Recent content by 12john

  1. 1

    Mastering Combinatorics: Exploring the Formula for Permutations

    My combinatorics professor has a MA, PhD from Princeton University. On our test, she asked I handwrote, but transcribed in Latex, my answer below. How can I improve this? What else should I've written? Professor awarded me merely 50%. She wrote
  2. 1

    How can I easily Uncouple this slide and lock on an office chair?

    While my hunky husband was lifting the chair up, and my brawny brother pushing the frame down, I kept hitting the top of the slide with a screwdriver, to try to loosen the slide. But these parts are still wedged too tightly! We ran out of energy and ideas! How can we life hack this please...
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    Why can't I quote the quotations in the original post containing MathJax?

    Please see the screenshot below. Why doesn't your website quote my 2 original quotations containing MathJax?
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    I Why did I lose 60% on my proof of Generalized Vandermonde's Identity?

    My tests are submitted and marked anonymously. I got a 2/5 on the following, but the grader wrote no feedback besides that more detail was required. What details could I have added? How could I perfect my proof? Beneath is my proof graded 2/5.
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    Calculate ways to form a committee of 3 from 8, without division?

    I grok, am NOT asking about, the answers below. Rather, how can I calculate the final answer DIRECTLY, without division? I don't know why my Latex isn't rendering here? Please see: [web link redacted by the Mentors] Orange underline 1. Unquestionably, $\color{#FFA500}{4 \times 3/2} = 3!$ But...
  6. 1

    Why did my roller luggage's wheels stop turning smoothly?

    Two weeks ago, my carry on worked perfectly. But last week the detachable wheels stopped rotating smoothly, when I tried to glide my carry on. The wheels budge JUST A TAD when you push them hard, but it should be EFFORT LESS! Please see two pictures below. I see nothing jammed in the wheels. I...
  7. 1

    Can some liquid hand soaps smudge your eyeglass lenses?

    My control variables are 1. water hardness level, as I live in Florida, and I lodged at a Ritz Carlton also in Florida. I'm not, in any way, affiliated with any corporation herein. I'm not, in any way, affiliated with any corporation herein. 2. my eyeglasses with $700 USD Nikon SeeMax Ultimate...
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    Is it safe to cover a floor lamp with an Aluminum metal pie plate?

    The "actual problem right now" is that (1) the downward light isn't bright enough, and (2) all the upward light (illuminating the ceiling) is wasting electricity and resources.
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    Biology Why do these biology textbooks write 'differential' as an adjective?

    Are these books using 'differential' correctly? Why not just write 'different'? 1. Handbook of the Biology of Aging edited by Edward J. Masoro, Steven N. Austad. p 480. 2. The Cambridge Companion to the Philosophy of Biology edited by David L. Hull, Michael Ruse. p 46. 3. p 78. 4. Dictionary...
  10. 1

    Is it safe to cover a floor lamp with an Aluminum metal pie plate?

    Please see the image below. I'm trying to convert my IKEA NYFORS floor lamp into a reading light, by covering the top with an Aluminium pie plate. Will this be a fire or electrical hazard? Does anyone foresee any dangers or risks? As I have 3 of these floor lamps in my attic, I don't want to...
  11. 1

    Intersection of Tangents to Hyperbola and 1/x

    Homework Statement Homework Equations The Attempt at a Solution \text{Differentiate }{{C}_{2}}:\text{ }\dfrac{d{{y}_{2}}}{dx}=\dfrac{x}{y} \text{Therefore, use }Q(-a,-b)\text{ for MQ: }{{y}_{2}}-(-b)=\dfrac{-a}{-b}\left( x-(-a) \right)\text{ }\Leftrightarrow...
  12. 1

    Why Repeated Roots instead of Two Distinct Roots

    Thank you HallsofIvy. I'm going sum up your answer. Please let me know if it's right or wrong. Did I miss anything? If t gives a point on the locus (NOT C) which two normals to C can be drawn to, there CAN in fact be two different values of t that satisfy 0=at^3 - th + 2at-k. So this...
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    Why Repeated Roots instead of Two Distinct Roots

    Greetings all. I hope it's OK to post here. My issue here is with the theory and not with the actual algebra or calculus. I understand this calculus question on parametric curves except why there must be a double root instead of just a repeated root in the last part. Please see the red...
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