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Margaret [11]
3 years ago
15

Sin (x/2)= √2- sin (x/2) solve for the exact solutions in the interval (0, 2π)

Mathematics
1 answer:
serg [7]3 years ago
5 0

sin\left( \frac{x}{2} \right)=\sqrt{2}-sin\left( \frac{x}{2} \right)\implies sin\left( \frac{x}{2} \right)+sin\left( \frac{x}{2} \right)=\sqrt{2}\implies 2sin\left( \frac{x}{2} \right)=\sqrt{2} \\\\\\ sin\left( \cfrac{x}{2} \right)=\cfrac{\sqrt{2}}{2}\implies sin^{-1}\left[ sin\left( \cfrac{x}{2} \right) \right]=sin^{-1}\left( \cfrac{\sqrt{2}}{2} \right) \implies \cfrac{x}{2}= \begin{cases} \frac{\pi }{4}\\\\ \frac{3\pi }{4} \end{cases} \\\\[-0.35em] ~\dotfill

\cfrac{x}{2}=\cfrac{\pi }{4}\implies \boxed{x=\cfrac{\pi }{2}}~\hfill \cfrac{x}{2}=\cfrac{3\pi }{4}\implies \boxed{x=\cfrac{3\pi }{2}}

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A researcher surveyed 80 adults and found that 22 regularly run for exercise and 18 regularly swim for exercise.
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Whenever the questions asks for the probability and has "or" you have to add the two probabilities. In the same way, "and" implies multiplication. Therefore, the probability that someone swims is:
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GenaCL600 [577]

Answer:

The least common denomator of 10 and 8 is 40

Step-by-step explanation:

8                  10

16                 20

24                  30

32                   40              

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