1. Let q-p" be a prime power. Show that X+ 1 is irreducible in F [X] if and only if q=3 mod4. (Hint: Use the fact that F is cyclic, also since its an if and only if please prove both directions)

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A: Given  e3x=8 Taking ln (i.e., loge ) on both sides we get ln (e3x)=ln 8 ⇒3x=ln 8          [Applying…

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A: Solve by squarring both side

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A: Given:- Numbers are 56 and 34  To find:- LCM of (56, 34)  Method:- i use prime Factorization method

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A: We have to find the LCM of 77 and 18.

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A: Total female = 133+43 = 178 Total "did not graduate" = 55+43 = 98 Grand total= (126+55+133+43)  =…

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A: Let's find.

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A: Given the function

Q: 3. Identify all the cycles at each node of the directed graph above.

A: Cycle is defined as a path that start and end at the same vertex.

Q: Solve the initial-value problem Ÿ' = AŸ + Ġ for -3 0 0 0 1 1 2 0 1 A = with Ÿ (0) - %3D 0 0 0 0 17

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A: The objective is to evaluate the value for

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A: Given expression: 2+2

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A: Given,          A triangle is shown below :

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A: Given: The figure,

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Q: 20 . 35 60.

A: Given equation: 20=3560 Consider the missing term be 'x' 20x=3560 The objective is to find the value…