Let SF(n) be the squarefree function of n. Hence, SF(1) = 1 and SF(p¹p2²...pr) SF(n). P1P2...Pr. Prove the following: ²(d)o(d) = = d|n

Q: let f(x)= X be 1 213 (-√5 < X<√) Y.V Pind P{/X/7/1.5},

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Q: C. Simplify the following Boolean expression and Implement the simplified function F. F = xy' +…

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Q: 1. Let f ( x) =5x+ 4 and 8( x) =2r – 6, find the following: a. (f + g) ( x) b. (f – 8) ( x) c.…

A: The given functions are f(x) = 5x + 4 and g(x) = 2x – 6. Composite function: A composite function is…

Q: Let P(x) = 2x² – 5x – 12 = (1 – 4)(2a +3). Which of the following is true? O A. For 1E[-2/7, 1),…

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Q: Bwalya was born in 1980. In two leap years to come, Shabalala was born. In which year was Shabalala…

A: Given, Bwalya was born in 1980. We know that 1980 is a leap year. Also, we have a leap year come…

Q: Show directly that f(n) = n2 + 3n3 Î (n3). That is, use the definitions of O and W  to show that…

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Q: determine L−1[F].

A: Inverse Laplace transformation of function

Q: 5- Solve the folowing linear algebraie equations using the Gauss elimination method: 3x -2x2 + 7x3 =…

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Q: Section I 3. Suppose that X is a discrete random variable with pmf |4- r|+ 4 f(z) for =-6,-3,0,3,6,…

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Q: 1. Suppose P(A) = 4/10, P(B) = 5/10, and P(AB) = 2/10. (a) Compute P(AC). (b) Compute P(AUB). (c)…

A: As per our guidelines we are suppose to answer only three sub parts.…

Q: determine L−1[F].

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Q: iii. P(AN B) = P(A) N P(B). iv. P(A) UP(B) C P(AUB)

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Q: -25 -3e c) s+2

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Q: determine L−1[F].

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Q: Evaluate the function at the given value of the input r6) = -9 p³ – 2 7 + 2, tmd r (-). O1.375-

A: Here we have to put the value of 'p' in the given function to get the solution.

Q: Determine L−1[F(s)]for the given F. Q) F(s)=6/(s−4)3

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Q: so be it r = 3xi + yi – 2zk and f (r) = –- where r| = find all of grad(f) and div ()

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Q: 3. Let h(x) = (f og)(x). Given f(x) = 3x2 +5 and g(x) = Vx – 3. a. Evaluate h(4). b. Determine fx).

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Q: * Find the derivative lic F (+) = (+³-2+ +1) (2+²

A: Given query is to find the derivative of the expression.

Q: Suppose P(A) = 0.4 and P(B) and B, show that 0.1 ≤ P(An B) ≤ 0.4. = 0.7. With no other assumptions…

A: We have given thatP(A) = 0.4P(B) = 0.7We have to show that0.1 ≤ P(AB) ≤ 0.4

Q: -3 1] Find P(A) for p(x) = x² + x – 2 where A 2.

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Q: B.1. Consider the function f: NR given by 4n • ( [47] - √₂). 3 f(n) = n Prove that f(n) is O(n²).

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Q: determine L−1[F].

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Q: 2F. n 1 ;;1=2" (b), (26)

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Q: Determine L−1[F(s)]for the given F. Q) F(s)= 3/(s−2)2+9

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Q: If L-[F(s)] = f(t), evaluate f(0) given by the expression F(s) : (s+2) %3D s2 (s+1)'

A: Solution

Q: Determine L−1[F(s)]for the given F. Q) F(s)=s+4/s2+6s+13

A: Consider the given function: Here the objective is to find the Inverse Laplace Transformation of…

Q: Let r(t) = (a) Find 7 (t). (b) Find Ñ (t). (c) Find K (t)

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Q: demonstrate that

A: We have to demonstrate

Q: Find 00 x² (x²+4) (x²+2x+2) dx

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Q: determine L−1[F].

A: Given Data The function is F(s)=4/(s+2)3.   The general inverse transform rule is,