Stitz-Zeager_College_Algebra_e-book

# A b c d e f g x g f x f h x h

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Unformatted text preview: gravitational force F exerted on the two objects varies directly with the product of the two masses and inversely with the square of the distance between their centers of mass. Solution. 1. Applying the deﬁnition of direct variation, we get F = kx for some constant k . 2. Since P and V are inversely proportional, we write P = k V . 3. There is a bit of ambiguity here. It’s clear the volume and height of the cone is represented by the quantities V and h, respectively, but does r represent the radius of the base or the square of the radius of the base? It is the former. Usually, if an algebraic operation is speciﬁed (like squaring), it is meant to be expressed in the formula. We apply Deﬁnition 4.4 to get V = khr2 . 4. Even though the problem doesn’t use the phrase ‘varies jointly’, the fact that the current I is given as relating to two diﬀerent quantities implies this. Since I varies directly with V but inversely with R, we write I = kV . R 5. We write the product of the masses mM a...
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