| mike25-003 Find all continuous functions $f(x)$ satisfying $$ \int_0^xf(t) dt=\left[f(x)\right]^2+C $$ (Hint: Differentiate both sides with respect to $x$.) |
| mike26-008 Three useful properties of exponentials are given below (note: they are true in any positive base as well as in base 10). \begin{align*} 10^x10^y&=10^{x+y}\\ \frac{10^x}{10^y}&=10^{x-y}\\ (10^x)^r&=10^{rx}\\ \end{align*}
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| mike28-007 In a certain village, there are 50 couples. As it turns out, everyone in the village is having an affair. This despite a particularly gruesome custom which requires a wife, upon discovering that her husband is having an affair, to kill him the following morning. Even more oddly, the women in the town talk quite freely about their activities! In fact they are all perfectly aware that any woman who is having an affair will tell EVERY other woman in the village except, of course, for the wife of the man with whom they are having the affair. Yet life there goes on quite peacefully since no woman can know for sure that her husband is actually having an affair. One day, a well revered wise man visits the village and announces that someone is having an affair. What happens after this? |
| msu-precalc02-013 Suppose there are eight coins identical in every respect, yet one is counterfeit and weighs less than the others. The only tool you have to determine which coin is a counterfeit is a balance. What is the minimum number of times necessary to use the balance to determine which coin is counterfeit? |
| msu-precalc03-007 The position of a tennis ball at time $t$ which is thrown up into the air if given by the function $f(t)=32t-16t^2$. \\
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