mendietaabi555
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The point P = (x, - 2/7) lies on the unit circle shown below. What is the value of x in simplest form?

The Point P X 27 Lies On The Unit Circle Shown Below What Is The Value Of X In Simplest Form class=

Sagot :

Answer: [tex]x = \frac{3\sqrt{5}}{7}\\\\[/tex]

Explanation:

The equation of the unit circle is [tex]x^2+y^2 = 1\\\\[/tex]

Plug in y = -2/7 and solve for x

[tex]x^2+y^2 = 1\\\\x^2+\left(-\frac{2}{7}\right) = 1\\\\x^2+\frac{4}{49} = 1\\\\x^2 = 1-\frac{4}{49}\\\\x^2 = \frac{49}{49}-\frac{4}{49}\\\\x^2 = \frac{45}{49}\\\\x = \sqrt{\frac{45}{49}} \ \ \text{ ... x is positive}\\\\x = \frac{\sqrt{45}}{\sqrt{49}}\\\\x = \frac{\sqrt{9*5}}{7}\\\\x = \frac{\sqrt{9}*\sqrt{5}}{7}\\\\x = \frac{3\sqrt{5}}{7}\\\\[/tex]

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