Question 250253
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We know the formula distance equals rate times time.  Since the rate is fixed at 60 mph, we can say:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ d\ =\ 60t]


by substitution.


But we were asked for <b>d</b>istance as a function of <b>t</b>ime, so:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ d(t)\ =\ 60t]


Any time you are asked to express <b>f</b>ernblatz as a function of e<b>x</b>tra special sauce, you simply write *[tex \LARGE f(x)\ =\] [some expression involving *[tex \LARGE x]].  In general abstract mathematics, *[tex \LARGE f(x)], *[tex \LARGE g(x)], etc. make dandy function descriptors.  But when you are describing physical phenomenon (like your distance to time relationship), it often makes good sense to describe the function and the independent variable(s) using symbols that are more mnemonic.


You will see this again and again.  Examples:


A rectangle has a length 3 meters longer than its width.


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ A(w)\ =\ w^2\ +\ 3w]


The height of a projectile projected upward at an initial velocity from an initial height:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ h(t)\ =\ -\frac{1}{2}gt^2\ +\ v_ot\ +\ h_o]


and so on...


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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