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2 years ago

Simplify EXPLAIN your answer.

Mathematics

1 answer:

krek1111 [17]2 years ago

8 0

$\frac{x-5}{ x^{3} +27} + \frac{2}{ x^{2} -9} = \frac{x-5}{ x^{3}+27 } + \frac{2}{(x+3)(x-3)} \\ \\ long-division.. \\ (x^{3} +27)/(x+3) = x^{2} -3x+9 \\ \\ \frac{x-5}{(x+3)( x^{2} -3x+9)} + \frac{2}{(x+3)(x-3)} \\ \\ \frac{x-5}{(x+3)( x^{2} -3x+9)}* \frac{x-3}{x-3} + \frac{2}{(x+3)(x-3)} * \frac{x^{2} -3x+9}{ x^{2} -3x+9} = \frac{(x-5)(x-3)+2( x^{2} -3x+9)}{(x+3)(x-3)( x^{2} -3x+9)}$

$\frac{(x-5)(x-3)+2( x^{2} -3x+9)}{(x+3)(x-3)( x^{2} -3x+9)} = \frac{ x^{2} -8x+15+2x^{2} -6x+18}{(x+3)(x-3)( x^{2} -3x+9)} \\ \\ \frac{ 3x^{2} -14x+33}{(x+3)(x-3)( x^{2} -3x+9)}$

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Given:

The height of the bird at time t is given by the function $h(t)=-4.9t^2+6t+50$

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The time can be determined by substituting h(t) = 0 in the function.

Thus, we have;

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Thus, we get;

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Simplifying, we get;

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The values of t are given by

$t=\frac{-6 + 31.87}{-9.8}$ and $t=\frac{-6 - 31.87}{-9.8}$

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