Let be a rational prime, with p = 1(mod 4). Prove that p is the product of two Gaussian primes that are not associates.

Q: B. by using Rules of Replacement 1. [p V (~p ^q)] → (p A q) 2. {~ (pvq) v [(~p^ q) v ~q]} «→ ~ (pvq)

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Q: would the expansion not be  1-3x+6x^2-10x^3  ? And how did you calculate the range please ?

A: Yes, the correct expansion is as follows: 1−3x+6x2−10x3+15x4

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Q: 19. Solve y'(1) + y(t) = sin t; y(0) = 1 by Laplace transfrom. %3D

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Q: Valid or Invalid? Use truth table.

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Q: х, + 3x, — 2х; + 2x5 2x, + 6х, — 5х,- 2х4 + 4xs 3x, = -1 + 15x, = + 8x, + 4x; + 18х, 5x; + 10х, 5…

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Q: If m rst = 164, what is m<RVT?

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Q: 1. Use a Chain rule to find aw aw and if w = x?, = sin(r²s) ar as

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Q: Theorem: Every normed vector space is a metric space but the converse is not true in general Proof

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Q: 1. Solve the system by Gaussian elimination x+y-5z =-18 3x-3y+z 6 x+3y-2z = -13

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A: Given:   f(x)=e-x(x2+5x+2)+1a=0, b=-1 To find the roots using bisection method

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Q: Let U={a,b,c,d,e,f,g,h,k}, A={a,b,c,g}, B={d,e,f,g}, C={a,c,f} and D={f,h,k} 1. Compute: a.) A UB…

A: To evaluate the given set operations.

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A: To find the solution of the given question :-

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Q: 17. Evaluate L{y"(1) + 2y'(1) + y(1)}; y'(0) = -1, y(0) = 5. Let L {y()} = {s). A) (s°+2s+ 1)Y(s) –…

A: Here we use basic laplace transform

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Q: 1- nullspace af now equivalent to the for the 1 1- 2. C. that puy -2 B. assume matrix pand Let A

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Q: (b) Show that any nonzero element of the ring QIV2 = {a + bv2 | a, b e Q} is invertible, that is,…

A: b)  We have given that ,  ℚ2 = a + b2 / a , b ∈ ℚ We need to show that , for any non-zero element of…

Q: r(t) ti+ 8 sin(t)j + 8 cos(t)k u(t) + 8 sin(t)j + 8 cos(t)k (a) r'(t) = (b) r"(t) = (c) D[r(t) ·…

A: Note: We are allowed to solve three subparts at a time so upload remaining parts as next question.

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Q: 土

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Q: A 100-L tank was initially empty, but is to be filled with salt-and-water solution. The way the…

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