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Given this unit circle, what is the value of x? (x, -7/10)(1,0)​

Given This Unit Circle What Is The Value Of X X 71010 class=

Sagot :

Answer:

x = - [tex]\frac{\sqrt{51} }{10}[/tex]

Step-by-step explanation:

the equation of a circle centred at the origin is

x² + y² = r² ( r is the radius )

The radius of a unit circle is r = 1

substitute (x, - [tex]\frac{7}{10}[/tex] ) into the equation and solve for x

x² + (- [tex]\frac{7}{10}[/tex] )² = 1²

x² + [tex]\frac{49}{100}[/tex] = 1 ( subtract [tex]\frac{49}{100}[/tex] from both sides )

x² = 1 - [tex]\frac{49}{100}[/tex] = [tex]\frac{51}{100}[/tex] ( take square root of both sides )

x = ± [tex]\sqrt{\frac{51}{100} }[/tex] = ± [tex]\frac{\sqrt{51} }{10}[/tex]

since the point is in the 3rd quadrant then x < 0

x = - [tex]\frac{\sqrt{51} }{10}[/tex]

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