Suppose an integer from 1 through 1,000 is chosen at random. Find the probability that the integer is a multiple of 3 or a multiple of 5. (select the correct answer) 31.2% ○ 25.8% ○ 14.2% 46.7%

Q: (a) Let r(t) = (√√t² – 1, e¹t, ln(2t — 4)). (i) Find the domain of r(t). (ii) Find lim3 r(t). (iii)…

A: Step 1:Step 2:Step 3:

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A: Approach to solving the question: Detailed explanation: Examples: Key references:

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A: Step 1: Step 2: Step 3: Step 4:

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A: Steps and explanations are as follows:In case of any doubt, please let me know. Thank you.

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A: Step 1: Step 2: Step 3:

Q: 10. Consider the following recurrence relation: P(n) = { 1 if n = 0 P(n-1)+n2 if n > 0. (a) Compute…

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Q: Diagonalize the matrix if possible the eigenvalues are as follow λ=3,4 4 0 2 2 3 4 0 0 3

A: Step 1:

Q: Find the general solution of the following first order linear ODEs: 1 (a) y' + ½/y = 3 cos(2t), t >…

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Q: 4. Find the line integral: a. Let r(t) = 2ti+ find fr(t)dt b. Let r(t) = 2e3 + find fr(t)dt

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Q: e) Consider the flow ϕt (v) = e^(tA) v, v in R^(n) generated by the linear system x' = Ax where A in…

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Q: b) Compute S i) C = √z: 121=4} 22²+2+1 dz, where iv) c=fz: 121=4} 22+4 ii) C = {z: 17-61-2} \ii) C=…

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Q: refer  to  image  below.  It  has  both  parts  of  same  question.

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Q: Good Day, Kindly assist me with differentiating the following. Regards

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Q: 3.- Check the veracity of the following identities: sec(0) - cos(0) 1 + sin(0), = tan 0

A: Solution-

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Q: IVP mean initial value problem

A: If you have any further requirement , please comment.

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Q: Solve the differential equation บ'' "-y-12y=-4-5₁(t), y(0) = −2, y'(0) = 1 using Laplace transforms.…

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Q: (d) The Frenet-Serret equations are given by dT ི||ž「ལྦ KN -KT+TB -TN Using these equations, prove…

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Q: Provide explanations and clear calculations

A: complete explanation is mentioned above answer

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Q: The matrix 4 0 0 A 0 4-8 -4 4 -8] has eigenvalues -4, 0, and 4. Find its eigenvectors. The…

A: Step 1: Step 2: Step 3: Step 4: