I need help to answer these two questions. Also, please explain the answers. Thank you.    Discrete Mathematics: 1.) Find c,k to show f(n) = 3n + 2 is O(n) 2). Find c,k to showf(n) = 7n² + 4 is O(n²)

Q: Find r(t) and v(t) if a(t) = tk, v(0) = 15i, r(0) = 14j.

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Q: Refer to the figure below. Find a + b - (c + d) - (e - f). -3 z+ ()-" + C:()-" ()- 1 1 a t+ b Ans :…

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Q: m-1 * If Σ (8k + 5) = 4m² + m − 5, then which of the following is equal to the - k=1 simplification…

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Q: •La Evaluate doc (1+√

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Q: Please answer parts b, c, and d

A: The objective of this question is to determine whether each of the given series converges or…

Q: 3. (E1.7-Q8) Find A², A-2, and A-k (where k is any integer). -6 0 0 0 0 30 0 5

A: To find , , and  (where  is any integer).

Q: Which expression below is equivalent to x4 − 4x³y + 6x²y² − 4xy³ + y4 O (x + y)4 (x - y)4 (x-2y)4

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Q: For each pair of statements, choose the one that is true 04 (3,4)} (a) o (4} e {3, 4)} (b) oh c {g.…

A: A set is a well defined collection of elements. It is usually denoted by A, B, C etc. If 'a' is a…

Q: 2. Determine the following sets: a) {r €R: (3n EN\{0}) 2n – 1 < nx < 7n - 2} b) {r ER: (Vn EN\{0})…

A: An interval is nothing but a subset of the set of real numbers. When the two endpoints are included…

Q: satisfies the equation? 2n+1 3n Σ b>2 olmak üzere 19 4n+1 eşitliğini sağlayan b sayısı 4. n=1…

A: We have to solve given problem:

Q: M² Prove by M I that 1+4+9+ ·· +n³²= £m(n+1)(2n+1)

A: we have to prove that 1+4+9+...+n2=n(n+1)(2n+1)6

Q: The solution is (-2,-3).

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Q: each st

A: The equation is given as 8+3|2x−11|&gt;1. Subtract 8 from both sides. 3|2x−11|&gt;-7 Divide by 3.…

Q: Find the equation represented in the table below. 7 1 21 2 63 3 189 O f(x)= 3 -7* O f(x)=7:3* O…

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Q: c) n° n° + 2n is a multiple 3 for all n 2 1.

A: To show: n3+2n is a multiple 3 for all n≥1. Statement used: Principal of Mathematical Induction:…

Q: (b) Determine whether 6|(n³-n), for each integer n ≥ 0.

A: 13) b We prove that n3-n is divisible by 6 by using mathematical induction   Basis step: For n=0…

Q: ind all solutions for n EN for which P(n, 4) = 12P(n, 2).

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Q: (k² – k) = O a. n? O b. n(n + 1)(2n + 1) O c. 6n + (n +1)(2n + 1) O d. (n + 1) O e. 플 (12-1) O f. 00…

A: the given expression is: ∑k=1n k3-k we have to find the value of the given expression.

Q: S X (x²+5) O dx none of these answers ○ In (x² + 5) + c ○ In (x² + 5) + c 1 (22² +5) + c

A: let   G=∫x(x2+5)dx

Q: (b) 6 + 7 + 8 + 9 + ... + k

A: (b) Given that 6+7+8+9+...+k The objective is to find the sum. The formula for sum of numbers are,…

Q: by definition r(n+1) = n!

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Q: (4) Suppose xo = 2√3, yo = 3, Prove that 2xn-14-1 Xn-1+Yn-1 and Yn √n Yn-1 for all n € N. = (b) x =…

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Q: 2. Completely simplify O(+1), x4, x-4 3(x+4) 2(x-4) O4, x4, x-4 2(x+4) 3 O4), x4, x 2(x-4) −4 3…

A: To simplify the given rational expression

Q: n (A)-0) k Simplify the equation shown here. with n≥k and n, ke Z+ (In the answer choices, nCk…

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Q: Please don't provide handwritten solution..

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Q: Evaluate. (Be sure to check by differentiating!) Slu? + 1)* x² dx (x³ + 1)³ A + C (x³ + 1)5 В + C…

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Q: Which of the following is true? A All of the above (D-xXD+x)=(D+xXD-x) (2D-1X3D+2)= (3D+2X2D-1)…

A: We know     (a+b)(a-b)= a2-b2= (a-b)(a-b)

Q: f (п) — Зп + 5 9 (п) — п — 1 (и) Find (f o g) (-Зп) o g)

A: The given functions are:fn=3n+5 and gn=n-1To find:fοg-3n

Q: 6. Prove the statement below Suppose x, y € R. Then x³ + x²y = y² + xy if and only if y=x² or y=-x.

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Q: The expression E ( (?) -Σ- () is equivalent to O n²-n 3 3 6.

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Q: c) What can you conclude about this series? Select all that applies. O The series converges because…

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Q: Exercise 2.6. Prove the following. For each, m and n are integers. Exercise 2.5. Prove the…

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