**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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