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hodyreva [135]
3 years ago
14

Write three functions. In the first function, y should vary directly with x. In the second function, y should vary inversely wit

h x. In the third function, the relationship between x and y should be neither inverse variation nor direct variation.
Mathematics
2 answers:
xxTIMURxx [149]3 years ago
8 0

1) y = kx . . . . . for some constant k

.. Here y is directly proportional to x , where k is the constant of proportionality


2) y = k/x . . . . for some constant k

.. Here y is inversely proportional to x , again k is the constant of proportionality.


3) y = 2x +52

..

Here y is linearly related to the x , it is neither directly proportional nor inversely proportional.

motikmotik3 years ago
7 0
Asked and answered elsewhere.
brainly.com/question/8880788
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With some simple rearrangement, we can rewrite the numerator as

2x^3 - 3x^2 - x + 4 = 2(x^3 - x) - 3x^2 + x + 4 \\\\ ~~~~~~~~ = 2x(x^2-1) - 3(x^2 - 1) + x + 1 \\\\ ~~~~~~~~ = (2x-3)(x^2-1) + x+1

Then factorizing the difference of squares, x^2-1=(x-1)(x+1), we end up with

\dfrac{2x^3 - 3x^2 - x + 4}{x^2 - 1} = \dfrac{(2x-3)(x-1)(x+1) + x+1}{(x-1)(x+1)} \\\\ ~~~~~~~~ = \boxed{2x-3 + \dfrac1{x-1}}

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