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Square!
  • Given r=f(θ), we are generally not concerned with r′=f′(θ); that describes how fast r changes with respect to θ

    You're using the derivative of a polar equation as the basis for what a tangent line is. But as the textbook explains, that doesn't give you a tangent line or describe the slope at that point. I never bothered defining what "tangent" means, but since this seems so important to you why don't you try coming up with a reasonable definition?

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  • I think we fundamentally don't agree on what "tangent" means. You can use

    x=f(θ)cosθ, y=f(θ)sinθ to compute dydx

    as taken from the textbook, giving you a tangent line in the terms used in polar coordinates. I think your line of reasoning would lead to r=1 in polar coordinates being a line, even though it's a circle with radius 1.

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  • Given r=f(θ), we are generally not concerned with r′=f′(θ); that describes how fast r changes with respect to θ

    I think this part from the textbook describes what you're talking about

    Instead, we will use x=f(θ)cosθ, y=f(θ)sinθ to compute dydx.

    And this would give you the actual tangent line, or at least the slope of that line.

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  • Polar Functions and dydx

    We are interested in the lines tangent a given graph, regardless of whether that graph is produced by rectangular, parametric, or polar equations. In each of these contexts, the slope of the tangent line is dydx. Given r=f(θ), we are generally not concerned with r′=f′(θ); that describes how fast r changes with respect to θ. Instead, we will use x=f(θ)cosθ, y=f(θ)sinθ to compute dydx.

    From the link above. I really don't understand why you seem to think a tangent line in polar coordinates would be a circle.

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  • A straight line in polar coordinates with the same tangent would be a circle.

    I'm not sure that's true. In non-euclidean geometry it might be, but aren't polar coordinates just an alternative way of expressing cartesian?

    Looking at a libre textbook, it seems to be showing that a tangent line in polar coordinates is still a straight line, not a circle.

  • Picture this
  • When you say red pill, do you mean this one?

    The concept of red and blue pills has since been widely used as a political metaphor in the United States, especially among online hate culture, where "taking the red pill" or being "red-pilled" means becoming aware of purported political biases inherent in society ... The supposed truths revealed to those who refer to themselves as "red pilled" often include conspiracy theories, as well as antisemitic, white supremacist, and misogynistic beliefs.

  • "Modding is pretty big" says Baldur's Gate 3 director as over 1m mods are installed in less than 24 hours
  • 1. OWNERSHIP

    By accepting these terms, you acknowledge and agree that you do not own or have any proprietary rights in the Game or any Mods you create, except as specifically mentioned here. Any Mods you create are your property only if they consist only of your original creative work. To the extent that any element of your Mod includes or is derived from the Game's intellectual property (such as code, themes, characters, names, stories, dialogue, locations, artwork, sounds, music, and visual effects), you agree that all intellectual property rights therein, whether they are registered or not, are owned by Larian Studios and its licensors.

    I'm not sure I believe you about your first point.

  • An important update on Concord - Being taken offline September 6th, refunds to be issued
  • Apex Legends is a battle royale, Gigantic and Battleborn are (were) more like MOBAs, Paladins and Dirty Bomb don't work on linux. I haven't played all of these games, but I don't think they're as interchangeable as you're implying.

  • Gun shops that sold weapons trafficked into Washington, DC, sued by nation’s capital and Maryland
  • In the United States, a straw purchaser of a firearm at a federally licensed firearm dealership who lies about the identity of the ultimate possessor of the gun can be charged with making false statements on a federal Firearms Transaction Record, which is a felony. Note that in this case, purchasing the item for another person is ipso facto illegal, regardless of that person's status as a legal possessor.

    from Wikipedia

    I guess if you're buying up a lot of guns with the intent to resell/distribute them, that would count as straw purchasing.

  • Anon casts a healing spell
  • Casting an Arcane Spell in Armor: A character who casts an arcane spell while wearing armor must usually make an arcane spell failure check. The number in the Arcane Spell Failure Chance column on Table 6–6 is the percentage chance that the spell fails and is ruined. If the spell lacks a somatic component, however, it can be cast with no chance of arcane spell failure.

    https://aonprd.com/Rules.aspx?ID=361

    It was a rule in Pathfinder, so presumably it was a rule in 3e.

  • The Worst TV Show Finales
  • I think it's just that Discovery didn't want to let it end. After Adam and Jamie left, they had like 2 more seasons with new hosts. I actually don't know if the quality of the show dropped, I never really gave it a chance.

  • InitialsDiceBearhttps://github.com/dicebear/dicebearhttps://creativecommons.org/publicdomain/zero/1.0/„Initials” (https://github.com/dicebear/dicebear) by „DiceBear”, licensed under „CC0 1.0” (https://creativecommons.org/publicdomain/zero/1.0/)LT
    ltxrtquq @lemmy.ml
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