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7nadin3 [17]
3 years ago
14

Paula has containers of colored sand that she uses for sand art. She has 1/3 cup of each blue, gray,and orange. She has 2/3 cup

of each of yellow and red. She has 1/2 cup of purple and 1cup of green. If Paula uses a cup of sand for each picture, how many pictures will she be able to make?
Mathematics
1 answer:
tangare [24]3 years ago
8 0
3 pictures.

1/3 + 1/3 + 1/3 = 3/3 = 1
2/3 + 2/3 = 4/3 = 1 1/3

1 + 1 + 1 1/3 + 1/2
   2 + 1 1/3 + 1/2

1 1/3 * 3 = 1 2/6
   1/2 * 3 =    3/6
              = 1 5/6

2 + 1 5/6
3 5/6

Paula can make 3 pictures.

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1200 students at the school

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Let x be the total number of students at the school

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Considering only the values of β for which sinβtanβsecβcotβ is defined, which of the following expressions is equivalent to sinβ
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Answer:

\tan(\beta)

Step-by-step explanation:

For many of these identities, it is helpful to convert everything to sine and cosine, see what cancels, and then work to build out to something.  If you have options that you're building toward, aim toward one of them.

{\tan(\theta)}={\dfrac{\sin(\theta)}{\cos(\theta)}    and   {\sec(\theta)}={\dfrac{1}{\cos(\theta)}

Recall the following reciprocal identity:

\cot(\theta)=\dfrac{1}{\tan(\theta)}=\dfrac{1}{ \left ( \dfrac{\sin(\theta)}{\cos(\theta)} \right )} =\dfrac{\cos(\theta)}{\sin(\theta)}

So, the original expression can be written in terms of only sines and cosines:

\sin(\beta)\tan(\beta)\sec(\beta)\cot(\beta)

\sin(\beta) * \dfrac{\sin(\beta) }{\cos(\beta) } * \dfrac{1 }{\cos(\beta) } * \dfrac{\cos(\beta) } {\sin(\beta) }

\sin(\beta) * \dfrac{\sin(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}}{\cos(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}} * \dfrac{1 }{\cos(\beta) } * \dfrac{\cos(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}} {\sin(\beta) \!\!\!\!\!\!\!\!\!\!\!\!\!\!\!\!{---}}

\sin(\beta) *\dfrac{1 }{\cos(\beta) }

\dfrac{\sin(\beta)}{\cos(\beta) }

Working toward one of the answers provided, this is the tangent function.


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