#help-39 | Mathematics | Page 50

sonic rivet Oct 29, 2023, 6:28 PM

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but we still have the -(-ab) term at the end

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in this case -(-12*10) = 120

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so we can write rc - 12r - 10c = rc - 12r - 10c + 120 - 120

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we are allowed to write this because we add then subtract 120, so its like adding 0, changes nothing

torn willow Oct 29, 2023, 6:30 PM

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rb is 10r

sonic rivet Oct 29, 2023, 6:30 PM

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oh woops

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a = 10, b = 12

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wait what

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no

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yes

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yes

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alright I have to go

torn willow Oct 29, 2023, 6:32 PM

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what?

sonic rivet Oct 29, 2023, 6:33 PM

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but rc - 12r - 10c + 120 - 120 = (r-10)(r-12) - 120 = 1 since r - 12r - 10c = 1 from above

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so (r-10)(r-12) = 121

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and now you consider all the different factors for 121

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which are 1, 11 and 121

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so you can check em all but you'll see that you need c-10 = 11 and r - 12 = 11

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from which we get c = 21 and r = 23

torn willow Oct 29, 2023, 6:35 PM

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sonic rivet but rc - 12r - 10c + 120 - 120 = (r-10)(r-12) - 120 = 1 since r - 12r - 10c = 1 ...

how did u figure out this equation?

sonic rivet Oct 29, 2023, 6:35 PM

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rc - 12r - 10c = 1 is what we established before

torn willow Oct 29, 2023, 6:35 PM

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k

sonic rivet Oct 29, 2023, 6:35 PM

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but rc - 12r - 10c = rc - 12r - 10c + 120 - 120 = (r-10)(r-12) - 120

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so 1 = (r-10)(r-12) - 120

torn willow Oct 29, 2023, 6:36 PM

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where did that 120 came from

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?

sonic rivet Oct 29, 2023, 6:37 PM

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I made it appear artificially so that I could use that (r-10)(c-12) = rc - 12r - 10c + 120

torn willow Oct 29, 2023, 6:37 PM

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artificially?

sonic rivet Oct 29, 2023, 6:37 PM

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rc - 12r - 10c + 120 - 120 <= notice that I add and then subtract 120

torn willow Oct 29, 2023, 6:38 PM

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WDYM?

sonic rivet Oct 29, 2023, 6:38 PM

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well just it seems useless

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but its not uselesss

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adding + 120 - 120 to a term seems a bit dumb, like adding +0

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but the +120 gets swept up into (r-10)(c-12), while the -120 gets left behind and sticks around until the end

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alright, bye

torn willow Oct 29, 2023, 6:39 PM

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why do we need to use 120?

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i dont get it

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<@&286206848099549185>

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<@&286206848099549185>

pearl pondBOT Oct 29, 2023, 7:06 PM

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@torn willow Has your question been resolved?

torn willow Oct 29, 2023, 7:06 PM

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<@&286206848099549185> can someone pls help me

foggy carbon Oct 29, 2023, 7:08 PM

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you have this equation
rc = 12r + 10c + 1

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turns out it can be factored

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rc - 12r - 10c = 1
(r - 10)(c - 12) - 120 = 1
(r - 10)(c - 12) = 121

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121 = 11 times 11

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so the only thing that makes sense is
r - 10 = 11
r = 21

c - 12 = 11
c = 23

foggy carbon Oct 29, 2023, 7:11 PM

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torn willow <@&286206848099549185>

there are 21 * 23 = 483 chairs

pearl pondBOT Oct 29, 2023, 7:36 PM

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@torn willow Has your question been resolved?

torn willow Oct 29, 2023, 7:43 PM

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but how is it 120

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@foggy carbon

foggy carbon Oct 29, 2023, 8:07 PM

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torn willow <@209300311091838977>

(r - 10)(c - 12) = rc - 12r - 10c + 120

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rc - 12r - 10c = 1
(rc - 12r - 10c + 120) - 120 = 1
(r - 10)(c - 12) - 120 = 1
(r - 10)(c - 12) = 121

torn willow Oct 29, 2023, 8:08 PM

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foggy carbon (r - 10)(c - 12) = rc - 12r - 10c + 120

how do u factorise it without common factor

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there are three methods that i know for factorisation:
common factor
difference between two squares
trinomials

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which method do u use?

foggy carbon Oct 29, 2023, 8:11 PM

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it is similar to completing the square

torn willow Oct 29, 2023, 8:12 PM

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what is completing the square

foggy carbon Oct 29, 2023, 8:12 PM

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for example, if you have
x^2 + 6x = 1

you do
(x^2 + 6x + 9) - 9 = 1
(x + 3)^2 - 9 = 1
(x + 3)^2 = 10

foggy carbon Oct 29, 2023, 8:13 PM

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foggy carbon rc - 12r - 10c = 1 (rc - 12r - 10c + 120) - 120 = 1 (r - 10)(c - 12) - 120 = 1 (...

here it is similar but instead of x^2 it is rc

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so the expansion gets you r term + c term

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which you use to factor it

torn willow Oct 29, 2023, 8:14 PM

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alright i will check about that in the internet too

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tysm

foggy carbon Oct 29, 2023, 8:14 PM

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torn willow alright i will check about that in the internet too

yes do that

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and np

torn willow Oct 29, 2023, 8:14 PM

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can somebody also help me with another question?

foggy carbon Oct 29, 2023, 8:14 PM

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make a new help channel

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close this first

torn willow Oct 29, 2023, 8:15 PM

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k

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.close

pearl pondBOT Oct 29, 2023, 8:15 PM

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pearl pondBOT Oct 29, 2023, 8:41 PM

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midnight haven Oct 29, 2023, 8:59 PM

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The parabol equation:
y = x^2 −4x + 4

-Vertex (2,0)
x = -b/2a = 2
y = 0

AOS = 2
with y intercept
x = 0
y = 4
-with x intercept
y = 0
x = -b ± √(b^2-4ac) / 2a
x1 = 3,4
x2 = 0,6

pearl pondBOT Oct 29, 2023, 8:59 PM

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midnight haven The parabol equation: y = x^2 −4x + 4 -Vertex (2,0) x = -b/2a = 2 y = 0 - AOS ...

midnight haven Oct 29, 2023, 9:00 PM

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The question that i am having trouble with is: find the highest and lowest point of parabola

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I know its opening up bc of the positive a but vector is the highest or the lowest point?

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And how to find the other point

copper kestrel Oct 29, 2023, 9:09 PM

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a parabola that opens up has no highest point (it’s just infinity)

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therefore the vertex is the lowest point

midnight haven Oct 29, 2023, 9:16 PM

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Oh thanks

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I understood

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.close

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pearl pondBOT Oct 29, 2023, 9:40 PM

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bleak rock Oct 29, 2023, 9:46 PM

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pearl pondBOT Oct 29, 2023, 9:47 PM

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bleak rock

bleak rock Oct 29, 2023, 9:54 PM

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This is from my class in calculus

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<@&286206848099549185>

dim tangle Oct 29, 2023, 10:02 PM

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you can build it up from the basic sinx and arcsinx, then use the interval of sinx and the translation of arcsinx to show that they both undergo the same transformations in range/domain. proofing is not my strong suit so hopefully someone else can chime in.

bleak rock Oct 29, 2023, 10:08 PM

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oh alright i will try this, thx

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Never mind i still don't know what answer is correct

cursive wraith Oct 29, 2023, 10:17 PM

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huh? what else would arcsin be defined as except for the inverse of sin on [-pi/2,pi/2] ?

pearl pondBOT Oct 29, 2023, 10:25 PM

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@bleak rock Has your question been resolved?

bleak rock Oct 29, 2023, 10:27 PM

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the inverse of sin on [3pi/2,5pi/2]?

solid ivy Oct 29, 2023, 10:38 PM

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Naw arcsin always has range in [-pi/2, pi/2]

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You might be thinking of Arcsin(x), which returns all angle values theta that satisfy sin(theta) =x

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Capitalization matters catthumbsup

bleak rock Oct 29, 2023, 10:41 PM

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oh

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oh well thanks then

pearl pondBOT Oct 29, 2023, 11:12 PM

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@bleak rock Has your question been resolved?

pearl pondBOT Oct 29, 2023, 11:39 PM

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proud oracle Oct 29, 2023, 11:42 PM

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can you shear in both x and y direcitons?

i have matrix
[2 1]
[1 2]

is it a 1. stretch in both x and y by factor of 2
and 2. a shear in x and y?

pearl pondBOT Oct 29, 2023, 11:42 PM

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proud oracle can you shear in both x and y direcitons? i have matrix [2 1] [1 2] is it ...

tranquil plinth Oct 29, 2023, 11:44 PM

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How do you mean that?

proud oracle Oct 29, 2023, 11:45 PM

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tranquil plinth How do you mean that?

matrix transforatmion

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Matrix x Vector

tranquil plinth Oct 29, 2023, 11:46 PM

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https://shad.io/MatVis/

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theres this aplication where you can visualize Matrix Transformations

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That's your transformation

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That's where you start

proud oracle Oct 29, 2023, 11:56 PM

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tranquil plinth

thanks

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what's the applicaiton

pearl pondBOT Oct 30, 2023, 12:11 AM

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@proud oracle Has your question been resolved?

pearl pondBOT Oct 30, 2023, 12:26 AM

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gentle vapor Oct 30, 2023, 12:43 AM

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pearl pondBOT Oct 30, 2023, 12:43 AM

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gentle vapor

gentle vapor Oct 30, 2023, 12:44 AM

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Im stuck on this question

plush bramble Oct 30, 2023, 12:58 AM

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gentle vapor Im stuck on this question

!show

pearl pondBOT Oct 30, 2023, 12:58 AM

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gentle vapor Im stuck on this question

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

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topaz plover Oct 30, 2023, 3:04 AM

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did i do this right

pearl pondBOT Oct 30, 2023, 3:04 AM

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topaz plover did i do this right

pearl pondBOT Oct 30, 2023, 3:19 AM

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@topaz plover Has your question been resolved?

topaz plover Oct 30, 2023, 3:19 AM

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<@&286206848099549185>

pearl pondBOT Oct 30, 2023, 3:49 AM

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@topaz plover Has your question been resolved?

topaz plover Oct 30, 2023, 4:07 AM

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<@&286206848099549185>

vernal rune Oct 30, 2023, 4:21 AM

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topaz plover did i do this right

That all looks correct

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@topaz plover Has your question been resolved?

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alpine vortex Oct 30, 2023, 6:54 AM

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what does the vertical line with 1 and 0 mean

pearl pondBOT Oct 30, 2023, 6:54 AM

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alpine vortex what does the vertical line with 1 and 0 mean

tall flint Oct 30, 2023, 6:56 AM

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it means "evaluated at"

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so the first expression should be read as "the derivative of a^x, evaluated at x=0"

pearl pondBOT Oct 30, 2023, 7:09 AM

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tribal idol Oct 30, 2023, 6:14 PM

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pearl pondBOT Oct 30, 2023, 6:14 PM

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tribal idol

tribal idol Oct 30, 2023, 6:15 PM

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what would be an approach to prove these?

I was thinking of using the definition of uncountability and the fact that B dominates A
hence there exists a bijection from A to some C where C is a subset of B
but i kinda dk how to continue
ah and I prolly would need to use the fact that N is being dominated by A since A is uncountable

pearl pondBOT Oct 30, 2023, 6:30 PM

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@tribal idol Has your question been resolved?

pearl pondBOT Oct 30, 2023, 7:02 PM

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@tribal idol Has your question been resolved?

tribal idol Oct 30, 2023, 7:54 PM

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I need help with b)

sacred crest Oct 30, 2023, 8:51 PM

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tribal idol

Does that strange <= mean it has more elements?

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Oh you need help with b

tribal idol Oct 30, 2023, 8:51 PM

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sacred crest Does that strange <= mean it has more elements?

That means is dominated by so yea

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Basically if A <= N it is countable

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But yea I finished a) already thanks anyway :D

sacred crest Oct 30, 2023, 8:53 PM

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tribal idol

Could you explain what the notation in b means?

tribal idol Oct 30, 2023, 8:53 PM

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sacred crest Could you explain what the notation in b means?

Yes ofcccc

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So the set S contains all functions that map finite binary sequences to infinite ones

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That’s why I thought of using cantors diagonalizations argument to prove this by just assuming S is countable and then assuming S having the functions f1 f2 and so on

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But then I somehow need to be smart and construct a new function that is different from all these

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To prove S is uncountable

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I think I was pretty close by just stating f1(0) is some infinite binary sequence then f2 is a different one and then I just take the diagonal and take the complement of it

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So every 0 turns into 1 and every one turns into 0

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And then I would have a new value for a function g for which g(0) equals this complement

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But I’m not quite sure if that works tbh

sacred crest Oct 30, 2023, 8:57 PM

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That should work

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If you can prove that the functions f: {0} -> {0, 1}^infinity is uncountable then you’ve proven the statement

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And you can define every function f(0) in a list and then use the diagonalization proof

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I don’t see why there should be a problem with that

tribal idol Oct 30, 2023, 8:59 PM

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sacred crest If you can prove that the functions f: {0} -> {0, 1}^infinity is uncountable the...

But does it also work for {0,1}?

sacred crest Oct 30, 2023, 8:59 PM

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Well if f(0) is different for every function then every f is different

tribal idol Oct 30, 2023, 8:59 PM

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sacred crest If you can prove that the functions f: {0} -> {0, 1}^infinity is uncountable the...

And if I I would prove it this way do i just say the set u have defined here is being dominated by the set S, therefore S is also uncountable?

tribal idol Oct 30, 2023, 9:00 PM

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sacred crest Well if f(0) is different for every function then every f is different

Oh yea mb that’s the same

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Yea okay

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Thanks so much!!

sacred crest Oct 30, 2023, 9:00 PM

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Glad I could help!

tribal idol Oct 30, 2023, 9:01 PM

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.close

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nimble osprey Oct 30, 2023, 9:06 PM

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hi

pearl pondBOT Oct 30, 2023, 9:06 PM

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nimble osprey hi

nimble osprey Oct 30, 2023, 9:06 PM

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if $T:V\to V$ linear transformation (V real vector space) such that $T^2=-Id$ then dim(V) is even

fluid axle Oct 30, 2023, 9:07 PM

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hi

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tried anything yet ?

nimble osprey Oct 30, 2023, 9:08 PM

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yes

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i see that T satisfy that polynomial P(X)=X^2+1

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and i think i can use that to finish the problem,...

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the vector space is real

fluid axle Oct 30, 2023, 9:10 PM

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well you seem on the right track, one hint : look at determinants

jolly parrotBOT Oct 30, 2023, 9:10 PM

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everg

nimble osprey Oct 30, 2023, 9:10 PM

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mhh..

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ohh

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$0<det(T^2)=det(-id)=(-1)^n$

jolly parrotBOT Oct 30, 2023, 9:11 PM

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everg

nimble osprey Oct 30, 2023, 9:11 PM

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implies n is even

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thank you!

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.close

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velvet meadow Oct 30, 2023, 9:16 PM

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pearl pondBOT Oct 30, 2023, 9:16 PM

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velvet meadow

nimble osprey Oct 30, 2023, 9:18 PM

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wow you have a beautiful animated avatar

sacred crest Oct 30, 2023, 9:23 PM

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velvet meadow

What do you need help with?

velvet meadow Oct 30, 2023, 9:25 PM

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can you guys give me a hand with 1 and 2?

velvet meadow Oct 30, 2023, 9:25 PM

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nimble osprey wow you have a beautiful animated avatar

thank you very much-o

sacred crest Oct 30, 2023, 9:25 PM

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1 is gonna be for @nimble osprey not me

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What would your approach be for 2? @velvet meadow

nimble osprey Oct 30, 2023, 9:27 PM

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sacred crest 1 is gonna be for <@696748240758112316> not me

why? you are also an undergrad

sacred crest Oct 30, 2023, 9:28 PM

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nimble osprey why? you are also an undergrad

No I’m a high schooler

velvet meadow Oct 30, 2023, 9:28 PM

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sacred crest Oct 30, 2023, 9:28 PM

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nimble osprey why? you are also an undergrad

I just do Uni maths in my free time so I chose the undergrad role

sacred crest Oct 30, 2023, 9:29 PM

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velvet meadow

Right, so what do we need to show in order to show that F is injective/not injective?

velvet meadow Oct 30, 2023, 9:33 PM

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mmm

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I think if the kernel of F is the zero vector

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then F is injective

sacred crest Oct 30, 2023, 9:39 PM

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@nimble osprey Confirm this please, idk enough about matrices

velvet meadow Oct 30, 2023, 9:47 PM

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look

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@here

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you see

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im a king

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king_cheems

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http://linear.ups.edu/fcla/section-ILT.html

sacred crest Oct 30, 2023, 9:49 PM

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velvet meadow

Im gonna be honest, I don’t even know what a kernel is 😅

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But congrats!

velvet meadow Oct 30, 2023, 9:49 PM

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🤣

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no worries just google around

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thats what im doing

sacred crest Oct 30, 2023, 9:50 PM

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My approach would have been to set up an equation for F(x)=F(y) and then deduce that x=y

nimble osprey Oct 30, 2023, 9:52 PM

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ok

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i ll help you

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mh.. maybe he is gone

sacred crest Oct 30, 2023, 9:53 PM

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Depends on who you mean

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Other person will reappear right after a ping

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Ain’t that right @velvet meadow

nimble osprey Oct 30, 2023, 9:53 PM

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so for first one:

velvet meadow Oct 30, 2023, 9:54 PM

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pepe_Hmm

eternal tulip Oct 30, 2023, 9:54 PM

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sacred crest Im gonna be honest, I don’t even know what a kernel is 😅

kernel is essentially like 'every input that takes you to '0' '

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typically called nullspace in linalg also

nimble osprey Oct 30, 2023, 9:55 PM

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fix a basis for example (the most simple) $e_1=(1 0 0)^t,e_2=(0 1 0)^t, e_3=(0 0 1)^t$ right ?ù

jolly parrotBOT Oct 30, 2023, 9:55 PM

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everg

eternal tulip Oct 30, 2023, 9:55 PM

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there are more general concepts of it that you will discover if you go into deeper mathematics, but it's always that basic concept

nimble osprey Oct 30, 2023, 9:55 PM

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now the matrix will be ...

velvet meadow Oct 30, 2023, 9:56 PM

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identity pepe_Hmm

nimble osprey Oct 30, 2023, 9:56 PM

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$$\left(\begin{matrix} 1 & 1&1\0&1&0\-1&0&1 \end{matrix}\right)$$

velvet meadow Oct 30, 2023, 9:57 PM

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badtex

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whaaaaaaaat

jolly parrotBOT Oct 30, 2023, 9:57 PM

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everg

nimble osprey Oct 30, 2023, 9:58 PM

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do this make sense?

velvet meadow Oct 30, 2023, 9:59 PM

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nimble osprey Oct 30, 2023, 9:59 PM

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right?

velvet meadow Oct 30, 2023, 10:00 PM

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yes

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teradoge

nimble osprey Oct 30, 2023, 10:00 PM

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now

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1 is done

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do you know determinant ?

#

@velvet meadow

#

ok so

velvet meadow Oct 30, 2023, 10:01 PM

#

nimble osprey Oct 30, 2023, 10:01 PM

#

if determinat is different from zero then the matrix is invertible

#

i.e. F is invertible, then F is both surjective and injective

#

lets compute the determinant

#

its different from zero! (if you don t trust me then compute it by yourself !)

velvet meadow Oct 30, 2023, 10:04 PM

#

its 2

nimble osprey Oct 30, 2023, 10:04 PM

#

ok nice

velvet meadow Oct 30, 2023, 10:04 PM

#

I did calculator teradoge

nimble osprey Oct 30, 2023, 10:04 PM

#

and our filed its not $\mathbb F_2$

jolly parrotBOT Oct 30, 2023, 10:04 PM

#

everg

nimble osprey Oct 30, 2023, 10:04 PM

#

so $2\neq 0$

jolly parrotBOT Oct 30, 2023, 10:04 PM

#

everg

nimble osprey Oct 30, 2023, 10:05 PM

#

2 is done

#

#

its obvious that x_2=1

#

can you finish by your self?

#

i'll take it like a yes

pearl pondBOT Oct 30, 2023, 10:19 PM

#

@velvet meadow Has your question been resolved?

velvet meadow Oct 30, 2023, 10:27 PM

#

yes

#

x2 = 1

#

then we have

#

x1 +x3 = 1

#

x3 - x1 = -1

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thus x3 = 0

#

@here

#

thus x1 = 1

#

@nimble osprey

#

x1 = 1
x2 = 1
x3 = 0

#

now F(x) =
2
1
-1

#

@here

nimble osprey Oct 30, 2023, 10:31 PM

#

velvet meadow x1 +x3 = 1

sorry, you re right

#

gg

velvet meadow Oct 30, 2023, 10:32 PM

#

teradoge

nimble osprey Oct 30, 2023, 10:32 PM

#

super giga chad

velvet meadow Oct 30, 2023, 10:32 PM

#

tysm you are awesome

#

catthumbsup

nimble osprey Oct 30, 2023, 10:33 PM

#

i know thank you 😉

velvet meadow Oct 30, 2023, 10:33 PM

#

.close

pearl pondBOT Oct 30, 2023, 10:33 PM

#

Channel closed

Closed by @velvet meadow

Use .reopen if this was a mistake.

nimble osprey Oct 30, 2023, 10:33 PM

#

you too

pearl pondBOT Oct 31, 2023, 1:10 AM

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dire snow Oct 31, 2023, 1:19 AM

#

pearl pondBOT Oct 31, 2023, 1:19 AM

#

dire snow

dire snow Oct 31, 2023, 1:19 AM

#

do I need to take the inverse of everything?

marsh crater Oct 31, 2023, 1:26 AM

#

Yes

#

but you can also left multiply be the inverse of the first matrix then find the inverse of the result

#

But I think both methods take around the same amount of time

pearl pondBOT Oct 31, 2023, 1:34 AM

#

@dire snow Has your question been resolved?

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pearl pondBOT Oct 31, 2023, 2:37 AM

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pearl pondBOT Oct 31, 2023, 2:54 AM

#

Channel closed

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glossy roost Oct 31, 2023, 2:54 AM

#

.close

pearl pondBOT Oct 31, 2023, 3:04 AM

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fickle sable Oct 31, 2023, 3:07 AM

#

how do i slove number 6 in this question

pearl pondBOT Oct 31, 2023, 3:07 AM

#

fickle sable how do i slove number 6 in this question

fickle sable Oct 31, 2023, 3:07 AM

#

signal atlas Oct 31, 2023, 3:09 AM

#

4^(m+2)=4^m(4^2)

fickle sable Oct 31, 2023, 3:10 AM

#

how do i get that?

signal atlas Oct 31, 2023, 3:10 AM

#

fickle sable how do i get that?

it is a property of exponents

#

$x^ax^b = x^{a+b}$

jolly parrotBOT Oct 31, 2023, 3:11 AM

#

Cure Miracle

fickle sable Oct 31, 2023, 3:11 AM

#

ohh ok

#

so how do i isolate m?

signal atlas Oct 31, 2023, 3:12 AM

#

next you can pull out 4^m

#

distributive property

fickle sable Oct 31, 2023, 3:13 AM

#

ok i see it now

#

yeah i just solved it

#

thanks!

signal atlas Oct 31, 2023, 3:13 AM

#

Np

pearl pondBOT Oct 31, 2023, 3:28 AM

#

@fickle sable Has your question been resolved?

#

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fringe juniper Oct 31, 2023, 3:40 AM

#

could anyone help me

Screenshot_2023-10-30_at_11.37.17_AM.png

pearl pondBOT Oct 31, 2023, 3:40 AM

#

fringe juniper could anyone help me

fringe juniper Oct 31, 2023, 3:40 AM

#

i asked earlier but i don’t think anyone was available

#

i did something wrong somewhere and i’m not sure what it is

dense goblet Oct 31, 2023, 3:42 AM

#

i don't think relative minimum/maximum means what you think it means

fringe juniper Oct 31, 2023, 3:44 AM

#

dense goblet i don't think relative minimum/maximum means what you think it means

but wouldn’t x8 be an abs min?

dense goblet Oct 31, 2023, 3:44 AM

#

it's both

#

the question says to put abs though

fringe juniper Oct 31, 2023, 3:45 AM

#

yeah thats what I did

dense goblet Oct 31, 2023, 3:45 AM

#

x8 isn't the problem

fringe juniper Oct 31, 2023, 3:45 AM

#

also for x1 i switched it to none

#

ohh

#

would x5 be the problem?

dense goblet Oct 31, 2023, 3:46 AM

#

i don't think so, no

#

what about x9

fringe juniper Oct 31, 2023, 3:47 AM

#

OHH

#

that was the problem

#

got it 😭

fringe juniper Oct 31, 2023, 3:47 AM

#

dense goblet what about x9

thank you bro

pearl pondBOT Oct 31, 2023, 4:02 AM

#

@fringe juniper Has your question been resolved?

pearl pondBOT Oct 31, 2023, 4:17 AM

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short oak Oct 31, 2023, 5:46 AM

#

How do I solve this question using Integral substitution? ... when i get du/dx of x+3, I cannot cancel out the x in the front ...

pearl pondBOT Oct 31, 2023, 5:46 AM

#

short oak How do I solve this question using Integral substitution? ... when i get du/dx o...

short oak Oct 31, 2023, 5:46 AM

#

signal atlas Oct 31, 2023, 5:49 AM

#

u=x+3 implies x=u-3. Try substituting the outside x

short oak Oct 31, 2023, 5:52 AM

#

Can you show me the woeking out

#

The answer is a but not too sure

signal atlas Oct 31, 2023, 5:54 AM

#

We will use u=x+3. As I mentioned x=u-3. If we substitue we get

Integral((u-3)sqrtu)

This simplifies to

Integral(usqrtu-3sqrtu)

From here it is trivial integration

pearl pondBOT Oct 31, 2023, 6:07 AM

#

@short oak Has your question been resolved?

pearl pondBOT Oct 31, 2023, 6:22 AM

#

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wheat otter Oct 31, 2023, 6:35 AM

#

The graph of the function has an extremum at the edge of the domain of definition
At point 4 = x.
A. Find a.
B. Find the minimum value and the maximum value of the function. Maybe the translation is bad but if you know please help me.

pearl pondBOT Oct 31, 2023, 6:35 AM

#

wheat otter The graph of the function has an extremum at the edge of the domain of definitio...

wheat otter Oct 31, 2023, 6:38 AM

#

so my thought was to do a - x^2 >= 0. Since its the edge of the definition its a - x^2 = 0. And plug in 4 as x and find a = 16 tell me if im correct

#

so the function is now: y = 1 + sqrt(16 - x^2). If not tell me please

#

And if i want to find the minimum value since there is nothing smaller then 0 in the y
min: y = 1 + 0(the min value of sqrt) = 1

pearl pondBOT Oct 31, 2023, 7:03 AM

#

@wheat otter Has your question been resolved?

pearl pondBOT Oct 31, 2023, 7:33 AM

#

@wheat otter Has your question been resolved?

pearl pondBOT Oct 31, 2023, 8:03 AM

#

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earnest zephyr Oct 31, 2023, 8:32 AM

#

is it correct?

pearl pondBOT Oct 31, 2023, 8:32 AM

#

earnest zephyr is it correct?

blazing saffron Oct 31, 2023, 8:35 AM

#

No

earnest zephyr Oct 31, 2023, 8:36 AM

#

can you teach me

blazing saffron Oct 31, 2023, 8:36 AM

#

How did you get the second row

earnest zephyr Oct 31, 2023, 8:37 AM

#

i just follow my teacher step

#

and its wrong

blazing saffron Oct 31, 2023, 8:38 AM

#

Why dont you just substitue 2 in the original equation

earnest zephyr Oct 31, 2023, 8:38 AM

#

how to subtitue

blazing saffron Oct 31, 2023, 8:40 AM

#

Limit as x goes to 2 means that as x gets closer and closer to 2 and thats going to be the value of the limit, and because you go infinitely close to 2, x becomes 2

earnest zephyr Oct 31, 2023, 8:40 AM

#

ookee

blazing saffron Oct 31, 2023, 8:40 AM

#

Its the same thing you did in the end of line 2

#

Just the beginning is wrong

earnest zephyr Oct 31, 2023, 8:43 AM

#

where i can write "lim", how can i correct it?

blazing saffron Oct 31, 2023, 8:44 AM

#

Correct

earnest zephyr Oct 31, 2023, 8:44 AM

#

what about my writing?

blazing saffron Oct 31, 2023, 8:44 AM

#

Also correct

light helm Oct 31, 2023, 8:45 AM

#

the lim is dropped after subbing in

earnest zephyr Oct 31, 2023, 8:45 AM

#

subbing where

light helm Oct 31, 2023, 8:46 AM

#

the value your evaluating at

earnest zephyr Oct 31, 2023, 8:46 AM

#

until 0/1?

light helm Oct 31, 2023, 8:46 AM

#

as you sub the x=2, you no longer write the limit

earnest zephyr Oct 31, 2023, 8:47 AM

#

okee

#

thank you very much,, i learned something neww

light helm Oct 31, 2023, 8:47 AM

#

the reason why you initial attempt is invalid is you tried to apply lhop without checking whether the conditions are satisfied

earnest zephyr Oct 31, 2023, 8:48 AM

#

aaa,, so subtitue first

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right?

light helm Oct 31, 2023, 8:48 AM

#

yeh, usually a good idea

earnest zephyr Oct 31, 2023, 8:48 AM

#

what if its 0/0?

#

.close

pearl pondBOT Oct 31, 2023, 8:51 AM

#

Channel closed

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pearl pondBOT Oct 31, 2023, 4:29 PM

#

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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hybrid basin Oct 31, 2023, 5:20 PM

#

Hello

pearl pondBOT Oct 31, 2023, 5:20 PM

#

hybrid basin Hello

hybrid basin Oct 31, 2023, 5:21 PM

#

What equations can I use for this question?

plucky oriole Oct 31, 2023, 5:23 PM

#

take $y= x^{2x^{2}}$

jolly parrotBOT Oct 31, 2023, 5:24 PM

#

Hack With Techno Boy

plucky oriole Oct 31, 2023, 5:24 PM

#

and now take log on both sides

#

then take derivative on both sides of eqn

#

you have to find dy/dx

hybrid basin Oct 31, 2023, 5:27 PM

#

$\frac{dy}{dx}=\frac{4x\ln\left(x\right)+2x}{y}$

jolly parrotBOT Oct 31, 2023, 5:27 PM

#

LE SSERAFIM

hybrid basin Oct 31, 2023, 5:27 PM

#

plucky oriole you have to find dy/dx

Like this?

#

And sub y from the original equation?

plucky oriole Oct 31, 2023, 5:28 PM

#

$\frac{1}{y}\frac{dy}{dx}=4x\ln\left(x\right)+2x$

jolly parrotBOT Oct 31, 2023, 5:28 PM

#

Hack With Techno Boy

hybrid basin Oct 31, 2023, 5:28 PM

#

Oh

#

lol

#

Right

#

Thank you

#

.close

pearl pondBOT Oct 31, 2023, 5:29 PM

#

Channel closed

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plucky oriole Oct 31, 2023, 5:29 PM

#

arigato

pearl pondBOT Oct 31, 2023, 5:30 PM

#

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river sun Oct 31, 2023, 6:53 PM

#

Prove by induction the identity

$$
\frac{(n+1)\cdot(n+2)\dots(2n-1)\cdot2n}{1\cdot3\cdot5\cdot\dots\cdot(2n-1)}=2^n
$$
for any natural $n.$

pearl pondBOT Oct 31, 2023, 6:53 PM

#

river sun Prove by induction the identity $$ \frac{(n+1)\cdot(n+2)\dots(2n-1)\cdot2n}{1\c...

jolly parrotBOT Oct 31, 2023, 6:53 PM

#

aaaaaaaa

river sun Oct 31, 2023, 6:53 PM

#

how

#

Prove by induction the identity
$$\frac{(n+1)\cdot(n+2)\dots(2n-1)\cdot2n}{1\cdot3\cdot5\cdot\dots\cdot(2n-1)}=2^n$$
For any natural $n.$

Proof:

Step 1. Base case n = 1

$$\frac{(2(1)-1)\cdot2(1)}{(2(1)-1)}=2^1$$
$$\frac{2}{1}=2$$

Step 2. Assume this is true is true blah blah

$$\frac{(2k-1)\cdot2k}{(2k-1)}=2^k$$

Step 3. Now how do i do $k+1$

jolly parrotBOT Oct 31, 2023, 7:00 PM

#

aaaaaaaa

river sun Oct 31, 2023, 7:01 PM

#

Step 3. k + 1 part???????? idk what im doing

$$\frac{(2(k+1)-1)\cdot2(k+1)}{(2(k+1)-1)}=2^{k+1}$$
$$\frac{(2k+2-1)\cdot2(k+1)}{(2(k+1)-1)}=2^{k+1}$$
$$\frac{(2k+2-1)\cdot2(k+1)}{(2k+2-1)}=2^{k+1}$$
$$\frac{(2k+1)\cdot2(k+1)}{(2k+1)}=2^{k+1}$$
$$2(k+1) = 2^{k+1}$$
$$2k+2 = 2^{k+1}$$

sharp quest Oct 31, 2023, 7:04 PM

#

that's not what the identity says in the problem

river sun Oct 31, 2023, 7:04 PM

#

oh

jolly parrotBOT Oct 31, 2023, 7:04 PM

#

aaaaaaaa

river sun Oct 31, 2023, 7:04 PM

#

damn

#

so im doing everything wrong?

#

idk how to do it

#

what am i supposed to do

#

$$
\frac{(n+1)\cdot(n+2)\dots(2n-1)\cdot2n}{1\cdot3\cdot5\cdot\dots\cdot(2n-1)}=2^n
$$

jolly parrotBOT Oct 31, 2023, 7:05 PM

#

aaaaaaaa

sharp quest Oct 31, 2023, 7:06 PM

#

you cut off the first part of the fraction. Your n+1 part only has this

#

you need the whole thing

river sun Oct 31, 2023, 7:06 PM

#

what whole thing

#

im so confused

sharp quest Oct 31, 2023, 7:07 PM

#

jolly parrot **aaaaaaaa**

^^^

river sun Oct 31, 2023, 7:07 PM

#

even the 1 3 5

sharp quest Oct 31, 2023, 7:07 PM

#

yes

river sun Oct 31, 2023, 7:07 PM

#

what do i do with the dots

sharp quest Oct 31, 2023, 7:07 PM

#

the dots are to imply 'this pattern continues until' whatever the last term is

river sun Oct 31, 2023, 7:08 PM

#

$$
\frac{(n+1)\cdot(n+2)(2n-1)\cdot2n}{1\cdot3\cdot5\cdot(2n-1)}=2^n
$$

sharp quest Oct 31, 2023, 7:08 PM

#

so the denominator is the product of odd integers, until you get to 2n-1

jolly parrotBOT Oct 31, 2023, 7:08 PM

#

aaaaaaaa

river sun Oct 31, 2023, 7:08 PM

#

this is what i need?

sharp quest Oct 31, 2023, 7:10 PM

#

jolly parrot **aaaaaaaa**

so if $n=4$ then your fraction is $\frac{5\cdot 6\cdot7\cdot8}{1\cdot3\cdot5\cdot7}$

jolly parrotBOT Oct 31, 2023, 7:11 PM

#

Zybikron

river sun Oct 31, 2023, 7:11 PM

#

ohhhhhhh

sharp quest Oct 31, 2023, 7:12 PM

#

river sun this is what i need?

no, you need every integer between n+1 and 2n and every odd integer between 1 and 2n-1

river sun Oct 31, 2023, 7:12 PM

#

how do i prove this

#

$$
\frac{(k+1)(k+2)\dots(2k-1)\cdot2k}{1\cdot3\cdot5\cdot\dots(2k-1)}=2^k
$$

#

i assume this is true

#

right?

#

then do k+1

sharp quest Oct 31, 2023, 7:13 PM

#

no, you don't have all the terms you need in between, that's what the .... was for

jolly parrotBOT Oct 31, 2023, 7:13 PM

#

aaaaaaaa

river sun Oct 31, 2023, 7:13 PM

#

?

#

what

sharp quest Oct 31, 2023, 7:15 PM

#

yes, so you assume that's true.
Now use the formula again with n+1, and use your assumption to show that it is equal to 2^n+1

river sun Oct 31, 2023, 7:15 PM

#

sharp quest yes, so you assume that's true. Now use the formula again with n+1, and use your...

idk how to do the k+1 part

#

im confused

sharp quest Oct 31, 2023, 7:15 PM

#

<@&268886789983436800>

river sun Oct 31, 2023, 7:16 PM

#

$$\frac{((k+1)+1)((k+1)+2)\dots(2(k+1)-1)\cdot2(k+1)}{1\cdot3\cdot5\cdot\dots(2(k+1)-1)}=2^{k+1}$$

$$\frac{((k+2)((k+3)\dots(2k+2-1)\cdot2(k+1)}{1\cdot3\cdot5\cdot\dots(2k+2-1)}=2^{k+1}$$

$$\frac{(k+2)(k+3)\dots(2k+1)\cdot2(k+1)}{1\cdot3\cdot5\cdot\dots(2k+1)}=2^{k+1}$$

$$\frac{(k+2)(k+3)\dots(2k+1)\cdot2(k+1)}{1\cdot3\cdot5\cdot\dots(2k+1)}=2^k \cdot 2$$

$$\frac{(k+2)(k+3)\dots2(k+1)}{1\cdot3\cdot5\cdot\dots(2k-1)}=2^k \cdot 2$$

sharp quest Oct 31, 2023, 7:17 PM

#

yep

river sun Oct 31, 2023, 7:18 PM

#

sharp quest yep

on the right path?

sharp quest Oct 31, 2023, 7:20 PM

#

yep

river sun Oct 31, 2023, 7:21 PM

#

sharp quest yep

idk what to do next

sharp quest Oct 31, 2023, 7:21 PM

#

there's a 2k+1 in the numerator and denominator.

river sun Oct 31, 2023, 7:21 PM

#

im stuck now

river sun Oct 31, 2023, 7:21 PM

#

sharp quest there's a 2k+1 in the numerator and denominator.

o

sharp quest Oct 31, 2023, 7:22 PM

#

$2^{k+1} \neq 2^k + 2$

jolly parrotBOT Oct 31, 2023, 7:22 PM

#

Zybikron

river sun Oct 31, 2023, 7:22 PM

#

oh shit meant to do

#

multiply

jolly parrotBOT Oct 31, 2023, 7:23 PM

#

aaaaaaaa

river sun Oct 31, 2023, 7:23 PM

#

do i keep the dots

sharp quest Oct 31, 2023, 7:23 PM

#

that last equation is wrong

river sun Oct 31, 2023, 7:23 PM

#

oh im trippin

#

oops

#

lemme fix

sharp quest Oct 31, 2023, 7:24 PM

#

when you cancel the 2k+1 you're left with the 2(k+1) in the numerator, and the last term of the denominator is now (2k-1)

river sun Oct 31, 2023, 7:24 PM

#

oh

#

wait

#

why 2k-1

sharp quest Oct 31, 2023, 7:25 PM

#

the denominator is the product of every odd integer from 1 to 2k+1

#

the odd below 2k+1 is 2k-1, so that's the last term now.

river sun Oct 31, 2023, 7:26 PM

#

$$\frac{((k+1)+1)((k+1)+2)\dots(2(k+1)-1)\cdot2(k+1)}{1\cdot3\cdot5\cdot\dots(2(k+1)-1)}=2^{k+1}$$

$$\frac{((k+2)((k+3)\dots(2k+2-1)\cdot2(k+1)}{1\cdot3\cdot5\cdot\dots(2k+2-1)}=2^{k+1}$$

$$\frac{(k+2)(k+3)\dots(2k+1)\cdot2(k+1)}{1\cdot3\cdot5\cdot\dots(2k+1)}=2^{k+1}$$

$$\frac{(k+2)(k+3)\dots(2k+1)\cdot2(k+1)}{1\cdot3\cdot5\cdot\dots(2k+1)}=2^k \cdot 2$$

$$\frac{(k+2)(k+3)\dots2(k+1)}{1\cdot3\cdot5\cdot\dots(2k-1)}=2^k \cdot 2$$

jolly parrotBOT Oct 31, 2023, 7:26 PM

#

aaaaaaaa

sharp quest Oct 31, 2023, 7:26 PM

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yes

river sun Oct 31, 2023, 7:26 PM

#

do i expand

#

k+2 and k+3

sharp quest Oct 31, 2023, 7:27 PM

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jolly parrot **aaaaaaaa**

now, notice that you can move the (k+1) to the front of the numerator and you have your inductive hypothesis

river sun Oct 31, 2023, 7:28 PM

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whatt

sharp quest Oct 31, 2023, 7:28 PM

#

river sun Oct 31, 2023, 7:28 PM

#

$$\frac{((k+1)+1)((k+1)+2)\dots(2(k+1)-1)\cdot2(k+1)}{1\cdot3\cdot5\cdot\dots(2(k+1)-1)}=2^{k+1}$$

$$\frac{((k+2)((k+3)\dots(2k+2-1)\cdot2(k+1)}{1\cdot3\cdot5\cdot\dots(2k+2-1)}=2^{k+1}$$

$$\frac{(k+2)(k+3)\dots(2k+1)\cdot2(k+1)}{1\cdot3\cdot5\cdot\dots(2k+1)}=2^{k+1}$$

$$\frac{(k+2)(k+3)\dots(2k+1)\cdot2(k+1)}{1\cdot3\cdot5\cdot\dots(2k+1)}=2^k \cdot 2$$

$$\frac{(k+1)(k+2)(k+3)\dots2}{1\cdot3\cdot5\cdot\dots(2k-1)}=2^k \cdot 2$$

jolly parrotBOT Oct 31, 2023, 7:28 PM

#

aaaaaaaa

river sun Oct 31, 2023, 7:29 PM

#

what was inductivve hypothesis

sharp quest Oct 31, 2023, 7:29 PM

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jolly parrot **aaaaaaaa**

^^^

#

so all of this is equal to 2^k

river sun Oct 31, 2023, 7:30 PM

#

sharp quest so all of this is equal to 2^k

ok what how 😭

sharp quest Oct 31, 2023, 7:31 PM

#

what do you get when you replace all of that with 2^k?

river sun Oct 31, 2023, 7:32 PM

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how is all the equivalent to 2^k

sharp quest Oct 31, 2023, 7:34 PM

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jolly parrot **aaaaaaaa**

that's what this says

river sun Oct 31, 2023, 7:41 PM

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im lost

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i understand how i got here

$$\frac{(k+1)(k+2)(k+3)\dots2}{1\cdot3\cdot5\cdot\dots(2k-1)}=2^k \cdot 2$$

jolly parrotBOT Oct 31, 2023, 7:42 PM

#

aaaaaaaa

river sun Oct 31, 2023, 7:42 PM

#

after than im lost

pearl pondBOT Oct 31, 2023, 7:57 PM

#

@river sun Has your question been resolved?

river sun Oct 31, 2023, 8:26 PM

#

.close

pearl pondBOT Oct 31, 2023, 8:26 PM

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thorny stream Oct 31, 2023, 9:10 PM

#

pearl pondBOT Oct 31, 2023, 9:10 PM

#

thorny stream

thorny stream Oct 31, 2023, 9:13 PM

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nvm

rough stream Oct 31, 2023, 9:13 PM

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Need the gradient before anything

thorny stream Oct 31, 2023, 9:13 PM

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i got it

#

.close

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gloomy summit Oct 31, 2023, 9:25 PM

#

Could someone explain what it is asking me to do here?

pearl pondBOT Oct 31, 2023, 9:25 PM

#

gloomy summit Could someone explain what it is asking me to do here?

rough stream Oct 31, 2023, 9:26 PM

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Find a span of UnW

gloomy summit Oct 31, 2023, 9:27 PM

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From what I’m understanding, I need to find a vector of 3 dimensions which is in the span of U and W.
However, the y direction has a span (-1,4) and (5,11) respectively and hence I’m confused as there are no numbers which overlap

gloomy summit Oct 31, 2023, 9:27 PM

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rough stream Find a span of UnW

Right, but that’s confusing me because the y component doesn’t have any numbers in common, thus I’m confused

rough stream Oct 31, 2023, 9:28 PM

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U is a plane in 3-space
W is a different plane in 3-space

We can agree there, right?

gloomy summit Oct 31, 2023, 9:28 PM

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Yep👍🏼

rough stream Oct 31, 2023, 9:29 PM

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The intersection of those two planes is probably going to be a line

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But could also be nothing, I'm up for surprises

gloomy summit Oct 31, 2023, 9:29 PM

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Worth finding a line equation then
Will compute this now and see what happens

rough stream Oct 31, 2023, 9:30 PM

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Okay! Let me know if you get stuck or anything

frosty mauve Oct 31, 2023, 9:39 PM

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An amount of chlorine is added to a swimming pool that contains pure water. The concentration of chlorine, c, in the pool at t hours is given by c(t) = 2t/2+ t where c is measured in milligrams per litre. What happens to the concentration of chlorine in the pool during the 3rd hour

gloomy summit Oct 31, 2023, 9:40 PM

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rough stream Okay! Let me know if you get stuck or anything

Bit stuck on finding out the intersection point ngl

unborn abyss Oct 31, 2023, 9:40 PM

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frosty mauve An amount of chlorine is added to a swimming pool that contains pure water. The ...

!occupied

pearl pondBOT Oct 31, 2023, 9:40 PM

#

frosty mauve An amount of chlorine is added to a swimming pool that contains pure water. The ...

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

gloomy summit Oct 31, 2023, 9:41 PM

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But I understand that it’ll be a 1 x 3 column vector (obviously)

rough stream Oct 31, 2023, 9:41 PM

#

I am seeing a nice general method here:
https://math.stackexchange.com/questions/25371/how-to-find-a-basis-for-the-intersection-of-two-vector-spaces-in-mathbbrn

Mathematics Stack Exchange

How to find a basis for the intersection of two vector spaces in $\...

What is the general way of finding the basis for intersection of two vector spaces in $\mathbb{R}^n$?

Suppose I'm given the bases of two vector spaces U and W:
$$ \mathrm{Base}(U)= \left{ \left(1...

gloomy summit Oct 31, 2023, 9:42 PM

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Ooo let me have a look

rough stream Oct 31, 2023, 9:42 PM

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But when I started commenting, I was gonna suggest "get the equations for both planes, find their intersection"

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But that might be more work and less general

gloomy summit Oct 31, 2023, 9:43 PM

#

#

Now this method I have no clue how to go about it

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But elementary row operations may work

rough stream Oct 31, 2023, 9:45 PM

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It is suggesting getting the nullspace of a matrix, where the matrix is all of your vectors as columns

gloomy summit Oct 31, 2023, 9:45 PM

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Ooohhh wait that might work

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Oh wow I never even knew you could do that

#

Let me try

rough stream Oct 31, 2023, 9:46 PM

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Or, wait, the negative of the vectors in the other space

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Everything in W goes in negative

gloomy summit Oct 31, 2023, 9:48 PM

#

#

Only 1 more try😭

gloomy summit Oct 31, 2023, 9:50 PM

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rough stream Or, wait, the negative of the vectors in the other space

Like this?

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W went negative

rough stream Oct 31, 2023, 9:53 PM

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,w matrix nullspace {{-2,-19,1,16},{-1,4,-5,-11},{5,-5,-5,10}}

jolly parrotBOT Oct 31, 2023, 9:53 PM

#

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rough stream Oct 31, 2023, 9:54 PM

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Oh wait that's not the right size lol

gloomy summit Oct 31, 2023, 9:54 PM

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Can’t be right hmm

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Other way round must be

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The transpose right?

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Now I’m sooo confused lol

rough stream Oct 31, 2023, 10:05 PM

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Alright mb this method isn't as good as I thought.

We can grab an equation for both planes by using a cross product, then solve for the intersection.

Get one vector off that, this is a solution

gloomy summit Oct 31, 2023, 10:06 PM

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rough stream Alright mb this method isn't as good as I thought. We can grab an equation for...

How do you do that?

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Well

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I get that U and W are planes

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But cross product off those? How?

rough stream Oct 31, 2023, 10:21 PM

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Any two vectors on them

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Easiest would be the vectors listed in the basis

rough stream Oct 31, 2023, 10:22 PM

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gloomy summit Could someone explain what it is asking me to do here?

#

,w cross product of (-2,-1,5) and (-19,4,-5)

jolly parrotBOT Oct 31, 2023, 10:23 PM

#

Results provided by WolframAlpha

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gloomy summit Oct 31, 2023, 10:23 PM

#

#

There must be a way to do it by finding the null space

#

I’ve row reduced

rough stream Oct 31, 2023, 10:24 PM

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I like that idea too, but the theory doesn't quite line up. It happens to work in the link because the matrix is square

gloomy summit Oct 31, 2023, 10:25 PM

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😢

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Alright cool

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Found that cross product, now the other one

rough stream Oct 31, 2023, 10:25 PM

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But the plane in U is given by
-15x - 105y - 27z = 0

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Lame method I know. I wonder how they expected you to do it

gloomy summit Oct 31, 2023, 10:27 PM

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Other one is -105x - 70y + 91z = 0

rough stream Oct 31, 2023, 10:28 PM

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Can equate those for x

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Get ANY (y,z), use those to get an x

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You've got me interested in a better way to do this type of problem. This is going to bother me lol

gloomy summit Oct 31, 2023, 10:29 PM

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rough stream Can equate those for x

What do you mean by this

gloomy summit Oct 31, 2023, 10:30 PM

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rough stream You've got me interested in a better way to do this type of problem. This is goi...

It’s a real annoying problem this one lll

#

lol

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The only one I’ve been struggling on

gloomy summit Oct 31, 2023, 10:30 PM

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rough stream Get ANY (y,z), use those to get an x

Ohh wait I get it

#

So like (1,2) and then compute

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For y,z

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Cool

rough stream Oct 31, 2023, 10:31 PM

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Multiply the top by -7,
105x + 735y + 189z = 0
-105x - 70y + 91z = 0

#

Add

gloomy summit Oct 31, 2023, 10:31 PM

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I’ve row reduced it already, looks atrocious

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And doesn’t seem possible to do

gloomy summit Oct 31, 2023, 10:35 PM

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rough stream Multiply the top by -7, 105x + 735y + 189z = 0 -105x - 70y + 91z = 0

I think there must be a way with the nullspace

#

Otherwise I genuinely give up

rough stream Oct 31, 2023, 10:39 PM

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Huh? We have it

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665y + 280z = 0

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We want ANY solution to that. One is (y, z) = (280, -665)

#

Plug those back into either plane to get an x

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That (x,y,z) should be accepted

gloomy summit Oct 31, 2023, 10:49 PM

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That’s a rather big value for x

gloomy summit Oct 31, 2023, 10:49 PM

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rough stream That (x,y,z) should be accepted

Would that still stand here?

rough stream Oct 31, 2023, 10:55 PM

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Yeah

pearl pondBOT Oct 31, 2023, 11:04 PM

#

@gloomy summit Has your question been resolved?

gloomy summit Oct 31, 2023, 11:04 PM

#

rough stream Yeah

It didn’t ):

#

Nvm

#

Thanks for your help

pearl pondBOT Oct 31, 2023, 11:37 PM

#

@gloomy summit Has your question been resolved?

pearl pondBOT Nov 1, 2023, 12:07 AM

#

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hollow meadow Nov 1, 2023, 12:17 AM

#

Hello, I was wondering how L'H rule works when you have an Infinity over another infinity

pearl pondBOT Nov 1, 2023, 12:17 AM

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hollow meadow Hello, I was wondering how L'H rule works when you have an Infinity over another...

hollow meadow Nov 1, 2023, 12:18 AM

#

#

after taking the derivative of both the top and the bottom, i get 1/(sqrt2x *e^x)

#

<@&286206848099549185>

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<@&286206848099549185>

rough stream Nov 1, 2023, 12:52 AM

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Alright. Now the limit tends to 1/inf = 0

hollow meadow Nov 1, 2023, 12:52 AM

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OH

#

that makes sense.. thank you!

#

.close

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steep hawk Nov 1, 2023, 1:04 AM

#

If I wanted to find real roots of the above equation, how should I start? I do not want to simply graph this for different values of a. Would an approach like Newton's method work here?

pearl pondBOT Nov 1, 2023, 1:04 AM

#

steep hawk If I wanted to find real roots of the above equation, how should I start? I do n...

#

@steep hawk Has your question been resolved?

snow sail Nov 1, 2023, 1:20 AM

#

steep hawk If I wanted to find real roots of the above equation, how should I start? I do n...

this looks cubic? so, you can just write the answers

#

its not fun

#

alternatively yea, some kind root-finding algorithm

steep hawk Nov 1, 2023, 1:20 AM

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nah, you gotta find possible values of a. Found this another way. This has to do with dynamical systems

snow sail Nov 1, 2023, 1:21 AM

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oh, well why didnt you say so :p

steep hawk Nov 1, 2023, 1:21 AM

#

Just figured it out rn lol

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dim rover Nov 1, 2023, 1:28 AM

#

need to derive ln(1+x/100)

pearl pondBOT Nov 1, 2023, 1:28 AM

#

dim rover need to derive ln(1+x/100)

dim rover Nov 1, 2023, 1:28 AM

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should be easy but im overthinking it

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im tired

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ln(x) = 1/x

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whats the chain rule for ln tho

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is it everything inside

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so 1/1+x/100 * d/dx (1+x/100)

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1

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1

lunar lichen Nov 1, 2023, 1:30 AM

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yes

dim rover Nov 1, 2023, 1:30 AM

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wtf

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then 1/1+X/100 * 1/100

lunar lichen Nov 1, 2023, 1:31 AM

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yh

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oh no

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nvm

#

should be

#

just simplify and you get 1/1+x

dim rover Nov 1, 2023, 1:38 AM

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.close

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prisma igloo Nov 1, 2023, 2:15 AM

#

pearl pondBOT Nov 1, 2023, 2:15 AM

#

prisma igloo

prisma igloo Nov 1, 2023, 2:15 AM

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Prove the identity, help

#

@ me

pearl pondBOT Nov 1, 2023, 2:17 AM

#

prisma igloo @ me

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

prisma igloo Nov 1, 2023, 2:31 AM

#

.close

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unborn cosmos Nov 1, 2023, 2:57 AM

#

Screen_Shot_2023-11-01_at_1.56.57_PM.png

pearl pondBOT Nov 1, 2023, 2:57 AM

#

unborn cosmos

unborn cosmos Nov 1, 2023, 2:57 AM

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for b), have they taken the cauchy product?

pearl pondBOT Nov 1, 2023, 3:12 AM

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restive oxide Nov 1, 2023, 3:34 AM

#

a59a754305d34203804a7480e4b6a8betplv-ejcjvp0zxf-webp-scale330126.png

pearl pondBOT Nov 1, 2023, 3:35 AM

#

restive oxide

pearl pondBOT Nov 1, 2023, 3:41 AM

#

restive oxide

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

restive oxide Nov 1, 2023, 3:41 AM

#

Have to find the limit

limpid roost Nov 1, 2023, 3:56 AM

#

Exp(log

pearl pondBOT Nov 1, 2023, 4:01 AM

#

@restive oxide Has your question been resolved?

restive oxide Nov 1, 2023, 4:23 AM

#

this questions is from a L'hopital section of my book, so I imagine to find the solution it wants me to apply L'hopital

plush bramble Nov 1, 2023, 4:25 AM

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restive oxide this questions is from a L'hopital section of my book, so I imagine to find the ...

You do that after EndTimes' hint

pearl pondBOT Nov 1, 2023, 4:53 AM

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@restive oxide Has your question been resolved?

restive oxide Nov 1, 2023, 4:53 AM

#

.close

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lunar oasis Nov 1, 2023, 2:13 PM

#

To prove the trigonometric identity (\frac{1-\cos(x)}{\sin(2x)} = \tan(x)), we'll start with the left-hand side (LHS) and manipulate it to show that it's equal to the right-hand side (RHS).

LHS:
(\frac{1-\cos(x)}{\sin(2x)})

First, we'll use the double angle identity for sine:
(\sin(2x) = 2\sin(x)\cos(x))

Now, the expression becomes:
(\frac{1-\cos(x)}{2\sin(x)\cos(x)})

Next, let's split the fraction into two terms:
(\frac{1}{2\sin(x)\cos(x)} - \frac{\cos(x)}{2\sin(x)\cos(x)})

Now, we can simplify each term:
(\frac{1}{2\sin(x)\cos(x)} = \frac{1}{2} \cdot \frac{1}{\sin(x)\cos(x)} = \frac{1}{2}\csc(x)\sec(x))

And for the second term:
(-\frac{\cos(x)}{2\sin(x)\cos(x)} = -\frac{1}{2\sin(x)} = -\frac{1}{2}\csc(x))

Now, the LHS becomes:
(\frac{1}{2}\csc(x)\sec(x) - \frac{1}{2}\csc(x))

Combine the terms:
(\frac{1}{2}\csc(x)(\sec(x) - 1))

Now, we know that (\sec(x) = \frac{1}{\cos(x)}), so we can rewrite (\sec(x) - 1) as (\frac{1}{\cos(x)} - 1):

(\frac{1}{2}\csc(x)\left(\frac{1}{\cos(x)} - 1\right))

Now, let's simplify the expression further:
(\frac{1}{2}\csc(x)\left(\frac{1-\cos(x)}{\cos(x)}\right))

Finally, you can see that (\frac{1-\cos(x)}{\cos(x)}) is equal to (\tan(x)), so we have:

(\frac{1}{2}\csc(x)\tan(x) = \frac{1}{2}\cdot\frac{\sin(x)}{\cos(x)} = \frac{1}{2}\tan(x) = \tan(x))

So, we have shown that the LHS is equal to the RHS, and the identity (\frac{1-\cos(x)}{\sin(2x)} = \tan(x)) is proven.

pearl pondBOT Nov 1, 2023, 2:13 PM

#

lunar oasis To prove the trigonometric identity $\frac{1-\cos(x)}{\sin(2x)} = \tan(x)$, we...

jolly parrotBOT Nov 1, 2023, 2:13 PM

#

Vaibhav

lunar oasis Nov 1, 2023, 2:13 PM

#

.close

pearl pondBOT Nov 1, 2023, 2:13 PM

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Channel closed

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lunar oasis Nov 1, 2023, 2:15 PM

#

To prove the identity (\frac{1 - \cos(x)}{\sin(2x)} = \tan(x)), you can start by using trigonometric identities to simplify the left side of the equation:

(\frac{1 - \cos(x)}{\sin(2x)} = \frac{1 - \cos(x)}{2\sin(x)\cos(x)})

Now, let's work on the numerator:

(1 - \cos(x) = \sin^2(x)) (using the Pythagorean identity (\sin^2(x) + \cos^2(x) = 1))

Now, substitute this back into the equation:

(\frac{\sin^2(x)}{2\sin(x)\cos(x)})

Now, simplify the expression:

(\frac{\sin(x)}{2\cos(x)} = \frac{\sin(x)}{\cos(x)} \cdot \frac{1}{2} = \frac{1}{2} \tan(x))

So, we have shown that (\frac{1 - \cos(x)}{\sin(2x)} = \frac{1}{2} \tan(x),) which proves the identity.

jolly parrotBOT Nov 1, 2023, 2:16 PM

#

Vaibhav

lunar oasis Nov 1, 2023, 2:16 PM

#

.close

old marsh Nov 1, 2023, 2:18 PM

#

#latex-testing

pearl pondBOT Nov 1, 2023, 2:38 PM

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midnight haven Nov 1, 2023, 2:48 PM

#

[
\int_0^1 \prod_{n=0}^\infty \m{\exp_x}{\m{\exp_x}{xn+1}}\dd x
]

pearl pondBOT Nov 1, 2023, 2:48 PM

#

midnight haven \[ \int_0^1 \prod_{n=0}^\infty \m{\exp_x}{\m{\exp_x}{xn+1}}\dd x \]

jolly parrotBOT Nov 1, 2023, 2:48 PM

#

midnight haven Nov 1, 2023, 2:48 PM

#

so this is absolutely very crazy, but what exactly is the trick to computing this?

#

or does it plain out not compute/diverge?

limber oasis Nov 1, 2023, 2:51 PM

#

why is it exp_x and not just exp ?

midnight haven Nov 1, 2023, 2:52 PM

#

Because i hate exponents

#

anyways [
\m {\exp_x}a = x^a
]

jolly parrotBOT Nov 1, 2023, 2:52 PM

#

limber oasis Nov 1, 2023, 2:52 PM

#

but yeah this product diverges because e^x >= x so for x, n != 0 each factor is > 1

#

by a long shot

#

so this has no hope of converging

#

oh nvm

cursive wraith Nov 1, 2023, 2:52 PM

#

?

#

at least write exp(ln(x) ...)

limber oasis Nov 1, 2023, 2:52 PM

#

it's not e^a, it's x^a

cursive wraith Nov 1, 2023, 2:53 PM

#

converges

#

recall that prod(exp...) = exp(...)

limber oasis Nov 1, 2023, 2:53 PM

#

limber oasis so this has no hope of converging

so this didn't apply at all

midnight haven Nov 1, 2023, 2:54 PM

#

cursive wraith recall that prod(exp...) = exp(...)

so like how does this translate

cursive wraith Nov 1, 2023, 2:55 PM

#

$\prod_{n=0}^\infty \exp(\ln(x)\exp(\ln(x)(xn+1))) = \exp(\ln(x)\sum_{n=0}^\infty\exp(\ln(x)(xn+1)))$

jolly parrotBOT Nov 1, 2023, 2:55 PM

#

rafilou2003

cursive wraith Nov 1, 2023, 2:56 PM

#

so... geometric sum should be ez

pearl pondBOT Nov 1, 2023, 3:09 PM

#

@midnight haven Has your question been resolved?

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green arrow Nov 1, 2023, 4:41 PM

#

Does anyone know how to solve this? (Rationalize de dominator or the numbers that are down) Thank You

pearl pondBOT Nov 1, 2023, 4:41 PM

#

green arrow Does anyone know how to solve this? (Rationalize de dominator or the numbers tha...

green arrow Nov 1, 2023, 4:43 PM

#

in 3.1

#

<@&286206848099549185>

finite geode Nov 1, 2023, 4:53 PM

#

green arrow Nov 1, 2023, 4:55 PM

#

oh, I can do that?

#

Thank You very much, I apreciate it

finite geode Nov 1, 2023, 4:56 PM

#

No worries!

pearl pondBOT Nov 1, 2023, 5:10 PM

#

@green arrow Has your question been resolved?

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tall cargo Nov 1, 2023, 5:29 PM

#

Does anybody know how to solve this limit without l'Hopitals rule and without Taylor series substitution?

pearl pondBOT Nov 1, 2023, 5:29 PM

#

tall cargo Does anybody know how to solve this limit without l'Hopitals rule and without Ta...

tall cargo Nov 1, 2023, 5:30 PM

#

The result is supposed to be a

cursive wraith Nov 1, 2023, 5:32 PM

#

$\lim_{x\to x_0}\frac{f(x)-f(x_0)}{x-x_0}$

jolly parrotBOT Nov 1, 2023, 5:32 PM

#

rafilou2003

tall cargo Nov 1, 2023, 5:32 PM

#

We're not supposed to just use the limit definition I'm pretty sure

#

is there some way to add an x to scrap the bottom x?

cursive wraith Nov 1, 2023, 5:33 PM

#

?

cursive wraith Nov 1, 2023, 5:33 PM

#

jolly parrot **rafilou2003**

when f is differentiable, what is this?

tall cargo Nov 1, 2023, 5:34 PM

#

That is the general definition of a limit right?

#

Where delta x becomes infintesimaly smaall

tall cargo Nov 1, 2023, 5:36 PM

#

tall cargo Where delta x becomes infintesimaly smaall

or well approaches x0, but x0 is zero in this case so infintesimaly small

#

but we're not allowed to solve it like that

tall flint Nov 1, 2023, 5:43 PM

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It's not the definition of a limit

#

It's the limit definition of something (one of two limit definitions actually)

tall cargo Nov 1, 2023, 5:44 PM

#

Oh my bad

#

The point is, they want us to solve the limit by somehow bringing an x down from e^(ax) and scrapping the denominator x

#

Not allowed to use l'Hopital, limit definitions, (Taylor) series substitution. They want us to solve it using the properties of e and ln

pearl pondBOT Nov 1, 2023, 6:01 PM

#

@tall cargo Has your question been resolved?

tall cargo Nov 1, 2023, 6:02 PM

#

.close

pearl pondBOT Nov 1, 2023, 6:02 PM

#

Channel closed

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vale kindle Nov 1, 2023, 6:14 PM

#

Hello. Not sure where I went wrong in this problem here. I somehow got the correct maximum, just none of the variables to get there.

pearl pondBOT Nov 1, 2023, 6:14 PM

#

vale kindle Hello. Not sure where I went wrong in this problem here. I somehow got the corre...

vale kindle Nov 1, 2023, 6:19 PM

#

You can use a computer to do the pivoting for you btw, that’s why there are only test ratios as work shown for pivoting on the table. I used https://www.math.cmu.edu/~bkell/pivot.html for this, but I’m sure there are like a lot of these things out there probably

pearl pondBOT Nov 1, 2023, 6:34 PM

#

@vale kindle Has your question been resolved?

pearl pondBOT Nov 1, 2023, 7:12 PM

#

@vale kindle Has your question been resolved?

pearl pondBOT Nov 1, 2023, 8:13 PM

#

@vale kindle Has your question been resolved?

vale kindle Nov 1, 2023, 8:37 PM

#

<@&286206848099549185> Using my ping since it's been >2 hrs lol

north smelt Nov 1, 2023, 8:40 PM

#

is this matrix question

vale kindle Nov 1, 2023, 8:40 PM

#

Mostly, yes. I messed up somewhere when pivoting (I think), and I've done it a few times now and come up with the same thing each time

#

There's a chance I set up the equations/inequalities for the word problem incorrectly as well, but I'm more confident in those

north smelt Nov 1, 2023, 8:42 PM

#

i am also doing matrix and maybe i might pull it off let me just try

pearl pondBOT Nov 1, 2023, 10:41 PM

#

@vale kindle Has your question been resolved?

vale kindle Nov 1, 2023, 11:20 PM

#

Solved it, nvm

#

The solution was to not have that one sentence in the word problem equate to 2 equations, the ones that start with -y and end with 0. They are supposed to be one inequality, meaning the equation I was supposed to have was x-y+z+d=0 and then go from there

#

Thanks though

#

.close

pearl pondBOT Nov 1, 2023, 11:21 PM

#

Channel closed

Closed by @vale kindle

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pearl pondBOT Nov 2, 2023, 12:04 AM

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languid quest Nov 2, 2023, 12:12 AM

#

A cube with an open lid with dimensions 5x5x5 feet is tilted (rotated) 45 degrees.

How much less water can hold it from its original position??

pearl pondBOT Nov 2, 2023, 12:12 AM

#

languid quest A cube with an open lid with dimensions 5x5x5 feet is tilted (rotated) 45 degree...

languid quest Nov 2, 2023, 12:12 AM

#

I got it can hold 125 square feet of water

#

But after 45 degrees idk

restive briar Nov 2, 2023, 12:15 AM

#

Think about what it would look like once you rotate it 45 degrees

pearl pondBOT Nov 2, 2023, 12:28 AM

#

@languid quest Has your question been resolved?

languid quest Nov 2, 2023, 12:29 AM

#

restive briar Think about what it would look like once you rotate it 45 degrees

The height would be sqrt2/2 times the original right?

#

Or .7

pearl pondBOT Nov 2, 2023, 12:59 AM

#

@languid quest Has your question been resolved?

pearl pondBOT Nov 2, 2023, 2:00 AM

#

@languid quest Has your question been resolved?

pearl pondBOT Nov 2, 2023, 4:00 AM

#

@languid quest Has your question been resolved?

vestal tapir Nov 2, 2023, 4:24 AM

#

languid quest The height would be sqrt2/2 times the original right?

the height is not what you want to find

languid quest Nov 2, 2023, 4:57 AM

#

vestal tapir the height is not what you want to find

Then what

#

Isn't it just height * length * width

vestal tapir Nov 2, 2023, 4:58 AM

#

this is about how water behaves around open lids

#

here's your thing

#

pearl pondBOT Nov 2, 2023, 8:57 AM

#

@languid quest Has your question been resolved?

languid quest Nov 2, 2023, 12:14 PM

#

vestal tapir

Right it'll always be horizontal

pearl pondBOT Nov 2, 2023, 8:15 PM

#

@languid quest Has your question been resolved?

pearl pondBOT Nov 3, 2023, 12:15 PM

#

@languid quest Has your question been resolved?

midnight haven Nov 4, 2023, 2:10 AM

#

@languid quest whats happens when you tilt and open container 45 degrees and is full of water

#

half of the water is emptyed

#

using trigonometry and pythag we can sovle for the volume

languid quest Nov 4, 2023, 2:14 AM

#

midnight haven half of the water is emptyed

Oh

#

OH

#

That makes so much sense

#

Ok how about like a not nice number

midnight haven Nov 4, 2023, 2:15 AM

#

yes

languid quest Nov 4, 2023, 2:15 AM

#

Like 44 degrees

#

How would I calculate that mathematically

#

Wait a minute

#

Isn't the length actually longer now

#

While the height of the water has been like

#

Decreased

#

Not by half

#

A little more than half

#

More like times sqrt2 divide 2

midnight haven Nov 4, 2023, 2:16 AM

#

hold on

languid quest Nov 4, 2023, 2:16 AM

#

Alr

languid quest Nov 4, 2023, 2:17 AM

#

languid quest The height would be sqrt2/2 times the original right?

This is what I thought earlier

midnight haven Nov 4, 2023, 2:18 AM

#

im back i just needed pen and paper

#

so the side that the water will fall out of is the side we are focasing on

#

using trigonometry we ca solve for the horizontal line that the water makes

languid quest Nov 4, 2023, 2:23 AM

#

Alr

midnight haven Nov 4, 2023, 2:31 AM

#

srry my phones flat

#

i cant upload the solution

#

@languid quest here is the solution

#

,rotate

jolly parrotBOT Nov 4, 2023, 2:43 AM

#

midnight haven Nov 4, 2023, 2:43 AM

#

ok their

#

but this only solves the area of the shaded area

#

gtg

#

<@&286206848099549185> this guy has been waiting for 2 days. please help him out

#

oh and the question is;
A cube with an open lid with dimensions 5x5x5 feet is tilted (rotated) 44 degrees.

How much less water can hold it from its original position??

torpid quest Nov 4, 2023, 2:52 AM

#

Ok let me see

#

Ok in like 10 minutes I can send you my diagram inshaAllah

midnight haven Nov 4, 2023, 2:54 AM

#

jolly parrot

oh and once you find the area of this side, times it by the depth to get the volume

#

cya

torpid quest Nov 4, 2023, 3:03 AM

#

#

This is how I saw the problem

#

@midnight haven

harsh silo Nov 4, 2023, 3:04 AM

#

languid quest A cube with an open lid with dimensions 5x5x5 feet is tilted (rotated) 45 degree...

consider the cross section of the cube which is perpendicular to the body diagonol, this will be square and the height of water that can be held will be equal to the length of the side of this square.

the side of this square cross section can be found by dividing the body diagonal by √2.

the body diagonol is given by d=s√3 where s is the side of the cub so d=5√3,

so the side of the square cross section is (5√3)/√2

the volume of water the cube can hold when tilted is then the area of the square cross-section times the height of the cube

the area of the square is the side length squared, and the height is the same as the side length of the cube (5 feet).
A = ((5√6)/2)²
A = 37.5 ft²

V = A * 5 = 37.5 * 5 = 187.5

the difference is then given by
187.5-555 = 62.5

midnight haven Nov 4, 2023, 3:05 AM

#

torpid quest

oh shoot i approched the problem at the wrong angle

harsh silo Nov 4, 2023, 3:06 AM

#

wait nvm fucked it up

midnight haven Nov 4, 2023, 3:06 AM

#

yes

#

remember their is water in the container

#

the open lid is tiped 44 degrees

#

how much water is their left

torpid quest Nov 4, 2023, 3:07 AM

#

Well after the diagram I gave you

#

You could just divide the area of the triangle with 46° that doesn't have any water by the total area of the square, to get the percentage of water lost

#

And the multiply that percentage by 125 to get the amount of water lost

midnight haven Nov 4, 2023, 3:09 AM

#

wait i have a different approch

midnight haven Nov 4, 2023, 3:13 AM

#

torpid quest

here

#

use the cosine rule to solve the missing angles and sides

torpid quest Nov 4, 2023, 3:14 AM

#

Yes that would make sense

torpid quest Nov 4, 2023, 3:15 AM

#

midnight haven here

midnight haven Nov 4, 2023, 3:15 AM

#

nice

torpid quest Nov 4, 2023, 3:15 AM

#

torpid quest

midnight haven Nov 4, 2023, 3:16 AM

#

then we could use area of a triangle

#

$A=1/2abSin(A)$

jolly parrotBOT Nov 4, 2023, 3:16 AM

#

Mr. Macro

torpid quest Nov 4, 2023, 3:17 AM

#

torpid quest

midnight haven Nov 4, 2023, 3:17 AM

#

oh shoot yeah

torpid quest Nov 4, 2023, 3:17 AM

#

Yeah

#

Tho x would be 5

midnight haven Nov 4, 2023, 3:17 AM

#

yes

torpid quest Nov 4, 2023, 3:18 AM

#

And then y would be 5tan(46°)

#

And you can get the area of the triangle through base x height /2

midnight haven Nov 4, 2023, 3:19 AM

#

jolly parrot **Mr. Macro**

or using this

torpid quest Nov 4, 2023, 3:19 AM

#

Yeah you can do that too

midnight haven Nov 4, 2023, 3:19 AM

#

it works with all angled triagles

torpid quest Nov 4, 2023, 3:20 AM

#

Wdym by "angled triangles"???

midnight haven Nov 4, 2023, 3:20 AM

#

non right angle triangles

torpid quest Nov 4, 2023, 3:21 AM

#

Also works on right triangles

midnight haven Nov 4, 2023, 3:21 AM

#

yes

torpid quest Nov 4, 2023, 3:21 AM

#

And this is a right triangle BTW. 44-46-90

midnight haven Nov 4, 2023, 3:21 AM

#

💀 my brain borken today

torpid quest Nov 4, 2023, 3:21 AM

#

Anyways doesn't matter just go finish the problem

midnight haven Nov 4, 2023, 3:22 AM

#

@languid quest i hope this helps

languid quest Nov 4, 2023, 3:22 AM

#

OH HEY

#

IM ABT TO SLEEP

midnight haven Nov 4, 2023, 3:22 AM

#

oh

languid quest Nov 4, 2023, 3:22 AM

#

Cuz I'm in the east

midnight haven Nov 4, 2023, 3:23 AM

#

im in the west

languid quest Nov 4, 2023, 3:23 AM

#

midnight haven <@306574358262841354> i hope this helps

TYSM THO IT PROBS DID

languid quest Nov 4, 2023, 3:23 AM

#

midnight haven im in the west

8:23 pm for u?

#

It's almost midnight for me

torpid quest Nov 4, 2023, 3:23 AM

#

11:23pm for me

languid quest Nov 4, 2023, 3:23 AM

#

jolly parrot **Mr. Macro**

Wait what formula was this again

midnight haven Nov 4, 2023, 3:23 AM

#

2:23pm for me

languid quest Nov 4, 2023, 3:23 AM

#

So ur in europe

midnight haven Nov 4, 2023, 3:23 AM

#

languid quest Wait what formula was this again

area of a triangle, or you can use 1/2bh

torpid quest Nov 4, 2023, 3:23 AM

#

I'm in Canada

languid quest Nov 4, 2023, 3:23 AM

#

Huh

#

Is that like

#

Uh

#

I don't recognize that formula

#

But I do

#

From like trig class

#

Law of sines??

#

Wait no

languid quest Nov 4, 2023, 3:24 AM

#

midnight haven area of a triangle, or you can use 1/2bh

Yeah that's better 😂

midnight haven Nov 4, 2023, 3:25 AM

#

since its a right angle triangle you can just use 1/2bh

#

welp thanks @torpid quest for helping out when my brain was broken

torpid quest Nov 4, 2023, 3:26 AM

#

No problem 🙂

midnight haven Nov 4, 2023, 3:26 AM

#

tbh you did all the thinking

#

and i was busy munching on some food lol 😁

midnight haven Nov 4, 2023, 3:27 AM

#

languid quest Yeah that's better 😂

do you need any further assistence

languid quest Nov 4, 2023, 3:27 AM

#

midnight haven do you need any further assistence

Nope but I'm gonna def read it tmr LOL

#

Can I leave it open

#

I'm abt to sleep

#

Tysm all for ur hell

#

Help

torpid quest Nov 4, 2023, 3:28 AM

#

No problem 🙂

torpid quest Nov 4, 2023, 3:29 AM

#

languid quest Can I leave it open

Yeah I think that's ok

languid quest Nov 4, 2023, 3:29 AM

#

Yay

midnight haven Nov 4, 2023, 3:29 AM

#

the bot might auto close tho

torpid quest Nov 4, 2023, 3:29 AM

#

If it did you can dm me

midnight haven Nov 5, 2023, 8:14 AM

#

woah

#

this channel is still open?

silk junco Nov 5, 2023, 11:04 AM

#

midnight haven this channel is still open?

OP can .close it

nimble osprey Nov 5, 2023, 5:05 PM

#

.close

pearl pondBOT Nov 5, 2023, 5:05 PM

#

Channel closed

Closed by @nimble osprey

Use .reopen if this was a mistake.

pearl pondBOT Nov 5, 2023, 6:17 PM

#

Available help channel!

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

boreal crest Nov 5, 2023, 6:19 PM

#

Hello I need help identifying this type of chart and how to make it in excel

pearl pondBOT Nov 5, 2023, 6:19 PM

#

boreal crest Hello I need help identifying this type of chart and how to make it in excel

old marsh Nov 5, 2023, 6:22 PM

#

Boxplot looks like

#

The blue diamond maybe represents mean?

#

Red median

boreal crest Nov 5, 2023, 6:23 PM

#

I will send the whole chart for context

#

#

Would you know how to reproduce this in excel

old marsh Nov 5, 2023, 6:24 PM

#

Do u have a table of values or is that all u have

boreal crest Nov 5, 2023, 6:24 PM

#

that's all i have

old marsh Nov 5, 2023, 6:24 PM

#

So u need the chart to be made by excel? U can’t just copy and paste?

boreal crest Nov 5, 2023, 6:25 PM

#

No i'm saying If i wanted to reproduce a similar model with my own numbers

#

How would I go about doing that

#

To make it look exactly like that

old marsh Nov 5, 2023, 6:27 PM

#

Not sure sorry

#

If u had a table I could help, but not sure how to make it without the values

boreal crest Nov 5, 2023, 6:28 PM

#

got it, thanks

#

.close

pearl pondBOT Nov 5, 2023, 6:28 PM

#

Channel closed

Closed by @boreal crest

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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

crystal storm Nov 5, 2023, 6:33 PM

#

someone help me solve these questions i totally forgot about them and i have to submit it before 12 am

Screenshot_2023-11-05-20-31-05-581_org.readera.jpg

Screenshot_2023-11-05-20-33-07-707_org.readera.jpg

pearl pondBOT Nov 5, 2023, 6:33 PM

#

crystal storm someone help me solve these questions i totally forgot about them and i have to ...

crystal storm Nov 5, 2023, 6:34 PM

#

i already solved the first 3 questions but i dont think i can finish this in time 😭😭😭

limpid lily Nov 5, 2023, 6:35 PM

#

!occupied

pearl pondBOT Nov 5, 2023, 6:35 PM

#

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

#

@crystal storm Has your question been resolved?

plush bramble Nov 5, 2023, 6:50 PM

#

crystal storm i already solved the first 3 questions but i dont think i can finish this in tim...

Pick ONE problem and show your attempt here

crystal storm Nov 5, 2023, 6:52 PM

#

i solved question 4 and 5 but im not sure if i did it correctly

#

#

mind my dirty ass hand writing im in a hurry

#

#

question 5

#

can someone check if this is right?

plush bramble Nov 5, 2023, 7:17 PM

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Your number 4 has a couple typos that may have algebra errors. P(T) you wrote 98/100+3/100 but should be product. Then just a minor typo in the P(T) = 49/1000 denominator

crystal storm Nov 5, 2023, 7:20 PM

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oh shit yeah

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you're right

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my bad

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soooo 4.9%

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anything else that's not right?

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I'm ganna move on and solve question 6 in the mean time

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bruhh now that i am rechecking and calculating again my answer for Q4 part b is 2/5

crystal storm Nov 5, 2023, 7:58 PM

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2 hours left and I've solved till 6

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please let me know if im making any errors

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crystal storm Nov 5, 2023, 8:07 PM

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crystal storm

Question 8's Solution

crystal storm Nov 5, 2023, 8:09 PM

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crystal storm

actually i think im supposed to add instead of multiply

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im not sure

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Question 9's Solution

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not very confident about my work so please let me know if anything is wrong

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im ganna submit it at the last 10 mins

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<@&286206848099549185>

pearl pondBOT Nov 5, 2023, 8:54 PM

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@crystal storm Has your question been resolved?

crystal storm Nov 5, 2023, 8:55 PM

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one hour left 😕

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all of my other friends got different answers too 😭

pearl pondBOT Nov 5, 2023, 9:55 PM

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@crystal storm Has your question been resolved?

crystal storm Nov 5, 2023, 9:56 PM

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fuck it im submitting it

pearl pondBOT Nov 5, 2023, 9:56 PM

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Channel closed

Closed by @crystal storm

Use .reopen if this was a mistake.

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atomic quail Nov 5, 2023, 9:58 PM

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Hi I've a problem with that :

pearl pondBOT Nov 5, 2023, 9:58 PM

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atomic quail Hi I've a problem with that :

atomic quail Nov 5, 2023, 9:59 PM

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I have to use the change of variable x = sin(t)

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And then I know that sqrt(1-sin²) = cos² and Finally I get pi/6 but it's false

plush bramble Nov 5, 2023, 10:02 PM

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You missed dx in your substitution

atomic quail Nov 5, 2023, 10:03 PM

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I don't understand, I mutliplied by cos(t) and then I get dt instead of dx ?

plush bramble Nov 5, 2023, 10:04 PM

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dx = cos(t)dt but you substituted dx=dt/cos(t)

atomic quail Nov 5, 2023, 10:05 PM

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Oh okey

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plush bramble Nov 5, 2023, 10:05 PM

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Yea

atomic quail Nov 5, 2023, 10:05 PM

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Thanks !

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.close

pearl pondBOT Nov 5, 2023, 10:06 PM

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Channel closed

Closed by @atomic quail

Use .reopen if this was a mistake.

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Available help channel!

Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.