Question 1201676
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In most textbooks or other references, s being inversely proportional to the square root of t would be described by introducing a proportionality constant k and using the equation {{{s=k/sqrt(t)}}}.<br>
In practice, it is nearly always easier to think in terms of the product of s and the square root of t being constant.<br>
So with the given information that s is 28 when t is 64, we have<br>
{{{s*sqrt(t)=28*sqrt(64)=28*8=224}}}<br>
So however s or t changes, the product of s and the square root of t will always be 224.<br>
So....<br>
a) find S when t is 81:<br>
{{{S*sqrt(81)=224}}}
{{{9S=224}}}
{{{S=224/9}}}<br>
b) find t when s is 60:<br>
{{{60*sqrt(t)=224}}}
{{{sqrt(t)=224/60=56/15}}}
{{{t=(56/15)^2=3136/225}}} = 13.94 rounded to 2 decimal places.<br>
The other tutor pointed out that your error in part b was taking a square root when you should have been squaring.  You are far less likely to make that kind of error if you work inverse variation problems in the manner described above.<br>