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Exercise 2 Find a formula for Y in terms of X

Exercise 2 Find a formula for Y in terms of X-example-1
User Roys
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1 Answer

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6 votes

Given:

y is inversely proportional to square of x.

The equation is written as,


\begin{gathered} y\propto(1)/(x^2) \\ y=(c)/(x^2)\ldots\ldots\ldots c\text{ is constant} \end{gathered}

Also y = 0.25 when x = 5.


\begin{gathered} y=(c)/(x^2) \\ 0.25=(c)/(5^2) \\ 25*0.25=c \\ c=(25)/(4) \end{gathered}

So, the equation of y interms of x is,


y=(25)/(4x^2)

When x increases,


\begin{gathered} \lim _(x\to\infty)y=\lim _(x\to\infty)((25)/(4x^2)) \\ =(25)/(4)\lim _(x\to\infty)((1)/(x^2)) \\ =0 \end{gathered}

Hence, the value of x increases then y decreases.

User Shondel
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