Suppose we randomly select a subset of positive integers. How large must the subset be, if we want to make sure that we have chosen at least one pair of integers a, b such that 19|(b − a)?

Q: when x = 3.57 using quadratic Approximate y Lagrange Interpolating polynomial up to 3rd degree. Use ...

A: Given table is xi yi 3.1 20.1810 3.2 22.5280 3.3 25.0470 3.4 27.7440 3.5 30.6250 3.6 ...

Q: Exercise.2 Prove that cos-1 z =- In(z ± Vz? – 1)

A: The given problem is to prove the given inverse complex trigonometric identity. cos-1(z)=1/j ln(z+√(...

Q: 2-5s (s-6)(s2 +16)

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Q: Inverting a transform for matrix: 0.375 0 0.927 5 0.608 0.755 -0.246 2.787 -0.7 0.656 0.283 4.92 0 1

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Q: " + 4x' + 4x = 4e24, r(0) = 0, r' (0) = 1.

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Q: The following table gives retail values of a 2017 Corvette for various odometer readings. Odometer R...

A: we have given the table that gives retail values of a 2017 Corvette for various odometer readings. (...

Q: 4. Find the solution of the following set of simultaneous equations by ' conditions y(0) = x(0) = 0 ...

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Q: Find the closed form for the generating function for the following sequences: a) (9,0), (9,1), (9,2)...

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Q: Find a basis for the solution set of the following system: X1 + x2 – 3x3 + x4 = 0 - X1 + x2 + x3 – x...

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Q: 8 8 -2 -3 -2 4 and B = 6. A = 3 8. 2 3 2 -1 -2 -4 and D= 5 C - 7 4 4 8

A: matrix multiplication problem  find -3C ,C  given

Q: Solve the given differential equation by undetermined coefficient: y′′ − 2y′ + 5y = e^x cos(2x)

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Q: 5. Let A = {n E Z; n is odd} and B = {n € Z; 3n² + 7 is even}. Prove that A = B.

A: Given that              A=n∈ℤ ; n is odd   and   B=n∈ℤ; 3n2+7 is even

Q: Find an equation for the graph sketched below -구 -5 -4 -3 -2 -1 -2 -6 f(x) =| Preview %3D

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Q: 9. Consider an inhomogeneous differential equation f"(x) = e". a) 'Guess' a solution of the inhomoge...

A: Consider the inhomogeneous differential equation: f'''x=ex

Q: Compute for the cross product of the following pairs of vectors (-4, 3, 0) and (6, 2, -5). Then, ver...

A:

Q: Prove that every group of order 675 has a normal Sylow 5-subgroup.

A: Theorem: If number of Sylow p-subgroup of a group G is unique, then that subgroup is normal. Let G b...

Q: Let V = (-5, 00). For u, v E V and a € R define vector addition by u H v := uv+ 5(u + v) + 20 and sc...

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Q: Don't use calculator to solve.

A: Newton-Raphson method uses the formula: xn+1=xn-f(xn)f'(xn) to perform the iterations and to approxi...

Q: 5. Find the extremum points of the function (the minimum and maximum points, the values of the funct...

A: Given:y=2x3-15x2+36x-14

Q: Consider the parallelepiped with adjacent edges u = 4i + 3j + k v = i+j+ 4k w = i+ 9j + 2k Find the ...

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Q: s' S 5 The value of 5' 5 5' is:

A: We need to find the given determinant.

Q: 5. Find the solution of the differential equation y"(t) - 3y'(t) + 2y(t) = 4 y(0) =y'(0) = O using L...

A: Given differential equation is y''(t) - 3y'(t) + 2y(t) = 4 with y(0) = y'(0) = 0

Q: a) Find the 4th approximation of the positive root of the function f(x) = x ^ 4 - 7 using the bisect...

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Q: 2x5y' = y(3x*+y?) %3D

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Q: Use the inner product (u, v) = 2u;V1 + uzV2 in R2 and the Gram-Schmidt orthonormalization process to...

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Q: Plz solve this particular soloution like the example that i attached Solve using second method that ...

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Q: d*y d³y (b) F(0) = F'(0) = F'" (0) = 0 = Cos t F"(0) = 1 dt4 dt3 12

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Q: 5. Let A = {n E Z; n is odd} and B = {n € Z; 3n² +7 is even}. Prove that A = B.

A: 5. 

Q: 1. (C'B)A" 3 4 B 3= 4 2 A = -1 C = 3. 1 2. tr(4ET – D) 1

A: This is a problem of linear transformation.

Q: If the sum of seven consecutive integers is zero, what is the biggest of the seven integers? x, x + ...

A: Let the consecutive integers be x, x+1, x+2, x+3, x+4, x+5, and x+6. Then,         x + (x+1) + (x+2)...

Q: 3.1. Prove that the square of a rational number is rational, using direct proof.

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Q: Give an example of a sequence of continuous functions: fn: [0, 1] R that is pointwise convergent but...

A: Consider the function fx=0, x is irrational in 0,1mn, x is rational in 0,1. This function is called ...

Q: 7. A tank initially contains 60 gallons of brine in which there is dissolved 8 lbs. of salt. Brine c...

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

Q: Prove 1-3. 1. Show that the sum of two lower triangular matrices is a lower triangular.

A: We have to prove that the sum of two lower triangular matrix is a lower triangular.

Q: • (d) ((A – B) + D / ((E + F) * G)) • (e) ( A – 2 * (B + C) / D * E) + F

A: (d) Prefix :           (A-B) + D/((E+F)*G)          -> +(A-B) D/((E+F)*G)          -> +-AB/D((...

Q: (b) The function f : R Ris defined as follows: -r, if r1 f(r) = {r. Plot the function, and say wheth...

A: Given f:Z →Za ) f(x) = n+1, if n is evenn-3, if n is oddTo check one-one or injective Case 1: x and ...

Q: g3 – 4x2 x(r+ 8)(x - 2) (x +2)3 8(7r- 4) f(x) = with f'(x) = and f"(x) = (x + 2)² ' (x +2)4 d. Const...

A: we have to use following relation between f , f' and f" * when f'(x) >0 => function increasing...

Q: QUESTION 1 Compute the area of the shaded region. f(x) = 2 2. 4. 24 256 16 8

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Q: Writing logical notations to compound statements Let p: Man is rational. q: A century is 100 years. ...

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Q: 7. Let z be a root of the polynomial p(z) = (z + 1)" + z". Show that %3D 1 Re z = - 2

A: For the solution follow the next step.

Q: Use the plurality with elimination method to determine the winner of the election. Four students are...

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Q: 4.x2 with f'(x) = x(x+8)(x - 2) (x+ 2)3 8(7x – 4) (x +2)4 f(x) = and f"(x) = %3D (x + 2)2 a. Find th...

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Q: 6s – 5 3. '. 452 4s +7

A: The inverse Laplace transformation formula states that L-1ss2+a2=cosat, L-1as2+a2=sinat. Simplify th...

Q: Let the rref of a matrix A be, 0 -2 1 0 0 1 0 0 2 -5 0 -3 1 6 Determine A if the first, second and f...

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Q: Use the appropriate test to determine if the series given is absolutely convergent, conditionally co...

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Q: 6. Compute the orthogonal projection of = onto the line L through 4 and the origin. -5 고 52

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Q: Use Root Test to determine whether the series E(-1)"en² sin²n n=1 absolutely converges, conditionall...

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Q: Sunset bus leaves lautoka at 7.15 am andreaches Pacific harbour at 10.15 am covering distance of a 2...

A: Time from 7:15 am to 10:15 am is 3 hours,  Total distance is 210 km  The average speed of the bus is...

Q: Find parametric equations for the line. (Use the parameter t.) The line through (-8, 4, 7) and paral...

A: we have given the line through (-8, 4, 7) and  parallel to the line 12x=13y=z+1 we have to find the ...

Q: 1. h(t) = t 2 sin(2t) 2. g(t) = t 3/2 3. f(t) = (10t) 3/2

A: