1. Given: Let p = Line a is parallel to line b Let q = Some prime numbers are odd Letr = 3+4 > 6 Let s = All irrational numbers are real numbers Write the following propositions using p, q, r, s and logical connectives. a. p^qvs b. rVr c. (q v¬s) Ar d. (r^ p) →→s e. ((p V¬q) ^r) →→s

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Q: 5. Solve 3y" (x) + 2y'(x) - 8y(x) = 0, y(0) = 6, y'(0) = 18

A: 3y''x+2y'x-8yx=0y0=6y'0=18

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A: Given that the function f is graphed below:                      .

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Q: Do all with explanation

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A: The answer provided below has been developed in a clear step by step manner.

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Q: How is the graph of f(x) = logx transformed to get the graph of g(x) = logx^5?

A: we see that the  first graph given is  f(x)=logx  whereas the second graph given is g(x)=logx5  note…