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Diano4ka-milaya [45]
3 years ago
12

NASA cameras film a rocket launcher vertically from the launch pad, 3 miles away. When the angle between the camera and the grou

nd is 60 degrees, and is changing at a rate of 1.5 rad/minute. Find the rockets velocity at that moment.
Mathematics
1 answer:
Nimfa-mama [501]3 years ago
8 0
The height of the rocket is found in terms of the angle as
.. h/(3 mi) = tan(θ)
.. h = (3 mi)*tan(θ)

Then the rate of change of height (vertical velocity) is
.. h' = (3 mi)*sec(θ)^2*θ'
.. h' = (3 mi)*4*(1.5 rad/min)
.. h' = 18 mi/min

The rocket's velocity is 18 miles per minute at that moment.
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Explanation:


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Now, we get the z-score for 720 seconds by the following formula:

\text{z-score} =  \frac{x - \mu}{\sigma}

where 

t = \text{time for the auditor to finish his work } = 720 \text{ seconds}
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So, the z-score of 720 seconds is given by:

\text{z-score} = \frac{x - \mu}{\sigma}
\\
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\\
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Let

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Since the time is normally distributed, the probability for t > 720 is the same as the probability for z > 1.2. In terms of equation:

P(t \ \textgreater \  720) 
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\\ = 1 - P(z \leq 1.2)
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\\  \boxed{P(t \ \textgreater \  720)  = 0.115}

Hence, there is 11.5% chance that the auditor will spend more than 12 minutes in an invoice. 
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