Question 1061689
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If we assume that air resistance is proportional to the square of the velocity, then the time t in seconds 
required for an object to reach a velocity v in feet per second is given by: 
t=9/24ln 24+v/24-v, 0 < v < 24 
determine the velocity, to the nearest hundredth foot per second of the object after 1.3 seconds 
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<pre>
If your formula is

t = {{{(9/24)*ln((24+v)/(24-v))}}} 


then they want you to solve this equation for "v":

1.3 = {{{(9/24)*ln((24+v)/(24-v))}}}.


It is equivalent to

{{{1.3*(24/9)}}} = {{{ln((24+v)/(24-v))}}}    or

{{{ln((24+v)/(24-v))}}} = 3.4666,

{{{(24+v)/(24-v)}}} = {{{e^3.4666)}}},

{{{(24+v)/(24-v)}}} = {{{2.71828^3.4666}}},

{{{(24+v)/(24-v)}}} = 32.03   (approximately).


====> 24 + v = 32.03*(24 - v)  ====>  v + 32.03v = 32.03*24 - 24  ====>  v = {{{744.72/(1+32.03)}}} = 22.55  (approximately).
</pre>

Solved.  The answer is v = 22.55.


<U>Check</U>.  {{{(9/24)*ln((24+22.55)/(24-22.55))}}} = 1.3.   Correct !