If gasoline costs $ 3.77 per gallon when you pay with a credit card, but $0.08 per gallon less if you pay with cash, how much do
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Parameterize the ellipsoid using the augmented spherical coordinates:
Then the Jacobian for the change of coordinates is
which has determinant
Then the volume of the ellipsoid is given by
where
denotes the spaced contained by the ellipsoid. In particular, we have the definite integral and volume
Then the Jacobian for the change of coordinates is
which has determinant
Then the volume of the ellipsoid is given by
where