$\frac{6+\sqrt{27} }{4-\sqrt{3} } = \frac{r+s\sqrt{3} }{13} \\We\ may\ multiply\ the\ numerator\ and\ denominator\ with\ (4+\sqrt{3} ).\\Hence,\\\frac{(6+\sqrt{27})(4+\sqrt{3}) }{13} = \frac{r+s\sqrt{3} }{13} \\Hence,\\24+6\sqrt{3} +4\sqrt{27} +9= r+s\sqrt{3}\\24+6\sqrt{3} +4*3\sqrt{3} } +9= r+s\sqrt{3}\\24+6\sqrt{3} +12\sqrt{3}+9 = r+s\sqrt{3}\\33+18\sqrt{3} = r+s\sqrt{3}\\Hence,\\r=33, s=18$

5 0

3 years ago

Sarah is researching the connection between the time students spend watching television and their performance in school. Her stu

lubasha [3.4K]

Her studies indicate that there is an inverse relationship between TV time and GPA, and that a student who watched 15 hours of TV per week can be expected to have a GPA of 3.5

In equation form

15 = k(1/3.5)

Solve for k

K = 15 * 3.5

<span>K = 52.5 is the constant of variation</span>

6 0

2 years ago

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