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42 votes
42 votes
Y is inversely proportional to x².
When x = 4, y = 2.
Find y when x = 1 divided by 2

User Rishabh Jhalani
by
2.9k points

1 Answer

14 votes
14 votes


\textbf{Heya !}


\bigstar\textsf{Given:-}

  • y is inversely proportional to
    \sf{x^2}.


\bigstar\textsf{To\quad find:-}

  • If y=2 when x=4, what is y when x=
    (1)/(2) ?

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\bigstar\textsf{Solution\quad steps:-}

If y is inversely proportional to x^2, the equation looks as shown below:-


\sf{\longmapsto{y=\cfrac{k}{x^2}}, where k -- constant of proportionality

Plug in all values


\sf{\longmapsto{2=\cfrac{k}{4^2}} , simplifying --


\sf{\longmapsto{2=k/16}

multiply by 16 both sides


\sf{\longmapsto 2*16=k}}


\sf{\longmapsto{32=k}}

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Plug 32 into the second equation:-


\sf{\longmapsto y=\cfrac{32}{\bigg(\cfrac{1}{2}\bigg)^2}}

simplify the complex fraction


\longmapsto\sf{y=\cfrac{32}{\cfrac{1}{4}}

divide fractions


\sf{\longmapsto{y=\cfrac{32}{1}/\cfrac{1}{4}}=\cfrac{32}{1}\cdot}\cfrac{4}{1}}=128}

`hope that was helpful to u ~

User Maweeras
by
2.9k points