A cell phone tower has a reach of 5 miles in every direction. The cell tower is centered 3 miles
1 answer:
Answer:
73:29 minutes:seconds
Step-by-step explanation:
Since we want to know the time we're in cell-tower range, we can convert the coordinates of the problem to time. At 8 miles per hour, each mile is 1/8 of an hour, or 7.5 minutes.
From the designated origin, the tower is 3 miles, or 22.5 minutes, east and 6 miles, or 45 minutes, north. The turning point in our bike ride is 2 miles, or 15 minutes, east of our origin. Cell phone coverage will be had within 5 miles, or 37.5 minutes, of the tower location. The relevant circle and north-south travel line are shown in the attachment.
The equation of the cell coverage circle is ...
(x -22.5)^2 +(y -45)^2 = 37.5^2
Analytically, we're interested in the y-values where x = 15. Solving for those, we get ...
(15 -22.5)^2 + (y -45)^2 = 37.5^2
(y -45)^2 = 37.5^2 -7.5^2 = 1350
The values of time after our turning point where we enter and exit cell coverage are ...
y = 45 ± √1350
The difference between these times is 2√1350 minutes, 73.4847 minutes.
The fraction of a minute corresponds to 29.08 seconds
We will receive cell coverage for 73 minutes 29.08 seconds.
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