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  1. pka

    "American" English only?

    Please SEE HERE. This is a English Language website. Please post accordingly.
  2. pka

    pka disagrees with teaching graphs before limits

    Well I completely disagree that one needs to have a graph to work this question. w(x)=\begin{cases}-x^3+1 & x\le 1 \\2|x-1|-2 & 1<x<3\\ (x-5)^2-2 & 3\le x \end{cases} Look the right column. We have (-\infty, 1]\cup(1,3)\cup [3,\infty)=\Re, the set of real numbers. That tells us that the set of...
  3. pka

    pka disagrees with a valid method

    I almost never reply if it requires completing someone else's proof. But in this case the suggested proof is so ridiculous as to cry out for a correction. 1) \(m(\widehat{AB})=m(\angle AOB)\); the central angle theorem. 2) \(m(\widehat{AB})=2m(\angle ACB)\); the inscribed angle theorem. 3)...
  4. pka

    pka's not-so-fond memory

    AH! Synthetic Division that is not so fond memory from my childhood. I don't think that it has crossed my path in at least fifty years. I thought that had gone the way of finding the square root by hand. Guess not. Have these math-ed types heard of Computer Algebra Systems?
  5. pka

    pka found a scary math joke

    This thread is one of the scary mathematics jokes I have seen in a long time!
  6. pka

    LOG vs LN

    The current usage is \(\log(x)\) for natural logarithm. SEE HERE
  7. pka

    pka hates degree measure

    I understand functions that are defined on numbers. But what are degrees? If you say that they are numbers, then tell me what numbers?
  8. pka

    Coronavirus leads to stress

    @Will Red, you are a pitiful TROLL. Anyone who tries to capsulize on our current nation tragedy is truly despicable. If you can show that you have a PhD/MD is a research area well then O.K., otherwise butt out!
  9. pka

    Need for a Helpers Forum

    As many of you know that in my former life I read/edited thousands of test questions. But the above question is a complete and utter mystery to me. Mostly I have had some idea, no matter how vague, of what is going on. But not with this one. There are at least two helpers who seem to understand...
  10. pka

    Systemic Nth roots of a number

    There are six sixth roots of -12+5i see here. See that there are six of them. Each of them is on a circle centered at the origin of radius |-12+5i|^{1/6}=\large\sqrt[6]{13} However, the salient feature is the fact the the are evenly spaced on the circle and the central angle between any to...
  11. pka

    LaTeX trouble

    See this post
  12. pka

    Another discussion about notation

    In my experience in courses dealing with functions the notation fg(x) means f(x)\cdot g(x). Just as f+g(x) means f(x)+g(x) or the addition of functions then fg(x) means multiplication of functions. In this case fg(x)=gf(x)=3x^3+x^2. It appears that you are assuming that it is f\circ...
  13. pka

    Digging Post Holes ... Pile High and Deep

    I have no idea what the box method is. But whatever it is, it is useless in factoring. Having won a citywide factoring contest years ago, I can tell you how to learn factoring. My algebra teacher then gave me a sheet of four hundred problems. They all looked like (7x-4)(2x+5). When I objected...
  14. pka

    Instructors who take great offense

    I fear that teacher has no idea that sets are not ordered. If so the teacher will take great offence at told s/he in incorrect.
  15. pka

    Off Topic

    @mmm4444bot are you going to ban me now?
  16. pka

    Wolfram Alpha's graphing

    See PLOT I PLOT II Do you use WolframAlphaPro? That may be your confusion.
  17. pka

    Extracurricular

    If you really want to learn about even and odd functions then try to show that: every function is the sum of an even function and an odd function.
  18. pka

    Stand-Up Comic Fail

    From somewhere over the rainbow.
  19. pka

    Solve |-4t| = -24 ..... trick question

    This Question, \large{-2|2t|=-24} is exactly the same as \large{|t|=6} which is exactly the same as \large{|-4t|=24} which is exactly the same as \large{|2t|=12}. It is a sad commentary on the state of basic mathematics education if anyone cannot see the solution of \large{|-4t|=-24} is less...
  20. pka

    Origin of calculus

    You don't need either integration or differentiation; just the ability to count and estimate. How many square units are shaded in? This is a standard exercise in beginning calculus. The whole idea is to get students to realize what the course is all about. Many who have taught calculus do not...
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