Answer the following questions about rational and irrational numbers.1. Prove or disprove: If a and b are rational numbers then a^b is rational.2. Prove or disprove: If a and b are irrational numbers then a^b is irrational.

Q: Solve the simultaneous linear congruences 3x = 2 (mod 5), 3x = 4 (mod 7), 3x = 6 (mod 11).

A: We have:3x ≡ 2 (mod 5)3x ≡ 4 (mod 7)3x ≡ 6 (mod 11)Step 1: Convert each equation to the form x ≡ a…

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A: compensatory growth

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Q: . Expand sinh z in Taylor's series at zo = πi, and show that lim sinh: καπί κ - п - - 1.

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Q: matrix 3

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A: Step 1:            Step 4:           Step 5:          Final AnswerUsing Simpson's Rule with n=4 will…

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Q: You recieve a case of fresh Michigan cherries that weighs 8.2 kg. You will be making cherry pies.…

A: Convert 8.2 kg to poundsSince 1 kg = 2.20462 lbs,  8.2×2.20462=18.08 lbs Account for the yield…

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A: Step 1: Solve the Homogeneous SystemThe homogeneous system is represented as:      X′=[−13​3−1​]Find…

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Q: Question 1: (10 points) Determine whether the following Realation is an Equivalent Relation or not,…

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Q: Q/ Give an Such that L(G) example of a simple graph G is Euler but G is not.

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Q: Below, let A, B, and C be sets. 1) Prove (AUB) nC = (ANC) U (BNC).

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Q: x 1 3 5 7 f -1 3 15 35 7 • Sea) dx from the faible find: 1 f(x) dx by Sempeson method 8 2 if S .dx…

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Q: 2. Disprove the following by finding counterexamples: 3. (a) For all sets A and B, AU (BNA) = B. (b)…

A: Note : U is the universal set.

Q: Pls help ASAP

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