(i) Deduce that the difference in the number of integers in the numerator and denominator of (* 2N N which are divisible by q is [2N/q] – 2|N/q]. (ii) Show that this quantity equals either o or 1.

Q: Draw a line to show how the white king can move out of check .Remember two kings can never move next...

A: This is the problem of LP. finite math.

Q: Consider the series E (In(2n + 1) – In(2n – 1)). (a) Let a, = In(2n + 1) – In(2n – 1). Does {an} con...

A: We have to check whether given series and sequence is convergent or divergent.

Q: A population P obeys the logistic model. It satisfies the equation dP 0.24P 1 for P> 0. dt 4900

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Q: 10. X 20 30 40 50 P(X) 0.05 0.35 0.4 0.2 11. X 1 3 4 P(X) 0.4 0.3 0.2 1 12. X 7 9. 12 14 4 13 3 P(X)...

A: 10. If P(X = x) >= 0 for all x        Also if we sum the probabilities over all x, the sum is (0....

Q: Use cylindrical coordinates. Evaluate (x - y) dV, where E is the solid that lies between the cylinde...

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Q: Jhosep wants a tv for his birthday that originally cost $740. Right now, the tv is on sale for 40% o...

A: Given, Jhosep wants a tv for his birthday that originally cost $740. Right now, the tv is on sale fo...

Q: III. For each of the following series, determine whether it is convergent or divergent. Justify your...

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Q: 7k Let ak = Which of the following inequalities is/are true for any positive integer k? k2 +| sin k|...

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Q: Consider the system of differential equations dx = 0.3x – 0.02xy - dt dy 0.2y + 0.016xy dt Where x a...

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Q: The lengths of each side of a rectangular prism are doubled. What is the ratio of the surface area o...

A: Let the rectangular prism has l units length, w units width and h units height. Now the lengths of e...

Q: Proposition 14. The Fibonacci numbers are defined to be F1 = F2 = 1 and F, = Fn-1+ Fn-2 for n > 3. T...

A: Given The Fibonacci number are defined as F1=F2=1  & Fn =Fn-1+Fn-2 , n≥3 then we have to show th...

Q: · exist and are harmonic. 18.6. Let be a simple closed contour described in the positive sense, 3+78...

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Q: Test for convergence the series 3.6.9 ... 3n ( 1 ) Σ n = 1 x" (x > 0), 7.10.13 ... (3n + 4) I1 = 2.4...

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Q: Find the Laplace transform of each of the following functions: 1. f (t) = t2 – 3t + 5 || -

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

Q: Σe0 = 1+z+ = 1+ x + -k=0 2! 3! 4! + +

A: This is a question oof Mclaurin series.

Q: 6+ -0 -3 -4 The plot above is created with the parametric equations S¤(t) = a cos(bt) l y(t) = c sin...

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Q: Use cylindrical coordinates. Find the volume of the solid that is enclosed by the cone z = x² + y2 a...

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Q: List the eigenvalues of A. The transformation XHAX is the composition of a rotation and a scaling. G...

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Q: Proposition 7. Let a, b, c, d E Z and n be a positive integer. If a = b (mod n) andc = d (mod n), th...

A: a ≡ b (mod n) ➞ n|(b-a) a ≡ b (mod n) ➞ b ≡ a (mod n)

Q: Obtain the values of the following integrals. sin?nz+cos²nz A) dz on the contour |z – il = 3 (z-1)(z...

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

Q: +oo 1 (2n)! ( a) Σ ( c) Σ-1)" 4n2 – 8n + 3 n=1 2" n=1 +00 In n (b) Σ-1)" n2 n=2

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Q: Determine whether each of the following statements is true. If true, prove it. If false, give a coun...

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Q: 2. f (t) = 2 cosh² 3t

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Q: Solve xy' (2y - 1) = y (1 - x)

A: Solve xy' (2y - 1) = y (1 - x)

Q: (t – 4)y' + In(t + 1)y = 5t, y(3) = - 2 Find the interval in which the solution of the initial value...

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Q: Choi Home Repair needs to accumulate $22,000 in 6 years to purchase new equipment. What sinking fund...

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Q: Proposition 7. Let a, b, c, d E Z and n be a positive integer. If a = b (mod n) andc = d (mod n), th...

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Q: IV. Determine whether the given series is convergent or divergent. Justify your answers. 1 (2n)! (a)...

A: Note: Since you ask multiple question, only first question will be addressed here. It is given that,...

Q: Evaluate the line integral (y dr+yrdy) taken in clockwise sense along the hexagon whose vertices are...

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Q: 3. b c def f gh a bcd efgh 8 8. 7 7 7 6. 4 4 4 3 21金 2 1 曾 a b c def g. h 1 a b c 1 49 Convrigu 土 三 ...

A: how white can escape from the check :-

Q: Determine whether each of the following statements is true. If true, prove it. If false, give a coun...

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for y...

Q: Evaluate the integral of (t-i)^3 from 0 to 1 where i=sqrt(-1) choices:  a. -5/4 b. 7/4 c. 4/3 d...

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Q: The equation x5 + x4 − 5 = 0 has one real solution. Approximate it by Newton’s Method.

A: This is a problem of Newton Raphson method.

Q: 1. Find the Fourier transform of f(t) defined by: 0 t<0 e-6t t20 f(t A. (6- jw)/(36+ w^2) B. (6 + ja...

A: Fourier transform of the pice wise function

Q: Find (2+j5) O 0.00934 - j0.265 O 0.0265 - j0.00934 O 0.00934 -j0.0265 0.265-j0.00934

A: Solution:-

Q: .Find the flaw in the following proof. JECTURE: If n is a prime number, then 2"- 1 is also prime. UM...

A: Please concentrate when you  see  this  answer.  

Q: Proposition 12. Let n be a поппедative integer. Then 3|(52n - 1). Hint: Try induction on n. Proof.

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Q: 2. f(t) = -7(e^3t)[sinh(2t)] A. -14 / (s^2 – 6s + 5) B. (-7s + 21) / (s^2 – 6s + 5) C. -14 / (s^2 - ...

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Q: Give the Maclaurin series expansion of f(x) = ln(3-2x). Determine its interval of convergence by fin...

A: Differentiate the expression of f(x) to obtain the expression of f'(x), f''(x), f'''(x),⋯⋯⋯⋯⋯,fn(x)....

Q: 00 20 00 02 C = 2000 0001 0 010 0100 y D = 0 200 1000

A: let λ be an eigenvalue of C.

Q: PROBLEM: lim CSch 2 ATTEMPT: CSch csch x In %3D Ix1 _csch x = In I+ (0)= In ! (히 %3D In Ito 4. 101 1...

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Q: I ind the second derivative(y") of the following functions and simplify the final results. 1. y = x ...

A: Differentiate using the rules of derivative.

Q: Write an equation for the line through center a circle (x² + y² + 4x+6y = 3) which make an angle) wi...

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Q: Question 6 i P Consider a room in the shape of a 4 m cube, 4 meters on each side. A bug at point P w...

A: We need  to find shortest distance between two diagonally opposite corners of the cube .(along the s...

Q: a) Solve the system of congruences: x 3 mod 4 x= 5 mod 7 b) Solve the system of congruences: X 3 mod...

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Q: Evaluate |1 – cos40 de O 1/(2v2) V2/2 O None of the choices O 1/2

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Q: 6. When finding the determinant using cofactor expansion, it is necessary to select the row or colum...

A: As per Bartleby guidelines we're supported to answer only first three subparts. Kindly repost rest.

Q: Q.2 Find the vertex point and show in graph: y=2x²-4x+4

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Q: +o0 Σ)

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