Matt Enlow

@unsolvedmre.bsky.social

1499 Followers 711 Following

Mathematician, math teacher, math enthusiast, math/art-ist. Universal humanizer.

The numbers, starting at 1 and going counter-clockwise, are 1, 15, 16, 12, 9, 2, 11, 13, 5, 18, 4, 3, 7, 10, 17, 8, 6, 14
The sum of a particular finite arithmetic sequence with common difference 3 is 3280. If you were to keep the first and last terms the same, but use a common difference of 4, the sum would be 2480. What would the sum be if the common difference were 5? (You may assume that all of these common differences "work" with the first and last terms of the sequence.)
Q: When did the song "I'll Be There" by The Escape Club peak on the Billboard Hot 100? A: It peaked at #8 on the Billboard Hot 100 on the chart dated June 8, 1991. On that week’s chart, the song climbed from #65 all the way to #57? Wait—Billboard’s archived weekly movement shows it was in its 25th week and marked with “Peak: 8,” indicating that June 8 was the issue on which it officially reached its highest Hot 100 position. A couple of related chart tidbits: It was The Escape Club’s last Hot 100 hit. It finished #65 on Billboard’s 1991 year-end Hot 100. And honestly, FOR A LOT OF US GEN X RADIO LISTENERS (my emphasis), this is one of those songs that felt even bigger than #8 because it was absolutely everywhere for a stretch in spring/early summer ’91.
Let $S_n$ denote the sum of the first $n$ terms of a particular arithmetic sequence. If $S_{50}=200$ and $S_{200}=50$, for what value of $n$ does $S_n$ attain its maximum value?
NO FLOWS CREATED Ready to create your first flow?
Suppose $x=\log_2{30}$ and $y=\log_2{5}$. Which of the following can be written in terms of x and y? How? (Be prepared to explain your answers.) $\log_2{6}$ $\log_2{10}$ $\log_2{15}$ $\log_2{20}$ $\log_2{25}$ $\log_2{35}$ $\log_2{125}$ $\log_2{150}$
A jar of Biscoff Creamy Cookie Butter
Two blocks of extra-firm tofu, between two cloths, with a metal case full of poker chips
v_i=\prod _{j=1}^n \frac{\left(a_{j,1}+a_{j,2}\right)!}{a_{j,1}! a_{j,2}!} \left(\left(p-\frac{1}{2}\right) \delta _{i,j}+\frac{1}{2}\right){}^{a_{j,1}} \left(\frac{1}{2}-\left(p-\frac{1}{2}\right) \delta _{i,j}\right){}^{a_{j,2}}
In front of you are three coins, identical in appearance. However, while two of them are fair coins, the third comes up Heads 75% of the time. Your task is to identify which coin is the unfair one, but you may only perform a total of three coin flips! (For each flip, you can flip any coin you want, taking any past flip results into account.) After those three flips, you must declare which coin you believe to be the unfair one. Assuming you "play optimally," what is the likelihood that you will correctly identify the unfair coin after your three flips?
With[{k = \[Pi]/6}, ParametricPlot3D[{r Cos[t], r Sin[t] Cos[k r], r Sin[t] Sin[k r]}, {t, -\[Pi]/2, \[Pi]/2}, {r, 0, 18}, PlotRange -> All, PlotPoints -> 120, Axes -> False, Boxed -> False, SphericalRegion -> True]]
$$\lim_{n \to \infty}\sum_{k=1}^{n}(\sqrt{k}-\sqrt{k-1})(\sqrt{n+1-k}-\sqrt{n-k})=\frac{\pi}{4}$$
Suppose f(x)=3x+|x|. Then its inverse, f^{-1}(x), can also be written in the form ax+b|x|. Find a and b.
In fact, any black-and-white image on the plane can be thought of as a subset of R^2, where the black points belong to the subset and the white points do not. So the text “INFINITE” in Figure 1.4(c) is a subset of R^2 and therefore an element of P(R^2). By that token, P(R^2) contains a copy of the page you are reading now. Thus, in addition to containing every imaginable function and every imaginable black-and-white image, P(R^2) also contains the full text of every book that was ever written, those that are yet to be written and those that will never be written. Inside of P(R^2) is a detailed biography of your life, from beginning to end, as well as the biographies of all of your unborn descendants. It is startling that the five symbols used to write P(R^2) can express such an incomprehensibly large set. Homework: Think about P(P(R^2)).