Suppose that $$ y $$ varies inversely with $$ x $$, and $$ y=10 $$ when $$ x=2 $$. (a) Write an inverse variation equation that relates $$ x $$ and $$ y $$. Equation: $$ \square $$ (b) Find $$ y $$ when $$ x=25 $$. $$ y=\square $$

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1. Since $$ y $$ varies inversely with $$ x $$, the relationship can be written as  
   $$
   y = \frac{k}{x},
   $$  
   where $$ k $$ is the constant of variation.

2. When $$ y=10 $$ and $$ x=2 $$, substitute into the equation to find $$ k $$:  
   $$
   10 = \frac{k}{2}.
   $$  
   Multiply both sides by 2 to get  
   $$
   k = 10 \times 2 = 20.
   $$

3. The inverse variation equation that relates $$ x $$ and $$ y $$ is  
   $$
   y = \frac{20}{x}.
   $$

4. To find $$ y $$ when $$ x=25 $$, substitute $$ x=25 $$ into the equation:  
   $$
   y = \frac{20}{25} = \frac{4}{5}.
   $$

Equation: $$ y = \frac{20}{x} $$  
$$ y = \frac{4}{5} $$ when $$ x = 25 $$.
(a) The inverse variation equation is $$ y = \frac{20}{x} $$. (b) When $$ x = 25 $$, $$ y = \frac{4}{5} $$.

Suppose that varies inversely with , and when .
(a) Write an inverse variation equation that relates and .
Equation:
(b) Find when .

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Suppose that varies inversely with , and when . (a) Write an inverse variation equation that relates and . Equation: (b) Find when .