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- Missouri Conducts Controversial Execution of Marcellus WilliamsSeptember 25, 202419 Comments
- Open Mic for the week of 9/23/2024September 23, 2024146 Comments
- From The Financial Times: From Taipei to Budapest: the mysterious trail of exploding pagersSeptember 18, 202412 Comments
- Open Mic for the week of 9/16/2024September 16, 2024378 Comments
- Group Discussion: The Push For Social Media Warning LabelsSeptember 12, 202411 Comments
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- LeeEsq on Open Mic for the week of 9/23/2024My theory and it is mine is that people expect Jews to deal with a certain amount of anti-Semitism a…
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Oh, and I was hoping for an example of a problem.
“See? This is the math we *USED* to teach!”
There’s a page from a math book from the 1920s here. Impenetrable at first glance but, nope, you can do these in your head.
Even if it’s been decades.Report
oh, wait
maybe you can only do #14 in your headReport
Most of the problems are amenable to a change of variable and the quadratic formula. Then once you realize that most of the answers are going to be small integers, or at least based on small integers, you can solve a number of them in your head by just trying small integers to see which work.Report
While I can sing the Quadratic to the tune of “Pop Goes the Weasel”, I can’t do it in my head anymore.
Sigh.Report
No, but for the first problem, you can run through small integers in your head and find that 1 and 4 work (so also -1 and -4). For the second, 2 and 3 work (also -2 and -3). For number eight, you chunk through the numbers that have integral fourth roots (1, 16, 81, 196, etc) to find that 196 works.
I always told my calculus students that if they were working one of my test problems and the algebra suddenly became unmanageable, they should back up because they had made a mistake. I wasn’t testing whether they could do overly complicated algebraic manipulation.Report
I don’t think you need the quadratic formula for any of these. There are enough moving parts that you’d probably want scratch paper, but these all seem fairly easily factorable.Report