vn (4n > 5n) Determine the truth…

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Q: 3. Solve the system of congruences Show the steps used. 3x = 2 7x3 8x 7 mod 7 mod 11 mod 19.

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Q: find the general solution by finding the homogeneous solution and a particular solution. please help…

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Q: a. Find f'(-2) and f"(-2) b. At which value(s) of x does f(x) have a relative extremum on [2,6]?…

A: f' (-2) = 1f'' (-2) = -(1/2)

Q: 2. Solve for m, 2 2m² = 3 - 5m

A: (.) Given,

Q: Charlie's Pizza orders all of its pepperoni, olives, anchovies, and mozzarella cheese to be shipped…

A: Given information:The time interval between reviews, .Lead time, .The average demand for pepperoni…

Q: Let R4 have the Euclidean inner product. Find a unit vector with a positive first component that is…

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Q: n(n + 1) 2 Use the formula S =- 1+ 2+ 3+ ... + 980 = to find the sum of 1 + 2 + 3 + ... + 980.

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Q: Problem #8: Let R4 have the Euclidean inner product. Find a unit vector with a positive first…

A: .

Q: Eigen vectors and Eigen values

A: Given system of differential equationsX′=[01−10]XCoefficients matrix A=[01−10]Characteristic…

Q: Simplify the expression by combining like terms. 4x²-3y² + 3z-5z - 5y²

A: In this question, we will simplify the expression by combining like terms.

Q: Find the arc length s of the vector function r(t) = 11 cos³ (t)i + 11 sin³ (†)j + k from t = 0 to t…

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Q: . Let A and B be square n x n matrices. Show that det AB = det BA even though in general, AB ‡ BA. •…

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Q: (c) Find the limit of Σ r=N+l N (3r+1)(3r-2) as N →∞0.

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Q: 1. Prove that the function f(x) = x² sin x + 4x 3 has exactly one root in [0, 2]. Perform the…

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Q: Show that the identity k n = n 72 n k k-1, olds for all integers 1 <k<n and use it to prove that n…

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Q: In 1980, America's GDP per capita was approximately $30,000 (measured in today's dollars). How much…

A: According to the given data:America's GDP per capita in 1980  = $ 30,000America's GDP per capita in…

Q: 3. Prove that n! > 2" for every integer n ≥ 4.

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Q: 2 1 0 -1 -2 -3 -4 3 F(x, y) = 4x + 4y²j F(x, y) = 4y²i + 4xj F(x, y) = 4yi + 4x²j F(x, y) = 4x²i +…

A: We have to identify the vector field

Q: Rewrite each of the sets described below in set builder notation.

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Q: Choose 2 Are the vectors -2 11. 2 [B]+ -2+ If they are linearly dependent, find scalars that are not…

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Q: List all the elements of the following set. Use set notation and the listing method to describe the…

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Q: Please label each part of your solution with the corresponding A, B, C. Consider the curve defined…

A: Let us consider the polar curve, .(a)Find the all values of  such that .Further,It implies that the…

Q: Let V be the vector space of symmetric 2 x 2 matrices and W be the subspace W-spand W = span{ a.…

A: We need to find two elements X and Y.

Q: I see that parts 1-3 are answered but can you help me with 4-6?

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Q: Consider the following tableau for a particular Linear Program (LP) being solved using the M-Method:…

A: Given Information:Tabuleau for particular LPP using big M method is given as…

Q: 2. Recall that a number m is said to be square free if ď² | m for d≥ 1 implies that d = 1.…

A: The idea is to carefully apply the Chinese Remainder Theorem.

Q: 1. Find all solutions of the congruence 5x+3x²+x+3 = 0 mod 30. You should do this by factoring the…

A: The congruence .To Find:Solution of the above congruence.

Q: he coordinates of point P are (-3,8) and the coordinates of point Q are (5,3), M is the midpoint of…

A: Result: If  . Let M be the mid point of the line PQ then .

Q: Let a, b ∊ R, and suppose that for every ɛ>0 we have a≤b + ɛ. Show that a≤b.

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Q: Your Cd pays a return of 5.95 & Apr Compounded daily.  a) Find the Periodic Interest. b) Find the…

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Q: Let x, y, z be (non-zero) vectors and suppose w = x - 3y + z. If z = x - 3y, then w = 00000 x+ Using…

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Q: 1. Let p and q be the propositions p: I bought a lottery ticket this week; q: I won the million…

A: Let p : I bought a lottery ticket.     q : I won the million dollar jackpot.a) I bought a lottery…

Q: Find the area of the region that lies inside the first curve and outside the second curve. r = 19…

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Q: If F = {0, 1, x} is a field with three elements, then (x + 1) + x is equal to

A: Given that  is a field.Then is abelian group under addition and  is abelian group under…

Q: Let K be a finite normal extension of a field F. If a, ß are any two elements of K conjugate over F,…

A: Statement : Let K be a finite normal extension of a field F. If a and b are any two elements of K…

Q: 1. Solve using algebra. Show the EXACT solution. No graphing solution is accepted. Clearly display…

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Q: (a) Let 0 < a < 1. Show the series or converges uniformly on [-a, a] to ₁¹. n=0 (b) Does the series…

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Q: The function f is defined by f(x) = x² - 2 - 4 sin (3x² + 5). Let l be the line tangent to the graph…

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Q: 5. (x + 2y + 3) dx + (3x + 9y - 5) dy = 0

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Q: The trace of a square n x n matrix A = (aj) is the sum a₁1 + a22 + ... +ann of the entries on its…

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Q: Problem #1: Let Problem #1(a): A = Problem #1(b): 5 0 1 4 -6 0 (a) Find the characteristic…

A: To find eigenvalues and corresponding eigen vector.

Q: Let a and b be positive integers with ged(a, b) = 1. Show that if d > ab, then as + tb = d has a…

A: 4. Given that a and b be positive integers with gcd(a, b)=1.     To prove that if then has a…

Q: Prove that if R is an equivalence relation on a set A, then the inverse relation R−1 is an…

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Q: B. Express the ff atticher whit with general Form quadortic function. 1. 2 9=C++3) ²-3 FLAMU

A: The general form of a quadratic function is

Q: 1. A car travels at a constant speed and burns g(x) liters of gas per kilometer, where x is the…

A: 1. Given that a car travels at a constant speed and burns g(x) liters of gas per kilometer,…

Q: 1. Show that there is no monic polynomial p(2) = 2" +an-12-¹+...+ao such that [p(2)| < 1 for all…

A: To show that there is no monic polynomial p(z)=zn+an−1zn−1+…+a0 such that |p(z)|&lt;1 for all z with…

Q: Assume that the recursively defined sequence converges and find its limit. a₁ = 3, an+ 1 42 1+ an…

A: The recursively defined sequence is a1 = 3 ,an+1 = 42/(1+an) and which is convergent.

Q: Prove that 1-²-2+2-3- + + 1 n(n+1) = n n+1 for all n E N.

A: The given problem is to prove the given following identity,Given 1/1•2 + 1/2•3 + .. + 1/n(n+1) =…