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inysia [295]
3 years ago
12

A robot can complete 8 tasks in 5/6 hour. each task takes the same amount of time.

Mathematics
2 answers:
matrenka [14]3 years ago
7 0

Answer:

A robot can complete 8 tasks in hour = \frac{5}{6}

A robot can complete 1 task in hour = \frac{\frac{5}{6}}{8}

A robot can complete 1 task in hour = \frac{5}{48}

So,  it take \frac{5}{48} hours the robot to complete the task

A robot can complete tasks in  \frac{5}{6} hour = 8

A robot can complete tasks in  1 hour = \frac{8}{\frac{5}{6}}

                                                           =9.6

So,  the robot complete 9 tasks in one hour.

nikklg [1K]3 years ago
3 0
5/6 hour = 5/6 × 60 = 300/6 = 50 minutes

8 tasks in 50 minutes
1 task = 50/8 = 6 1/4 minutes

a. robot completes task in 6 1/4 minutes

b. #tasks per hour =
#of tasks × time takes to do task < or = 60
n × 6.25 = 60
6.25n = 60.
n= 60/6.25 = 9.6

robot can complete 9 tasks in one hour
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Answer:

\cot(x)+\cot(\frac{\pi}{2}-x)

\cot(x)+\tan(x)

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\csc(x)[\frac{1}{\cos(x)}]

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\csc(x)\csc(\frac{\pi}{2}-x)

Step-by-step explanation:

I'm going to use x instead of \theta because it is less characters for me to type.

I'm going to start with the left hand side and see if I can turn it into the right hand side.

\cot(x)+\cot(\frac{\pi}{2}-x)

I'm going to use a cofunction identity for the 2nd term.

This is the identity: \tan(x)=\cot(\frac{\pi}{2}-x) I'm going to use there.

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Let's just do it all together without all the words now:

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\csc(x)[\frac{\cos^2(x)+\sin^2(x)}{\cos(x)}]

\csc(x)[\frac{1}{\cos(x)}]

\csc(x)[\sec(x)]

\csc(x)[\csc(\frac{\pi}{2}-x)]

\csc(x)\csc(\frac{\pi}{2}-x)

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