# differential calculus

when a certain polyatomic gas undergoes adiabatic expansion,its pressure p and volume V satisfy the equation pV^1.3 =k,where k is constant.Find the relationship between the related rates dp/dt and dV/dt.

this is a problem of related rates please show all solutions and diagram thanks

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1. p v^1.3 = k

p d/dt (v^1.3) + v^1.3 dp/dt = 0

1.3 p v^.3 dv/dt + v^1.3 dp/dt = 0

1.3 p dv/dt = - v dp/dt

1.3 dv/dt /v = - dp/dt /p

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2. thanks =) we have arrived at the same answer

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