#help-36 | Mathematics | Page 51

final saddleBOT Sep 17, 2023, 5:52 PM

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Channel closed

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wind river Sep 17, 2023, 5:52 PM

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I understand that S is an element of the power set of [n]

fossil geyser Sep 17, 2023, 6:00 PM

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final saddle

Hey the bot is gonna lock this channel, you should make a new one

final saddleBOT Sep 17, 2023, 6:02 PM

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wind river Sep 17, 2023, 6:06 PM

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gotcha

final saddleBOT Sep 17, 2023, 6:06 PM

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wind river gotcha

wind river Sep 17, 2023, 6:06 PM

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steep sequoia Sep 17, 2023, 6:06 PM

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wind river

!status

final saddleBOT Sep 17, 2023, 6:06 PM

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wind river

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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

wind river Sep 17, 2023, 6:07 PM

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1

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i dont know where to begin

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the idea i have rn is

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ik that i have to use

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simple induction

steep sequoia Sep 17, 2023, 6:07 PM

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Yeah. That's what i did.

wind river Sep 17, 2023, 6:07 PM

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and that S is an element of the power set of [n]

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and that the summation

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is adding up all the elements

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in the power set

steep sequoia Sep 17, 2023, 6:07 PM

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wind river and that S is an element of the power set of [n]

Except for the phi of course.

wind river Sep 17, 2023, 6:07 PM

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phi?

steep sequoia Sep 17, 2023, 6:08 PM

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wind river is adding up all the elements

their factorials.

steep sequoia Sep 17, 2023, 6:08 PM

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wind river phi?

Empty set.

wind river Sep 17, 2023, 6:08 PM

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ah yeah

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since its nonempty

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so for

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the example they gave

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{{1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3}}

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so 1/1 + 1/2 + 1/3 + 1/1x2 + 1/3x1 + 1/2x3 + 1/2x3x1

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uhh

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so the base case is easy

steep sequoia Sep 17, 2023, 6:10 PM

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Yeah.

wind river Sep 17, 2023, 6:10 PM

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the IH would be the summation of [k] where Sk = [a1 a2 a3 ... ak]

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and 1/S! = k

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now i need to show the [k+1] holds

steep sequoia Sep 17, 2023, 6:11 PM

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Yes.

wind river Sep 17, 2023, 6:11 PM

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how i do this is where

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im lost

subtle lava Sep 17, 2023, 6:11 PM

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wind river Sep 17, 2023, 6:11 PM

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uh

steep sequoia Sep 17, 2023, 6:12 PM

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So, [k+1] is just [k] U {k+1}.

wind river Sep 17, 2023, 6:12 PM

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@subtle lava wrong channel friend

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yeah

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thats what i was thinking

steep sequoia Sep 17, 2023, 6:12 PM

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subtle lava

Open your own help channel. Refer #❓how-to-get-help

wind river Sep 17, 2023, 6:13 PM

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so Sk U Sk+1

steep sequoia Sep 17, 2023, 6:13 PM

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Umm... why are you doing that?

wind river Sep 17, 2023, 6:13 PM

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i was thinking

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that

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for the summation

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we would need

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the elements that doesnt include k+1

steep sequoia Sep 17, 2023, 6:13 PM

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Sk+1 already includes Sk.

wind river Sep 17, 2023, 6:13 PM

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oh yeah

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mb

steep sequoia Sep 17, 2023, 6:14 PM

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steep sequoia Sk+1 already includes Sk.

This is the key point.

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You know that Summation(S!) for [k+1] will have all the terms of summation(S!) for [k].

wind river Sep 17, 2023, 6:15 PM

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yeah

steep sequoia Sep 17, 2023, 6:15 PM

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So, you write {Summation(S!) for [k+1]} as {summation(S!) for [k]} + <some extra terms>.

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Then you show that those extra terms sum up to exactly 1.

wind river Sep 17, 2023, 6:16 PM

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hm

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yea hsince

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Sk! = k

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by IH

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uhh

steep sequoia Sep 17, 2023, 6:17 PM

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Yes

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So, we'll show that S! for [k+1] is k+1.

wind river Sep 17, 2023, 6:17 PM

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yeah

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the extra terms

steep sequoia Sep 17, 2023, 6:18 PM

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Now, you can easily write those extra terms if you notice what is special about them.

wind river Sep 17, 2023, 6:18 PM

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would be all the summations that include k+1

steep sequoia Sep 17, 2023, 6:18 PM

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Yes.

wind river Sep 17, 2023, 6:18 PM

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uh the power set of k+1?

steep sequoia Sep 17, 2023, 6:18 PM

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All those terms which have k+1.

wind river Sep 17, 2023, 6:18 PM

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yeah

steep sequoia Sep 17, 2023, 6:18 PM

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wind river uh the power set of k+1?

Umm... No. That's just k+1 and phi.

wind river Sep 17, 2023, 6:19 PM

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the powerset not including the empty**

steep sequoia Sep 17, 2023, 6:19 PM

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you can say it this way: Power set of [k+1] - Power set of [k]

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However, this notation doesn't really help us much.

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Try to think about them in terms of combinations.

wind river Sep 17, 2023, 6:20 PM

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uhh

wind river Sep 17, 2023, 6:23 PM

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steep sequoia Now, you can easily write those extra terms if you notice what is special about ...

what's special is that its the summation of all the terms which have k+1

steep sequoia Sep 17, 2023, 6:23 PM

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Yes

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Think about it. All the set that are in Power set of [k] - if we just add (k+1) to them, we get almost all the terms which have (k+1).

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Only one term is left. Which one?

wind river Sep 17, 2023, 6:27 PM

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k+1?

wind river Sep 17, 2023, 6:27 PM

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steep sequoia Think about it. All the set that are in Power set of [k] - if we just add (k+1) ...

i did this on my whiteboard but it didnt really give me anything

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like if k+1 was 3

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the original power set is

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{1} {2} {1 2}

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and then adding in k+1

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we get

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{1 k+1} {2 k+1} {1 2 k+1}

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so k+1 is missing?

steep sequoia Sep 17, 2023, 6:28 PM

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Yes

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So, after all, You have -
{S! for [k+1]} = {S! for [k]} + S! for sets in [{k+1} {1 k+1} {2 k+1} {1 2 k+1}]

wind river Sep 17, 2023, 6:30 PM

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mhm

steep sequoia Sep 17, 2023, 6:30 PM

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Now, try writing product for those sets.

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You'll see something magical happen. 😌

wind river Sep 17, 2023, 6:31 PM

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uh

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S! for k simplifies to k

wind river Sep 17, 2023, 6:31 PM

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steep sequoia So, after all, You have - {S! for [k+1]} = {S! for [k]} + S! for sets in [{k+1}...

i thought k+1 wasnt included

steep sequoia Sep 17, 2023, 6:31 PM

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Why not?

wind river Sep 17, 2023, 6:32 PM

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{k+1} {1 k+1} {2 k+1} {1 2 k+1}

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{k+1} should be missing no?

steep sequoia Sep 17, 2023, 6:32 PM

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Why should it be missing?

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Is that not a set having k+1 ?

wind river Sep 17, 2023, 6:32 PM

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since the empty set isnt included?

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am i being dumb

steep sequoia Sep 17, 2023, 6:34 PM

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{k+1} isn't an empty set.

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It has one element.

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Empty sets have no element.

steep sequoia Sep 17, 2023, 6:34 PM

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wind river {1} {2} {1 2}

See. You were taking {1} and {2} here for k=2.

wind river Sep 17, 2023, 6:35 PM

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right

steep sequoia Sep 17, 2023, 6:35 PM

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Why won't you take {3} ?

wind river Sep 17, 2023, 6:35 PM

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wind river {1 k+1} {2 k+1} {1 2 k+1}

and then adding k+1 (3) would give

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this

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oooog

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wait your right mb

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i get it we have to include k+1

steep sequoia Sep 17, 2023, 6:37 PM

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Good.

steep sequoia Sep 17, 2023, 6:38 PM

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wind river i thought k+1 wasnt included

Now write all the S! terms for those sets having {k+1}.

wind river Sep 17, 2023, 6:38 PM

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wind river {k+1} {1 k+1} {2 k+1} {1 2 k+1}

1/k+1 + 1/k+1 + 1/2k+2 + 1/2k+2

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which is

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uhh

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3/k+1

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and since k is 2

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3/3 = 1

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in the case where k is arbitrary

wind river Sep 17, 2023, 6:42 PM

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steep sequoia Now write all the S! terms for those sets having {k+1}.

ik it would be k+1/k+1?

steep sequoia Sep 17, 2023, 6:42 PM

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Yes

wind river Sep 17, 2023, 6:42 PM

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how do i derive this properly?

steep sequoia Sep 17, 2023, 6:42 PM

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But you need to show it using variables.

wind river Sep 17, 2023, 6:43 PM

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using variables

steep sequoia Sep 17, 2023, 6:43 PM

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Can't do using some values.

wind river Sep 17, 2023, 6:43 PM

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yeah

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it'd be

steep sequoia Sep 17, 2023, 6:43 PM

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Let me write it out for you and it should give you some hint.

wind river Sep 17, 2023, 6:43 PM

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gotcha

steep sequoia Sep 17, 2023, 6:48 PM

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$k + \left( \left[\frac{1}{k+1}\right] + \left[\frac{1}{(k+1) \cdot 1} + \frac{1}{(k+1) \cdot 2} + \cdots\right] + \left[\frac{1}{(k+1) \cdot (1\cdot2)} +\frac{1}{(k+1) \cdot (1\cdot3)} + \cdots\right] + \cdots \text{ so on for 3 terms taken with k+1 in S! and then 4 and so on...} + \left[\frac{1}{1\cdot 2\cdot 3\cdot 4 \cdots k \cdot k+1}\right]\right)$

wind river Sep 17, 2023, 6:48 PM

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damn

steep sequoia Sep 17, 2023, 6:48 PM

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Gosh.

wind river Sep 17, 2023, 6:49 PM

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right

steep sequoia Sep 17, 2023, 6:50 PM

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Open that in browser and see in bigger fonts.

wind river Sep 17, 2023, 6:50 PM

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yeah i got u

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OH

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since theres k+1 terms

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the 1s add up to k+1?

steep sequoia Sep 17, 2023, 6:50 PM

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No.

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You are trying to create ways to get 1. 😐

wind river Sep 17, 2023, 6:51 PM

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lol i thought i had something there

steep sequoia Sep 17, 2023, 6:51 PM

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Properly look at the expression and see if you manipulate it somehow.

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Maybe factor something out.

wind river Sep 17, 2023, 6:51 PM

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do i have to use the IH again?

steep sequoia Sep 17, 2023, 6:51 PM

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Remember - First k is S! for [k] so you can ignore that.

steep sequoia Sep 17, 2023, 6:52 PM

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wind river do i have to use the IH again?

Kinda.

soft zealotBOT Sep 17, 2023, 6:53 PM

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Enemagneto

wind river Sep 17, 2023, 6:54 PM

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uhhh

steep sequoia Sep 17, 2023, 6:54 PM

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Ah. Fixed finally.

steep sequoia Sep 17, 2023, 6:54 PM

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wind river uhhh

Ignore me. Look at the expression.

wind river Sep 17, 2023, 6:54 PM

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hm

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can i say

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that

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everything after the inital 1/k+1

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simplifies to k+1?

steep sequoia Sep 17, 2023, 6:55 PM

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How are you saying that?

wind river Sep 17, 2023, 6:55 PM

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by the IH

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or rather sorry

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nvm

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we were trying to get to that

steep sequoia Sep 17, 2023, 6:56 PM

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Do thus.

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Which factor do you see in all the terms inside the parentheses?

wind river Sep 17, 2023, 6:56 PM

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k+1

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oh k?

steep sequoia Sep 17, 2023, 6:56 PM

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Not k+1. All the terms are in denominator.

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How are you getting k+1 ?

steep sequoia Sep 17, 2023, 6:56 PM

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wind river oh k?

Do you see any k factor in 1/(k+1) ?

wind river Sep 17, 2023, 6:57 PM

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no

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uhhhh

steep sequoia Sep 17, 2023, 6:57 PM

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wind river k+1

You are on the right track here.

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It's just not k+1.

wind river Sep 17, 2023, 6:57 PM

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is it 1?

steep sequoia Sep 17, 2023, 6:57 PM

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EVERYTHING IS IN DENOMINATOR.

wind river Sep 17, 2023, 6:57 PM

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hmm

steep sequoia Sep 17, 2023, 6:57 PM

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wind river is it 1?

Does taking 1 as factor ever help?

wind river Sep 17, 2023, 6:58 PM

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never

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sorry factors

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in the denominator?

steep sequoia Sep 17, 2023, 6:58 PM

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Come on. (1/(k+1)) is the factor.

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not k+1.

wind river Sep 17, 2023, 6:58 PM

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right mb

steep sequoia Sep 17, 2023, 6:59 PM

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Take that as factor from the parentheses.

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What do you get inside the parentheses?

wind river Sep 17, 2023, 7:00 PM

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1/k+1([1] + [1/1 + 1/2 + ...] + [1/2 + 1/3 + ....] + .... + [1/1x2x3x4xk])

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ohh

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the

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parantheses

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simplifies now

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to k

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by IH

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and (1/k+1)*k

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or wait

wind river Sep 17, 2023, 7:06 PM

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steep sequoia What do you get inside the parentheses?

it simplifies

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to k+1

steep sequoia Sep 17, 2023, 7:06 PM

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Yes

wind river Sep 17, 2023, 7:06 PM

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since its 1/k+1 ( 1 + k)

steep sequoia Sep 17, 2023, 7:06 PM

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So that becomes 1.

wind river Sep 17, 2023, 7:06 PM

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which is now 1

steep sequoia Sep 17, 2023, 7:06 PM

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Overall k + 1

wind river Sep 17, 2023, 7:06 PM

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yeah

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ok i just gotta write this out in latex now

wind river Sep 17, 2023, 7:09 PM

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steep sequoia Overall k + 1

thanks for the help

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sorry for being slow lmao

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.close

final saddleBOT Sep 17, 2023, 7:09 PM

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fringe holly Sep 17, 2023, 7:15 PM

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Use continuity to evaluate the limit.
lim
𝜃→3𝜋⁄2
sin(tan(cos(𝜃)

final saddleBOT Sep 17, 2023, 7:15 PM

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fringe holly Use continuity to evaluate the limit. lim 𝜃→3𝜋⁄2 sin(tan(cos(𝜃)

fringe holly Sep 17, 2023, 7:15 PM

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How do I got about solving this

tired walrus Sep 17, 2023, 7:17 PM

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$\lim_{\theta \to 3\pi/2} \sin(\tan(\cos(\theta)))$

soft zealotBOT Sep 17, 2023, 7:17 PM

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Ann

tired walrus Sep 17, 2023, 7:17 PM

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this?

fringe holly Sep 17, 2023, 7:17 PM

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yes

tired walrus Sep 17, 2023, 7:17 PM

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well, sin, cos and tan are continuous functions (except tan at odd multiples of pi/2...)

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do you know what continuity means for limits

fringe holly Sep 17, 2023, 7:18 PM

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that it will go to -infinity or positive infinite

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like you can draw the graph without lifting your pencil

tired walrus Sep 17, 2023, 7:20 PM

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not quite the answer i was looking for...

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continuity means that $\lim_{x \to c} f(x) = f(c)$

soft zealotBOT Sep 17, 2023, 7:20 PM

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Ann

tired walrus Sep 17, 2023, 7:20 PM

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meaning you can just plug shit in

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mostly

fringe holly Sep 17, 2023, 7:23 PM

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so the limit of that function wouldn't be continuous because of tan and the 3 is making it an odd number

final saddleBOT Sep 17, 2023, 7:38 PM

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@fringe holly Has your question been resolved?

final saddleBOT Sep 17, 2023, 7:53 PM

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near sedge Sep 17, 2023, 8:10 PM

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This is a lagrange function, but how he goes from this to this:

final saddleBOT Sep 17, 2023, 8:10 PM

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near sedge This is a lagrange function, but how he goes from this to this:

near sedge Sep 17, 2023, 8:11 PM

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I didnt get that lambda_t+1

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apparently it's a simplification from this paper: https://www.jstor.org/stable/pdf/2234070.pdf

final saddleBOT Sep 17, 2023, 8:40 PM

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@near sedge Has your question been resolved?

final saddleBOT Sep 17, 2023, 9:11 PM

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@near sedge Has your question been resolved?

final saddleBOT Sep 17, 2023, 9:41 PM

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sonic thistle Sep 17, 2023, 9:48 PM

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Can I just put these all under one sqrt?

rn_image_picker_lib_temp_22b858d8-f29f-4fa1-a40d-47ebb840d402.jpg

final saddleBOT Sep 17, 2023, 9:48 PM

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sonic thistle Can I just put these all under one sqrt?

brave cloak Sep 17, 2023, 9:49 PM

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No

sonic thistle Sep 17, 2023, 9:49 PM

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Sqrt of -x^2 +x +28

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So how do you add them together?

brave cloak Sep 17, 2023, 9:50 PM

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I don't think you can add them you just leave them like that

sonic thistle Sep 17, 2023, 9:50 PM

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Ohhh

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But you can add them under certain conditions right? If they have the same something?

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Sorry I am trying to remember stuff from 9 months ago

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Oh its when its multiplied

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They can all go under

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Sorry thank you!

brave cloak Sep 17, 2023, 9:54 PM

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sonic thistle They can all go under

Yes right

brave cloak Sep 17, 2023, 9:54 PM

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sonic thistle Sorry thank you!

No problem

sonic thistle Sep 17, 2023, 9:54 PM

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.close

final saddleBOT Sep 17, 2023, 9:54 PM

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sullen warren Sep 17, 2023, 10:06 PM

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Ok this is more just making sure I did the diagram right than anything at the moment
So the question is
Draw a Venn-style diagram, which displays the relation aRb , for a∈A and b∈B, where R maps each digit to the vowel(s) which occurs in the name of the digit.

B = five vowels of the English alphabet```
Are the sets respectively. This is what I have right now for my diagram. 
          A                    B          
 ----------------------------------------
|        0= E,O         |          A = a   |
|        1= E,O         |          E = e    |
|        2= O            |          I = i       |
|        3= E             |         O = o     |
|        4= O,U        |         U = u     |
|        5= E,I           |                       |
|        6= I              |                       |
|        7= E             |                       |
|        8= E,I           |                       |
|        9= E,I           |                       |
|                             |                       |
 -----------------------------------------

final saddleBOT Sep 17, 2023, 10:06 PM

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sullen warren Ok this is more just making sure I did the diagram right than anything at the mo...

sullen warren Sep 17, 2023, 10:06 PM

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I just want to make sure that I did the diagram properly is all really, idk if this is the right place for this or not

final saddleBOT Sep 17, 2023, 10:21 PM

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@sullen warren Has your question been resolved?

sullen warren Sep 17, 2023, 10:30 PM

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No

final saddleBOT Sep 17, 2023, 10:42 PM

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Channel closed

The owner is missing!

final saddleBOT Sep 18, 2023, 1:07 AM

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soft jewel Sep 18, 2023, 1:14 AM

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final saddleBOT Sep 18, 2023, 1:14 AM

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soft jewel

soft jewel Sep 18, 2023, 1:14 AM

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is this wrong j cuz i forgot m

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should it have been m * this

final saddleBOT Sep 18, 2023, 1:29 AM

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@soft jewel Has your question been resolved?

final saddleBOT Sep 18, 2023, 1:44 AM

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final saddleBOT Sep 18, 2023, 3:19 PM

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gilded apex Sep 18, 2023, 3:21 PM

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rearange to H

final saddleBOT Sep 18, 2023, 3:21 PM

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gilded apex rearange to H

steady olive Sep 18, 2023, 3:21 PM

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I’m not sure how to do this do I do it by integration of parts and how do I start

gilded apex Sep 18, 2023, 3:21 PM

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rearange to H

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final saddleBOT Sep 18, 2023, 3:36 PM

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@gilded apex Has your question been resolved?

gilded apex Sep 18, 2023, 3:37 PM

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help pls 🙂

final saddleBOT Sep 18, 2023, 4:07 PM

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@gilded apex Has your question been resolved?

final saddleBOT Sep 18, 2023, 4:37 PM

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lusty charm Sep 18, 2023, 6:27 PM

#

how come 6 is not a correct answer

final saddleBOT Sep 18, 2023, 6:27 PM

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lusty charm how come 6 is not a correct answer

tired walrus Sep 18, 2023, 6:31 PM

#

is 36i+2j parallel to 36i-2j?

lusty charm Sep 18, 2023, 6:32 PM

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i dont rlly understand how a vector component works.

i thought the coeffficient of i is like the slope and coefficient of j is like the y-intercept?

final saddleBOT Sep 18, 2023, 6:47 PM

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@lusty charm Has your question been resolved?

final saddleBOT Sep 18, 2023, 7:02 PM

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pulsar surge Sep 18, 2023, 7:11 PM

#

Hey guys. I need to help to control if my answer is correct

final saddleBOT Sep 18, 2023, 7:11 PM

#

pulsar surge Hey guys. I need to help to control if my answer is correct

pulsar surge Sep 18, 2023, 7:11 PM

#

(picture of my calculation, it's a little a messy but hope someone can help me)

#

I got 19

glad glacier Sep 18, 2023, 7:15 PM

#

correct

pulsar surge Sep 18, 2023, 7:15 PM

#

Thanks😊

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.close

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obtuse pulsar Sep 18, 2023, 7:33 PM

#

i need help

final saddleBOT Sep 18, 2023, 7:33 PM

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obtuse pulsar i need help

obtuse pulsar Sep 18, 2023, 7:34 PM

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.close

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grave hinge Sep 18, 2023, 7:48 PM

#

Can anyone confirm this is correct (turning velocity time graph to acceleration time graph) got a test with this question in 10 mins 😭

final saddleBOT Sep 18, 2023, 7:48 PM

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grave hinge Can anyone confirm this is correct (turning velocity time graph to acceleration ...

fossil geyser Sep 18, 2023, 7:50 PM

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Yeah for a sketch without a scale that seems fine

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Acc is positive when vel is increasing, etc

grave hinge Sep 18, 2023, 7:52 PM

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Is the part where I made the acceleration higher then normal also good?

fossil geyser Sep 18, 2023, 7:52 PM

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Yeah the slope of the velocity seems higher there so that checks out

grave hinge Sep 18, 2023, 7:52 PM

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Alr thx

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.close

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slender tide Sep 18, 2023, 8:36 PM

#

I'm needing helpi with this exercise. I will be translating since it is in portuguese:

"If cotgx + tgx = 8, when 0 < x < π/2, so which is the value of: (sinx + cosx)² "

final saddleBOT Sep 18, 2023, 8:36 PM

#

slender tide I'm needing helpi with this exercise. I will be translating since it is in portu...

slender tide Sep 18, 2023, 8:40 PM

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I did an exercise similar to that one some time ago by equaling the denominators, so that's what I tried here:

cosx/ sinx + sinx/ cosx = 8 (now multiplying cosx/sinx by cosx and sinx/cosx by sinx)

cosx² + sinx² / sinx . cosx = 8

1 / sinx . cosx = 8

#

have i done anything wrong until this point?

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and if i'm right, how can I continue this?

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the template says that the answer is 5/4 but I don't know how to get to that number

#

@unkempt moon

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Sorry, wrong ping

#

<@&286206848099549185>

final saddleBOT Sep 18, 2023, 9:12 PM

#

@slender tide Has your question been resolved?

slender tide Sep 18, 2023, 9:27 PM

#

<@&286206848099549185>

final saddleBOT Sep 18, 2023, 9:57 PM

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upper sigil Sep 18, 2023, 10:16 PM

#

im second guessing myself

final saddleBOT Sep 18, 2023, 10:16 PM

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upper sigil im second guessing myself

upper sigil Sep 18, 2023, 10:16 PM

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but

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i would just plug in 28 and solve

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right

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or would i do the irc at 28? or does it literally just want

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at 28

fierce mesa Sep 18, 2023, 10:19 PM

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i would say m(v)=28

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and go from there yes

upper sigil Sep 18, 2023, 10:19 PM

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yeah so plug in 28 for v

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right

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or are you saying solve for v

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thats the same thing isnt it

fierce mesa Sep 18, 2023, 10:21 PM

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given 28 is the height needed to throw, m=28 in this case as opposed to v=28, as v represents the velocity instead of height

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so m(v), as a function of v, will be substituted to be 28, following which you will solve for v

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as stated: 'find the ideal velocity of Romeo's throw'

upper sigil Sep 18, 2023, 10:21 PM

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ah

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that makes sense

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because its max height as a functuion of velocity

fierce mesa Sep 18, 2023, 10:22 PM

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yeps

upper sigil Sep 18, 2023, 10:22 PM

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if it said what is the max height if romeo throws the flowers at 28 feet per second or something

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then id plug in

#

got it

#

.close

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#

supple copper Sep 18, 2023, 10:38 PM

#

Yes

final saddleBOT Sep 18, 2023, 10:38 PM

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tranquil pine Sep 18, 2023, 10:50 PM

#

final saddleBOT Sep 18, 2023, 10:50 PM

#

tranquil pine

tranquil pine Sep 18, 2023, 10:51 PM

#

Need help to prove Q2c wih strong induction

final saddleBOT Sep 18, 2023, 11:06 PM

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@tranquil pine Has your question been resolved?

final saddleBOT Sep 18, 2023, 11:36 PM

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@tranquil pine Has your question been resolved?

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final saddleBOT Sep 19, 2023, 12:03 AM

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obtuse pagoda Sep 19, 2023, 12:14 AM

#

final saddleBOT Sep 19, 2023, 12:14 AM

#

obtuse pagoda

obtuse pagoda Sep 19, 2023, 12:14 AM

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Can someone explain the highlighted part

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Don't know what I'm doing wrong

final saddleBOT Sep 19, 2023, 12:29 AM

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@obtuse pagoda Has your question been resolved?

obtuse pagoda Sep 19, 2023, 12:29 AM

#

<@&286206848099549185>

barren galleon Sep 19, 2023, 12:33 AM

#

obtuse pagoda <@&286206848099549185>

4-a+b=4+(-1)a+(-1)(-b)=4+(-1)(a-b)=4-(a-b)

final saddleBOT Sep 19, 2023, 12:59 AM

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@obtuse pagoda Has your question been resolved?

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atomic spindle Sep 19, 2023, 8:19 PM

#

final saddleBOT Sep 19, 2023, 8:19 PM

#

atomic spindle

atomic spindle Sep 19, 2023, 8:19 PM

#

the dum program is so specific

#

idk which step it wants

novel rover Sep 19, 2023, 8:24 PM

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It wants which piecewise function to execute

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As x approaches 0 from the left which equation do you use?

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You put it in the space

atomic spindle Sep 19, 2023, 8:27 PM

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^-

atomic spindle Sep 19, 2023, 8:28 PM

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novel rover It wants which piecewise function to execute

thats wrong

novel rover Sep 19, 2023, 8:29 PM

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Oh it's the derivative mb, just put the derivative in the space

atomic spindle Sep 19, 2023, 8:32 PM

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like ik the derivative equation

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does it want me to substitute in

vital crag Sep 19, 2023, 8:35 PM

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atomic spindle like ik the derivative equation

show

atomic spindle Sep 19, 2023, 8:36 PM

#

f'(x) = lim h->0 [f(x+h) - f(x)]/h

vital crag Sep 19, 2023, 8:37 PM

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yea apply that to both functions in f(x)

atomic spindle Sep 19, 2023, 8:39 PM

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so just substitute

atomic spindle Sep 19, 2023, 8:41 PM

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vital crag yea apply that to both functions in f(x)

it really doesn't like variables

#

so idk

vital crag Sep 19, 2023, 8:41 PM

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you're supposed to find f'(x)

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and input that to the box

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not limit definitions

atomic spindle Sep 19, 2023, 8:43 PM

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um

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well f'(x) = lim h->0 [(4(x+h)-6(x+h)^2)-(4x-6x^2)]/h

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im not sure what im supposed to do w that

vital crag Sep 19, 2023, 8:44 PM

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find the limit!

#

also, that's only for x < 0. you'll need to find f'(x) for x>=0

atomic spindle Sep 19, 2023, 8:47 PM

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4-12x

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i believe

vital crag Sep 19, 2023, 8:47 PM

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atomic spindle 4-12x

yes. this is what you put in the first box

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this means x < 0

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so you differentiate this piece of the function

atomic spindle Sep 19, 2023, 8:48 PM

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it doesn't like that either

vital crag Sep 19, 2023, 8:48 PM

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what did you input

#

screenshot it

atomic spindle Sep 19, 2023, 8:48 PM

#

._.

vital crag Sep 19, 2023, 8:49 PM

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atomic spindle well f'(x) = lim h->0 [(4(x+h)-6(x+h)^2)-(4x-6x^2)]/h

then it's this but with x=0 and h=x

atomic spindle Sep 19, 2023, 8:51 PM

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f'(x) = lim h->0 [(4(0+x)-6(0+x)^2)-(4(0)-6(0)^2)]/x

#

(4x-6x^2)/x

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4-6x

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oh that was it

#

ok i got it thx

#

.close

final saddleBOT Sep 19, 2023, 8:54 PM

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final saddleBOT Sep 19, 2023, 9:22 PM

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vocal atlas Sep 19, 2023, 9:23 PM

#

guys

final saddleBOT Sep 19, 2023, 9:23 PM

#

vocal atlas

vocal atlas Sep 19, 2023, 9:23 PM

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mistake ?

#

they didnt put -

severe canyon Sep 19, 2023, 9:24 PM

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They used the minus on the exponent to swap numerator and the denominator

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(they did what is usually called reciprocal of a fraction)

vocal atlas Sep 19, 2023, 9:24 PM

#

fr

severe canyon Sep 19, 2023, 9:25 PM

#

$${\left(\frac{a}{b}\right)}^{-1} = \frac{b}{a}$$

soft zealotBOT Sep 19, 2023, 9:25 PM

#

Alberto Z.

vocal atlas Sep 19, 2023, 9:25 PM

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ye like

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oh shit

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oh shit

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feeet

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sometimes my brain malfunction

#

like im slow rn

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and i lose 33% of skill

#

and therefore i didnt catch this

#

make it 500x and i lose all skill gg

#

🇮🇱 Israeli military wins and dominates whole world gg

#

.close

final saddleBOT Sep 19, 2023, 9:27 PM

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jolly vector Sep 19, 2023, 10:00 PM

#

final saddleBOT Sep 19, 2023, 10:00 PM

#

jolly vector

jolly vector Sep 19, 2023, 10:00 PM

#

what does this mean

final saddleBOT Sep 19, 2023, 10:15 PM

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hushed musk Sep 19, 2023, 10:33 PM

#

Help I get how 16 comes from 2 but how do i know how many places to move the decimal.

final saddleBOT Sep 19, 2023, 10:33 PM

#

hushed musk Help I get how 16 comes from 2 but how do i know how many places to move the dec...

winter sleet Sep 19, 2023, 10:35 PM

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represent as a fraction

hushed musk Sep 19, 2023, 10:36 PM

#

Omg tysm 😭

#

.close

final saddleBOT Sep 19, 2023, 10:36 PM

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haughty grove Sep 19, 2023, 10:42 PM

#

can someone help me wotht he following calculation! 2+2=?

final saddleBOT Sep 19, 2023, 10:43 PM

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shell plover Sep 19, 2023, 10:50 PM

#

so i got the points (0,3) and (3,0) but idk where that what seems to be (-1.5, 0) comes from on the left

final saddleBOT Sep 19, 2023, 10:50 PM

#

shell plover so i got the points (0,3) and (3,0) but idk where that what seems to be (-1.5, 0...

shell plover Sep 19, 2023, 10:50 PM

#

ping if you know it

brave cloak Sep 19, 2023, 10:55 PM

#

shell plover so i got the points (0,3) and (3,0) but idk where that what seems to be (-1.5, 0...

substituting -1.5 for x in the first equation at x<0

shell plover Sep 19, 2023, 10:56 PM

#

brave cloak substituting -1.5 for x in the first equation at x<0

yeah but in reality im not given a graph so how woudl i know to use -1.5

brave cloak Sep 19, 2023, 10:57 PM

#

if the function is given let f(x)=0 and solve for x

shell plover Sep 19, 2023, 10:58 PM

#

wdym f(x) isnt = to 0 here

brave cloak Sep 19, 2023, 10:59 PM

#

(-1.5,0) means that f(x)=0 at x=1.5 so if you can't tell what the value of x is from the graph or the graph is not give use the function

shell plover Sep 19, 2023, 11:04 PM

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im sorry i really dont get it so my thing is if f(x) = 0 and f(x) = 2x +3 then 0 = 2x + 3 then x = 3/2

vital crag Sep 19, 2023, 11:09 PM

#

shell plover im sorry i really dont get it so my thing is if f(x) = 0 and f(x) = 2x +3 then 0...

2(3/2) + 3=?

final saddleBOT Sep 19, 2023, 11:19 PM

#

@shell plover Has your question been resolved?

shell plover Sep 19, 2023, 11:20 PM

#

vital crag 2(3/2) + 3=?

doesnt tha equal 9

#

how is that related

vital crag Sep 19, 2023, 11:30 PM

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shell plover doesnt tha equal 9

that's pluging in your value of x to 2x + 3

#

#

also that doesn't equal 9

#

2 (3/2) = 3

#

3 + 3 = ?

#

use a calculator to verify

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#

warm ether Sep 20, 2023, 12:07 AM

#

When you used the product rule you forgot the ln on the sin

royal gust Sep 20, 2023, 12:08 AM

#

Don't forget to chain-rule the ln(sin

final saddleBOT Sep 20, 2023, 12:20 AM

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@tranquil pine Has your question been resolved?

final saddleBOT Sep 20, 2023, 12:35 AM

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#

✅

final saddleBOT Sep 20, 2023, 12:52 AM

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@tranquil pine Has your question been resolved?

final saddleBOT Sep 20, 2023, 1:07 AM

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woven girder Sep 20, 2023, 1:11 AM

#

Given: limit as h approaches 0 of [4(h-2)^2+8(h-2)]/h

final saddleBOT Sep 20, 2023, 1:11 AM

#

woven girder **Given:** limit as h approaches 0 of [4(h-2)^2+8(h-2)]/h

woven girder Sep 20, 2023, 1:12 AM

#

I have identified that this is the h-gap method of dinging the derivative. I need to find f(x) and what is the value of x in question.

#

I am unsure of what to do.

final saddleBOT Sep 20, 2023, 1:27 AM

#

@woven girder Has your question been resolved?

woven girder Sep 20, 2023, 1:27 AM

#

@vast sonnet

#

<@&286206848099549185>

woven girder Sep 20, 2023, 1:27 AM

#

woven girder <@1146448870218399806>

Wrong ping, sorry.

final saddleBOT Sep 20, 2023, 1:57 AM

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@woven girder Has your question been resolved?

woven girder Sep 20, 2023, 2:21 AM

#

woven girder **Given:** limit as h approaches 0 of [4(h-2)^2+8(h-2)]/h

Does anyone know how to find the parent function from the derivative definition?

final saddleBOT Sep 20, 2023, 3:21 AM

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@woven girder Has your question been resolved?

final saddleBOT Sep 20, 2023, 4:21 AM

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vagrant wraith Sep 20, 2023, 4:49 AM

#

i was wondering whether to solve lim sin x/x=1 as x approaches 0, we could use small angle approximation on sin x?

final saddleBOT Sep 20, 2023, 4:49 AM

#

vagrant wraith i was wondering whether to solve lim sin x/x=1 as x approaches 0, we could use s...

vagrant wraith Sep 20, 2023, 4:50 AM

#

but a friend told me this is circular since small angle approximation is defined using lim sin/x as x approaches 0

#

is this right?

tired walrus Sep 20, 2023, 4:59 AM

#

yeah it is circular

final saddleBOT Sep 20, 2023, 5:05 AM

#

@vagrant wraith Has your question been resolved?

final saddleBOT Sep 20, 2023, 5:20 AM

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regal sail Sep 20, 2023, 6:58 AM

#

что такое отношение чисел?

final saddleBOT Sep 20, 2023, 6:58 AM

#

regal sail что такое отношение чисел?

hidden kernel Sep 20, 2023, 6:59 AM

#

regal sail что такое отношение чисел?

a/b

final saddleBOT Sep 20, 2023, 7:13 AM

#

@regal sail Has your question been resolved?

final saddleBOT Sep 20, 2023, 7:28 AM

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open shore Sep 20, 2023, 7:49 AM

#

how do you solve $4x^3-10x^2-1=0$

final saddleBOT Sep 20, 2023, 7:49 AM

#

open shore how do you solve $4x^3-10x^2-1=0$

hazy sequoia Sep 20, 2023, 7:50 AM

#

open shore how do you solve $4x^3-10x^2-1=0$

Is it one variable or 2?

open shore Sep 20, 2023, 7:51 AM

#

oh oops one

soft zealotBOT Sep 20, 2023, 7:51 AM

#

annyeong

hazy sequoia Sep 20, 2023, 7:52 AM

#

no way of factoring it that I can see

open shore Sep 20, 2023, 7:52 AM

#

the answer is a very long decimal

hazy sequoia Sep 20, 2023, 7:53 AM

#

Does the question ask you to solve it a certain way?

#

Maybe with a graphing calculator?

rich tide Sep 20, 2023, 7:54 AM

#

wait I have seen this polynomial

open shore Sep 20, 2023, 7:55 AM

#

nope

#

im guessing you can use a normal calculator but not sure how

desert mantle Sep 20, 2023, 7:55 AM

#

there is the cubic formula. it's painful to use but it does work

open shore Sep 20, 2023, 7:56 AM

#

hmm

desert mantle Sep 20, 2023, 7:56 AM

#

can you give us a picture of the problem statement

rich tide Sep 20, 2023, 7:56 AM

#

Okay the roots are highly irrational. You need to use cubic formula

hazy sequoia Sep 20, 2023, 7:56 AM

#

It seems likely that they mean for you to solve it with a graphing calculator, but who knows

open shore Sep 20, 2023, 7:57 AM

#

ok thanks at least i know that im not stupid

#

.close

final saddleBOT Sep 20, 2023, 7:58 AM

#

Channel closed

Closed by @open shore

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final saddleBOT Sep 20, 2023, 3:10 PM

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dim laurel Sep 20, 2023, 3:16 PM

#

Something that’s always confused me is how can you multiply a function without x

final saddleBOT Sep 20, 2023, 3:16 PM

#

dim laurel Something that’s always confused me is how can you multiply a function without x

dim laurel Sep 20, 2023, 3:16 PM

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For example

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If f: x → y then f = f(x)/x which is not true but yet fx ≠ f(x) so then how is fg possible

#

g isn’t defined because in this case g can be anything

#

I am confused on this notation and what it means

jade laurel Sep 20, 2023, 3:18 PM

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f = f(x)/x?

dim laurel Sep 20, 2023, 3:19 PM

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right which isn’t true

jade laurel Sep 20, 2023, 3:19 PM

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yes

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what are u doing

dim laurel Sep 20, 2023, 3:19 PM

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so then what do they mean when they write a homomorphism like f * g

jade laurel Sep 20, 2023, 3:20 PM

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i mean

dim laurel Sep 20, 2023, 3:20 PM

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Is it just a shorter version of the same thing

jade laurel Sep 20, 2023, 3:20 PM

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f * g

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f: x-> y

dim laurel Sep 20, 2023, 3:20 PM

#

f(x) * g = f * g?

jade laurel Sep 20, 2023, 3:20 PM

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g: z -> y

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ur writing composition right

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or

dim laurel Sep 20, 2023, 3:22 PM

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I guess what I’m trying to ask here is what’s the origin of f(x) and how does it differ from f cause you also have cases like ℤ[x]

jade laurel Sep 20, 2023, 3:22 PM

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what do you mean differ?

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how are u defining f?

#

like as the function right?

dim laurel Sep 20, 2023, 3:22 PM

#

dim laurel If f: x → y then f = f(x)/x which is not true but yet fx ≠ f(x) so then how is f...

^

#

Defined as a homomorphism that maps x to y

jade laurel Sep 20, 2023, 3:23 PM

#

then fg means the compsition

dim laurel Sep 20, 2023, 3:23 PM

#

Could you elaborate I’m unfamiliar with that term

jade laurel Sep 20, 2023, 3:24 PM

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if u have two maps

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f: x->y

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g: y->z

dim laurel Sep 20, 2023, 3:25 PM

#

Ohhh

jade laurel Sep 20, 2023, 3:25 PM

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their composition g \circ f

dim laurel Sep 20, 2023, 3:25 PM

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Would it be then fg: x -> z?

jade laurel Sep 20, 2023, 3:25 PM

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gf

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but change the domains and yeah

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basicly

dim laurel Sep 20, 2023, 3:25 PM

#

But I thought fg starts with x

#

fg would be z -> x then?

#

.close

final saddleBOT Sep 20, 2023, 3:35 PM

#

Channel closed

Closed by @dim laurel

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wispy plank Sep 20, 2023, 3:48 PM

#

how do i calculate percent equations (G:350,00€ %: 5) we gotta find out what W is

final saddleBOT Sep 20, 2023, 3:48 PM

#

wispy plank how do i calculate percent equations (G:350,00€ %: 5) we gotta find out what W i...

tired walrus Sep 20, 2023, 3:49 PM

#

i don't think anybody knows what the letters G and W stand for.

#

can you show the original problem?

#

even if it is not in english.

final saddleBOT Sep 20, 2023, 4:03 PM

#

@wispy plank Has your question been resolved?

final saddleBOT Sep 20, 2023, 4:18 PM

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final saddleBOT Sep 20, 2023, 6:32 PM

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sonic crescent Sep 20, 2023, 6:35 PM

#

Whats the domain and range of this?

The domain would be Z -> Z right

final saddleBOT Sep 20, 2023, 6:35 PM

#

sonic crescent Whats the domain and range of this? The domain would be Z -> Z right

severe canyon Sep 20, 2023, 6:35 PM

#

The domain is a set, it can't be "Z -> Z"

#

Anyway, the domain is Z, and the range is also Z

sonic crescent Sep 20, 2023, 6:36 PM

#

ohh ok, so what does Z -> Z really mean?

severe canyon Sep 20, 2023, 6:37 PM

#

sonic crescent ohh ok, so what does Z -> Z really mean?

The writing "Z -> Z" means that the function takes in input values from the set Z and spits out (returns) values in the set Z

sonic crescent Sep 20, 2023, 6:37 PM

#

ohh

severe canyon Sep 20, 2023, 6:37 PM

#

The arrow stands for "from Z to Z"

sonic crescent Sep 20, 2023, 6:38 PM

#

so R -> Z would mean the function takes in a real number and only spits out an integer?

severe canyon Sep 20, 2023, 6:38 PM

#

Yep

sonic crescent Sep 20, 2023, 6:38 PM

#

thank you!

severe canyon Sep 20, 2023, 6:38 PM

#

You're welcome 😊

sonic crescent Sep 20, 2023, 6:38 PM

#

.close

final saddleBOT Sep 20, 2023, 6:38 PM

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Channel closed

Closed by @sonic crescent

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final saddleBOT Sep 20, 2023, 8:16 PM

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slender ridge Sep 20, 2023, 8:17 PM

#

final saddleBOT Sep 20, 2023, 8:17 PM

#

slender ridge

slender ridge Sep 20, 2023, 8:18 PM

#

im confused on how im supposed to write the formula

languid yoke Sep 20, 2023, 8:23 PM

#

basically you're just solving for the shaded area in terms of theta

#

you would do that by doing
[area of triangle] - [area of sector]

slender ridge Sep 20, 2023, 8:32 PM

#

languid yoke basically you're just solving for the shaded area in terms of theta

how do I know the area if I dont have the angle

languid yoke Sep 20, 2023, 8:34 PM

#

you just write an expression in terms of theta

#

do you get what that means

slender ridge Sep 20, 2023, 8:40 PM

#

would it be this?

#

@languid yoke

languid yoke Sep 20, 2023, 8:43 PM

#

yes!

#

except you can use r=10 for the pi*r^2

#

but yeah that's basically the idea just make sure to simplify

slender ridge Sep 20, 2023, 8:44 PM

#

bruh

#

did I do smth wrong

#

#

this is the answer apparently

#

idk how

final saddleBOT Sep 20, 2023, 9:20 PM

#

@slender ridge Has your question been resolved?

#

Channel closed

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zenith quarry Sep 20, 2023, 9:28 PM

#

Why is it 1/3 as the constant that spills out and not 1/9?

final saddleBOT Sep 20, 2023, 9:28 PM

#

zenith quarry Why is it 1/3 as the constant that spills out and not 1/9?

charred chasm Sep 20, 2023, 9:29 PM

#

what's u here?

zenith quarry Sep 20, 2023, 9:29 PM

#

okay i just thought about that- i guess u=1/3 x

charred chasm Sep 20, 2023, 9:29 PM

#

that's right

zenith quarry Sep 20, 2023, 9:30 PM

#

but then where does the 9 constant term come from?

charred chasm Sep 20, 2023, 9:30 PM

#

that was the original problem, no?

#

or are you asking where it went?

zenith quarry Sep 20, 2023, 9:30 PM

#

where it went sorry

#

like if i distribute the 3 it looks like it doesn't work

charred chasm Sep 20, 2023, 9:30 PM

#

ah, then try factoring out 9 from the denominator

#

start with 1/(x^2 +9)

#

factor out 9 from the denominator

zenith quarry Sep 20, 2023, 9:31 PM

#

i feel like i get 1/9 * 1/(x^2/9 + 1)

charred chasm Sep 20, 2023, 9:31 PM

#

great

#

now do u -sub

manic herald Sep 20, 2023, 9:31 PM

#

zenith quarry Why is it 1/3 as the constant that spills out and not 1/9?

because dx = 3 du

charred chasm Sep 20, 2023, 9:32 PM

#

with u = x/3

zenith quarry Sep 20, 2023, 9:32 PM

#

oooooooooooooooooooooh okay okay

charred chasm Sep 20, 2023, 9:32 PM

#

does that make sense now?

zenith quarry Sep 20, 2023, 9:32 PM

#

thank u sm!!! yes yes

charred chasm Sep 20, 2023, 9:32 PM

#

cool

#

gl

zenith quarry Sep 20, 2023, 9:32 PM

#

i am so . rusty with my calc 2 crying

#

its ok ill get there 🙏

#

.close

final saddleBOT Sep 20, 2023, 9:33 PM

#

Channel closed

Closed by @zenith quarry

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chrome zinc Sep 20, 2023, 9:41 PM

#

how does someone solve the a/b part i don't even know what a binary operation is

final saddleBOT Sep 20, 2023, 9:41 PM

#

chrome zinc how does someone solve the a/b part i don't even know what a binary operation is

winter sleet Sep 20, 2023, 9:42 PM

#

takes two inputs

chrome zinc Sep 20, 2023, 9:42 PM

#

i can use any number on this right?

#

as long as it's not 0?

warm ether Sep 20, 2023, 9:43 PM

#

any 2 rational numbers that are non-zero

winter sleet Sep 20, 2023, 9:43 PM

#

Q - rational

chrome zinc Sep 20, 2023, 9:45 PM

#

so do i something else after i give a number to the entire equation?

#

do i solve it or i just leave it like that?

warm ether Sep 20, 2023, 9:48 PM

#

what you have showed is a definition, theres no working to be done from what youve shown

chrome zinc Sep 20, 2023, 9:49 PM

#

oh wait so i just replace it and that's it??

warm ether Sep 20, 2023, 9:49 PM

#

wdym replace it

chrome zinc Sep 20, 2023, 9:49 PM

#

ill just give a number and thats it

warm ether Sep 20, 2023, 9:49 PM

#

what are you using this definition for

chrome zinc Sep 20, 2023, 9:49 PM

#

nothing

#

that's the entire thing

warm ether Sep 20, 2023, 9:50 PM

#

or are you trying to prove it maps back to the rationals

chrome zinc Sep 20, 2023, 9:50 PM

#

there's nothing else attached to the original question despite being homework

#

u just have to define it and that's it

#

oh when i meant nothing it's homework

#

alright i think i got it thanks mate

#

.close

final saddleBOT Sep 20, 2023, 10:06 PM

#

Channel closed

Closed by @chrome zinc

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final saddleBOT Sep 20, 2023, 10:26 PM

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faint wing Sep 20, 2023, 10:34 PM

#

I need help with this: A parallelogram has a height of 3 ft and a base of 8 ft. Find the area of each shape that composes the parallelogram. What is the total area of thes special quadrilateral?
8 ft x 3 ft x 3 ft x 4.25 ft.

final saddleBOT Sep 20, 2023, 10:34 PM

#

faint wing I need help with this: A parallelogram has a height of 3 ft and a base of 8 ft. ...

faint wing Sep 20, 2023, 10:35 PM

#

<@&286206848099549185>

mental roost Sep 20, 2023, 10:36 PM

#

!15m

final saddleBOT Sep 20, 2023, 10:36 PM

#

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.

winter sleet Sep 20, 2023, 10:36 PM

#

stop opening new channels and spamming helpers

mental roost Sep 20, 2023, 10:36 PM

#

#❓how-to-get-help

faint wing Sep 20, 2023, 10:36 PM

#

i need help but noone coming

rancid idol Sep 20, 2023, 10:36 PM

#

!patience

final saddleBOT Sep 20, 2023, 10:36 PM

#

Please wait patiently, and do not interrupt other channels with your question. Helpers in this server are volunteers, and the server cannot guarantee that someone will be able to help you. By being impatient or begging, you will only turn potential helpers away.

In the meantime, please make sure your channel contains the original question, clearly describes what you have already tried, and states exactly what you are having trouble with. This increases your chances of getting a good response.

faint wing Sep 20, 2023, 10:38 PM

#

ok imma wait

#

if i dont get help in 10 mins imma be mad

#

A parallelogram has a height of 3 ft and a base of 8 ft. Find the area of each shape that composes the parallelogram. What is the total area of thes special quadrilateral?
8 ft x 3 ft x 3 ft x 4.25 ft.

mental roost Sep 20, 2023, 10:39 PM

#

remember that people help here, they dont work here

unique eagle Sep 20, 2023, 10:39 PM

#

Lol, none of us are getting paid to help, you can get mad all you want

faint wing Sep 20, 2023, 10:39 PM

#

ik im just saying

mental roost Sep 20, 2023, 10:39 PM

#

kindness often leads to quicker help

winter sleet Sep 20, 2023, 10:39 PM

#

better draw a diagram in the mean time

faint wing Sep 20, 2023, 10:40 PM

#

????

iron mist Sep 20, 2023, 10:40 PM

#

You don’t even have a diagram 💀

faint wing Sep 20, 2023, 10:40 PM

#

i do

grim badger Sep 20, 2023, 10:40 PM

#

faint wing i do

In the meantime, please make sure your channel contains the original question, clearly describes what you have already tried, and states exactly what you are having trouble with. This increases your chances of getting a good response.

iron mist Sep 20, 2023, 10:40 PM

#

Can’t help here when we have no idea what the figure looks like

faint wing Sep 20, 2023, 10:40 PM

#

i alr had it written 10 mins ago 💀

#

imma show it

#

gimme a sec

#

here.

#

#

.close

final saddleBOT Sep 20, 2023, 10:46 PM

#

Channel closed

Closed by @faint wing

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final saddleBOT Sep 20, 2023, 11:18 PM

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ornate harness Sep 20, 2023, 11:30 PM

#

how would i solve this

final saddleBOT Sep 20, 2023, 11:30 PM

#

ornate harness how would i solve this

ornate harness Sep 20, 2023, 11:30 PM

#

initial velocity = 0 m/s

#

t isnt given

#

acceleration is what i would have to solve for right?

#

oh wait

#

i solve

#

nvm i got it chat

#

if i set final velocity to 18

#

initial to 0

#

it will give me the acceleration

#

which i can use to figure out the final velocity for the last car as it passes the railway worker

#

chat is this right?

vestal frigate Sep 20, 2023, 11:33 PM

#

Yeah you want to find its acceleration and then figure out how fast it would be going 180+75 meters from t=0

ornate harness Sep 20, 2023, 11:34 PM

#

cuz the dude is 180m away

#

so i can set displacement to 180+75

#

solve for vf

final saddleBOT Sep 20, 2023, 11:49 PM

#

@ornate harness Has your question been resolved?

#

Channel closed

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lusty charm Sep 20, 2023, 11:54 PM

#

can someone explain where the vector projection formula comes from? like for this example, why square the bottom and multiply by v?

final saddleBOT Sep 20, 2023, 11:54 PM

#

lusty charm can someone explain where the vector projection formula comes from? like for thi...

rancid idol Sep 20, 2023, 11:56 PM

#

it can be restated as v hat

#

v hat is v / |v|

#

v hat being the unit vector in the direction of v

winged python Sep 20, 2023, 11:59 PM

#

Oh, I'm learning about this stuff rn, here's a page from my online textbook that might help

lusty charm Sep 21, 2023, 12:03 AM

#

that makes so much sense

lusty charm Sep 21, 2023, 12:03 AM

#

winged python Oh, I'm learning about this stuff rn, here's a page from my online textbook that...

thank you very much!

#

i'll save this

winged python Sep 21, 2023, 12:04 AM

#

I can dm you the full chapter's link too (it's free + online) if you're interested

lusty charm Sep 21, 2023, 12:04 AM

#

yooo that's great

winged python Sep 21, 2023, 12:04 AM

#

You can find explanations for other calc III stuff there, like cross product and etc.

lusty charm Sep 21, 2023, 12:04 AM

#

please do

#

.close

final saddleBOT Sep 21, 2023, 12:07 AM

#

Channel closed

Closed by @lusty charm

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tacit knot Sep 21, 2023, 12:08 AM

#

How do I know which to subtract by without seeing the graph

final saddleBOT Sep 21, 2023, 12:08 AM

#

tacit knot How do I know which to subtract by without seeing the graph

tacit knot Sep 21, 2023, 12:09 AM

#

Or do I have to visualize it every time..

warm ether Sep 21, 2023, 12:12 AM

#

i mean, its probably the most efficient way to go about it, if you do them the wrong way round youll get negative area for said integral so just change the sign

winged python Sep 21, 2023, 12:13 AM

#

tacit knot How do I know which to subtract by without seeing the graph

You can probably input a random value between the intervals as x, and use that to see which function is on the bottom and which function is on the top without using the graph

final saddleBOT Sep 21, 2023, 12:24 AM

#

@tacit knot Has your question been resolved?

final saddleBOT Sep 21, 2023, 12:39 AM

#

Channel closed

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final saddleBOT Sep 21, 2023, 1:02 AM

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nimble quartz Sep 21, 2023, 1:50 AM

#

I have a really annoying thing to prove

final saddleBOT Sep 21, 2023, 1:50 AM

#

nimble quartz I have a really annoying thing to prove

nimble quartz Sep 21, 2023, 1:50 AM

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0 and 1 are in a set

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and for any two elements in the set, their average is also in it so it is inductive

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i need to prove if 1/6 is in the set

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<@&286206848099549185>

vital crag Sep 21, 2023, 2:08 AM

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Can you prove that any numbers of the form 2^(-n) are in the set?

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n>=1

nimble quartz Sep 21, 2023, 2:08 AM

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I think so yeah

vital crag Sep 21, 2023, 2:08 AM

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Hmm nevermind I'm not sure if that's useful

nimble quartz Sep 21, 2023, 2:09 AM

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I’m not sure about how to structure the proof too

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i think it’s supposed to be structural induction

final saddleBOT Sep 21, 2023, 2:25 AM

#

@nimble quartz Has your question been resolved?

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slender ridge Sep 21, 2023, 2:49 AM

#

final saddleBOT Sep 21, 2023, 2:49 AM

#

slender ridge

slender ridge Sep 21, 2023, 2:49 AM

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how do I make the bottom not x so it not undefined

strange shore Sep 21, 2023, 2:50 AM

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you cant

slender ridge Sep 21, 2023, 2:50 AM

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bruh

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.close

final saddleBOT Sep 21, 2023, 2:50 AM

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slender ridge Sep 21, 2023, 2:52 AM

#

#

what do I do?

#

do I multiply by the congrugate

obtuse heath Sep 21, 2023, 2:54 AM

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You should first type .reopen so the channel doesn't become available

slender ridge Sep 21, 2023, 2:54 AM

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oh

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.reopen

final saddleBOT Sep 21, 2023, 2:55 AM

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✅

slender ridge Sep 21, 2023, 2:55 AM

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thx

obtuse heath Sep 21, 2023, 2:55 AM

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slender ridge how do I make the bottom not x so it not undefined

You can, by simplifying the expression

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Always do it when you can

slender ridge Sep 21, 2023, 2:57 AM

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how do I do that

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like how do I go about that

obtuse heath Sep 21, 2023, 2:58 AM

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First subtract the fractions on the numerator

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Then use (a/b)/c=a/(bc)

final saddleBOT Sep 21, 2023, 3:12 AM

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@slender ridge Has your question been resolved?

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kindred timber Sep 21, 2023, 3:45 AM

#

#

how is this wrong

final saddleBOT Sep 21, 2023, 3:45 AM

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kindred timber

kindred timber Sep 21, 2023, 3:45 AM

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i ran out of submissions

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but i cant see how this is wrong

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dont you just integrate by component?

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or did i miss something

robust mulch Sep 21, 2023, 3:47 AM

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Do they want exact answers?

kindred timber Sep 21, 2023, 3:47 AM

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no but they never don't accept it

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wdym

robust mulch Sep 21, 2023, 3:47 AM

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Ok lemme check you number rq

kindred timber Sep 21, 2023, 3:47 AM

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go for it

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#

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i made sure to check it too

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just in case

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but these are the numbers I get

robust mulch Sep 21, 2023, 3:48 AM

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Hmm

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Perhaps they wanted you to use i j and k

kindred timber Sep 21, 2023, 3:48 AM

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made it wants it in not component form

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but its never marked me wrong for that before

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its always been interchangeable

robust mulch Sep 21, 2023, 3:49 AM

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Is this cengage?

kindred timber Sep 21, 2023, 3:49 AM

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yes

robust mulch Sep 21, 2023, 3:49 AM

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I dont think they like <>

kindred timber Sep 21, 2023, 3:49 AM

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robust mulch Sep 21, 2023, 3:49 AM

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Oh

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Nvm then

kindred timber Sep 21, 2023, 3:49 AM

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ok i mean as long as I did it right its fine ig

runic oyster Sep 21, 2023, 3:49 AM

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Cengage doesn't like decimal answers sometimes

kindred timber Sep 21, 2023, 3:49 AM

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i see

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weird

robust mulch Sep 21, 2023, 3:50 AM

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Yeah ypu probably want to use fractions next time

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I cant see what else would have been wrong

kindred timber Sep 21, 2023, 3:50 AM

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ok damn

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thanks

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.close

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tranquil pine Sep 21, 2023, 4:21 AM

#

<@&286206848099549185>

final saddleBOT Sep 21, 2023, 4:21 AM

#

tranquil pine <@&286206848099549185>

magic sparrow Sep 21, 2023, 4:22 AM

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!15mins

final saddleBOT Sep 21, 2023, 4:22 AM

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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.

tranquil pine Sep 21, 2023, 4:22 AM

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he4lopp

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hello

magic sparrow Sep 21, 2023, 4:23 AM

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tranquil pine Sep 21, 2023, 4:23 AM

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oh sorry

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can u help me get ready for a retake test i will send pics

#

#

are u there

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.close

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civic ether Sep 21, 2023, 4:49 AM

#

@summer snow for the same question i posted prior

24acbe8bbc1e43e2b85e8f43d494eb2dtplv-ejcjvp0zxf-webp-scale425415.png

final saddleBOT Sep 21, 2023, 4:49 AM

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civic ether <@420958138682834944> for the same question i posted prior

civic ether Sep 21, 2023, 4:49 AM

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now that i think about it

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can i never consider fractional powers of x?

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x = 2^(2.5) * 3^(1.5)

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in that case when squared it'll always have a 2^5 and 3^3 guanteed right

summer snow Sep 21, 2023, 4:51 AM

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That would be true, yeah

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It shouldn't change our answer in this case however

civic ether Sep 21, 2023, 4:54 AM

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summer snow It shouldn't change our answer in this case however

makes sense, but which is the actual right way to express your answer?

Would it be more valid for x = 2^(2.5) * 3^(1.5) or x = 2^3 3^2

in the first case, you'd have x^2 = 2^5 * 3^3 * k

in the second case, you'd have x^2 = 2^6 * 3^4 * k where the k could absorb the extras and also get to x^2 = 2^5 * 3^3 * k

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they both yield correct answers then ig, but if i was teaching someone then which way would i imply

summer snow Sep 21, 2023, 4:57 AM

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If I were to describe all possible values of x, I might say:

$x$ equals $2^\frac{5+x}{2}\cdot 3^\frac{3+y}{2} \cdot \sqrt{k}$ for nonnegative integers $x$, $y$, and $k$.

soft zealotBOT Sep 21, 2023, 4:58 AM

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@summer snow

civic ether Sep 21, 2023, 5:00 AM

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hmm okay

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i think i kind of figured

summer snow Sep 21, 2023, 5:00 AM

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Or I suppose that could be simplified to just
[ x = 2^\frac{5}{2} \cdot 3^\frac{3}{2} \cdot \sqrt{k} ]
For some nonnegative integer $k$

soft zealotBOT Sep 21, 2023, 5:00 AM

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@summer snow

civic ether Sep 21, 2023, 5:01 AM

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u can't have fractional exponents as multiples because that would imply non integral multiplies and that usually isn't a thing unless you're working with ring theory and the like

summer snow Sep 21, 2023, 5:01 AM

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Yeah, exactly

civic ether Sep 21, 2023, 5:02 AM

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yeah so ig that should be it

civic ether Sep 21, 2023, 5:02 AM

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soft zealot <@420958138682834944>

also shouldn't it be k

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k is scaled

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u wouldn't sqrt(k) in anticipation that it'll be k after squaring imo

summer snow Sep 21, 2023, 5:03 AM

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If you wanted to include it as part of the definition of $x$, you would have to take the square root, otherwise $x^2 = 864 \times 2$ (a possibile multiple of 864) wouldn't have a corresponding valid $x$ value

soft zealotBOT Sep 21, 2023, 5:03 AM

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@summer snow

summer snow Sep 21, 2023, 5:04 AM

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since no integer satisfies $n^2 = 2$

soft zealotBOT Sep 21, 2023, 5:04 AM

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@summer snow

summer snow Sep 21, 2023, 5:05 AM

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Ah, though I suppose that messes with the ability for x to be negative and still satisfy the equation

#

A better definition would then be $x = \pm 2^\frac{5}{2} \cdot 3^\frac{3}{2} \cdot k^\frac{1}{2}$

soft zealotBOT Sep 21, 2023, 5:06 AM

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@summer snow

civic ether Sep 21, 2023, 5:07 AM

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hmm okay fair enough

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thanks

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one more question

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https://cdn.discordapp.com/attachments/1081837589780234241/1154008669453832203/Screenshot_2023-09-20_at_6.56.29_pm.png

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obviously i can just use the formula

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but how about if i don't want to use the formula

summer snow Sep 21, 2023, 5:11 AM

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I think we can intuit without the formula that B should be larger, since set A and set B both have equally evenly spaced elements, and set B has a larger range

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i.e., the regularity means that the larger range causes it to by definition deviate further from the mean

civic ether Sep 21, 2023, 5:12 AM

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summer snow I think we can intuit without the formula that B should be larger, since set A a...

so standard deviation increases with population size provided each input is distinct?

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ofc with the given fact that the spacing is consistent

summer snow Sep 21, 2023, 5:14 AM

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It's not necessarily that it increases with population size

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,w standard deviation {1, 2, 3, 4, 5, 6, 7}

soft zealotBOT Sep 21, 2023, 5:14 AM

#

Results provided by WolframAlpha

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summer snow Sep 21, 2023, 5:14 AM

#

,w standard deviation {1, 3, 5, 7}

soft zealotBOT Sep 21, 2023, 5:14 AM

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Results provided by WolframAlpha

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summer snow Sep 21, 2023, 5:16 AM

#

It seems that standard deviation generally will increase as the distance from the maximum and minimum elements increases, and as the distance between each element increases

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So going from 1...7 to 1...8, our range increased, so std dev should increase

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from 1...7 to 1,3,...,7, our range stayed the same, but the space between elements increased, so our std dev increased, even though we had fewer elements

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A proof as to why this might be a general trend would be interesting but is outside the scope of what I'm available to do right now

civic ether Sep 21, 2023, 5:26 AM

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summer snow A proof as to why this might be a general trend would be interesting but is outs...

no problem, yeah it does make intuitive sense, thanks so much

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.close

final saddleBOT Sep 21, 2023, 5:26 AM

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broken fox Sep 21, 2023, 5:39 AM

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i don’t know what i did wrong here. it seems rigjt to me

final saddleBOT Sep 21, 2023, 5:39 AM

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broken fox i don’t know what i did wrong here. it seems rigjt to me

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@broken fox Has your question been resolved?

inland ice Sep 21, 2023, 6:09 AM

#

broken fox i don’t know what i did wrong here. it seems rigjt to me

Hi there!

Statement 4 is incorrect because something like statement one where you have m <CBE = m<1 + m<3 (For this you're saying both those angles equal up to that entire angle labeled by the letters C B and E) is not the same as saying m<1 + m<2 = m<3 + m<4 (These angles added together separately make the same angles but they do not conclusively make the exact same bigger angle like statement 1.)

Statement 5 is wrong because if you look back at the problem you can see that your statement: m<2 = m<4 was given hence was reflexive property would be incorrect

Statement 7 is wrong because m<1 and m<3 do not have an adjacent line between them that make them the same, well symmetry wise

Hope that helps and makes sense!

final saddleBOT Sep 21, 2023, 6:09 AM

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timber onyx Sep 21, 2023, 3:21 PM

#

final saddleBOT Sep 21, 2023, 3:21 PM

#

timber onyx

timber onyx Sep 21, 2023, 3:21 PM

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I’m confused on how to do this

final saddleBOT Sep 21, 2023, 3:36 PM

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@timber onyx Has your question been resolved?

timber onyx Sep 21, 2023, 3:41 PM

#

<@&286206848099549185>

timber onyx Sep 21, 2023, 3:59 PM

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<@&286206848099549185> hello?

frank swan Sep 21, 2023, 4:08 PM

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timber onyx <@&286206848099549185> hello?

Basicaly y=4(x+7)+1-1 , the input +7 with x will shift it to the left and the -1 will shift it down

timber onyx Sep 21, 2023, 4:09 PM

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the answer has it as y= 4x + 28

frank swan Sep 21, 2023, 4:10 PM

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Huh...?

timber onyx Sep 21, 2023, 4:11 PM

#

#

Yeah

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I’m just gonna ask my teacher

frank swan Sep 21, 2023, 4:12 PM

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K

timber onyx Sep 21, 2023, 4:13 PM

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Thanks though

frank swan Sep 21, 2023, 4:13 PM

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Welcome

timber onyx Sep 21, 2023, 4:13 PM

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frank swan Basicaly y=4(x+7)+1-1 , the input +7 with x will shift it to the left and the -1...

that’s the same thing I did lol but I’ll see how he gets the 28

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.close

final saddleBOT Sep 21, 2023, 4:13 PM

#

Channel closed

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frank swan Sep 21, 2023, 4:13 PM

#

timber onyx that’s the same thing I did lol but I’ll see how he gets the 28

Yeaa thx gg

final saddleBOT Sep 21, 2023, 4:14 PM

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grim hinge Sep 21, 2023, 4:35 PM

#

Stuck on this question

final saddleBOT Sep 21, 2023, 4:35 PM

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grim hinge Stuck on this question

grim hinge Sep 21, 2023, 4:35 PM

#

Hello, not quite sure what to do

warm ether Sep 21, 2023, 4:39 PM

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what is marginal functions worksheet 9

grim hinge Sep 21, 2023, 4:40 PM

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its the worksheet the question is pulled from

warm ether Sep 21, 2023, 4:41 PM

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is this everything you have?

grim hinge Sep 21, 2023, 4:42 PM

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I have that too

final saddleBOT Sep 21, 2023, 4:57 PM

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@grim hinge Has your question been resolved?

final saddleBOT Sep 21, 2023, 5:29 PM

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@grim hinge Has your question been resolved?

final saddleBOT Sep 21, 2023, 5:59 PM

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glad basalt Sep 21, 2023, 6:03 PM

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final saddleBOT Sep 21, 2023, 6:03 PM

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glad basalt

glad basalt Sep 21, 2023, 6:03 PM

#

#

this is the original expression

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Why is y-int 5, 0 not plotted in the graph?

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final tangle Sep 21, 2023, 6:05 PM

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wdym

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what's 5, 0 supposed to mean

glad basalt Sep 21, 2023, 6:06 PM

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y int?

final tangle Sep 21, 2023, 6:06 PM

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y int is plotted here, its -3/2

glad basalt Sep 21, 2023, 6:06 PM

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how come its not 5, 0?

final tangle Sep 21, 2023, 6:06 PM

#

wdym by 5,0

glad basalt Sep 21, 2023, 6:06 PM

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I think its 5, 0

#

?

final tangle Sep 21, 2023, 6:07 PM

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did you mean (5,0)?

glad basalt Sep 21, 2023, 6:07 PM

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final tangle y int is plotted here, its -3/2

did you mean (-3, 2) ?

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come on

final tangle Sep 21, 2023, 6:07 PM

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no

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i did not

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-3/2 is -3/2

glad basalt Sep 21, 2023, 6:07 PM

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so

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that means

final tangle Sep 21, 2023, 6:08 PM

#

its fine to represent intercepts with a single numerical value

glad basalt Sep 21, 2023, 6:08 PM

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(-3/2, 0)

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anyways

final tangle Sep 21, 2023, 6:08 PM

#

you however are either listing two values

glad basalt Sep 21, 2023, 6:08 PM

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y int means y is 0

final tangle Sep 21, 2023, 6:08 PM

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or giving something implying you meant (5,0) which isn't a y-intercept at all

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no

glad basalt Sep 21, 2023, 6:08 PM

#

hm

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fdsaaaaaaaaaaaaaaa

#

I guess I mean x intercept

final tangle Sep 21, 2023, 6:09 PM

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y-intercept as the name suggests is where the y-axis is intercepted

glad basalt Sep 21, 2023, 6:10 PM

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do they not plot the x intercept

final tangle Sep 21, 2023, 6:10 PM

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did you try evaluating this function at x=5?

glad basalt Sep 21, 2023, 6:10 PM

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final tangle did you try evaluating this function at x=5?

yes thats a hole (5, 1)

final tangle Sep 21, 2023, 6:10 PM

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() are NOT optional when writing a point

glad basalt Sep 21, 2023, 6:10 PM

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lol

final tangle Sep 21, 2023, 6:11 PM

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anyway you have your answer

glad basalt Sep 21, 2023, 6:11 PM

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thats the x int

final tangle Sep 21, 2023, 6:11 PM

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no?

glad basalt Sep 21, 2023, 6:11 PM

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final tangle anyway you have your answer

bu-

final tangle Sep 21, 2023, 6:11 PM

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your work indicates that you have a hole at (5,1)

#

supposedly you also reached that the function is undefined at x=5
and/or that f(x) isn't 0 when x=5

glad basalt Sep 21, 2023, 6:13 PM

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what does that tell us?

final tangle Sep 21, 2023, 6:13 PM

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yes thats a hole (5, 1)

glad basalt Sep 21, 2023, 6:13 PM

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why can't there be a hole there

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and also be a x int

final tangle Sep 21, 2023, 6:14 PM

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technically you could

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IF the function is 0 when x=5,

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but f(5) isn't 0

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its undefined

glad basalt Sep 21, 2023, 6:15 PM

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why do we only care about x = 5

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and that being a hole

final tangle Sep 21, 2023, 6:15 PM

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because that's what you're asking about

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specifically

glad basalt Sep 21, 2023, 6:15 PM

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OHHHHHHH

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ok

#

so if there were not a hole at x = 5

final tangle Sep 21, 2023, 6:16 PM

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(5,0) isn't an x-interecept becaue
f(5) isn't 0

glad basalt Sep 21, 2023, 6:16 PM

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that'd be an x intercept

final tangle Sep 21, 2023, 6:16 PM

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no

glad basalt Sep 21, 2023, 6:16 PM

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why not I set the whole function to = 0

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and got (5, 0)

final tangle Sep 21, 2023, 6:16 PM

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you can try

#

but you'd did some invalid stuff along the way to get that