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Stells [14]
2 years ago
13

Solve on [0,2pi). Answer in order from smallest to biggest cos x sin x = sin x

Mathematics
1 answer:
Musya8 [376]2 years ago
3 0

Answer:

0, π

Step-by-step explanation:

cos x sin x = sin x

cos x sin x - sin x = 0

sin x (cos x - 1) = 0

sin x = 0, x = 0, π

cos x - 1 = 0

cos x = 1, x = 0

So answers: 0, π

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A coach purchases 47 hats for his players and their families at a total cost of $302. The cost of a small hat is $5.50. A medium
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Answer:

The answer is below

Step-by-step explanation:

Let x represent the number of small hat purchased, y represent the number of medium hat purchased and z represent the number of large hat purchased.

Since a total of 47 hats where purchased,  hence:

x + y + z = 47    (1)

Also, he spent a total of $302, hence:

5.5x + 6y + 7z = 302     (2)

He purchases three times as many medium hats as small hats, hence:

y = 3x

-x + 3y = 0    (3)

Represent equations 1, 2 and 3 in matrix form gives:

\left[\begin{array}{ccc}1&1&1\\5.5&6&7\\-3&1&0\end{array}\right] \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}47\\302\\0\end{array}\right] \\\\\\\\ \left[\begin{array}{c}x\\y\\z\end{array}\right] =\left[\begin{array}{ccc}1&1&1\\5.5&6&7\\-3&1&0\end{array}\right] ^{-1} \left[\begin{array}{c}47\\302\\0\end{array}\right] \\\\\\ \left[\begin{array}{c}x\\y\\z\end{array}\right] = \left[\begin{array}{c}6\\18\\23\end{array}\right]

Therefore he purchases 6 small hats, 18 medium hats and 23 large hats

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3 years ago
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