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3 years ago

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Mulder and Scully are driving to the same town. Mulder leaves the office at 9:30a.m. averaging 57mph. Scully leaves at 10:00a

.m., following the same path and averaging 60 mph. At what time will Scully catch up with Mulder?

1 answer:

koban [17]3 years ago

6 0

Answer:

Scully will catch up with Mulder by 7:30 PM.

Step-by-step explanation:

Consider the provided information.

Mulder leaves the office at 9:30a.m. averaging 57mph.

Scully leaves at 10:00a.m., following the same path and averaging 60 mph.

Distance covered by Mulder between 9:30 AM and 10:00 AM:

$\frac{57}{2}= 28.5$ miles

Let t is the time taken by Scully to catch up with Mulder.

After leaving office Scully needs to cover extra distance of 28.5 miles because Mulder leaves the office earlier.

Therefore total distance cover by them is:

$28.5+57t=60t$

$28.5=60t-57t$

$28.5=3t\\t=9.5$

Hence, it would take 9 hours 30 minutes to catch up Mulder.

10 am + 9 hours 30 minutes = 7:30 pm

Therefore, Scully will catch up with Mulder by 7:30 PM.

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Step-by-step explanation:

Given

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Required

Solve (a) to (d)

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So:

$\sec^2(\theta) = (\frac{1}{\cos(\theta)})^2$

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This is calculated as:

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$\cot(\theta) = \frac{1}{\tan(\theta)}$

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Solving (c):

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In trigonometry:

$\cot(\frac{\pi}{2} - \theta) = \tan(\theta)$

Hence:

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Solving (d):

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So:

$\csc^2(\theta) = (\frac{1}{\frac{9}{\sqrt{82}}})^2$

$\csc^2(\theta) = (\frac{\sqrt{82}}{9})^2$

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