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Phoenix [80]
3 years ago
14

D%20%20%5C%3A%20lies%20%5C%3A%20in%20%5C%3A%20which%20%5C%3A%20quadrant" id="TexFormula1" title="the \: angle \: of \: measure \: \frac{31\pi}{6} \: lies \: in \: which \: quadrant" alt="the \: angle \: of \: measure \: \frac{31\pi}{6} \: lies \: in \: which \: quadrant" align="absmiddle" class="latex-formula">
​
Mathematics
1 answer:
Yakvenalex [24]3 years ago
7 0

Answer:

3rd quadrant

Step-by-step explanation:

  • First we just convert the angle from radians to degrees
  • \frac{31\pi radians }{6}*\frac{180degrees}{\pi radians}  =\frac{31*180}{6} degrees=930degrees
  • Now that's too big, all this means is if we start rotating from the positive y-axis in a circle we will cross the starting point 2 times, 2 full circles;
  • 930degrees-360degrees=570degrees\\570degrees-360degrees=210degrees  
  • Now in which quadrant it 210 degrees?
  • 0 degrees to 90 degrees is 1st quadrant
  • 90 degrees to 180 degrees is 2nd quadrant
  • 180 degrees to 270 degrees is 3rd quadrant
  • 270 degrees to 360 degrees is 4th quadrant
  • So our answer is the 3rd quadrant.
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\sf 2x=5\:x\:56 \\\\\sfx=\frac{5\:x\:56}{2} \\\\\sfx=\frac{5\:x\: \cancel{56}\:\:28}{ \cancel{2}} \\\\\sf=x=5\: x\: 28 \\\\\sfx=140 \\\\\sf\boxed{x=140}

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