19. Prove that for each integer a, 3 divides (a + 23a). Hint: sing Theorem 3 0g and tehnia

Q: QUESTION 13 Let ma and n be integers. By mZ + nZ is meant {a + ba EmZ,bEnZ} of all the sums of an el...

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Q: Given the vectors a=i + j + k,  b= i-j and c=i + 2j + k, determine the volume of tetrahedron

A: Given- Given the vectors a = i + j + k, b = i - j, and c = i + 2j + k.  To find- Determine the volum...

Q: x² Q 1 S ;dx (x sin x+cos x)2

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

Q: Solve the D.E. 3(3x +y) dx - 2xy dy = 0 A x- c(9x² +y°) B) x- c(x² + 9y³) © x- c(9x² +y°) D x- c(x² ...

A: Given Equation: 3(3x2+y2)dx-2xydy=0 ⇒3(3x2+y2)dx=2xydy ⇒dydx=3(3x2+y2)2xy------(i)    

Q: |15 18 16 11 12 L 25 E.

A: A Hamiltonian path is a path which starts at any vertex of the graph and visits every vertex  of the...

Q: Find the order and the degree of the differential equation cos x COS X A 2,4 B) 5, 8 © 5,4 5,2

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Q: Let f(u, v) be a differentiable function with f(0, 2) = 0, fu (0, 2) = 2 and f. (0, 2) = -3, g(z, y)...

A: Given fu,v is a differentiable function with f0,2=0, fu0,2=2 and fv0,2=−3. And given gx,y=fx2y+x,3x−...

Q: Is 2 a factor of 10b + 14? yes no Submit

A: We have to find is 2 is a factor of 10b + 14.

Q: [5 Consider matrices A =9 -11 11 and B =|0 -1] Two elementary matrices -4 c) 2. 8. 4 1 -1 3 -4 2. E ...

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Q: Argue about nature of mathematics, what is it, how it is expressed, represented and used

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Q: A bond issued by Ford on May 15, 1997 is scheduled to mature on May 15, 2097. If today is November 1...

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Q: - All are interrelated to each other except precise concise A. С. convention В. D. powerful All are ...

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Q: Part 2: Solve the system using Gauss elimination. 3x, - 2x, + x3 + 2x, = -2 -X + 3x2 + 4x3 + 3x4 = 4...

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Q: Prove that if mn and m + n are even integers, then both m and n are even integers. (Use proof by con...

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Q: Suppose that you add 3 to all observations in a sample. How does this change the sample mean? How do...

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Q: n(n+1)(2n+1) 2. Prove the following using induction: 1+ 4+ 9+ · ..+n² 6

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Q: A lottery ticket contains three letters followed by two digits. How many different tickets could be ...

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Q: The first definition of the logarithm was constructed by Napier and popularized through his posthumo...

A: We will use basic knowledge of analysis and set theory to answer this question using Binomial theore...

Q: Question 2 Define the function g(x, y) = [4 – (x – 1)²][1 – (y – 2)²]. (a) Find the local maximum po...

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Q: 9. Find integers which are inverse of 17 modulo 24. а) 7 b) 17 c) 13 d) –11 e) –7

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Q: If f(z) = eV8 2' then the simplify form of f(z) is: %3D A) f(z) = i e-2VZ %3D B) f(z) = -i e²vZ C) f...

A: given fz=e8-π2i simplify form of fz is? solution it is known that  eiθ=cosθ+isinθ thus e-π2i=cos-π2+...

Q: AD = 12.363 "(-1.2278 x 10-1"7² + 6.1946 x 10-°T + 6.015 x 10-)dT a. Use 6 segment Simpson's 1/3 Rul...

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Q: Eliminate the arbitrary constants of the equation y = Cje 2x + A y" - 2y' - 3y = 0 B y" - 4y' - 2y =...

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Q: 5. Let f(z) = + cos z. Let C be a simple contour (but not closed) from the initial point 22 + i 21 =...

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Q: 3. Let Px and Pw be perpendicular projection matrices with C(Pw) CC(Px). Show that Px - Pw is a perp...

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Q: QUESTION 9 Draw the subgroup lattice diagram for Z60

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Q: Draw a direction field for the differential equation y' = -y(1 – y). Based on the direction field, d...

A: We have ,                                                                           y' = - y (1 - y)...

Q: Solve the following: 1. (x-2iy)-(y-ix)=2+i, x=?; y=? Express in Polar Form: 1. 3+i4 2. -3+i4

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Q: The force of magnitude F = 193 lb acts along the edge of the triangular plate. Determine the moment ...

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Q: 102÷ x 12Z 16275° (a) 2215° (b) – 79. 3

A: It is known that complex notation in angle notation (Phasor): z=z∠θ°   and in Polar form it could be...

Q: Draw a direction field for the given differential equation. Based on the direction field, determine ...

A: It is given that ,                 y' = y (y - 4)2  (.) Equilibrium point & Equilibrium         ...

Q: Directions: Find the derivative of the following functions: 1. y = log,(x + 5)5 5. y = In x4 %3D 2. ...

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Q: Question 19 Find the two square roots of 4i. A v2 - v2i and -v2 - V2i B v2 + v2i and v2 - V2i (c) -v...

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Q: 10. Find solutions of the system of congruences x = 3 (mod 7), x = 1 (mod 5), x = 4 (mod 6). a) 964 ...

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Q: Consider a lake of constant volume V (gallons) containing at time t (weeks) an amount Q(t) (grams) o...

A: As per norms, we will be answering only first three subparts. If you need an answer to others kindly...

Q: 5. Decide which of these integers is congruent to 13 modulo 17. a) 81 b) 18 c) -38 d) 83 e) -11

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Q: 6. Determine which of these integers are prime. a) 7· 17 b) 1· 19 c) 109 d) 153 e) 187

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Q: The integral of the given function | cos 2x cos(-x)dx is equal sin 3x + 3 sinx А. + C 6 sin 3x – 3 s...

A: Introduction: The indefinite integral is the way to find the function that on differentiation, produ...

Q: 2. y" – 2y' = -4 y(0) = 0, y'(0) = 4

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Q: Solution of dy/dx + 2xy = y is (A) y = ce* B y = ce -? © y=ce*²_ - x (D y=ce*-x2

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Q: 1. Let z and w be complex numbers. (a) Show that |1+ z w² + |z – w2 = (1+|z|?)(1+ |w/?). (b) Show th...

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Q: II. Solve AABC subject to the given conditions. Round the lengths of sides and measures of the angle...

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Q: Solve the D.E. 3(3x2 + y?) dx - 2xy dy = 0 A x = c(x2 + 3y²) B x = c(9x² + y²) c) x = c(x² + 9y²) D ...

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Q: kimum and minimum r3 9y +1

A: Given as, f(x)=x3 -9x+1, -∞,∞

Q: 2. f(x)= 2x³ – 7

A: Given function is f:ℝ→ℝ such that fx = 2x3 - 7

Q: Question 6 5 12 B = |1 11 and C = |-9 1 -5 |. Which of the following 14 6 -11 [16 -7 4 -3 13 7 10 0 ...

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Q: 4. What is your estimate of the Odds Ratio (OR) from these data? O 0.44 ০০67 O 1.33 O 2.25

A: The odd ratio is a statistical method to make decisions  on making conclusion of various substance  ...

Q: Perform the following as indicated. Show your complete solution to earn maximum marks If (x + yi) /i...

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Q: Compute the average rate of change of f over the intervals [5, 6] and [7, 8]. rate of change over [5...

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Q: The Sanchez family takes out a $200,000 loan for their fixed-rate, 30-year mortgage. The annual inte...

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as...