Let's analyze the given equation [tex]\( h = \frac{V}{iw} \)[/tex].
1. Direct Variation with [tex]\( V \)[/tex]:
- Direct variation means that as one variable increases, the other variable increases proportionately.
- In the given equation, if [tex]\( V \)[/tex] increases while keeping [tex]\( i \)[/tex] and [tex]\( w \)[/tex] constant, [tex]\( h \)[/tex] will also increase. Therefore, [tex]\( h \)[/tex] varies directly with [tex]\( V \)[/tex].
2. Inverse Variation with [tex]\( i \)[/tex] and [tex]\( w \)[/tex]:
- Inverse variation means that as one variable increases, the other variable decreases proportionately.
- In the given equation, if either [tex]\( i \)[/tex] or [tex]\( w \)[/tex] increases while keeping the other variables constant, [tex]\( h \)[/tex] will decrease. Therefore, [tex]\( h \)[/tex] varies inversely with both [tex]\( i \)[/tex] and [tex]\( w \)[/tex].
Given this analysis, the correct description of the variation in the equation [tex]\( h = \frac{V}{iw} \)[/tex] is:
- [tex]\( h \)[/tex] varies directly with [tex]\( V \)[/tex] and inversely with [tex]\( i \)[/tex] and [tex]\( w \)[/tex].
Thus, the correct answer is:
[tex]\[ \boxed{h \text{ varies directly with } V \text{ and inversely with } i \text{ and } w.} \][/tex]
