Respuesta :
[tex]\bf \qquad \qquad \textit{inverse proportional variation} \\\\ \textit{\underline{y} varies inversely with \underline{x}}\qquad \qquad y=\cfrac{k}{x}\impliedby \begin{array}{llll} k=constant\ of\\ \qquad variation \end{array} \\\\[-0.35em] \rule{34em}{0.25pt}[/tex]
[tex]\bf \textit{we also know that } \begin{cases} \stackrel{f(x)}{y}=3\\ x=10 \end{cases}\implies 3=\cfrac{k}{10}\implies 30=k \\\\\\ therefore\qquad \qquad \boxed{y=\cfrac{30}{x}} \\\\\\ \textit{when x = 15, what is the value of \underline{y}?}\qquad \qquad \stackrel{f(x)}{y}=\cfrac{30}{15}\implies y=2[/tex]
The value of the f(x) when x = 15 is 2.
Given that,
- f(x) varies inversely with x and f(X)= 3 when x = 10.
- We need to find the value of f(x).
Based on the above information, the calculation is as follows:
[tex]y = k\div x\\\\3 = k \div 10[/tex]
k = 30
Now the value of x is
[tex]= 30 \div 15[/tex]
= 2
Therefore we can conclude that the value of the f(x) when x = 15 is 2.
Learn more: brainly.com/question/2919338
