Suppose p and q are distinct prime numbers. Find the number of positive integers x ≤pq such that neither p nor q divide x.

Q: 4 Sketch the graph of the following functions, within the specified domains and hence determine…

A: The graphs of the given functions are sketched and their ranges are determined as shown below.

Q: Find the Laplace transform of: 1. f(t) = e(-4t)[sin(2t) – cos(2t)]² 2. f(t) = V1+ sin t + (6t)13 +…

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Q: arympdoter ofthe Sキマルソープリ 14y-+リル+5=0 Find all the cunve 2.

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Q: 2e* xy" - (2x + 1)y' + (x + 1)y : x?

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Q: Design a function that meets the following criteria: The function must have both a numerator and…

A: Given: The function must have both a numerator and denominator. The function must be designed in…

Q: The complex number z is defined by z = 3·z + 4.j where z is real. a) Find, in terms of z, the real…

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Q: 10s2+5s+4 F(s) (s³–6s²+11s-6)(s³)

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Q: Perform the change of variables indicated in the problem to obtain the general solution to the…

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Q: 2) Solve the following initial value problem if t 1 if t 1 y(0) = y'(0) = 0.

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Q: 0<x< (11) f(x) =- 3D くx<2x

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Q: Calculate the value of the error with one decimal place for: z = x/y where x = 6.2 +/- 0.3 and y =…

A: Given that,z=xyx=6.2±0.3y=2.0±0.2The error with one decimal place is calculated as shown below.

Q: 5. Find the number of faces in the planar graph given below. d.

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Q: Evaluate (2x - y) dx + (x + 7y) dy. C: x-axis from (0, 0) to (0, -7) and (0, -7) to (2, -7) 351 2

A: Solution :-

Q: d) Prove that the composition of two surjective linear transformations is again a surjective linear…

A: (d) Let T:X→Y be a surjective linear transformation and S:Y→Z also be the surjective linear…

Q: Compute f(x)dx f(x) = { 2x if x<1 4 if x 21

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Q: 3 b.

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Q: Let (X1, d1) and (X2, d2) be metric spaces and f : X1 -> X2 be a continuous function. Prove that if…

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Q: Use a triple integral to find the volume of the given solid. The tetrahedron enclosed by the…

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Q: The graphs of the function f (r) =7-2 and g(x)= 3 are given below. %3D 10 9 f(x) = 7-x2 4 g(x) = 3…

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Q: (2x + 1)(x + 1)y" + 2xy' – 2y = (2x + 1),

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Q: The period T of a pendulum is determined by T = 27 with L the length of the pendulum and g the…

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Q: Find the inverse transform of the given functions: 4s2 -4s+1 1. F(s) = (s3-4s2+s+6)(s²+5)

A: To solve given question first we write the partial fraction decomposition of given function and then…

Q: 8. Interval -c<x< c; function, f(x) = ex

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Q: Find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P.…

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Q: e19z y" – 38y' + 361ly It is proposed as a particular solution yp= U(x)e19x + V(x)xe19 where U'(x)…

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Q: Consider the box shown below, where 0 <¤< 2,0< y< 1, and 0< z<1. The rectangular prism is subjected…

A: Given E=-2x2yi^-2xy2j^+2xy2zk^ where 0≤x≤2, 0≤y≤1, 0≤z≤1

Q: 5. If H = 122Z and K = 8Z are subgroups of (Z, +). Then H + K = ... %3D

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Q: (2) Compute 2" - 37+2 5n-1 by explaining clearly why the series converges, and then actually…

A: Series and sequences

Q: 5.2.7 Show that Ae³A™ = eABA' for any orthogonal matrix A.

A: To show: AeBAT=eABAT for any orthogonal matrix A.

Q: (26. Ax)= x//x² + 1

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Q: QUESTION 1 Which of the following is a general solution to the following 4x?y"+4xy'+ (4x2 – 25) y=0…

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Q: Consider the equation y" + ay' + by = f(x) the constants a and b are real and different from zero,…

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Q: 6) f(x) =xcos x 2n(-1)" • sin(nx) (n-1)(n+1)

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Q: Use a double integral to find the volume of the indicated solid. 8. X +y+2 8 00

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Q: Use (1) X = eAtc (1) to find the general solution of the given system. 1 1 1 X' = 1 X 2 -2 -2 | X(t)…

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Q: 4s2-4s+1 1. F(s) = (s3-4s2+s+6)(s²+5)

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Q: Evaluate the double integral. 8x?sin y dA; Risthe region that is bounded by y = x, y = -x', and y =…

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Q: Which of the followings is TRUE for f(x, y) = 3x – y + 6 on the circle a? + y? = 4. Lütfen birini…

A: Given function is fx,y=3x−y+6 and a circle is x2+y2=4. We have to find the maximum and minimum of…

Q: Give an example of a function f : (X1, d1) → (X2, d2) that sends compact sets to compact sets, but…

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Q: Evaluate L{t(uo - u1) +tu}.

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Q: Find Fourier series for the function f (x) = x\,- <x< T

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Q: Let f(z) = ((z – 3i)² + 9)ez- The Laurent series representation of f(z) in the domain 0 < |z – 3i| <…

A: Given function is fz=z−3i2+9e1z−3i. We have to find the Laurent's series representation of fz in the…

Q: Show that a6 +.

A: We start with the RHS of the identity and show that it equals the LHS. The detailed proof is given…

Q: Compute f(x)dx 2x if x <1 4 if x21 f(x) =

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Q: Find the Laplace transform of: f (t) = v1+ sin t + (8t)15 + t² cos 3t

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Q: Let, a1 = 3, a2 = 4 and for n > 3, an = 2an-1+an-2+ 5n, express an in terms of n.

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Q: 24. Find the general solution of (2x + 1)(x + 1)y" + 2xy' – 2y = (2x + 1)2, 1)-1 1:

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Q: Use any method to simplify the.complex fraction. 25z°x5 49 2 6 175x z° 21

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Q: DIRECTION: FIND THE LAPLACE TRANSFORM OF EVERY GIVEN EQUATION. SHOW YOUR COMPLETE SOLUTION. BOX YOUR…

A: Solution

Q: Use Brute Force to determine the lowest weight -43 21 18 37 35 29

A: We have to use Brute Force to determine the lowest weight Hamilton circuit for the graph below.…