To calculate elapsed time:
Count on in minutes from the earlier time to the nearest hour.
Count on in hours to the hour nearest to the later time.
Count in minutes to reach the later time.
The gap from 9:25 PM to 10 PM is 35 min. The gap from 6 AM to 6:15 AM is 15 min. So far, that accounts for 35+15 = 50 min. The gap from 10 PM to midnight is 2 hours (10+2 = 12). Then the gap from midnight to 6 AM is 6 hours. So we have 2+6 = 8 hours. Add on the minute portion we computed to get 8 hours, 50 minutes.
Answer: 8 hours, 50 minutes
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General vertex form:
Given :
Extract "spread factor" m
Complete the square
Write as a squared binomial and simplify the constant
Re-write to match signs of standard general form:
So there is an identity we'll need to use to solve this:
cos(x+y) = cosxcosy - sinxsiny
replace the numerator with the right hand side of that identity and we get:
(cosxcosy - sinxsiny)/cosxsiny
Separate the numerator into 2 fractions and we get:
cosxcosycosxsiny- sinxsiny/cosxsiny
the cosx's cancel on the left fraction, the siny's cancel on the right fraction and we're left with:
cosy/siny - sinx/cosx
which simplifies to:
coty - tanx
Step 1: 654.75-15.00= $639.75
Therefore the club made $639.75
