Question 178095
duration of a storm is dependent on the duration of the storm.
looking at what you showed for the function, i get:
{{{f(d) = .07*sqrt(d)^3}}}
or:
{{{f(d) = (.07*sqrt(d))^3}}}
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if i assume the first equation, then:
{{{f(d) = .07*sqrt(d)^3}}}
becomes:
{{{f(9) = .07*sqrt(9)^3}}}
{{{sqrt(9)}}} = 3
{{{3^3}}} = 27
.07 * 27 = 1.89
your answer would be 1.89 hours if the diameter of the storm is 9 miles.
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if i assume the second equation, then:
{{{f(d) = (.07*sqrt(d))^3}}}
becomes:
{{{f(9) = (.07*sqrt(9))^3}}}
{{{sqrt(9)}}} = 3
.07*3 = .21
{{{.21^3}}} = .009261 hours
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i would bet on the first interpretation where the answer is 1.89 hours, rather than the second interpretation where the number of hours is .009261.
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use my first interpretation as follows:
{{{f(d) = .07*sqrt(d)^3}}}
becomes:
{{{f(9) = .07*sqrt(9)^3}}}
this becomes:
{{{f(9) = .07*3^3}}}
which becomes:
{{{f(9) = .07*27}}}
which becomes:
{{{f(9) = 1.89}}}
your answer would be:
a storm with a diameter of 9 miles would have a duration of 1.89 hours.
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please note:
{{{sqrt(9)^3}}} is the same as {{{(9^(1/2))^3}}} is the same as {{{9^(3/2)}}} = 27.
you could have done it either way and gotten the same answer.
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