#help-49 | Mathematics | Page 14

magic stone Oct 24, 2023, 10:14 PM

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Because rational number is any number that can be represented as a/b with a and b being integers

lavish cairn Oct 24, 2023, 10:15 PM

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Can you say the steps

balmy brook Oct 24, 2023, 10:15 PM

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there is no step

lavish cairn Oct 24, 2023, 10:15 PM

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What do I do

balmy brook Oct 24, 2023, 10:16 PM

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sorry but what age are you ?

lavish cairn Oct 24, 2023, 10:17 PM

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I do 2x2 and it’s 1/4?

balmy brook Oct 24, 2023, 10:17 PM

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if you are under 13 y then you can't be here

lavish cairn Oct 24, 2023, 10:18 PM

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balmy brook there is no step

Ok can you tell me how to do it again

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Nvm

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I ddnt know to divide

balmy brook Oct 24, 2023, 10:23 PM

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are you below 13 ?

lavish cairn Oct 24, 2023, 10:33 PM

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Can u tell me how do do it pls

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Yo

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To

lavish cairn Oct 24, 2023, 10:36 PM

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balmy brook are you below 13 ?

Why🥲

balmy brook Oct 24, 2023, 10:40 PM

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lavish cairn Why🥲

If you are then you can’t be on the server and sorry but for me it’s seems that you are below 13

lavish cairn Oct 24, 2023, 10:42 PM

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Stop pls

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I didn’t say I’m under 13..

balmy brook Oct 24, 2023, 10:43 PM

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I know

lavish cairn Oct 24, 2023, 10:43 PM

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Help pls

balmy brook Oct 24, 2023, 10:44 PM

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Do you know any rational number inferior to 1/2 or 0.5 ?

lavish cairn Oct 24, 2023, 10:44 PM

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No

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Yes 0.4 I mean

balmy brook Oct 24, 2023, 10:45 PM

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Another ?

lavish cairn Oct 24, 2023, 10:45 PM

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0.3

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0.0

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0.99

lavish cairn Oct 24, 2023, 10:46 PM

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balmy brook Another ?

0.05

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Is one

balmy brook Oct 24, 2023, 10:46 PM

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And so on

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Now you need to write it as a fraction

lavish cairn Oct 24, 2023, 10:47 PM

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How

balmy brook Oct 24, 2023, 10:48 PM

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I don’t know how to explain it so watch this instead

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https://youtu.be/xYZQaRf_Rz8?si=nRMdve8hfD20pJsU

YouTube

The Organic Chemistry Tutor

How To Convert Decimals to Fractions

This math video tutorial explains how to convert decimals to fractions. It contains a few examples and practice problems showing you how to do it.

Fractions - Basic Introduction: https://www.youtube.com/watch?v=3TklZi6MeJ4
Simplifying Fractions: https://www.youtube.co...

▶ Play video

lavish cairn Oct 24, 2023, 10:48 PM

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Ok

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They are 25/100 and 5/10?

balmy brook Oct 24, 2023, 10:52 PM

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5/10 can be simplified as 1/2

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And 25/100 as 1/4

lavish cairn Oct 24, 2023, 10:53 PM

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Ok

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What is the number in the middle?

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1/3

balmy brook Oct 24, 2023, 10:55 PM

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What number ?

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1/3 work

lavish cairn Oct 24, 2023, 10:55 PM

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Ok thx you

midnight plankBOT Oct 24, 2023, 11:25 PM

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@lavish cairn Has your question been resolved?

vale apex Oct 24, 2023, 11:29 PM

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lavish cairn Oct 24, 2023, 11:43 PM

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.close

midnight plankBOT Oct 24, 2023, 11:43 PM

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north pivot Oct 24, 2023, 11:51 PM

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midnight plankBOT Oct 24, 2023, 11:51 PM

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north pivot

north pivot Oct 24, 2023, 11:51 PM

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what concept solves this question

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so i can go study it

upper kindle Oct 24, 2023, 11:54 PM

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Substitution

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Say the root of an equation is n, that means f(n) = 0

north pivot Oct 24, 2023, 11:59 PM

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isee thanks

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.close

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midnight plankBOT Oct 25, 2023, 2:55 AM

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arctic hollow Oct 25, 2023, 3:03 AM

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midnight plankBOT Oct 25, 2023, 3:03 AM

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arctic hollow

arctic hollow Oct 25, 2023, 3:03 AM

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Uhh for the first one Im thinking like

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Actually

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Idk😭

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400c+2600e<95000

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And for the second one

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20c+120e≤470

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Wat y'all's thoughts

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Oki i got it right

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.close

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midnight plankBOT Oct 25, 2023, 3:55 AM

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olive matrix Oct 25, 2023, 3:57 AM

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a few things...
when you say "think of literally any number" and then talk about random chance you need to define a distribution for those numbers

second, i don't understand what you mean - are you trying to guess the value of lim{x->inf} 1/x by guessing randomly somehow?

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do u mean like we each guess a real number and if we guess the same number you win? you're going to run into a lot of issues here, mostly around accurately sampling a random real (not just rational) number

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ok that's what i said yeah

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how do u describe an arbitrary real number in a finite amt of time?

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you also need a distribution but the normal distribution will be fine - note that uniform distribution over the reals is meaningless

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like we each write one down right?

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how do i do that for a real number that isn't rational?

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right so how do i communicate my guess to you

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and how do you check if it's right

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painstakingly write out your guess
how

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yep

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and, in fact, is 100% likely to be

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correct but it's 0% likely to be 2

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really it's 0% likely to be any specific value

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nope

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there are more irrationals than rationals

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rationals are countable

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rationals are pairs of integers

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or really smaller than pairs of integers since like 2/3 and 4/6 are the same

next rover Oct 25, 2023, 4:07 AM

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it doesn't count again, it's 1

olive matrix Oct 25, 2023, 4:07 AM

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here's a slightly depressing video:
https://www.youtube.com/watch?v=10rA45pb7dk

YouTube

Up and Atom

You Can't Measure Time

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https://www.patreon.com/upandatom

Visit the Up and...

▶ Play video

steep ledge Oct 25, 2023, 4:10 AM

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if you only want to prove that rationals are countable and irrationals are not, then it's just the fact that rationals are and it's not hard to prove (bijection between N² and Q is obvious) and that reals are uncountable
if you want to deduce that the probability of getting rational is 0 as Miku said, it's related to the way you define the probability distribution and your measure, which you'll study later

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intuitively, the reason is that you're more or less assuming an uniform distribution, and rationals are very rare in real numbers

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their Lebesgue measure is 0

olive matrix Oct 25, 2023, 4:11 AM

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yeah but that's not relevant

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rationale is specifically one integer over another

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with some restrictions

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uh

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what about it!

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?

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yes

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it's equal to 11/12

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two integers

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watch that video

steep ledge Oct 25, 2023, 4:18 AM

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not really meaningless, it's just that you're mashing several questions together at the same time
for example take a disc of radius 1, and throw a dart at it
while it's definitely possible to hit exactly (0, 0), the center, the probability is 0

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but it is definitely possible, since your dart has to hit some point of the disc

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it's once again related to measure theory, intuitively, what happens is that a specific point of the disc represents an area of 0, it doesn't have any area and it's negligible

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so you can only put a 0 weight on it

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but if I told you what's the probability my dart touches the left half, you would have answered 1/2

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since the left half is 1/2 of my area

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when you deal with infinite possibilities, the way you define probabilities has to avoid some problems, and the way to avoid that is to think with measure theory and a somewhat geometrical approach

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if you take a random real number, it's the same idea but with "1 dimension geometry"

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while you'll necessarily get a real number, with probability one, the probability to get a specific number is 0

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it doesn't mean you won't get it, it's just the only probability you can assign to it

olive matrix Oct 25, 2023, 4:27 AM

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I'd argue that the very idea of choosing a random real number from a continuous distribution is meaningless

btw she glosses over the proof that irrationals are uncountable in that video. it's called Cantor diagonalization and it's very cool, but it requires a lot of precision so that's probably why. I'd recommend looking it up, or trying it yourself (imagine i handed you an infinitely long list of real numbers. can you construct a real number that i missed?)

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it's easy to show that the chance would have to be smaller than any given positive number

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so, the only value we can assign it is zero

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or... zero plus epsilon but that again requires a lot of precision (what's epsilon? how does it work? what can i do with it?)

steep ledge Oct 25, 2023, 4:33 AM

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intuitively, a probability of 0 means it's almost surely impossible, but not necessarily impossible
something almost surely impossible is when the "area" is 0 because it's nothing compared to the whole probability which represents an area of 1, distributed over infinitely many points
to take my example above once again, the probability that my dart hits the target is 1, but the probability it hits (0, 0) is 0
and same for hitting (0, 1) etc
the probability of hitting either (0, 0) or (0, 1) would be 0 again, because these two points still don't define an area, a consequent part of my target

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but the probability of hitting the right half would be 1/2, because now the event of hitting the right half is not negligible compared to the whole target

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what happens is that you can't compare points to length, area, or volume etc, points don't have any sort of mass (relatively to an infinite set of points), but in the end, a point is still chosen

midnight plankBOT Oct 25, 2023, 4:43 AM

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@last slate Has your question been resolved?

olive matrix Oct 25, 2023, 4:55 AM

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fun fact: if you've heard of the Halting Problem, this is directly related to the same idea

midnight plankBOT Oct 25, 2023, 4:58 AM

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robust shale Oct 25, 2023, 5:02 AM

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midnight plankBOT Oct 25, 2023, 5:02 AM

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robust shale

lyric charm Oct 25, 2023, 5:02 AM

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what's the question

robust shale Oct 25, 2023, 5:02 AM

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So

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I'm sort of confused why my book will write it like (e/3)^n but personally I find writing e^n / 3^n to think about the behavior easier. Am I missing something?

lyric charm Oct 25, 2023, 5:05 AM

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writing this as (e/3)^n makes it more blatant that this is a geometric series with ratio less than 1

robust shale Oct 25, 2023, 5:07 AM

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hmmm

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okay that's fair

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So with this ratio, wouldn't the num and denom just keep growing?

main current Oct 25, 2023, 5:14 AM

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,w geometric series

grand pondBOT Oct 25, 2023, 5:14 AM

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Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

main current Oct 25, 2023, 5:14 AM

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Huh, didn't expect wolfram to run right into the good stuff. Normally never does

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There's a closed formula for geometric series.

robust shale Oct 25, 2023, 5:16 AM

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does this look right?

main current Oct 25, 2023, 5:18 AM

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For Σ 3(e/3)^n?

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Your sum is infinite

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So you don't need the n-1 power

robust shale Oct 25, 2023, 5:21 AM

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yeah I got here and figured 3 was the a and (e/3) was the common ratio

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darn

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that's wrong

midnight plankBOT Oct 25, 2023, 5:41 AM

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@robust shale Has your question been resolved?

midnight plankBOT Oct 25, 2023, 6:11 AM

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@robust shale Has your question been resolved?

midnight plankBOT Oct 25, 2023, 7:11 AM

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@robust shale Has your question been resolved?

midnight plankBOT Oct 25, 2023, 8:11 AM

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summer hornet Oct 25, 2023, 8:33 AM

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I have an ALU that handles the subtraction of 2 binary numbers. It works well for equations like 4 - 2, 4 - 5, or anything similar. But I've decided I want to be able to switch between signed (2's complement) and unsigned. Which works well and all but let's say I was to subtract 128 from 0. The expected output would be 128, but it actually puts out -128. Because the ALU "thinks" that 128 is in 2's complement which means it would be -128. Similar examples would include 11110000 - 00000000 which is equates to -16 in signed binary but to 240 in unsigned binary, but the ALU only supports signed so it will spit out -16 regardless of the signed/unsigned input.

Okay, maybe that was a bit of a confusing question. But TL;DR: how can my ALU work with unsigned inputs? I have a flag that will tell it whether or not the input is signed or unsigned, but I'm not sure how I would process that correctly.

midnight plankBOT Oct 25, 2023, 8:33 AM

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summer hornet I have an ALU that handles the subtraction of 2 binary numbers. It works well fo...

summer hornet Oct 25, 2023, 8:38 AM

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More examples for clarification would be:
(signed) 11111000 - 00000010 = 11110110 (-8 - 2 = -10)
(unsigned) 11111000 - 00000010 = 11110110 (248 - 2 = 246)
Which would be the same but both of them have the 'negative' flag output by the ALU meaning that the unsigned bit gets interpreted as -10

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So I guess it could be solved by changing the output of the negative flag, but how could I do that (currently the negative flag is based off last bit (the 'sign' bit))

midnight plankBOT Oct 25, 2023, 8:53 AM

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@summer hornet Has your question been resolved?

summer hornet Oct 25, 2023, 8:57 AM

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<@&286206848099549185>

midnight plankBOT Oct 25, 2023, 9:27 AM

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@summer hornet Has your question been resolved?

midnight plankBOT Oct 25, 2023, 10:33 AM

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@summer hornet Has your question been resolved?

summer hornet Oct 25, 2023, 11:59 AM

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I've decided to just make my whole system signed (no more help needed)

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.close

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worthy copper Oct 25, 2023, 12:08 PM

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Help I got stuck

midnight plankBOT Oct 25, 2023, 12:08 PM

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worthy copper Help I got stuck

last slate Oct 25, 2023, 12:08 PM

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what are you supposed to find?

worthy copper Oct 25, 2023, 12:09 PM

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x

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floral gulch Oct 25, 2023, 12:10 PM

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i dont think there is an integral ans maybe taking a log would help

floral gulch Oct 25, 2023, 12:10 PM

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worthy copper

yes

worthy copper Oct 25, 2023, 12:10 PM

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floral gulch i dont think there is an integral ans maybe taking a log would help

yeah I got stuck

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I am meant to use log base 10

floral gulch Oct 25, 2023, 12:11 PM

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you can use any base

worthy copper Oct 25, 2023, 12:11 PM

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really?

worthy copper Oct 25, 2023, 12:11 PM

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worthy copper

so this is correct?

floral gulch Oct 25, 2023, 12:11 PM

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yeah finally it would produce the same result

worthy copper Oct 25, 2023, 12:12 PM

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okok

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ty

floral gulch Oct 25, 2023, 12:12 PM

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yeah simplify and verify

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np

worthy copper Oct 25, 2023, 12:12 PM

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.close

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dusky relic Oct 25, 2023, 12:23 PM

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midnight plankBOT Oct 25, 2023, 12:23 PM

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dusky relic

dusky relic Oct 25, 2023, 12:23 PM

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Is my process correct???

slender walrus Oct 25, 2023, 12:23 PM

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no

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division by $\textbf{sin}$ is mega illegal

grand pondBOT Oct 25, 2023, 12:23 PM

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ℝαμΩℕωⅤ

dusky relic Oct 25, 2023, 12:24 PM

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So what is the correct way??

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To find the value of theta?

torn compass Oct 25, 2023, 12:24 PM

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take arcsin \ sin inverse

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to remove sin

dusky relic Oct 25, 2023, 12:25 PM

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Huh?

dusky relic Oct 25, 2023, 12:25 PM

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dusky relic Huh?

We are just starting trigonometry

torn compass Oct 25, 2023, 12:25 PM

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sinx = 0
sin^-1(sinx) = sin^-1 (0)
x = 0

slender walrus Oct 25, 2023, 12:26 PM

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<@&268886789983436800>

viral oak Oct 25, 2023, 12:26 PM

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dusky relic

think of sin(x) as a function that takes in x and returns some value. you cannot say f(x) / f = x

dusky relic Oct 25, 2023, 12:27 PM

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Im solving how to make the equation equal

viral oak Oct 25, 2023, 12:27 PM

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sin or f is not a variable that you can cancel

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but you can sometimes take the inverse of a function

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(right now) you can for sin

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taking the inverse of sin(x), gives you x. and taking sin of x, gives you sin(x)

slender walrus Oct 25, 2023, 12:28 PM

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1 = 2sin(x)
dividing both sides by 2 only gives you
1/2 = sin(x)
taking sin^-1, (its the function inverse NOT the same as 1/sin which is the multiplicative inverse)
gives you one solution for x

viral oak Oct 25, 2023, 12:28 PM

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<@&268886789983436800>

next rock Oct 25, 2023, 12:29 PM

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Got them

dusky relic Oct 25, 2023, 12:30 PM

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How do I inverse the 2sin?

slender walrus Oct 25, 2023, 12:30 PM

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1 = 2sin(x)
dividing both sides by 2 only gives you
1/2 = sin(x)
taking sin^-1, (its the function inverse NOT the same as 1/sin which is the multiplicative inverse)
gives you one solution for x

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there is an excpetion in notation when that power is -1.
$$\sin^2(x) = \sin(x) \cdot \sin(x)$$
but
$$\sin^{-1}(x) \redneq \frac{1}{\sin(x)}$$

grand pondBOT Oct 25, 2023, 12:31 PM

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ℝαμΩℕωⅤ

viral oak Oct 25, 2023, 12:32 PM

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maybe arcsin is a better way of expressing it...

slender walrus Oct 25, 2023, 12:32 PM

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gives the angle of the arc from initial to terminal

viral oak Oct 25, 2023, 12:32 PM

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grand pond **ℝαμΩℕωⅤ**

this might get confusing hahah.

dusky relic Oct 25, 2023, 12:33 PM

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Wait for context we are just starting trigonometry so I don't have much knowledge yet

slender walrus Oct 25, 2023, 12:34 PM

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try finding some videos on:
special trig angles and ratios
inverse trig

dusky relic Oct 25, 2023, 12:34 PM

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slender walrus try finding some videos on: special trig angles and ratios inverse trig

Okey im going to do that

viral oak Oct 25, 2023, 12:35 PM

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dusky relic Wait for context we are just starting trigonometry so I don't have much knowledg...

in any case, since i already written this: sin of t expresses the height of this triangle, when t is some value. taking the inverse of sin t is akin to finding t. when you have $$1/2 = sin x$$, taking the inverse you write $$arcsin(1/2) = x$$. this is akin to finding the angle x, when the height of this triangle is 1/2.

grand pondBOT Oct 25, 2023, 12:36 PM

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Ab

viral oak Oct 25, 2023, 12:36 PM

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this triangle refers to the triangle in the unit circle

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: ). that's a job for the people making the calculators, lol. There are some formulas you can use to approximate the value of arcsin(x) which you can search up if you want to. you can assume it works by magic^TM, and do your calculations for now...

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(actually written this as meant to answer akio. idk your background, srry)

midnight plankBOT Oct 25, 2023, 12:49 PM

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@dusky relic Has your question been resolved?

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last slate Oct 25, 2023, 1:11 PM

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ok

midnight plankBOT Oct 25, 2023, 1:11 PM

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last slate ok

last slate Oct 25, 2023, 1:11 PM

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so i've solved the hard part of the problem

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now the part that is supposed to be trivial

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i dont understand

viral oak Oct 25, 2023, 1:12 PM

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so which problem do you mean?

last slate Oct 25, 2023, 1:12 PM

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im taking a piture of it

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didnt mean to play guessing games

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a = -2 and b = -5 and c = 0

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why is it -2 and -5

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only way it can see is if you take your answer and plug into your very first equation with constants (a,b,c)

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because then you can see why a = -2 etc, but can you not solve the problem just by looking at the last matrix

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but that seems odd to me

shell wigeon Oct 25, 2023, 1:19 PM

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Maybe it's clearer if you solve a system of equations

robust isle Oct 25, 2023, 1:20 PM

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I mean what this row reduced form tells you is that is ax_1 + bx_2 + cx_3 = (8,2,-7), then c can be whatever you want, and a+3c = -2, and b+2c = -5

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so if you want fix c=0

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you get a=-2, b=-5

last slate Oct 25, 2023, 1:20 PM

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if i suppose c = 0

robust isle Oct 25, 2023, 1:20 PM

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honestly I always think of the linear system behind even if it's just in my head

last slate Oct 25, 2023, 1:21 PM

#

then yeah sure when i re-insert into the first equation i can see its trivial

#

a + 0 + 0 = -2

robust isle Oct 25, 2023, 1:21 PM

#

otherwise I fuck it up

last slate Oct 25, 2023, 1:22 PM

#

so the row reduced form doesnt tell you it automatically

#

you have to take what you found

shell wigeon Oct 25, 2023, 1:22 PM

#

Tbh you only need to know that the three vectors form a basis; you can get any vector from them

robust isle Oct 25, 2023, 1:22 PM

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they don't form a basis here lol

shell wigeon Oct 25, 2023, 1:23 PM

#

Oh true my mistake

last slate Oct 25, 2023, 1:24 PM

#

but why must it be c

#

that is 0

#

the first equation is (a,b,c) and then repeated

#

why do i now assume its (c,c,c) = 0?

robust isle Oct 25, 2023, 1:25 PM

#

the 3rd row of the row reduced form tells you no information

#

0 = 0

last slate Oct 25, 2023, 1:26 PM

#

i know

robust isle Oct 25, 2023, 1:26 PM

#

so one of a, b, c can be treated as a free variable

last slate Oct 25, 2023, 1:26 PM

#

but why doesnt that say then a + b + c = 0

robust isle Oct 25, 2023, 1:26 PM

#

there's infinitely many possible lin combos that work

#

(a,b,c) = (-2, -5, 0), (a,b,c) = (-5, -7, 1), (a,b,c) = (-8, -9, 2), ...

#

for each c, you get a lin combo

last slate Oct 25, 2023, 1:32 PM

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yes but from this picture alone

#

or does this picture only tell me there is on x3=x3

#

so there is one free varaibel

robust isle Oct 25, 2023, 1:33 PM

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well yeah

#

the last row represents 0a+0b+0c=0

#

so you only really have 2 linear equations to satisfy

#

(the 2 upper rows)

last slate Oct 25, 2023, 1:34 PM

#

yh

midnight plankBOT Oct 25, 2023, 1:49 PM

#

@last slate Has your question been resolved?

midnight plankBOT Oct 25, 2023, 2:04 PM

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spiral copper Oct 25, 2023, 6:53 PM

#

not really sure how to solve for b and theta in this problem

#

https://gyazo.com/2b3f52748a688a3eaa9fa3d2912ec43c

Gyazo

midnight plankBOT Oct 25, 2023, 6:53 PM

#

spiral copper not really sure how to solve for b and theta in this problem

spiral copper Oct 25, 2023, 6:54 PM

#

I know I use toa to solve B, but I'm not too sure how to get theta

midnight plankBOT Oct 25, 2023, 7:09 PM

#

@spiral copper Has your question been resolved?

midnight plankBOT Oct 25, 2023, 7:48 PM

#

@spiral copper Has your question been resolved?

unique cedar Oct 25, 2023, 7:52 PM

#

Gyazo is not supported for my iPad but just by your response, to solve theta do inverse tangent and divide b by 20

midnight plankBOT Oct 25, 2023, 8:18 PM

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upbeat herald Oct 25, 2023, 8:42 PM

#

midnight plankBOT Oct 25, 2023, 8:42 PM

#

upbeat herald

upbeat herald Oct 25, 2023, 8:42 PM

#

Dont understand how to do this one (similar figures)

#

First, I thought to do 4/x = 3/5

#

To get x = 20/3 but thats wrong

#

answer in back of the book says it's root x = 31 - 1

sour kelp Oct 25, 2023, 8:44 PM

#

Are you let; x=a?

upbeat herald Oct 25, 2023, 8:44 PM

#

wdym

viral laurel Oct 25, 2023, 8:44 PM

#

huh, getting to the same answer as you

sour kelp Oct 25, 2023, 8:44 PM

#

The angle is a

#

~~Not x ;-; (minor mistake lul)~~

upbeat herald Oct 25, 2023, 8:44 PM

#

oh you mean next to 5 cm? yeah, it's just supposed to show that both triangles are similar

sour kelp Oct 25, 2023, 8:44 PM

#

Oh wait nvm are we solving for x?

upbeat herald Oct 25, 2023, 8:44 PM

#

sour kelp Oh wait nvm are we solving for x?

yes

sour kelp Oct 25, 2023, 8:45 PM

#

ah I understand

upbeat herald Oct 25, 2023, 8:46 PM

#

im losing

#

mcfuckin mind

viral laurel Oct 25, 2023, 8:50 PM

#

Seems like your solution is correct.

upbeat herald Oct 25, 2023, 8:50 PM

#

yeah but

#

book says it's root 31 - 1

viral laurel Oct 25, 2023, 8:50 PM

#

Author can make mistakes

upbeat herald Oct 25, 2023, 8:50 PM

#

this book doesn't have a single mistake

#

screw it, ill talk to the teacher tomorrow

viral laurel Oct 25, 2023, 8:52 PM

#

Checked with example in geogebra, seems to be right...

shell wigeon Oct 25, 2023, 8:52 PM

#

Perhaps it's the answer to another question

viral laurel Oct 25, 2023, 8:53 PM

#

upbeat herald this book doesn't have a single mistake

Happens

upbeat herald Oct 25, 2023, 8:55 PM

#

.closed

#

.close

midnight plankBOT Oct 25, 2023, 8:55 PM

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fading hull Oct 26, 2023, 12:08 AM

#

Can someone explain where I went wrong because I got dne (does not exist) as the answer but it’s wrong

midnight plankBOT Oct 26, 2023, 12:08 AM

#

fading hull Can someone explain where I went wrong because I got dne (does not exist) as the...

hearty rune Oct 26, 2023, 12:09 AM

#

you cant take ln of each thing

lavish venture Oct 26, 2023, 12:11 AM

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use lhopital

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i mean really e^2x increases faster

#

so u just get infinity

#

but yea use lhopital

#

differentiate the top and bottom three times

#

u would get 8e^2x/ 6

#

so infinity

midnight plankBOT Oct 26, 2023, 12:14 AM

#

lavish venture so infinity

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

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last slate Oct 26, 2023, 12:29 AM

#

If 1/x + x = 3, then 1/(x^2) + x^2 =

midnight plankBOT Oct 26, 2023, 12:29 AM

#

last slate If 1/x + x = 3, then 1/(x^2) + x^2 =

last slate Oct 26, 2023, 12:29 AM

#

i tried solving for x, but that got me no where

#

i tried multiplying 1/x by x/x, so that I could have (x^2) in the denominator, but that didn't do anything

#

now i don't know what to do

#

please help

#

i'm sped as fuck

#

.close

midnight plankBOT Oct 26, 2023, 12:32 AM

#

Channel closed

Closed by @zealous forum

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last slate Oct 26, 2023, 12:33 AM

#

.reopen

midnight plankBOT Oct 26, 2023, 12:33 AM

#

✅

last slate Oct 26, 2023, 12:33 AM

#

this was so easyu

#

just use (a+b)^2 formula

#

.close

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cosmic river Oct 26, 2023, 12:43 AM

#

midnight plankBOT Oct 26, 2023, 12:43 AM

#

cosmic river

tacit rose Oct 26, 2023, 12:44 AM

#

cosmic river

Rationalize

#

Multiply 1/sqrt(3) by sqrt(3)/sqrt(3)

cosmic river Oct 26, 2023, 12:45 AM

#

what does rationalize mean

hearty rune Oct 26, 2023, 12:45 AM

#

make the denominator a rational number

#

rather than an irrational one

tacit rose Oct 26, 2023, 12:46 AM

#

It's just the process to eliminate radicals in the denominator

cosmic river Oct 26, 2023, 12:49 AM

#

ok thanks

midnight plankBOT Oct 26, 2023, 1:04 AM

#

@cosmic river Has your question been resolved?

midnight plankBOT Oct 26, 2023, 1:19 AM

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hardy shadow Oct 26, 2023, 1:23 AM

#

Given that I know all the green lengths and angles, I need to solve for theta1 for my final answer in terms of a difference of arctangents, I know if I find alpha I can get it, but I'm currently stuck and don't know what step I should take next

midnight plankBOT Oct 26, 2023, 1:23 AM

#

hardy shadow Given that I know all the green lengths and angles, I need to solve for theta1 f...

hardy shadow Oct 26, 2023, 1:24 AM

#

This is the question if anyone wants to read it as well

#

I've found $\cos(\theta_2)=\frac{(a_1)^2+(a_2)^2-x^2-y^2}{2a_1a_2}$

grand pondBOT Oct 26, 2023, 1:26 AM

#

Ninja

midnight plankBOT Oct 26, 2023, 1:41 AM

#

@hardy shadow Has your question been resolved?

midnight plankBOT Oct 26, 2023, 2:11 AM

#

@hardy shadow Has your question been resolved?

last slate Oct 26, 2023, 2:33 AM

#

you can ping the helpers

#

this is beyond my knowledge

#

try pinging them

midnight plankBOT Oct 26, 2023, 3:11 AM

#

@hardy shadow Has your question been resolved?

hardy shadow Oct 26, 2023, 3:11 AM

#

<@&286206848099549185>

hardy shadow Oct 26, 2023, 3:47 AM

#

.close

midnight plankBOT Oct 26, 2023, 3:47 AM

#

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last slate Oct 26, 2023, 3:51 AM

#

1+j to polar form

midnight plankBOT Oct 26, 2023, 3:51 AM

#

last slate 1+j to polar form

last slate Oct 26, 2023, 3:51 AM

#

how would I do that?

hearty rune Oct 26, 2023, 3:52 AM

#

do you know polar form?

last slate Oct 26, 2023, 3:55 AM

#

yes

#

I think

#

this right?

midnight plankBOT Oct 26, 2023, 4:11 AM

#

@last slate Has your question been resolved?

hearty rune Oct 26, 2023, 4:52 AM

#

yeah, sorry for my disappearance

#

do you know what r and theta are

midnight plankBOT Oct 26, 2023, 5:02 AM

#

@last slate Has your question been resolved?

midnight plankBOT Oct 26, 2023, 5:32 AM

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Channel closed

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waxen silo Oct 26, 2023, 5:38 AM

#

if f(2) = 4 does that mean the inverse will be f^-1(4)=2

midnight plankBOT Oct 26, 2023, 5:38 AM

#

waxen silo if f(2) = 4 does that mean the inverse will be f^-1(4)=2

hearty rune Oct 26, 2023, 5:40 AM

#

yes

fallen socket Oct 26, 2023, 5:40 AM

#

No

sick fossil Oct 26, 2023, 5:40 AM

#

waxen silo if f(2) = 4 does that mean the inverse will be f^-1(4)=2

There may not be an inverse

fallen socket Oct 26, 2023, 5:40 AM

#

f need not be an invertible function

sick fossil Oct 26, 2023, 5:40 AM

#

But if there is, then you're right

hearty rune Oct 26, 2023, 5:41 AM

#

ive been kerboodled, the lack of sleep is killing me, but ive come too far

waxen silo Oct 26, 2023, 5:51 AM

#

hold on I thought I didn't have the question but I found it

#

#

its part ii)

#

i explained why f(x) is an inverse because its an lnx graph

main current Oct 26, 2023, 5:52 AM

#

Problem is, it isn't. It's a 2x + ln(x) graph

waxen silo Oct 26, 2023, 5:53 AM

#

but it passes the horizontal line test

main current Oct 26, 2023, 5:53 AM

#

How do you know?

waxen silo Oct 26, 2023, 5:53 AM

#

because I graphed it on desmos

main current Oct 26, 2023, 5:53 AM

#

Any way you can prove it without using Desmos?

waxen silo Oct 26, 2023, 5:54 AM

#

all values of y have one corresponding x value

#

which allows it have an inverse

main current Oct 26, 2023, 5:55 AM

#

That's the definition of an invertible function, true! How do you know this function in particular is invertible?

waxen silo Oct 26, 2023, 5:55 AM

#

I saw it an it has ln in it

main current Oct 26, 2023, 5:56 AM

#

Note f(x) = ln(x) - 2x is not invertible

#

So if it passes a horizontal line test, then it for sure has no maximums or minimums

waxen silo Oct 26, 2023, 5:56 AM

#

I don't know then

main current Oct 26, 2023, 5:57 AM

#

Well, let me rephrase. If the function has a local maximum, then right below that maximum is a spot the function would fail a horizontal line test

waxen silo Oct 26, 2023, 5:58 AM

#

yes but this graph has no maximum or minimum

#

due to the nature of a log graph

main current Oct 26, 2023, 5:58 AM

#

If f has no local maximums/minimums, and is continuous on the domain, then it's gotta be invertible

#

Note that f(x) = ln(x) - 2x has a maximum

waxen silo Oct 26, 2023, 5:59 AM

#

but its 2x + lnx

main current Oct 26, 2023, 5:59 AM

#

waxen silo due to the nature of a log graph

Right. Just, recognizing a log isn't enough to say whether there's a maximum or minimum.

waxen silo Oct 26, 2023, 6:00 AM

#

its 1 mark

#

how much info do they need

#

also I want ii) to be answered

#

did my logic work out right in this context

#

becaue I got g'(2)=1

#

.close

midnight plankBOT Oct 26, 2023, 6:11 AM

#

Channel closed

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near ravine Oct 26, 2023, 6:14 AM

#

HELP

midnight plankBOT Oct 26, 2023, 6:14 AM

#

near ravine HELP

near ravine Oct 26, 2023, 6:14 AM

#

alr

lyric charm Oct 26, 2023, 6:14 AM

#

you should post your question rather than just yell "HELP"

near ravine Oct 26, 2023, 6:14 AM

#

oh mb

#

i am sorry

#

#

I need some assitance on fidning

#

angle number 3 in the middle row

lyric charm Oct 26, 2023, 6:15 AM

#

so part b, angle 3?

near ravine Oct 26, 2023, 6:15 AM

#

Yes.

lyric charm Oct 26, 2023, 6:16 AM

#

will be easier if we give names to things

#

give me a minute

near ravine Oct 26, 2023, 6:16 AM

#

alright

lyric charm Oct 26, 2023, 6:16 AM

#

you found angle 2 already

near ravine Oct 26, 2023, 6:17 AM

#

yes

#

122 degrees

lyric charm Oct 26, 2023, 6:17 AM

#

#

look at triangle BCD

near ravine Oct 26, 2023, 6:17 AM

#

Yes

lyric charm Oct 26, 2023, 6:17 AM

#

do you notice anything about it

near ravine Oct 26, 2023, 6:17 AM

#

ik that there are 2 congruent tick marks

lyric charm Oct 26, 2023, 6:18 AM

#

indeed, two of the sides are congruent

#

what does this mean

near ravine Oct 26, 2023, 6:18 AM

#

lyric charm Oct 26, 2023, 6:18 AM

#

yes those are the congruent sides

#

what do we call a triangle with two congruent sides?

near ravine Oct 26, 2023, 6:18 AM

#

Isoceles?

lyric charm Oct 26, 2023, 6:18 AM

#

isosceles, yes

near ravine Oct 26, 2023, 6:18 AM

#

noice

lyric charm Oct 26, 2023, 6:18 AM

#

you've already used the main property of isosceles triangles on ABC to find angle 1

#

do it again in the same fashion

near ravine Oct 26, 2023, 6:19 AM

#

ohh

#

so

#

180-122

#

58

#

58/2

#

#

Thank you

#

I have one more question sorry

lyric charm Oct 26, 2023, 6:20 AM

#

yes?

near ravine Oct 26, 2023, 6:20 AM

#

this one will be on my test so I have to really study this one

#

I dont know anyting baout it

#

lyric charm Oct 26, 2023, 6:20 AM

#

oh god two col proofs

near ravine Oct 26, 2023, 6:20 AM

#

this one really confuses me

lyric charm Oct 26, 2023, 6:21 AM

#

uh yeah sorry i am not touching this lmao

#

best if you open a new channel w/ this question though

near ravine Oct 26, 2023, 6:21 AM

#

oh alr

lyric charm Oct 26, 2023, 6:21 AM

#

so just .close this one and repost that pic in a new channel

near ravine Oct 26, 2023, 6:21 AM

#

so

#

open it

#

in help 10

#

.close

midnight plankBOT Oct 26, 2023, 6:22 AM

#

Channel closed

Closed by @near ravine

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whole moon Oct 26, 2023, 7:03 AM

#

The questions are in regards to those with a question mark next to it.
I don't understand how to find where a function is odd or even about. For "normal" functions i can just check whether f(-x) = f(x) and so on.

midnight plankBOT Oct 26, 2023, 7:03 AM

#

whole moon The questions are in regards to those with a question mark next to it. I don't u...

verbal rain Oct 26, 2023, 7:06 AM

#

even means f(x) = f(-x)
odd means f(-x) = -f(x)

whole moon Oct 26, 2023, 7:08 AM

#

But how do i figure out at which point a certain figure is odd or even about? If you look at 15. It says it's odd about (2,0)

verbal rain Oct 26, 2023, 7:09 AM

#

i guess by about it means using that value as the origin of symmetry

#

origin for odd, axis for even.

#

so for (15), when x = 2, thats obv the asymptote

whole moon Oct 26, 2023, 7:12 AM

#

.close

midnight plankBOT Oct 26, 2023, 7:12 AM

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Channel closed

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midnight plankBOT Oct 26, 2023, 6:09 PM

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hallow mauve Oct 26, 2023, 6:14 PM

#

hi

midnight plankBOT Oct 26, 2023, 6:14 PM

#

hallow mauve hi

hallow mauve Oct 26, 2023, 6:14 PM

#

can someone pls help me with this?

#

midnight plankBOT Oct 26, 2023, 6:29 PM

#

@hallow mauve Has your question been resolved?

hallow mauve Oct 26, 2023, 6:29 PM

#

<@&286206848099549185>

midnight plankBOT Oct 26, 2023, 6:59 PM

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@hallow mauve Has your question been resolved?

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hallow mauve Oct 26, 2023, 7:36 PM

#

.reopen

grizzled lance Oct 26, 2023, 8:26 PM

#

midnight plankBOT Oct 26, 2023, 8:26 PM

#

grizzled lance

grizzled lance Oct 26, 2023, 8:26 PM

#

@storm spindle

#

I think I solved A2 and A3

#

but im lost on a1

storm spindle Oct 26, 2023, 8:27 PM

#

grizzled lance I think I solved A2 and A3

Yeah those seem to be the easy ones 😅

#

Could have certainly helped you with those

#

Imma try my luck on the first one though

grizzled lance Oct 26, 2023, 8:27 PM

#

I appreciate it

#

theres also this which I havent looked at yet, so idk how hard it is

#

I'll attempt it after we tackle A1

storm spindle Oct 26, 2023, 8:28 PM

#

grizzled lance theres also this which I havent looked at yet, so idk how hard it is

Looks reasonably simple at first glance

#

Not as easy as A2 and A3 though

midnight plankBOT Oct 26, 2023, 8:42 PM

#

@grizzled lance Has your question been resolved?

storm spindle Oct 26, 2023, 8:52 PM

#

grizzled lance

Yeah A1 is very difficult

#

Lol nvm

#

😂

#

It’s super easy once you take the right approach

midnight plankBOT Oct 26, 2023, 8:57 PM

#

Channel closed

Closed due to timeout

Use .reopen if this was a mistake.

storm spindle Oct 26, 2023, 8:58 PM

#

@grizzled lance

#

Reopen this ffs

#

@grizzled lance fast

midnight plankBOT Oct 26, 2023, 8:58 PM

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#

daring lark Oct 26, 2023, 9:02 PM

#

Am i on the right track? Or am i not going anywhere

#

Oh wait i did a mistake

midnight plankBOT Oct 26, 2023, 9:03 PM

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Channel closed

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midnight plankBOT Oct 26, 2023, 9:20 PM

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tiny gate Oct 26, 2023, 9:28 PM

#

If I want to determine if a matrix B is orthogonal, is it sufficient to use B x It’s transpose= identity matrix

midnight plankBOT Oct 26, 2023, 9:28 PM

#

tiny gate If I want to determine if a matrix B is orthogonal, is it sufficient to use B x ...

hazy bear Oct 26, 2023, 9:29 PM

#

tiny gate If I want to determine if a matrix B is orthogonal, is it sufficient to use B x ...

it is sufficient to check if B times its transpose (B^T) equals the identity matrix (I)

#

the product of the matrix and its transpose is the identity matrix

tiny gate Oct 26, 2023, 9:31 PM

#

Thank you

#

.close

midnight plankBOT Oct 26, 2023, 9:35 PM

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crude lichen Oct 26, 2023, 9:51 PM

#

how do i get cos(y) - 1. because sin(x + y) - sin(x) = sin(y) shouldnt the same relationship be for cos(x + y) - cos(x)?

midnight plankBOT Oct 26, 2023, 9:51 PM

#

crude lichen how do i get cos(y) - 1. because sin(x + y) - sin(x) = sin(y) shouldnt the same ...

crude lichen Oct 26, 2023, 9:54 PM

#

.close

midnight plankBOT Oct 26, 2023, 9:54 PM

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midnight plankBOT Oct 26, 2023, 11:47 PM

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remote fossil Oct 26, 2023, 11:50 PM

#

I’m not sure if I’m losing my mind or what but I completely forgot how to simplify this

midnight plankBOT Oct 26, 2023, 11:50 PM

#

remote fossil I’m not sure if I’m losing my mind or what but I completely forgot how to simpli...

remote fossil Oct 26, 2023, 11:50 PM

#

And the few Answers said I was wrong

#

Sooo 😅

blissful trench Oct 26, 2023, 11:50 PM

#

remote fossil I’m not sure if I’m losing my mind or what but I completely forgot how to simpli...

Use exponent rules

remote fossil Oct 26, 2023, 11:51 PM

#

These?

blissful trench Oct 26, 2023, 11:51 PM

#

Yes

remote fossil Oct 26, 2023, 11:51 PM

#

Oh ok

#

Thanks!

#

.close

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midnight plankBOT Oct 27, 2023, 2:58 AM

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gilded chasm Oct 27, 2023, 3:09 AM

#

Solve for x.```

midnight plankBOT Oct 27, 2023, 3:09 AM

#

gilded chasm ```3^(2x-5) = 87 Solve for x.```

gilded chasm Oct 27, 2023, 3:11 AM

#

ive been told that you have to find a common base but 87 isnt perfect

#

nvm

#

.close

midnight plankBOT Oct 27, 2023, 3:17 AM

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Channel closed

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tidal ice Oct 27, 2023, 3:56 AM

#

midnight plankBOT Oct 27, 2023, 3:56 AM

#

tidal ice

tidal ice Oct 27, 2023, 3:56 AM

#

Unsure about this question.

#

I know that s = r(theta)

#

Let me send a screenshot of the previous question since they're all connected.

#

cosmic elk Oct 27, 2023, 3:57 AM

#

tidal ice I know that s = r(theta)

right

#

you have arc length and you can find radius by dividing diameter by 2

tidal ice Oct 27, 2023, 3:57 AM

#

560/2

#

r = 260

cosmic elk Oct 27, 2023, 3:58 AM

#

ya

tidal ice Oct 27, 2023, 3:58 AM

#

1478.8 = 260(theta)

#

divide both sides by 260?

cosmic elk Oct 27, 2023, 3:58 AM

#

mhm

cosmic elk Oct 27, 2023, 3:59 AM

#

tidal ice 1478.8 = 260(theta)

*1474.8

tidal ice Oct 27, 2023, 3:59 AM

#

I got 5.672307692

#

good?

cosmic elk Oct 27, 2023, 4:00 AM

#

,calc 1474.8/260

grand pondBOT Oct 27, 2023, 4:00 AM

#

Result:

5.6723076923077

cosmic elk Oct 27, 2023, 4:00 AM

#

yeah

tidal ice Oct 27, 2023, 4:00 AM

#

Is that it?

cosmic elk Oct 27, 2023, 4:00 AM

#

now it wants you to convert to degrees

tidal ice Oct 27, 2023, 4:00 AM

#

Is it already not in degrees?

cosmic elk Oct 27, 2023, 4:00 AM

#

nope, s = r(theta) is where theta is in radians

tidal ice Oct 27, 2023, 4:01 AM

#

So we multiply by pi/180

#

,calc (1474.8/260) * pi/180

cosmic elk Oct 27, 2023, 4:01 AM

#

180/pi

grand pondBOT Oct 27, 2023, 4:01 AM

#

Result:

0.099000445416971

tidal ice Oct 27, 2023, 4:01 AM

#

oops.

#

,calc (1474.8/260) * 180/pi

grand pondBOT Oct 27, 2023, 4:02 AM

#

Result:

324.99929086882

cosmic elk Oct 27, 2023, 4:02 AM

#

yep

tidal ice Oct 27, 2023, 4:02 AM

#

then round to the nearest degree?

cosmic elk Oct 27, 2023, 4:02 AM

#

yeah ig

tidal ice Oct 27, 2023, 4:02 AM

#

Thanks!

cosmic elk Oct 27, 2023, 4:02 AM

#

np

tidal ice Oct 27, 2023, 4:02 AM

#

.close

midnight plankBOT Oct 27, 2023, 4:02 AM

#

Channel closed

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midnight plankBOT Oct 29, 2023, 5:59 PM

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wary mauve Oct 29, 2023, 6:00 PM

#

Hello can someone help me figure out how to start simplifying this

midnight plankBOT Oct 29, 2023, 6:00 PM

#

wary mauve Hello can someone help me figure out how to start simplifying this

wary mauve Oct 29, 2023, 6:00 PM

#

potent veldt Oct 29, 2023, 6:01 PM

#

Google trig identities catthumbsup

#

Specifically for cos(pi - x) and sin(pi - x)

wary mauve Oct 29, 2023, 6:02 PM

#

okay

steep hinge Oct 29, 2023, 6:02 PM

#

or use $sin(a+b)=sin(a)cos(b)+sin(b)cos(a)$

grand pondBOT Oct 29, 2023, 6:02 PM

#

everg

wary mauve Oct 29, 2023, 6:03 PM

#

no thats not the same?

#

wait

potent veldt Oct 29, 2023, 6:03 PM

#

Yeah that works too

steep hinge Oct 29, 2023, 6:03 PM

#

in this case $\pi-x+x=\pi$ and $sin(\pi)=0$

grand pondBOT Oct 29, 2023, 6:03 PM

#

everg

steep hinge Oct 29, 2023, 6:03 PM

#

wary mauve no thats not the same?

i used a,b general real numbers

potent veldt Oct 29, 2023, 6:03 PM

#

steep hinge in this case $\pi-x+x=\pi$ and $sin(\pi)=0$

Don't give away sols

wary mauve Oct 29, 2023, 6:03 PM

#

nono yea it wasnt the letters

potent veldt Oct 29, 2023, 6:03 PM

#

!nosols

wary mauve Oct 29, 2023, 6:03 PM

#

i realized after that the order of sin and cos doesnt matter

midnight plankBOT Oct 29, 2023, 6:03 PM

#

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

steep hinge Oct 29, 2023, 6:04 PM

#

potent veldt Don't give away sols

sura don t copy my answer pls

wary mauve Oct 29, 2023, 6:04 PM

#

i wont 😭

steep hinge Oct 29, 2023, 6:04 PM

#

you have a brain that works quite well

potent veldt Oct 29, 2023, 6:04 PM

#

idr if u do it now but don't do it in the future

#

Idrc

wary mauve Oct 29, 2023, 6:04 PM

#

steep hinge you have a brain that works quite well

i like to believe so

#

thank yall

#

.close

midnight plankBOT Oct 29, 2023, 6:04 PM

#

Channel closed

Closed by @wary mauve

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steep hinge Oct 29, 2023, 6:05 PM

#

sure you 'll go to mac donald if you copy the answer

potent veldt Oct 29, 2023, 6:05 PM

#

Should I call mods everg I'm

#

U don't seem to be taking it seriously

#

wasn't gonna bother but

wary mauve Oct 29, 2023, 6:05 PM

#

bro is freaking out

#

it's not a big deal at least I know how to solve it now

potent veldt Oct 29, 2023, 6:06 PM

#

ik

wary mauve Oct 29, 2023, 6:06 PM

#

and they didnt tell me to google

potent veldt Oct 29, 2023, 6:06 PM

#

Idc bout u getting this sol

#

Is that hes gonna do it again

wary mauve Oct 29, 2023, 6:06 PM

#

omg

#

i closed the channel

steep hinge Oct 29, 2023, 6:08 PM

#

992qqoloy wdym with Idrc?

potent veldt Oct 29, 2023, 6:08 PM

#

I don't rly care if u made the mistake of giving a sol from like not knowing

#

just that u don't seem to care bout not doing it in the future

#

Cus u were being all facetiosu

midnight plankBOT Oct 29, 2023, 6:10 PM

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potent veldt Oct 29, 2023, 6:10 PM

#

Basically idrc means I wanna give u the benefit of the doubt this time

midnight plankBOT Oct 29, 2023, 6:10 PM

#

potent veldt Basically idrc means I wanna give u the benefit of the doubt this time

steep hinge Oct 29, 2023, 6:10 PM

#

potent veldt Cus u were being all facetiosu

i am always facetiosu ...so they are indipendent events

potent veldt Oct 29, 2023, 6:10 PM

#

.close

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#

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last slate Oct 29, 2023, 6:29 PM

#

midnight plankBOT Oct 29, 2023, 6:29 PM

#

last slate

last slate Oct 29, 2023, 6:30 PM

#

WOuld this be correct

#

i am a bit uncertain :/

still rose Oct 29, 2023, 6:32 PM

#

that looks correct to me

last slate Oct 29, 2023, 6:32 PM

#

bit uncertain since it says -gradientV

still rose Oct 29, 2023, 6:32 PM

#

ah then just make it negative

#

that's just physics semantics lol

last slate Oct 29, 2023, 6:33 PM

#

feel like there should be negative sign in front of y^2/2

still rose Oct 29, 2023, 6:33 PM

#

use the definition when in doubt

last slate Oct 29, 2023, 6:33 PM

#

what branch of math is this under?

#

i have not seen this before yet it is a question

still rose Oct 29, 2023, 6:33 PM

#

multivar calc and/or physics

#

this is a fundamental law of multivar calc

#

for instance, let's say you have a curve

#

it's wonky, crazy, you know it starts as r_0, ends at r_1, and goes through a conservative vector field F

last slate Oct 29, 2023, 6:35 PM

#

conservative vector field

#

so it only cares about intial and final

still rose Oct 29, 2023, 6:35 PM

#

if you can find some f such that Δf = F, then instead of integrating along the curve, you can simply do f(r_1)-f(r_0)

#

whereas a non-conservative one will require you to suffer because the path matters and you have to parametricize it and suffer

last slate Oct 29, 2023, 6:37 PM

#

alright

#

what kind of math vidoes can i watch get the intution down?

#

what ought i search online?

midnight plankBOT Oct 29, 2023, 6:52 PM

#

@last slate Has your question been resolved?

fallow scarab Oct 29, 2023, 6:52 PM

#

Just do a bunch of problems

#

From your class's textbook preferably

#

Then search YouTube for example solved problems

last slate Oct 29, 2023, 6:54 PM

#

there arent any

#

i only knew what −∇V meant as assumed you should do as i did

midnight plankBOT Oct 29, 2023, 7:07 PM

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Channel closed

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last slate Oct 29, 2023, 7:14 PM

#

Can I use combinatorics to solve this problem?

midnight plankBOT Oct 29, 2023, 7:14 PM

#

last slate Can I use combinatorics to solve this problem?

last slate Oct 29, 2023, 7:15 PM

#

Could i use number theory?

#

I have a set of integers and I want to split them into three subsets with equal value ( the elements within sum to the same value )

main current Oct 29, 2023, 7:16 PM

#

<@&268886789983436800>

#

Thx ilu

#

@last slate
Basically no, because we can't make any assumptions about the input vector

last slate Oct 29, 2023, 7:19 PM

#

main current <@&268886789983436800>

what happened here

main current Oct 29, 2023, 7:19 PM

#

Advertiser

last slate Oct 29, 2023, 7:22 PM

#

main current <@456226577798135808> Basically no, because we can't make any assumptions about...

What field of mathematics do you think I can use?

main current Oct 29, 2023, 7:25 PM

#

Are you having trouble with the programming challenge?

last slate Oct 29, 2023, 7:26 PM

#

main current Are you having trouble with the programming challenge?

hmmCat I am trying not to program and instead just use math

#

simpler

#

i think

main current Oct 29, 2023, 7:27 PM

#

It's too random of a problem for math. We don't really know anything about this array, and can't say anything about this array

last slate Oct 29, 2023, 7:29 PM

#

What if I was to use the input to create a prefix sum array?

#

idk

#

Okay nvm

#

I guess I do have to program

#

I think I know a way to solve using prefix sum arrays and two pointers

#

TY for help

#

.close

midnight plankBOT Oct 29, 2023, 7:31 PM

#

Channel closed

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midnight plankBOT Oct 29, 2023, 7:50 PM

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halcyon escarp Oct 29, 2023, 8:09 PM

#

i need help on practicing plugging in my transformation. I always get the B incorrectly, so i want someone to explain how to plug it in correctly.

my step:
k(x) = 1/2 (3(x-4)-4
k(x) = 1/2 (3x-12)-4
k(x) = 3/2x-10 (my answer)

answer is y = 3/2x-6

midnight plankBOT Oct 29, 2023, 8:09 PM

#

halcyon escarp i need help on practicing plugging in my transformation. I always get the B inco...

fresh sparrow Oct 29, 2023, 8:11 PM

#

halcyon escarp i need help on practicing plugging in my transformation. I always get the B inco...

f(x)=3x-4, not 3(x-4)

#

that's the mistake

halcyon escarp Oct 29, 2023, 8:12 PM

#

fresh sparrow f(x)=3x-4, not 3(x-4)

i thought that the 3 was the b

fresh sparrow Oct 29, 2023, 8:12 PM

#

read the f(x) carefully

fresh sparrow Oct 29, 2023, 8:13 PM

#

halcyon escarp i thought that the 3 was the b

also this is so incomprehensible lol

halcyon escarp Oct 29, 2023, 8:13 PM

#

so

1/2 (3x-4)-4

fresh sparrow Oct 29, 2023, 8:13 PM

#

firstly you need to have the understanding

#

then cheatsheets

fresh sparrow Oct 29, 2023, 8:13 PM

#

halcyon escarp so 1/2 (3x-4)-4

yep

halcyon escarp Oct 29, 2023, 8:13 PM

#

OH I GOT IT NOW

fresh sparrow Oct 29, 2023, 8:13 PM

#

just like that

halcyon escarp Oct 29, 2023, 8:13 PM

#

alright give me a question

fresh sparrow Oct 29, 2023, 8:13 PM

#

like a random question?..

halcyon escarp Oct 29, 2023, 8:13 PM

#

uhhh sure

fresh sparrow Oct 29, 2023, 8:14 PM

#

halcyon escarp alright give me a question

or like wdym lol

#

some random question about function tranformations?

halcyon escarp Oct 29, 2023, 8:14 PM

#

nvm, i have a practice paper for transformation

#

it all good

#

thanks for the help

#

.close

midnight plankBOT Oct 29, 2023, 8:14 PM

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Channel closed

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unique cedar Oct 29, 2023, 8:22 PM

#

hi

midnight plankBOT Oct 29, 2023, 8:22 PM

#

unique cedar hi

unique cedar Oct 29, 2023, 8:23 PM

#

#

what does a^c mean in terms of sets

fresh sparrow Oct 29, 2023, 8:23 PM

#

complement

#

basically everything that is not in a

unique cedar Oct 29, 2023, 8:23 PM

#

ok. Thank you so much

#

.close

midnight plankBOT Oct 29, 2023, 8:23 PM

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Channel closed

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left hinge Oct 29, 2023, 8:38 PM

#

midnight plankBOT Oct 29, 2023, 8:38 PM

#

left hinge

left hinge Oct 29, 2023, 8:38 PM

#

pls help

olive path Oct 29, 2023, 8:40 PM

#

Taylor series?

left hinge Oct 29, 2023, 8:42 PM

#

I'm not sure

#

I need to expand until I get a coefficient with x^3 but idk where to start

midnight plankBOT Oct 29, 2023, 8:57 PM

#

@left hinge Has your question been resolved?

left hinge Oct 29, 2023, 8:58 PM

#

<@&286206848099549185>

wintry cave Oct 29, 2023, 9:03 PM

#

left hinge

did they give the value of the point of the series expansion ??

left hinge Oct 29, 2023, 9:13 PM

#

wintry cave did they give the value of the point of the series expansion ??

no

#

idk if its Taylor series, binomial expansion perhaps?

wintry cave Oct 29, 2023, 9:18 PM

#

it says series expansion

midnight plankBOT Oct 29, 2023, 9:46 PM

#

@left hinge Has your question been resolved?

midnight plankBOT Oct 29, 2023, 10:46 PM

#

@left hinge Has your question been resolved?

midnight plankBOT Oct 29, 2023, 11:46 PM

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idle briar Oct 29, 2023, 11:49 PM

#

im confused by this

midnight plankBOT Oct 29, 2023, 11:49 PM

#

idle briar im confused by this

idle briar Oct 29, 2023, 11:49 PM

#

#

here the context btw

#

MY FICTIOUS AMOUNT IS 19837 SO IM wondering if this method for iii is correct

midnight plankBOT Oct 30, 2023, 12:09 AM

#

@idle briar Has your question been resolved?

dense idol Oct 30, 2023, 12:46 AM

#

yeah part 3 looks right
but for part 2, i'd assume that the 10% deposit is on the price of the car, not on how much money you have

midnight plankBOT Oct 30, 2023, 12:56 AM

#

@idle briar Has your question been resolved?

midnight plankBOT Oct 30, 2023, 1:26 AM

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clever palm Oct 30, 2023, 1:34 AM

#

Need help on bottom stuff

midnight plankBOT Oct 30, 2023, 1:34 AM

#

clever palm Need help on bottom stuff

#

@clever palm Has your question been resolved?

midnight plankBOT Oct 30, 2023, 2:19 AM

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@clever palm Has your question been resolved?

midnight plankBOT Oct 30, 2023, 2:49 AM

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brittle shale Oct 30, 2023, 2:52 AM

#

<@&286206848099549185>

midnight plankBOT Oct 30, 2023, 2:52 AM

#

brittle shale <@&286206848099549185>

midnight plankBOT Oct 30, 2023, 2:53 AM

#

brittle shale <@&286206848099549185>

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

brittle shale Oct 30, 2023, 2:53 AM

#

Hello, I need help I'm stuck in a math situation and I don't understand.

tribal temple Oct 30, 2023, 2:54 AM

#

brittle shale Oct 30, 2023, 2:55 AM

#

rn_image_picker_lib_temp_d00e35ea-d487-4b1e-aaf0-112fc696116c.jpg

midnight plankBOT Oct 30, 2023, 2:55 AM

#

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

brittle shale Oct 30, 2023, 2:56 AM

#

I have begun but got stuck midway.

tacit rose Oct 30, 2023, 2:57 AM

#

What exactly are you stuck on?

brittle shale Oct 30, 2023, 2:57 AM

#

nvm, I cannot do this right now.

#

family issues

wary epoch Oct 30, 2023, 2:59 AM

#

If you can't do it right now, you should close this and repost the question later.

midnight plankBOT Oct 30, 2023, 3:12 AM

#

@brittle shale Has your question been resolved?

midnight plankBOT Oct 30, 2023, 3:27 AM

#

Channel closed

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orchid iris Oct 30, 2023, 3:46 AM

#

midnight plankBOT Oct 30, 2023, 3:46 AM

#

orchid iris

orchid iris Oct 30, 2023, 3:47 AM

#

how do you find the roots of cot4theta

#

its not a polynomial

#

i just dont really understand this solution

fallen vigil Oct 30, 2023, 3:48 AM

#

orchid iris how do you find the roots of cot4theta

Well cot is cos/sin, so when cos4theta is 0 cot4theta is 0

orchid iris Oct 30, 2023, 3:49 AM

#

i get that

#

so youre finding the roots of the cos?

#

so if you set both the lhs and rhs to zero

#

so both cot 4 theta = 0 and the big long cot expression to 0

#

if you find the roots of cot 4 theta, you also find the roots of the big long cot expression

#

since both are equal?

fallen vigil Oct 30, 2023, 3:57 AM

#

Yeah

orchid iris Oct 30, 2023, 3:58 AM

#

.close

midnight plankBOT Oct 30, 2023, 3:58 AM

#

Channel closed

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midnight plankBOT Oct 30, 2023, 9:18 PM

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open dew Oct 30, 2023, 9:21 PM

#

midnight plankBOT Oct 30, 2023, 9:21 PM

#

open dew

vale zephyr Oct 30, 2023, 9:22 PM

#

!status

midnight plankBOT Oct 30, 2023, 9:22 PM

#

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

steep hinge Oct 30, 2023, 9:22 PM

#

try to use quadratic formula

open dew Oct 30, 2023, 9:22 PM

#

alright

#

That's hella wrong

#

rn_image_picker_lib_temp_ac3062b6-f4a7-442c-bd4c-69f3b2a1ef9f.jpg

#

what did I mess up?

steep hinge Oct 30, 2023, 9:26 PM

#

are you interested in integer solution right ?

open dew Oct 30, 2023, 9:26 PM

#

Idk the answer is 2/5 and 1

#

I have no clue how to get that

steep hinge Oct 30, 2023, 9:28 PM

#

do sum and then divide by 12

open dew Oct 30, 2023, 9:28 PM

#

okay

#

wait like 54 ÷12?

steep hinge Oct 30, 2023, 9:29 PM

#

do that sum before

open dew Oct 30, 2023, 9:30 PM

#

yeah? then divide by 12?

#

OH I GET IT

#

here wait

#

I have -8 and 12? is that it

#

.close

midnight plankBOT Oct 30, 2023, 9:38 PM

#

Channel closed

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strange pond Oct 30, 2023, 9:41 PM

#

The bolded text is my response so far. I'm not sure what to say as my proof for scenario 2.

midnight plankBOT Oct 30, 2023, 9:41 PM

#

strange pond The bolded text is my response so far. I'm not sure what to say as my proof for ...

#

@strange pond Has your question been resolved?

strange pond Oct 30, 2023, 10:04 PM

#

<@&286206848099549185>

midnight plankBOT Oct 30, 2023, 10:34 PM

#

@strange pond Has your question been resolved?

midnight plankBOT Oct 30, 2023, 11:44 PM

#

@strange pond Has your question been resolved?

midnight plankBOT Oct 31, 2023, 1:45 AM

#

@strange pond Has your question been resolved?

#

Channel closed

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midnight plankBOT Nov 1, 2023, 4:59 PM

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leaden mural Nov 1, 2023, 5:19 PM

#

midnight plankBOT Nov 1, 2023, 5:19 PM

#

leaden mural

#

Please don't occupy multiple help channels.

leaden mural Nov 1, 2023, 5:20 PM

#

#

<@&286206848099549185>

midnight plankBOT Nov 1, 2023, 5:47 PM

#

@leaden mural Has your question been resolved?

leaden mural Nov 1, 2023, 6:14 PM

#

.close

midnight plankBOT Nov 1, 2023, 6:14 PM

#

Channel closed

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leaden mural Nov 1, 2023, 6:14 PM

#

.reopen

midnight plankBOT Nov 1, 2023, 6:14 PM

#

✅

midnight plankBOT Nov 1, 2023, 6:44 PM

#

@leaden mural Has your question been resolved?

last slate Nov 1, 2023, 6:56 PM

#

leaden mural

Shayad unit vector mai convert krke ho jaye?

#

p = (1/a)(unit vector of bxc)

#

@vale zephyr

leaden mural Nov 1, 2023, 6:58 PM

#

Tagging to whom?

vale zephyr Nov 1, 2023, 6:59 PM

#

bhai tu arjun hai na?, jo bar bar id badal ke question post krta hai?

leaden mural Nov 1, 2023, 7:00 PM

#

What???

vale zephyr Nov 1, 2023, 7:00 PM

#

last slate p = (1/a)(unit vector of bxc)

kya?

vale zephyr Nov 1, 2023, 7:00 PM

#

leaden mural What???

u know hindi right?

leaden mural Nov 1, 2023, 7:03 PM

#

Yes i know hindi but not fluently

midnight plankBOT Nov 1, 2023, 8:03 PM

#

@leaden mural Has your question been resolved?

midnight plankBOT Nov 1, 2023, 9:03 PM

#

Channel closed

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midnight plankBOT Nov 1, 2023, 9:52 PM

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last slate Nov 1, 2023, 9:55 PM

#

I'm doing this question and I keep getting ridiculous #s, what am I doing wrong

midnight plankBOT Nov 1, 2023, 9:55 PM

#

last slate I'm doing this question and I keep getting ridiculous #s, what am I doing wrong

last slate Nov 1, 2023, 10:00 PM

#

I have so far:
fx=y - 64x^-2 = 0 fxx = 128x^-3 fxy = 1
fy=x - 64y^-2 = 0 fyy = 128y^-3
Calculated using symbolab: x=8(8)^(1/5) , y=1/(8)^(2/5)

Hessian: 128^2(x^-3)(y^-3) - 1

midnight plankBOT Nov 1, 2023, 10:15 PM

#

@last slate Has your question been resolved?

last slate Nov 1, 2023, 10:29 PM

#

<@&286206848099549185>

limpid wraith Nov 1, 2023, 10:35 PM

#

last slate <@&286206848099549185>

Yes?

last slate Nov 1, 2023, 10:47 PM

#

the question

midnight plankBOT Nov 1, 2023, 11:17 PM

#

@last slate Has your question been resolved?

midnight plankBOT Nov 2, 2023, 12:20 AM

#

@last slate Has your question been resolved?

midnight plankBOT Nov 2, 2023, 1:02 AM

#

Channel closed

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midnight plankBOT Nov 2, 2023, 3:34 AM

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craggy arrow Nov 2, 2023, 3:37 AM

#

can someone explain how step 3 becomes step 4?

midnight plankBOT Nov 2, 2023, 3:37 AM

#

craggy arrow can someone explain how step 3 becomes step 4?

craggy arrow Nov 2, 2023, 3:38 AM

#

like im trying to calculate it but im never getting -40.2m/s

hard shard Nov 2, 2023, 3:39 AM

#

!show

midnight plankBOT Nov 2, 2023, 3:39 AM

#

Show your work, and if possible, explain where you are stuck.

hard shard Nov 2, 2023, 3:39 AM

#

How did you plug it into your calculator?

craggy arrow Nov 2, 2023, 3:39 AM

#

hard shard How did you plug it into your calculator?

like this

-√(35.0)^2+2(-9.81^2)(-20.0)

hard shard Nov 2, 2023, 3:40 AM

#

The ² is for the m/s²

#

You dont add it

#

It should be -sqrt((35.0)²+2(-9.81)(-20.0))

craggy arrow Nov 2, 2023, 3:40 AM

#

so i just do (-9.81)

hard shard Nov 2, 2023, 3:41 AM

#

Yeah

craggy arrow Nov 2, 2023, 3:41 AM

#

it gives me 6872

#

6872.603428

#

oh wait

hard shard Nov 2, 2023, 3:41 AM

#

Can you send like a screenshot or pictur of your calculator

craggy arrow Nov 2, 2023, 3:41 AM

#

i know why

#

cause i didnt put the square root over the whole hing

midnight plankBOT Nov 2, 2023, 3:57 AM

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@craggy arrow Has your question been resolved?

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spring heron Nov 2, 2023, 4:31 AM

#

midnight plankBOT Nov 2, 2023, 4:31 AM

#

spring heron

#

Please don't occupy multiple help channels.

spring heron Nov 2, 2023, 4:36 AM

#

oh sorry

nocturne jetty Nov 2, 2023, 4:43 AM

#

spring heron

what's the answer given

fallow scarab Nov 2, 2023, 4:47 AM

#

,w plot arcsin(1+x/2) + arcsin(x/2) - arccos(x) for -1<x<0

grand pondBOT Nov 2, 2023, 4:48 AM

#

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

fallow scarab Nov 2, 2023, 4:48 AM

#

spring heron

What's the question

nocturne jetty Nov 2, 2023, 4:53 AM

#

I got in range

midnight plankBOT Nov 2, 2023, 4:58 AM

#

@spring heron Has your question been resolved?

midnight plankBOT Nov 2, 2023, 5:13 AM

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topaz hamlet Nov 2, 2023, 5:24 AM

#

midnight plankBOT Nov 2, 2023, 5:24 AM

#

topaz hamlet

topaz hamlet Nov 2, 2023, 5:25 AM

#

A police car is located 40 feet to the side of a straight road.

A red car is driving along the road in the direction of the police car and is 140 feet up the road from the location of the police car. The police radar reads that the distance between the police car and the red car is decreasing at a rate of 75 feet per second. How fast is the red car actually traveling along the road?

#

i am really confused abt the wording

midnight plankBOT Nov 2, 2023, 5:40 AM

#

@topaz hamlet Has your question been resolved?

midnight plankBOT Nov 2, 2023, 6:10 AM

#

@topaz hamlet Has your question been resolved?

midnight plankBOT Nov 2, 2023, 6:40 AM

#

Channel closed

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round mural Nov 2, 2023, 7:04 PM

#

midnight plankBOT Nov 2, 2023, 7:04 PM

#

round mural

round mural Nov 2, 2023, 7:05 PM

#

Using rollers theorem to find when f’(x) = 0

#

I’m confused what to do next

lyric charm Nov 2, 2023, 7:06 PM

#

rollers theorem

#

🛼

round mural Nov 2, 2023, 7:06 PM

#

Here’s the other work:

lyric charm Nov 2, 2023, 7:07 PM

#

anyway rolle's theorem doesnt really help you find where f'(x) = 0

#

it only guarantees the existence of at least one such point in an interval

#

speaking of, on what interval are you considering this function

round mural Nov 2, 2023, 7:08 PM

#

round mural Nov 2, 2023, 7:15 PM

#

lyric charm speaking of, on what interval are you considering this function

What do I do next

lyric charm Nov 2, 2023, 7:15 PM

#

wait, what was the original function? sin(x/2)?

round mural Nov 2, 2023, 7:17 PM

#

Yeah

#

Mb

#

midnight plankBOT Nov 2, 2023, 7:33 PM

#

@round mural Has your question been resolved?

round mural Nov 2, 2023, 7:41 PM

#

.close

midnight plankBOT Nov 2, 2023, 7:41 PM

#

Channel closed

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placid vessel Nov 2, 2023, 7:48 PM

#

suppose you have a function like this:

midnight plankBOT Nov 2, 2023, 7:48 PM

#

placid vessel suppose you have a function like this:

placid vessel Nov 2, 2023, 7:49 PM

#

#

clearly it is not continuous

#

but if you were to define it as a pointwise function

#

what would the value be at x = 0?

#

it could be anything in [-1,1]

#

wait maybe it is continuous

#

no it isn't

languid scroll Nov 2, 2023, 7:50 PM

#

Not a function

placid vessel Nov 2, 2023, 7:51 PM

#

#

what i drew above is the pointwise limit of this sequence

#

so would that mean there is no pointwise limit?

dry lance Nov 2, 2023, 7:53 PM

#

is this occupied

placid vessel Nov 2, 2023, 7:53 PM

#

yes

hearty rune Nov 2, 2023, 7:53 PM

#

yes

lyric charm Nov 2, 2023, 7:54 PM

#

dry lance is this occupied

if it has somebody's name on it, it's occupied.

dry lance Nov 2, 2023, 7:54 PM

#

lyric charm if it has somebody's name on it, it's occupied.

ye just saw it thx

placid vessel Nov 2, 2023, 7:57 PM

#

just taking the limit as n tends to infinity of that piecewise function

#

i see that no f(x) can exist s.t. the sequence will converge to f

#

so is it possible that a sequence of functions has neither a pointwise nor a uniform limit?

midnight plankBOT Nov 2, 2023, 8:13 PM

#

@placid vessel Has your question been resolved?

midnight plankBOT Nov 2, 2023, 8:43 PM

#

@placid vessel Has your question been resolved?

#

Channel closed

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glossy pagoda Nov 2, 2023, 9:04 PM

#

hey i have a proof problem

midnight plankBOT Nov 2, 2023, 9:04 PM

#

glossy pagoda hey i have a proof problem

glossy pagoda Nov 2, 2023, 9:04 PM

#

a and b are positive integers

#

and i need to prove that the converse of this statement is true

trail quartz Nov 2, 2023, 9:07 PM

#

Like 4|a and 4|b then 4|ab?

glossy pagoda Nov 2, 2023, 9:07 PM

#

yh but it has that small line going through the line

#

meaning does not divide

glossy pagoda Nov 2, 2023, 9:07 PM

#

trail quartz Like 4|a and 4|b then 4|ab?

but i need to do converse

#

so

#

if 4 does not divide ab then 4 does not divide a and 4 does not divide b

#

i was thinking proof by contradiction

#

well i tried to do proof by contradiction but i struggled

trail quartz Nov 2, 2023, 9:09 PM

#

But you cant contradict something thats true

glossy pagoda Nov 2, 2023, 9:09 PM

#

proof by contradiction is done by assuming the opposite of the converse statement

#

the opposite of the converse statement will lead to a contradiction which we would come to a conclusion would be that the converse statement is true

trail quartz Nov 2, 2023, 9:12 PM

#

a and b have to be different right?

glossy pagoda Nov 2, 2023, 9:12 PM

#

yh

steep hinge Nov 2, 2023, 9:12 PM

#

what have you wanted prove ?

glossy pagoda Nov 2, 2023, 9:12 PM

#

cuz their a and b

glossy pagoda Nov 2, 2023, 9:12 PM

#

steep hinge what have you wanted prove ?

if 4 does not divide ab then 4 does not divide a and 4 does not divide b

#

4 does not divide 15 then 4 does not divide 5 and 4 does not divide 3

steep hinge Nov 2, 2023, 9:13 PM

#

if wlog 4|a then a=4k then ba=b4k=4(bk) then 4|ab contradiction

glossy pagoda Nov 2, 2023, 9:14 PM

#

xD

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im tryna understand it

steep hinge Nov 2, 2023, 9:15 PM

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take your time, and ask me anything you want ❤️

glossy pagoda Nov 2, 2023, 9:15 PM

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so thats the proof by contradiction

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what is wlog

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?

steep hinge Nov 2, 2023, 9:15 PM

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yes it is

glossy pagoda Nov 2, 2023, 9:15 PM

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steep hinge yes it is

i see

steep hinge Nov 2, 2023, 9:15 PM

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without loss of generality

glossy pagoda Nov 2, 2023, 9:15 PM

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oh

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wait

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so what would be the assumption

steep hinge Nov 2, 2023, 9:16 PM

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4|a or 4|b

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so "without loss of generality" i assumed 4|a

glossy pagoda Nov 2, 2023, 9:16 PM

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that if 4 does not divide ab then 4 divides a or 4 divides b, like that

steep hinge Nov 2, 2023, 9:16 PM

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yes