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First of all: knowing that v*m*t\neq{0} implies that none of the variables equals to zero.

Second of all: v^2*m^3*t^{-4}>0? --> \frac{v^2*m^3}{t^4}> 0? Now when this inequality holds true? Obviously as v^2 and t^4 are positive this inequality will hold true if and only m^3>0, or, which is the same, when m>0.

(1) m>v^2 --> m is more than some positive number (v^2), hence m is positive. Sufficient.

(2) m>t^{-4} --> m>\frac{1}{t^4} --> Again m is more than some positive number (\frac{1}{t^4} ), hence m is positive. Sufficient.

in both conditions the only variable that can change the sign of the expression is M. Since in both conditions we are told that M most be greater than some always positive number than in both condition we can answer the question if M is positive and thus the expression is positive.

Re: If v*m*t not = 0 , is v^2*m^3*t^{-4} > 0 ? [#permalink]
18 Dec 2013, 04:30

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