SOLUTION: To estimate how long a thunderstorm will last, meteorologist can use the formula t= square root of d^3 over 216, where t is the time in hours and d is the diameter of the storm in

Algebra ->  Radicals -> SOLUTION: To estimate how long a thunderstorm will last, meteorologist can use the formula t= square root of d^3 over 216, where t is the time in hours and d is the diameter of the storm in       Log On


   

Question 29056: To estimate how long a thunderstorm will last, meteorologist can use the formula t= square root of d^3 over 216, where t is the time in hours and d is the diameter of the storm in miles.
1) A thunderstorm is 8 miles in diameter. Estimate how long the storm will last. Give your answer in simplified form and as a decimal(homework asked this, not me)
2) Will a thunderstorm twice this diameter last twice as long?Explain.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
t+=++sqrt%28+d%5E3%29+%2F+216
[a] t+=+sqrt%288%5E3%29+%2F+216
t+=+sqrt%288%2A8%29+%2A+sqrt%284%2A2%29+%2F+216
t+=+8+%2A+2+%2A+sqrt%282%29+%2F+216
t+=+2+%2A+1.414+%2F+27
t+=+.1047
This is in hours
for minutes and seconds
.1047 hours x 60 minutes/hour = 6.284 minutes
.284 minutes x 60 seconds/minute = 17 seconds
so the time is 6 minutes 17 seconds
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twice the diameter would be 16 miles or 2*8 miles
t+=++sqrt%28+d%5E3%29+%2F+216
t+=+sqrt%28%282%2A8%29%5E3%29+%2F+216
t+=+sqrt%282%5E3%2A8%5E3%29+%2F+216
that's because (2*8) * (2*8) * (2*8) = (2*2*2) * (8*8*8)
[b] t+=+sqrt%282%5E3%29+%2A+sqrt%288%5E3%29+%2F+216}
notice the difference between [a] (the 2nd line) and [b]
the difference is the factor sqrt%282%5E3%29
so if you double the diameter this is the factor you multiply the time by
to get the new time.