Set A is the set of all natural numbers less than 30 that are divisible by 5.  Express the following using roster niotation and find the cardinality n(A).

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A: We have the system of equations as x1+x2+x3=56x1+7x2-3x3=5

Q: Let F be a field and aeF be such that [F (a): F]=5. Show that F(a)= F(x³).

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Q: Determine whether the sequence converges or diverges. 3+5n² a. an n+n² b. - cos² n 2n

A: a.  Given an = 3 + 5n2n + n2 Here limn→∞an = limn→∞3 + 5n2n + n2              = limn→∞3n2 + 51n + 1…

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Q: Estimate the following definite integrals using the Trapezoidal rule and Simpson's rule. Estimate…

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Q: Let F = Z, [x] (x³ + 3x + 2) and α=x+ (x+3x+. (x³+3x+2) €F. Find a³.

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Q: dv dt Given the following direction field for = 9.8 -0.196v and v(1) = 20, classify the equilibrium…

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Q: A a 5x5 real matrix & v₁,..., v5 linearly independent real vectors in 5 dimensional space: Av₁ = 4v₁…

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Q: Fourier cosine integral (a) representations : =x² + a² if 0a.

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