Respuesta :
[tex]\textbf{Heya !}[/tex]
✏[tex]\bigstar\textsf{Given:-}[/tex]✏
- y is inversely proportional to [tex]\sf{x^2}[/tex].
✏[tex]\bigstar\textsf{To\quad find:-}[/tex] ✏
- If y=2 when x=4, what is y when x=[tex]\frac{1}{2}[/tex] ?
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✏[tex]\bigstar\textsf{Solution\quad steps:-}[/tex] ✏
If y is inversely proportional to x^2, the equation looks as shown below:-
[tex]\sf{\longmapsto{y=\cfrac{k}{x^2}}[/tex], where k -- constant of proportionality
Plug in all values
[tex]\sf{\longmapsto{2=\cfrac{k}{4^2}}[/tex] , simplifying --
[tex]\sf{\longmapsto{2=k/16}[/tex]
multiply by 16 both sides
[tex]\sf{\longmapsto 2*16=k}}[/tex]
[tex]\sf{\longmapsto{32=k}}[/tex]
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Plug 32 into the second equation:-
[tex]\sf{\longmapsto y=\cfrac{32}{\bigg(\cfrac{1}{2}\bigg)^2}}[/tex]
simplify the complex fraction
[tex]\longmapsto\sf{y=\cfrac{32}{\cfrac{1}{4}}[/tex]
divide fractions
[tex]\sf{\longmapsto{y=\cfrac{32}{1}\div\cfrac{1}{4}}=\cfrac{32}{1}\cdot}\cfrac{4}{1}}=128}[/tex]
`hope that was helpful to u ~
