e. When is the greatest common factor of two numbers one of the two numbers? Explain your reasoning.

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A: the solution consists of substitution

Q: (d) s

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A: This question can be solved using the concept of differentiation of implicit and explicit function

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Q: the function y = x(x 6)².

A: To find the critical points for the given function

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Q: 6. 7. 8. dy x- -= x² + y y = x² + 4x; dx In y = C₁e* + c₂e-x; yy" - (y')² = y² In y y−³ = x³ (3ex +…

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Q: Qe Evaluate the following integrals, then reverse the integration order ( a) y dx dy.

A: Consider: ∫02∫04-y2y dx dy=∫02y x04-y2 dy=∫02y 4-y2-0dy=∫024y-y3dy=2y2-y4402=222-244-202-044=8-4=4…

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A: we have to find the solution of given differential equation.

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Q: 2. f(x) = (x + 2)²³ (x-1)

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A: Let's solve.

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Q: Find the solution of the IVP: (1 + y cos x) dx - sin x dy = 0, y(1/2) = 1. Then, evaluate y(1.603).

A: This question can be solved using the concept of linear differential equation.

Q: For the polynomial, one zero is given. Find all others. 4) P(x) = x3 - 7x2 + 15x - 25; 5

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A: See this solution in below.

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Q: 4 f(x)=x+acos x, where a is a positive constant and 0≤x≤ 2. Find the x-coordinates of all points,…

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