# Find the elasticity of demand at the price p=8.5 with the demand of p.x^2=498.75 the elasticity of demand is ED=

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You need to find the demand function, such that:

`p*x^2 = 498.75 => x^2 = 498.75/p => x = +-sqrt(498.75/p)`

You need to find the price elasticity of demand using the following formula, such that:

`ED = (dx)/(dp)*(p/x)`

`(dx)/(dp) = (d(sqrt(498.75/p)))/(dp) => (dx)/(dp) = (-498.75/p^2)/2sqrt(498.75/p) => (dx)/(dp) = (-sqrt(498.75p)/(2p^2))`

Replacing `(-sqrt(498.75p)/(2p^2))` for `(dx)/(dp)` and `sqrt(498.75/p)` for x yields:

`ED = (-sqrt(498.75p)/(2p^2))*(p/(sqrt(498.75/p)))`

`ED = -1/2 < 1`

**Hence, evaluating the price elasticity of demand yields `ED = -1/2 < 1,` thus the demad is price inelastic.**

`px^2= 498.75` `x=sqrt(498.75/p)` `sqrt(498.75) xx p^-(1/2)`

`dx/dp= sqrt(498.75) xx (-1/2) xx p^(-1/2-1)= (-1/2)sqrt(498.75)p^(-3/2)`

`ED=((dx)/(dp)) xx (p/x)= (-1/2)sqrt(498.75) p^(-3/2) xx p sqrt(p)/sqrt(498.75)=`

`= (-1/2) p^(-3/2+1+1/2)=(-1/2)<1`````

`A"ne"lastyc`

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