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If a curve is represented parametrically by the equation `x = 4t^(3)+3` and `y=4+3t^(4)` and `(((d^(2) x)/(dy^(2))))/(((dx)/(dy))^(n))` is constant then value of `n/2` is

Text Solution

Verified by Experts

The correct Answer is:
`83.9`
`(dx)/(dy)= - ((dx)/(dt))/((dy)/(dt))=(12 t^(2))/(12 t^(3))=1/t`
`(d^(2)x)/(dy^(2))=d/(dy)((dx)/(dy))=d/(dt)(1/t).(dt)/(dy)=(-1)/t^(2). 1/(12 t^(3))=(-1)/(12 t^(5))`
so `((-1)/(12 t^(5)))/((1/t)^(n))` is constant `implies n=5`
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