#help-10 | Mathematics | Page 280

woeful fulcrum Oct 29, 2023, 5:10 PM

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oh

severe reef Oct 29, 2023, 5:10 PM

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the rate of change of volume is constant

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implying the height is changing at a constant rate as well

woeful fulcrum Oct 29, 2023, 5:10 PM

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ohh so if i think logically about it the rate of the height stays the same as it decreases

severe reef Oct 29, 2023, 5:10 PM

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since volume is proportional to height

woeful fulcrum Oct 29, 2023, 5:11 PM

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so the same answer would apply if i was looking for the rate when the height is 4m for example

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right

severe reef Oct 29, 2023, 5:11 PM

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yes

woeful fulcrum Oct 29, 2023, 5:11 PM

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ok

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im gonna test my answer

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it was right yay

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tysm

severe reef Oct 29, 2023, 5:11 PM

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np

woeful fulcrum Oct 29, 2023, 5:13 PM

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.close

obtuse pebbleBOT Oct 29, 2023, 5:13 PM

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shadow lava Oct 29, 2023, 5:19 PM

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obtuse pebbleBOT Oct 29, 2023, 5:19 PM

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shadow lava

shadow lava Oct 29, 2023, 5:19 PM

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AX = XB + C

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B = 2I

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AX = X(2I) + C

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not sure where to go from here?
Can I do this?

(A^-1)AX = (A^-1)X(2I) + C

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or am I forgetting about C when I do that

royal basin Oct 29, 2023, 5:21 PM

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well you are

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but also left-multiplying by A^-1 won't help much here

shadow lava Oct 29, 2023, 5:21 PM

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Oh, I thought it could remove A from the LHS

royal basin Oct 29, 2023, 5:21 PM

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so you're fucking up both planning and execution

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this is as unhelpful as dividing both sides by 7 in the equation 7x = 2x + 9

shadow lava Oct 29, 2023, 5:21 PM

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OK

royal basin Oct 29, 2023, 5:22 PM

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anyway what you want to notice here is that $X \cdot 2I = 2I \cdot X = 2X$

warm shaleBOT Oct 29, 2023, 5:22 PM

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AnnGhost

shadow lava Oct 29, 2023, 5:22 PM

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so I'm on the right track here, but I'm stuck on next step..
AX = X(2I) + C

royal basin Oct 29, 2023, 5:22 PM

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the identity matrix and all scalar multiples thereof commute with everything

shadow lava Oct 29, 2023, 5:22 PM

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because all matrices are 2x2?

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how do we know that X is 2x2?

fervent cradle Oct 29, 2023, 5:23 PM

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in order for the addition on the RHS to make sense, we need X(2I) to be 2x2

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and we also need AX on the LHS to be 2x2

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so X must be 2x2

shadow lava Oct 29, 2023, 5:23 PM

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but do we know that X is 2x2? or just assuming

fervent cradle Oct 29, 2023, 5:23 PM

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ok

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so on the RHS we know that X(2I) is 2x2

royal basin Oct 29, 2023, 5:24 PM

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shadow lava because all matrices are 2x2?

no, this doesn't have to do with the size.

fervent cradle Oct 29, 2023, 5:24 PM

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so therefore we know that the number of rows of X is 2

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similarly on the LHS we know that AX is 2x2

royal basin Oct 29, 2023, 5:24 PM

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but you do know that X is 2×2 from the equation.

fervent cradle Oct 29, 2023, 5:24 PM

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where A is 2x2

shadow lava Oct 29, 2023, 5:24 PM

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fervent cradle so on the RHS we know that X(2I) is 2x2

we do?

fervent cradle Oct 29, 2023, 5:24 PM

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yes

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basically you can't add matrices unless they're the same dimension

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but we have like X(2I) + C

shadow lava Oct 29, 2023, 5:24 PM

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AH

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that's the giveaway

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OK

shadow lava Oct 29, 2023, 5:25 PM

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fervent cradle basically you can't add matrices unless they're the same dimension

this helps

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but X could either be

a scalar
2x2 matrix

royal basin Oct 29, 2023, 5:25 PM

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no, X cannot be a scalar

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it's said to be a matrix

fervent cradle Oct 29, 2023, 5:25 PM

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ok look it wants a matrix it just says that in the question

shadow lava Oct 29, 2023, 5:25 PM

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oh right

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ty

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AX = X(2I) + C

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so the identity disappears?

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AX = X2 + C

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AX = 2X + C

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all 3 of these equations are equal?

fervent cradle Oct 29, 2023, 5:27 PM

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yeah

shadow lava Oct 29, 2023, 5:27 PM

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warm shale **AnnGhost**

just based on this

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huh.. interesting

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and the identity goes away because it doesnt' change anything when multiplying same size matrix

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so it's kinda irrelevant

fervent cradle Oct 29, 2023, 5:27 PM

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sure

shadow lava Oct 29, 2023, 5:27 PM

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OK

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so now we are cooking with fire

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AX = 2X + C

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AX - 2X = C

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is that a good next step?

fervent cradle Oct 29, 2023, 5:28 PM

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yes

shadow lava Oct 29, 2023, 5:28 PM

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then I can factor out the X on LHS?

fervent cradle Oct 29, 2023, 5:28 PM

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yes

shadow lava Oct 29, 2023, 5:28 PM

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X(A - 2) = C

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wait

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sorry

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wrong side

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needs to be (A - 2)X = C

fervent cradle Oct 29, 2023, 5:28 PM

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good catch

shadow lava Oct 29, 2023, 5:28 PM

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now I divide both sides by A-2

fervent cradle Oct 29, 2023, 5:28 PM

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one more thing, you should really say

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(A - 2I)X = C

shadow lava Oct 29, 2023, 5:29 PM

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no division in matrices

fervent cradle Oct 29, 2023, 5:29 PM

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because you're doing matrix subtraction

shadow lava Oct 29, 2023, 5:29 PM

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shadow lava now I divide both sides by A-2

multiply by reciprocal instead

shadow lava Oct 29, 2023, 5:29 PM

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fervent cradle `(A - 2I)X = C`

would it be "wrong" to remove the I in this case?

fervent cradle Oct 29, 2023, 5:29 PM

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yes

shadow lava Oct 29, 2023, 5:29 PM

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damn

fervent cradle Oct 29, 2023, 5:29 PM

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because A - 2 doesn't really make sense

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matrix minus a scalar

shadow lava Oct 29, 2023, 5:29 PM

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oh right

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good call

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(A - 2I)X = C

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now I multiply both sides by 1/(A-2I)

fervent cradle Oct 29, 2023, 5:30 PM

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well

shadow lava Oct 29, 2023, 5:30 PM

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X = C/(A-2I)

fervent cradle Oct 29, 2023, 5:30 PM

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(A-2I)^-1 is the way we usually put it

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inverse

shadow lava Oct 29, 2023, 5:31 PM

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oh right, same thing as reciprocal

fervent cradle Oct 29, 2023, 5:31 PM

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the equivalent, yeah

shadow lava Oct 29, 2023, 5:31 PM

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interesting..

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that's so neat

past sand Oct 29, 2023, 5:31 PM

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Probably show that it exists first?

shadow lava Oct 29, 2023, 5:31 PM

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so it cancels out the (A - 2I)

fervent cradle Oct 29, 2023, 5:31 PM

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yes

shadow lava Oct 29, 2023, 5:31 PM

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on the LHS

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and I'm left with X = [(A-2I)^-1]C

fervent cradle Oct 29, 2023, 5:32 PM

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yeah

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and now you just need to find what that actually is with like matrix multiplication and inversion and stuff

shadow lava Oct 29, 2023, 5:32 PM

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I can't do thisX = C/(A-2I) because it's not clear if (A-2I) is on left or right side

fervent cradle Oct 29, 2023, 5:32 PM

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essentially yeah

shadow lava Oct 29, 2023, 5:32 PM

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but X = [(A-2I)^-1]C is very clear it's on left side of C

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OK tyvm

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now I just calculate

shadow lava Oct 29, 2023, 5:34 PM

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fervent cradle essentially yeah

wait, could I not just write it like this as well?
[(A-B)^-1]C

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since B = 2I

fervent cradle Oct 29, 2023, 5:35 PM

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sure

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it's the same

shadow lava Oct 29, 2023, 5:40 PM

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fervent cradle it's the same

i got X =
5 6 4 2

fervent cradle Oct 29, 2023, 5:40 PM

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cool

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you can just try it out to see if it works

shadow lava Oct 29, 2023, 5:41 PM

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fervent cradle you can just try it out to see if it works

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My A|I ~ I|A^-1 method might be using a chainsaw to cut a matchstick in half, but it gets the job done

fervent cradle Oct 29, 2023, 5:42 PM

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ah

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mistake

shadow lava Oct 29, 2023, 5:42 PM

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gawd dammit

shadow lava Oct 29, 2023, 5:42 PM

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fervent cradle mistake

where?

fervent cradle Oct 29, 2023, 5:42 PM

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two mistakes

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minor

shadow lava Oct 29, 2023, 5:43 PM

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hmmm, I did my multiplication wrong

fervent cradle Oct 29, 2023, 5:43 PM

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no the multiplication is right

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it's just, the subtraction

shadow lava Oct 29, 2023, 5:43 PM

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oh it's the signs

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99% of the way there and trip right before the finish line

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sadly, if I had this as my answer on exam. big fat 0 for everything

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they only give marks for correct answer and showing work

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so all that effort and time for nothing, just flushed down the toilet

shadow lava Oct 29, 2023, 5:45 PM

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shadow lava 99% of the way there and trip right before the finish line

i don't know if I necessarily agree with that. Does your university do the same thing?

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5 6 -2 -2

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that's what it should be, but all the work before the last 2 steps are correct

fervent cradle Oct 29, 2023, 5:48 PM

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that's how it goes

shadow lava Oct 29, 2023, 5:48 PM

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all or nothing

fervent cradle Oct 29, 2023, 5:48 PM

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well no

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ok they care about the working

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i'm saying, very common to get basically everything right but make a small arithmetic mistake

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but yeah more forgiving usually in my experience

shadow lava Oct 29, 2023, 5:49 PM

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so i should probably still get some marks for showing the work at least

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up until the very last fumble

fervent cradle Oct 29, 2023, 5:49 PM

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sure

shadow lava Oct 29, 2023, 5:49 PM

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marking math must be so time consuming, and subjective to the grader

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i'm sure the examiner sees all sorts of weird shit on exams

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they gotta determine if any of the mess is worth anything, which takes time, and it cannot be automated, only humans can do the job

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my guess is that math teachers really earn their pay, the good ones should be paid more imo, it feels like they are doing more work than other subjects. but i could also be very wrong.

fervent cradle Oct 29, 2023, 5:52 PM

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no clue

shadow lava Oct 29, 2023, 5:52 PM

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i've had a lot of exams that are simply multiple choice and get marked with dots on a score card by a computer

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math exams are never offered in this format unfortunately lol

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tyvm for the help @fervent cradle

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.close

obtuse pebbleBOT Oct 29, 2023, 5:53 PM

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honest flicker Oct 29, 2023, 5:54 PM

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obtuse pebbleBOT Oct 29, 2023, 5:54 PM

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honest flicker

honest flicker Oct 29, 2023, 5:55 PM

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I was thinking exponential because the common ratio thingy of the y's but the X's look kinda funky idk

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I think like exponential or maybe neither

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Idk

fervent cradle Oct 29, 2023, 6:05 PM

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try plotting the points and seeing what it looks like

honest flicker Oct 29, 2023, 6:06 PM

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It looks exponential

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So is that the asnwer fr

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@fervent cradle

fervent cradle Oct 29, 2023, 6:08 PM

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does it look exponential

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show your sketch

honest flicker Oct 29, 2023, 6:08 PM

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I already destroyed it

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😭

fervent cradle Oct 29, 2023, 6:08 PM

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ok do it again lol

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just rq

honest flicker Oct 29, 2023, 6:08 PM

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ITS EXPONENTIAL LOOKING

fervent cradle Oct 29, 2023, 6:08 PM

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it doesn't have to be beautiful

honest flicker Oct 29, 2023, 6:09 PM

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Plz believe

fervent cradle Oct 29, 2023, 6:09 PM

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ok well

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it's not exponential

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sketch better

honest flicker Oct 29, 2023, 6:09 PM

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.

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What it is

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Fr

fervent cradle Oct 29, 2023, 6:09 PM

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sketch it

honest flicker Oct 29, 2023, 6:10 PM

#

#

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@fervent cradle

fervent cradle Oct 29, 2023, 6:11 PM

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ok

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wait that does look exponential wtf

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ok i was wrong sorry

honest flicker Oct 29, 2023, 6:14 PM

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😭

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.close

obtuse pebbleBOT Oct 29, 2023, 6:17 PM

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tawdry vortex Oct 29, 2023, 6:19 PM

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obtuse pebbleBOT Oct 29, 2023, 6:19 PM

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tawdry vortex

tawdry vortex Oct 29, 2023, 6:19 PM

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this third one confuse me sadly

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like it cant be 1/2

alpine bison Oct 29, 2023, 6:20 PM

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i can't even read properly

tawdry vortex Oct 29, 2023, 6:20 PM

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oh

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,flip

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.flip

shrewd moon Oct 29, 2023, 6:20 PM

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No helpers want to help me

tawdry vortex Oct 29, 2023, 6:20 PM

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sad

uneven palm Oct 29, 2023, 6:20 PM

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,rotate

warm shaleBOT Oct 29, 2023, 6:20 PM

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Couldn't find an attached image in the last 10 messages.

tawdry vortex Oct 29, 2023, 6:20 PM

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uneven palm Oct 29, 2023, 6:20 PM

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tawdry vortex

,rotate

warm shaleBOT Oct 29, 2023, 6:21 PM

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shrewd moon Oct 29, 2023, 6:22 PM

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Bro this is grade 10 work

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That root 6 is 6^0.5

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And 6 is 36^0.5

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So u get 36^0.5x0.5

dusk ruin Oct 29, 2023, 6:24 PM

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ozioma do not directly give people answers, the point of this server to help people understand

spare prairie Oct 29, 2023, 6:24 PM

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this one is pre-calculus?

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Very simple material

uneven palm Oct 29, 2023, 6:24 PM

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shrewd moon Bro this is grade 10 work

no need for that

dusk ruin Oct 29, 2023, 6:24 PM

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and the level of the problem is irrelevant, so long as someone needs help with it

warm canopy Oct 29, 2023, 6:24 PM

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yeah stop commenting on how "simple" material is for you

shrewd moon Oct 29, 2023, 6:24 PM

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So x is equal to 0.25 or 1/4

daring sorrel Oct 29, 2023, 6:25 PM

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Also how do you not know he isnt in 10th? Absolutely useless comment

willow mauve Oct 29, 2023, 6:25 PM

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the point is not to give the answer

shrewd moon Oct 29, 2023, 6:25 PM

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Sorry

spare prairie Oct 29, 2023, 6:25 PM

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Lol

shrewd moon Oct 29, 2023, 6:25 PM

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My first time helping

spare prairie Oct 29, 2023, 6:25 PM

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SOmetime its good to be honest

daring sorrel Oct 29, 2023, 6:25 PM

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Im more worried about how he keeps asking for help with pretty much exact same questions

spare prairie Oct 29, 2023, 6:26 PM

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I never asked a question

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Or you talk about ozioma

shrewd moon Oct 29, 2023, 6:26 PM

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Yah me

daring sorrel Oct 29, 2023, 6:26 PM

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Im talking about ac lol

obtuse pebbleBOT Oct 29, 2023, 6:26 PM

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shrewd moon So x is equal to 0.25 or 1/4

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

spare prairie Oct 29, 2023, 6:26 PM

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Anyway the answer was very easy to get

tawdry vortex Oct 29, 2023, 6:29 PM

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Ok thnxs

shrewd moon Oct 29, 2023, 6:29 PM

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tawdry vortex Ok thnxs

U know when u have same bases u can cancel them out right?

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That's what I did there

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Got myself to a base of 36

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So the bases cancel out

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And they can cancel like that only when they r in opposite side of the = sign

tawdry vortex Oct 29, 2023, 6:41 PM

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yea

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I just realized this homework is so repetitve

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I Just went through 10 questions same damn thing they jsut ask it different ways

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.close

obtuse pebbleBOT Oct 29, 2023, 6:45 PM

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ember inlet Oct 29, 2023, 6:46 PM

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obtuse pebbleBOT Oct 29, 2023, 6:46 PM

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ember inlet

ember inlet Oct 29, 2023, 6:46 PM

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Im so confused and im lost O-o idk where to start even

obtuse pebbleBOT Oct 29, 2023, 7:01 PM

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@ember inlet Has your question been resolved?

obtuse pebbleBOT Oct 29, 2023, 7:45 PM

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@ember inlet Has your question been resolved?

ember inlet Oct 29, 2023, 7:46 PM

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<@&286206848099549185>

obtuse pebbleBOT Oct 29, 2023, 8:46 PM

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@ember inlet Has your question been resolved?

obtuse pebbleBOT Oct 29, 2023, 9:46 PM

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cosmic veldt Oct 29, 2023, 10:04 PM

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obtuse pebbleBOT Oct 29, 2023, 10:04 PM

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cosmic veldt

cosmic veldt Oct 29, 2023, 10:04 PM

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So I think the bounds are 0 to pi/2 by that last part but not sure what c(t) is?

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This is the formula btw

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worn yoke Oct 29, 2023, 10:05 PM

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what's the usual parametrization of the unit circle?

cosmic veldt Oct 29, 2023, 10:05 PM

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Basically the formula but different letters

cosmic veldt Oct 29, 2023, 10:05 PM

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worn yoke what's the usual parametrization of the unit circle?

(sint, cost) right?

worn yoke Oct 29, 2023, 10:05 PM

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other way round

cosmic veldt Oct 29, 2023, 10:06 PM

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Oh yeah cuz cosine is x and sine is y

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Oh is that it?

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(cos t, sin t)?

worn yoke Oct 29, 2023, 10:06 PM

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yes

cosmic veldt Oct 29, 2023, 10:06 PM

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Nice

obtuse pebbleBOT Oct 29, 2023, 10:21 PM

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@cosmic veldt Has your question been resolved?

obtuse pebbleBOT Oct 29, 2023, 10:36 PM

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lavish kayak Oct 29, 2023, 10:38 PM

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Can someone please give me an intuitive explaniation of what the mixed partial derivative means graphically?

obtuse pebbleBOT Oct 29, 2023, 10:38 PM

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lavish kayak Can someone please give me an intuitive explaniation of what the mixed partial d...

lavish kayak Oct 29, 2023, 10:38 PM

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I know that the second order partial derivative fxx and fyy just determine the concavity of the function created at a fixed x (or y) variable

obtuse pebbleBOT Oct 29, 2023, 10:53 PM

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@lavish kayak Has your question been resolved?

obtuse pebbleBOT Oct 29, 2023, 11:24 PM

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@lavish kayak Has your question been resolved?

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solid bear Oct 29, 2023, 11:30 PM

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I know the right answer is 3 but I. don't get why if someome could help me

Captura_de_pantalla_2023-10-29_a_las_20.30.06.png

obtuse pebbleBOT Oct 29, 2023, 11:30 PM

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solid bear I know the right answer is 3 but I. don't get why if someome could help me

brazen gorge Oct 29, 2023, 11:31 PM

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mind providing a translation?

solid bear Oct 29, 2023, 11:32 PM

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the answers 3 says a can be any number you want and b <0

brazen gorge Oct 29, 2023, 11:33 PM

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x-> -inf, so ae^x goes to 0

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same with e^x

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so you get be^-x/x^3

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$\lim_{x \to -\infty} \frac{be^{-x}}{x^3}$

warm shaleBOT Oct 29, 2023, 11:34 PM

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artemetra

brazen gorge Oct 29, 2023, 11:35 PM

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e^-x goes to +inf, x^3 goes to -inf

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therefore b must be negative to get -inf/-inf = +inf

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it's.. basically what you have there written already

solid bear Oct 29, 2023, 11:37 PM

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i just got confused cuz I thought -inf/-inf was indeterminate

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or is it only when is -inf/+inf

brazen gorge Oct 29, 2023, 11:39 PM

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solid bear i just got confused cuz I thought -inf/-inf was indeterminate

i also think that honestly

solid bear Oct 29, 2023, 11:41 PM

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so is it wrong?

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or is there another way to do it?

obtuse pebbleBOT Oct 29, 2023, 11:56 PM

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@solid bear Has your question been resolved?

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obtuse pebbleBOT Oct 30, 2023, 12:44 AM

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timid silo Oct 30, 2023, 12:46 AM

#

Can anyone recommend me a good video or resource on directional derivatives, thanks

obtuse pebbleBOT Oct 30, 2023, 12:46 AM

#

timid silo Can anyone recommend me a good video or resource on directional derivatives, tha...

tardy epoch Oct 30, 2023, 12:59 AM

#

timid silo Can anyone recommend me a good video or resource on directional derivatives, tha...

Why can't you just Google this

timid silo Oct 30, 2023, 1:01 AM

#

tardy epoch Why can't you just Google this

Alright, i got a video from khan academy

#

thnks

obtuse pebbleBOT Oct 30, 2023, 1:16 AM

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acoustic portal Oct 30, 2023, 1:34 AM

#

Question one

obtuse pebbleBOT Oct 30, 2023, 1:34 AM

#

acoustic portal Question one

acoustic portal Oct 30, 2023, 1:39 AM

#

<@&286206848099549185> Rigorous proof alert ⏰

#

I dont really want to answer but i dont know what to do

#

I know it converges to 1/2(a + b) but i dont know how to prove it

#

perhaps i can use the definition of cauchy sequence or somethinig but idk how to proceed with that

obtuse pebbleBOT Oct 30, 2023, 1:55 AM

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@acoustic portal Has your question been resolved?

acoustic portal Oct 30, 2023, 2:01 AM

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<@&286206848099549185> !!

obtuse pebbleBOT Oct 30, 2023, 2:31 AM

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@acoustic portal Has your question been resolved?

acoustic portal Oct 30, 2023, 2:45 AM

#

<@&286206848099549185> ☹️

tardy epoch Oct 30, 2023, 2:57 AM

#

acoustic portal I know it converges to 1/2(a + b) but i dont know how to prove it

Usual way is to assume the limit exists and is a variable, say c, then take the limit of the entire sequence and solve for c

obtuse pebbleBOT Oct 30, 2023, 3:45 AM

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@acoustic portal Has your question been resolved?

acoustic portal Oct 30, 2023, 3:47 AM

#

tardy epoch Usual way is to assume the limit exists and is a variable, say c, then take the ...

But for a recursive sequence, isn’t it much different v

tardy epoch Oct 30, 2023, 4:01 AM

#

Oh hmm

#

Try finding the first 5 terms and find a pattern

#

Then you can make some induction argument

acoustic portal Oct 30, 2023, 4:23 AM

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tardy epoch Try finding the first 5 terms and find a pattern

The terms are like

#

(1/2)^n * coefficient of a + coefficient of b where

#

The coefficients are jacobinan(?) numbers for

obtuse pebbleBOT Oct 30, 2023, 6:24 AM

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thick sun Oct 30, 2023, 8:32 AM

#

I need help finding the measure of the angle of the two intersecting bike trails, and the length of the pathway to the bridge (I also need help with the full solution)

obtuse pebbleBOT Oct 30, 2023, 8:32 AM

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thick sun I need help finding the measure of the angle of the two intersecting bike trails...

jagged falcon Oct 30, 2023, 8:42 AM

#

Okay, can you draw a simpler diagram on paper?

obtuse pebbleBOT Oct 30, 2023, 8:47 AM

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timid silo Oct 30, 2023, 9:07 AM

#

trying to find [
\lim_{n \to \infty} \f1n \p{n!}^{\ff1n}
]

obtuse pebbleBOT Oct 30, 2023, 9:07 AM

#

timid silo trying to find \[ \lim_{n \to \infty} \f1n \p{n!}^{\ff1n} \]

warm shaleBOT Oct 30, 2023, 9:07 AM

#

timid silo Oct 30, 2023, 9:07 AM

#

I did this to check to see if like I can find out if I can find an upper bound that diverges

#

[
\f1n \p{n!}^{\ff1n} = \p{\f1{n^n} n!}^{\ff1n} = \f1n\m\ln{\f1{n^n} n!} = \f1n\m\ln{\f1{n^n}\int_1^n x \dd x} =\f1n\m\ln{\f{n^2-1}{2n^n}}
]

warm shaleBOT Oct 30, 2023, 9:08 AM

#

timid silo Oct 30, 2023, 9:08 AM

#

but this probably converges thonk2

timid silo Oct 30, 2023, 9:08 AM

#

warm shale

I'm 99% sure this is some wicked limit of e I can't find

warm canopy Oct 30, 2023, 9:08 AM

#

A divergent upper bound would not tell you anything

tardy epoch Oct 30, 2023, 9:09 AM

#

Do you know Stirling's formula

timid silo Oct 30, 2023, 9:09 AM

#

oh sorry I probably mixed stuff up

timid silo Oct 30, 2023, 9:09 AM

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tardy epoch Do you know Stirling's formula

No probably not

#

Ah you mean that

#

would substituting n! for that make it work out

#

oh I guess n^n's cancel

#

so that's nice

warm canopy Oct 30, 2023, 9:12 AM

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n! = ∫_1^n x dx ? bhappy

timid silo Oct 30, 2023, 9:12 AM

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OHHH

timid silo Oct 30, 2023, 9:12 AM

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warm canopy n! = ∫_1^n x dx ?<:bhappy:924710573885755422>

.> but I was lazy sorry

#

ok thanks for telling me about this Stirling formula thingy really helpful

#

.close

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craggy tapir Oct 30, 2023, 9:19 AM

#

I need help with basically everything shown in this image. I'm very clueless on what to do or how to read it.

obtuse pebbleBOT Oct 30, 2023, 9:19 AM

#

craggy tapir I need help with basically everything shown in this image. I'm very clueless on ...

obtuse pebbleBOT Oct 30, 2023, 9:34 AM

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@craggy tapir Has your question been resolved?

craggy tapir Oct 30, 2023, 9:35 AM

#

<@&286206848099549185>

obtuse pebbleBOT Oct 30, 2023, 10:05 AM

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@craggy tapir Has your question been resolved?

craggy tapir Oct 30, 2023, 10:41 AM

#

.close

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weary bone Oct 30, 2023, 1:46 PM

#

My calculus teacher insists that none of the options are correct, but i got D
Could this just be a difference in the interpretation of the question?

obtuse pebbleBOT Oct 30, 2023, 1:46 PM

#

weary bone My calculus teacher insists that none of the options are correct, but i got D Co...

twin sapphire Oct 30, 2023, 1:48 PM

#

show your working out

#

and also f(5) =/=1 no?

weary bone Oct 30, 2023, 1:50 PM

#

It doesn’t equal, which is why I think she interpreted it differently

twin sapphire Oct 30, 2023, 1:50 PM

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i mean the question doesnt make sense then

weary bone Oct 30, 2023, 1:50 PM

#

Yeah…

twin sapphire Oct 30, 2023, 1:50 PM

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like theres no such tangent line

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as (5,1) isnt on the curve

weary bone Oct 30, 2023, 1:51 PM

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Could this be interpreted as (5,1) being a point on the tangent line, not on the graph?

#

I feel like that would be the only way

twin sapphire Oct 30, 2023, 1:51 PM

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oooh then this gets much harder

#

and there could be multiple answers

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i think there would be 2 answers

#

you can do that

weary bone Oct 30, 2023, 1:52 PM

#

Even with that interpretation, it would be y-1 = (10-2sqrt14)(x-5), which is not an option

twin sapphire Oct 30, 2023, 1:53 PM

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im not sure its that simple

#

for a tangent at point a

twin sapphire Oct 30, 2023, 1:54 PM

#

weary bone Even with that interpretation, it would be y-1 = (10-2sqrt14)(x-5), which is not...

you have y-(f(a)) = 10(x-a)

#

right?

weary bone Oct 30, 2023, 1:54 PM

#

that was my initial answer

twin sapphire Oct 30, 2023, 1:54 PM

#

so in this case

#

y-(a²-10) = 10(x-a)

#

and you also want

#

that for some value (x,y) = (5,1)

#

it holds true

#

so you have

#

1-(a²-10) = 10(5-a)

#

so you have to solve this quadratic in a

#

and this will lead you to the points

#

a

#

where the two tangent lines are possible

weary bone Oct 30, 2023, 1:57 PM

#

interesting

twin sapphire Oct 30, 2023, 1:57 PM

#

so we can solve it

#

-a² +10a -40 = 0

#

i think

#

theres no answer

weary bone Oct 30, 2023, 1:58 PM

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twin sapphire 1-(a²-10) = 10(5-a)

This equation doesn’t seem to have any solutions though

#

Yeah

twin sapphire Oct 30, 2023, 1:58 PM

#

we could plot it

#

,w plot x^2 -10

warm shaleBOT Oct 30, 2023, 1:58 PM

#

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twin sapphire Oct 30, 2023, 1:59 PM

#

its weird because visually it seems there should be such a tangent line

#

maybe i messed up somewhere

#

oh

#

the original is not with 10

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y-(f(a)) = f'(a)(x-a)

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1-(a²-10) = 2a(5-a)

#

a² -10a+10 = 0

#

,w solve x^2-10x+10=0

warm shaleBOT Oct 30, 2023, 2:02 PM

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twin sapphire Oct 30, 2023, 2:02 PM

#

and plug that back

#

two solutions

#

as i said

#

you got what i did?

weary bone Oct 30, 2023, 2:03 PM

#

yes I understand

twin sapphire Oct 30, 2023, 2:03 PM

#

ok

#

so $y - ((5 \pm \sqrt{15})^2 -10) = 2 (5 \pm \sqrt{15})(x-(5 \pm \sqrt{15}))$

warm shaleBOT Oct 30, 2023, 2:05 PM

#

Benjamin

twin sapphire Oct 30, 2023, 2:05 PM

#

its a bit convoluted

#

but its the only valid answer

#

its a tangent

#

and it goest through (5,1)

weary bone Oct 30, 2023, 2:06 PM

#

I see…

twin sapphire Oct 30, 2023, 2:06 PM

#

but the real answer

#

is that the question doesnt have an answer in what they wanted you to do

weary bone Oct 30, 2023, 2:06 PM

#

Yeah the question was written poorly

obtuse pebbleBOT Oct 30, 2023, 2:21 PM

#

@weary bone Has your question been resolved?

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#

silver plover Oct 30, 2023, 3:01 PM

#

how do the two equations at the bottom have no solutions?

#

u can calc t for when it equals 0, no?

unreal musk Oct 30, 2023, 3:04 PM

#

A solution for one won't be the solution for the other one catlove

silver plover Oct 30, 2023, 3:05 PM

#

unreal musk A solution for one won't be the solution for the other one <:catlove:92069876293...

oh yhhh

#

t has to be the same

#

for the vector to be (0,0)

#

makes sense, thanks

unreal musk Oct 30, 2023, 3:05 PM

#

SCgoodjob2 np

silver plover Oct 30, 2023, 3:05 PM

#

.close

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mint nebula Oct 30, 2023, 3:13 PM

#

In the exterior of the square ABCD there are equilateral triangles ADF and BCE. If DE intersected with CF = G, prove that the triangle AGB is equilateral

obtuse pebbleBOT Oct 30, 2023, 3:13 PM

#

mint nebula In the exterior of the square ABCD there are equilateral triangles ADF and BCE. ...

mint nebula Oct 30, 2023, 3:13 PM

#

obtuse pebbleBOT Oct 30, 2023, 3:28 PM

#

@mint nebula Has your question been resolved?

obtuse pebbleBOT Oct 30, 2023, 4:01 PM

#

@mint nebula Has your question been resolved?

mint nebula Oct 30, 2023, 4:01 PM

#

Dang.

#

Is it that hard as I thought? lol

obtuse pebbleBOT Oct 30, 2023, 5:01 PM

#

@mint nebula Has your question been resolved?

obtuse pebbleBOT Oct 30, 2023, 7:25 PM

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@mint nebula Has your question been resolved?

fathom flicker Oct 30, 2023, 11:53 PM

#

maybe try drawing some parallel lines

obtuse pebbleBOT Oct 31, 2023, 1:13 AM

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@mint nebula Has your question been resolved?

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wild kayak Oct 31, 2023, 5:23 AM

#

when using the a^2+b^2-= c^2 why cant i just square root the equasion to remove the ^2s?

obtuse pebbleBOT Oct 31, 2023, 5:23 AM

#

wild kayak when using the a^2+b^2-= c^2 why cant i just square root the equasion to remove ...

wild kayak Oct 31, 2023, 5:23 AM

#

like 9^2 +12^2 =c^2 equals 15

shut lagoon Oct 31, 2023, 5:26 AM

#

Because sqrt(a^2 + b^2) is (almost) never equal to a+b.

#

Exponentiation and surds aren't distributive like multiplication and addition are.

wild kayak Oct 31, 2023, 5:26 AM

#

but doesnt it remove the ^2>

#

ohh ok

#

thats confusing

shut lagoon Oct 31, 2023, 5:27 AM

#

I mean

#

In your example you say 9^2 + 12^2 = 15^2

#

But clearly 9 + 12 = 21, not 15

#

So you can't just sqrt both sides and hope for the best

#

I mean you can, but then you have $c = \sqrt{a^2 + b^2}$

warm shaleBOT Oct 31, 2023, 5:28 AM

#

Azyrashacorki

shut lagoon Oct 31, 2023, 5:28 AM

#

And this can't be simplified further.

wild kayak Oct 31, 2023, 5:29 AM

#

ok i havent learned that yet im just trying to learn the pythagorum therum

shut lagoon Oct 31, 2023, 5:29 AM

#

Yeah just know that the square root and exponentiation distribute over multiplication/division, but not over addition/subtraction.

#

$\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$

wild kayak Oct 31, 2023, 5:30 AM

#

ok kind of like factoring

warm shaleBOT Oct 31, 2023, 5:30 AM

#

Azyrashacorki

shut lagoon Oct 31, 2023, 5:30 AM

#

This works

#

At the end of the day

wild kayak Oct 31, 2023, 5:30 AM

#

yes ok i know thay

shut lagoon Oct 31, 2023, 5:30 AM

#

It's the exponents law

wild kayak Oct 31, 2023, 5:31 AM

#

ok

#

so you cant just ^2 away the root

#

like multiplying to remove division

shut lagoon Oct 31, 2023, 5:32 AM

#

I wouldn't say it like that, but I guess so. You just can't distribute the square root. For the same reason that you can't distribute squares $(a+b)^2 \neq a^2 + b^2$.

warm shaleBOT Oct 31, 2023, 5:32 AM

#

Azyrashacorki

pure kayak Oct 31, 2023, 5:33 AM

#

Someone explain to me wth is parametric form of a eqn of a straight line

shut lagoon Oct 31, 2023, 5:33 AM

#

!occupied

obtuse pebbleBOT Oct 31, 2023, 5:33 AM

#

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).

wild kayak Oct 31, 2023, 5:33 AM

#

ok that makes sense

pure kayak Oct 31, 2023, 5:34 AM

#

obtuse pebble Someone else is already using this help channel. If you need help with a questio...

Ok

shut lagoon Oct 31, 2023, 5:34 AM

#

If you have some roots you want to get rid of, like say you have $v = \sqrt{a}$.

warm shaleBOT Oct 31, 2023, 5:34 AM

#

Azyrashacorki

shut lagoon Oct 31, 2023, 5:34 AM

#

Then you can square both sides to get $v^2 = a$.

warm shaleBOT Oct 31, 2023, 5:34 AM

#

Azyrashacorki

shut lagoon Oct 31, 2023, 5:34 AM

#

This you can do

wild kayak Oct 31, 2023, 5:34 AM

#

or what about if it is a square root * a square troot

shut lagoon Oct 31, 2023, 5:35 AM

#

Yes this distributes

wild kayak Oct 31, 2023, 5:35 AM

#

then you could square to remove beacuse its multiplication right?

#

oohhhhok

shut lagoon Oct 31, 2023, 5:35 AM

#

square roots are just exponents 1/2

wild kayak Oct 31, 2023, 5:35 AM

#

they arent opposites?

shut lagoon Oct 31, 2023, 5:35 AM

#

So $a^{1/2}\cdot a^{1/2} = a^{1/2 + 1/2} = a^1 = a$

warm shaleBOT Oct 31, 2023, 5:35 AM

#

Azyrashacorki

wild kayak Oct 31, 2023, 5:36 AM

#

and 1/2 is a square root

shut lagoon Oct 31, 2023, 5:36 AM

#

wild kayak they arent opposites?

Yes.

wild kayak Oct 31, 2023, 5:36 AM

#

ok interesting

#

what is the oppostie of a square root?

shut lagoon Oct 31, 2023, 5:37 AM

#

The inverse would be squaring.

#

Similarly, you can think of division as a multiplication right? a/b = a * (1/b)

wild kayak Oct 31, 2023, 5:37 AM

#

ok

shut lagoon Oct 31, 2023, 5:37 AM

#

Well you can think of surds as exponents that are fractions.

wild kayak Oct 31, 2023, 5:37 AM

#

yes

shut lagoon Oct 31, 2023, 5:37 AM

#

Cube roots are 1/3

wild kayak Oct 31, 2023, 5:38 AM

#

yes

#

ok interesting i understand now i just need to fully wrap my head around it

shut lagoon Oct 31, 2023, 5:38 AM

#

Yeah it'll clock in with some practice

wild kayak Oct 31, 2023, 5:38 AM

#

ok cool i appreciate your help

#

i think thats all i need im going to keep practacing

#

!close

#

.close

obtuse pebbleBOT Oct 31, 2023, 5:39 AM

#

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spare phoenix Oct 31, 2023, 6:35 AM

#

hello

obtuse pebbleBOT Oct 31, 2023, 6:35 AM

#

spare phoenix hello

spare phoenix Oct 31, 2023, 6:35 AM

#

can someone help me with these questions and correct them for me
"List your 3 points you have identified. Write them to 2 decimal places.
(-1,2) (0,1) (1,3)

Write the equation you have found using this Step (write the three points on your parabola (labeling effectively) and use your knowledge of three variable, three equation systems to find a quadratic equation for your parabola. Need to find a, b, and c! (USE MODE, 5, 2)"

#

this is the points you might need it

Screen_Shot_2023-10-31_at_9.36.31_AM.png

obtuse pebbleBOT Oct 31, 2023, 6:52 AM

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#

royal basin Oct 31, 2023, 7:22 AM

#

#discussion

obtuse pebbleBOT Oct 31, 2023, 7:35 AM

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@timid silo Has your question been resolved?

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tired jackal Oct 31, 2023, 8:31 AM

#

I have a question here that is kinda confusing me, its SCM, but its basic math, its just a word problem. I already calculated shrinkage which is 326 units per month to meet 7500 sets per month, so now I'm just having trouble with question #3.

obtuse pebbleBOT Oct 31, 2023, 8:31 AM

#

tired jackal I have a question here that is kinda confusing me, its SCM, but its basic math, ...

tired jackal Oct 31, 2023, 8:34 AM

#

How I thought of solving it was 7500 x 12 = 90,000 sets per year sold and 7826 x 12 = 93912 to account for shrinkage.
So you're profiting off 90,000 sets per year, so 275 x 90,000 = 24,750,000 and then 200 x 93912 = 18,782,400 to account for all costs.
Now its just revenue - costs so 24,750,000 - 18,782,400 = 5,967,600 profit.

#

The actual answer to this question is 782,400, which makes no sense to me

#

.close

obtuse pebbleBOT Oct 31, 2023, 8:37 AM

#

Channel closed

Closed by @tired jackal

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timid silo Oct 31, 2023, 8:43 AM

#

hi
if u(x) = cos(x+1) and v(x) = x-1 then u(v(x)) is cos((x-1)+1) right
which is just cos(x)

obtuse pebbleBOT Oct 31, 2023, 8:43 AM

#

timid silo hi if u(x) = cos(x+1) and v(x) = x-1 then u(v(x)) is cos((x-1)+1) right which is...

shy vigil Oct 31, 2023, 8:47 AM

#

yes

obtuse pebbleBOT Oct 31, 2023, 8:58 AM

#

@timid silo Has your question been resolved?

obtuse pebbleBOT Oct 31, 2023, 9:13 AM

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bold brook Oct 31, 2023, 9:18 AM

#

i subtitue its -25/0 .

obtuse pebbleBOT Oct 31, 2023, 9:18 AM

#

bold brook i subtitue its -25/0 .

bold brook Oct 31, 2023, 9:18 AM

#

how to solve it?

sage dagger Oct 31, 2023, 9:19 AM

#

L 🏥

bold brook Oct 31, 2023, 9:19 AM

#

but if 2x - 6 / 1 = 4

sage dagger Oct 31, 2023, 9:19 AM

#

wow annnn

#

u would

bold brook Oct 31, 2023, 9:20 AM

#

using another way

sage dagger Oct 31, 2023, 9:20 AM

#

opencry

royal basin Oct 31, 2023, 9:20 AM

#

but even with l'hop: 2x-6 at x=1 gives -4, not 4

royal basin Oct 31, 2023, 9:20 AM

#

sage dagger u would

you're taking an L from me

sage dagger Oct 31, 2023, 9:20 AM

#

I give myself a W

bold brook Oct 31, 2023, 9:20 AM

#

i replace x as 5

#

which one is correct , -4 or 4 or -25/0

sage dagger Oct 31, 2023, 9:23 AM

#

You can’t divide by 0

bold brook Oct 31, 2023, 9:23 AM

#

yes

#

im confused

royal basin Oct 31, 2023, 9:30 AM

#

ah fuck.

#

shit.

#

i misread the thing sorry

obtuse pebbleBOT Oct 31, 2023, 9:38 AM

#

@bold brook Has your question been resolved?

pseudo swift Oct 31, 2023, 9:41 AM

#

also -25/0, you can't do l'hopital on that, it's only for 0/0 or infty/infty cases

bold brook Oct 31, 2023, 9:41 AM

#

so the answer is 4

#

right ?

pseudo swift Oct 31, 2023, 9:42 AM

#

your problem seems broken tbf

#

as written in the question, the limit doesn't even exist

bold brook Oct 31, 2023, 9:42 AM

#

yeah

#

that's make me confused

pseudo swift Oct 31, 2023, 9:42 AM

#

well ask your prof or whatever

bold brook Oct 31, 2023, 9:43 AM

#

she said the answer was there

pseudo swift Oct 31, 2023, 9:43 AM

#

,w lim x->5 (x^2-6x-20)/(x-5)

warm shaleBOT Oct 31, 2023, 9:43 AM

#

Results provided by WolframAlpha

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

pseudo swift Oct 31, 2023, 9:43 AM

#

well it's not

#

big L for your prof

bold brook Oct 31, 2023, 9:44 AM

#

what should i do? i need to chose between these option

#

😭

pseudo swift Oct 31, 2023, 9:44 AM

#

you don't

#

attach a screenshot of wolfram alpha and voila

bold brook Oct 31, 2023, 9:49 AM

#

ok

#

thanks

#

.close

obtuse pebbleBOT Oct 31, 2023, 9:49 AM

#

Channel closed

Closed by @bold brook

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obtuse pebbleBOT Oct 31, 2023, 10:39 AM

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timid silo Oct 31, 2023, 10:49 AM

#

obtuse pebbleBOT Oct 31, 2023, 10:49 AM

#

timid silo

timid silo Oct 31, 2023, 10:49 AM

#

anyone please 🤦‍♂️

royal basin Oct 31, 2023, 10:50 AM

#

!status

obtuse pebbleBOT Oct 31, 2023, 10:50 AM

#

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

timid silo Oct 31, 2023, 10:51 AM

#

4

royal basin Oct 31, 2023, 10:51 AM

#

show work and answer

#

@timid silo ?

timid silo Oct 31, 2023, 10:55 AM

#

my bad

#

royal basin Oct 31, 2023, 10:56 AM

#

do you understand how nonsensical the answer is lol

timid silo Oct 31, 2023, 10:56 AM

#

not at all 😭

royal basin Oct 31, 2023, 10:56 AM

#

oh wait no hold on i misread

#

thought you had a six figure tax total

#

but also why do you add 5092 tho.

timid silo Oct 31, 2023, 10:56 AM

#

was i supposed to minus

royal basin Oct 31, 2023, 10:57 AM

#

no

#

you were supposed to see you are in the third bracket: 45,001-120,000

#

the tax equals 32.5% of everything in excess of 45k, plus 5092

#

that's what you add 5092 to

#

not the original gross income

timid silo Oct 31, 2023, 10:58 AM

#

ohhh

royal basin Oct 31, 2023, 10:58 AM

#

the amount taxable in this bracket specifically is 97000-45000

timid silo Oct 31, 2023, 10:58 AM

#

still abit lost, whts the answer tho 😭

royal basin Oct 31, 2023, 11:01 AM

#

oh my bad typo

#

92,000 - 45,000

#

this difference is taxed at 32.5%

#

so the tax for this bracket is 32.5% * (92k - 45k)

#

and you add to that the total tax from the prev brackets which is 5092

timid silo Oct 31, 2023, 11:05 AM

#

20,367?

royal basin Oct 31, 2023, 11:12 AM

#

,calc (92000-45000)*0.325 + 5092

warm shaleBOT Oct 31, 2023, 11:12 AM

#

Result:

royal basin Oct 31, 2023, 11:12 AM

#

ok yeah

timid silo Oct 31, 2023, 11:13 AM

#

cheers bro

royal basin Oct 31, 2023, 11:15 AM

#

don't call me bro

#

please edit that out

obtuse pebbleBOT Oct 31, 2023, 11:28 AM

#

@edgy hull Has your question been resolved?

trail musk Oct 31, 2023, 11:43 AM

#

everyone's a bro

obtuse pebbleBOT Oct 31, 2023, 11:43 AM

#

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ivory spoke Oct 31, 2023, 12:05 PM

#

Are $\lnot (P \lor Q)$ and $(\lnot P \lor \lnot Q)$ the same?

obtuse pebbleBOT Oct 31, 2023, 12:05 PM

#

ivory spoke Are $\lnot (P \lor Q)$ and $(\lnot P \lor \lnot Q)$ the same?

warm shaleBOT Oct 31, 2023, 12:05 PM

#

Shinutsi

ivory spoke Oct 31, 2023, 12:06 PM

#

For instance in this example:

"Either John and Bill are both telling the truth, or neither of them is."

#

Does $(J \lor B) \lor \lnot(J \lor B)$ and $(J \lor B) \lor (\lnot J \lor \lnot B)$ both translate the statement correctly?

warm shaleBOT Oct 31, 2023, 12:08 PM

#

Shinutsi

timid silo Oct 31, 2023, 12:12 PM

#

warm shale **Shinutsi**

no

ivory spoke Oct 31, 2023, 12:12 PM

#

What's the difference?

timid silo Oct 31, 2023, 12:12 PM

#

[
\neg(P \vee Q) \equiv \neg P \wedge \neg Q
]

warm shaleBOT Oct 31, 2023, 12:13 PM

#

ivory spoke Oct 31, 2023, 12:13 PM

#

What how

#

wait

#

let me process

timid silo Oct 31, 2023, 12:15 PM

#

I will neither eat a burger or go out.

I will not eat a burger and I will not go out

ivory spoke Oct 31, 2023, 12:15 PM

#

OHHHHHHHHHHHHHHHHHHHHHHHH

#

damn

#

thank you

#

got it now

#

.close

obtuse pebbleBOT Oct 31, 2023, 12:15 PM

#

Channel closed

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obtuse pebbleBOT Oct 31, 2023, 12:57 PM

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patent fog Oct 31, 2023, 1:02 PM

#

did i derive C'(x1,x2) correctly?
fyi: a_n is an activation function, and although some values are the same (ie. w_1^1) every value is unique.

obtuse pebbleBOT Oct 31, 2023, 1:02 PM

#

patent fog did i derive C'(x1,x2) correctly? fyi: a_n is an activation function, and althou...

patent fog Oct 31, 2023, 1:03 PM

#

sorry its a bit complicated but to give some info, im deriving the gradient for weights in the first hidden layer

#

$c_n^m$ represents the "constants" that wont need to be derived, just need the value for chain rule

warm shaleBOT Oct 31, 2023, 1:04 PM

#

jtangkilla

obtuse pebbleBOT Oct 31, 2023, 1:19 PM

#

@patent fog Has your question been resolved?

obtuse pebbleBOT Oct 31, 2023, 1:57 PM

#

@patent fog Has your question been resolved?

patent fog Oct 31, 2023, 2:02 PM

#

bruh

#

damn ig no one wants to do chain rule 😭

mighty lava Oct 31, 2023, 2:45 PM

#

patent fog damn ig no one wants to do chain rule 😭

True

obtuse pebbleBOT Oct 31, 2023, 3:17 PM

#

@patent fog Has your question been resolved?

obtuse pebbleBOT Oct 31, 2023, 5:17 PM

#

@patent fog Has your question been resolved?

obtuse pebbleBOT Oct 31, 2023, 7:17 PM

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sharp anchor Oct 31, 2023, 7:29 PM

#

So my problem is " what are the maximum amount points you can fit in a sphere of a radius of 60. Each point has the dimensions of a 4x4x4 box and has to be 20 units away from every other box."

obtuse pebbleBOT Oct 31, 2023, 7:29 PM

#

sharp anchor So my problem is " what are the maximum amount points you can fit in a sphere of...

#

@sharp anchor Has your question been resolved?

sharp anchor Oct 31, 2023, 7:56 PM

#

I tried a triple integral but idk.

#

Used spherical coords

obtuse pebbleBOT Oct 31, 2023, 8:26 PM

#

@sharp anchor Has your question been resolved?

obtuse pebbleBOT Oct 31, 2023, 8:56 PM

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#

warm shaleBOT Oct 31, 2023, 8:59 PM

#

Abo Wisam

obtuse pebbleBOT Oct 31, 2023, 8:59 PM

#

Channel closed

Channel closed due to the original message being deleted.
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alpine bison Oct 31, 2023, 9:00 PM

#

induction?

obtuse pebbleBOT Oct 31, 2023, 9:09 PM

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vestal geode Oct 31, 2023, 9:20 PM

#

I have multiple questions

obtuse pebbleBOT Oct 31, 2023, 9:20 PM

#

vestal geode I have multiple questions

vestal geode Oct 31, 2023, 9:20 PM

#

Ill send them

tardy epoch Oct 31, 2023, 9:23 PM

#

just ask one at a time

vestal geode Oct 31, 2023, 9:23 PM

#

vestal geode Oct 31, 2023, 9:23 PM

#

tardy epoch just ask one at a time

Im gonna be real with you

#

I just wanna know the answers

tardy epoch Oct 31, 2023, 9:23 PM

#

too bad that's against the rules

#

#rules and #info

vestal geode Oct 31, 2023, 9:24 PM

#

Bet

#

How do i close

tardy epoch Oct 31, 2023, 9:26 PM

#

obtuse pebble

and read this

#

.close

obtuse pebbleBOT Oct 31, 2023, 9:26 PM

#

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undone sentinel Oct 31, 2023, 9:40 PM

#

The length of a box(say x) is only half of its width, and its height is 7 units larger than its length. If the volume of this box were to be 100^3, what would the box's length = x be? Round to the nearest hundredths necessary

obtuse pebbleBOT Oct 31, 2023, 9:40 PM

#

undone sentinel The length of a box(say x) is only half of its width, and its height is 7 units ...

undone sentinel Oct 31, 2023, 9:53 PM

#

<@&286206848099549185>

unborn coral Oct 31, 2023, 10:00 PM

#

I suggest naming the width y, and the height z, and expressing y and z in terms of x

undone sentinel Oct 31, 2023, 10:06 PM

#

unborn coral I suggest naming the width y, and the height z, and expressing y and z in terms ...

Can you show me how

unborn coral Oct 31, 2023, 10:09 PM

#

if you name the width y, and x is half of y, that would mean y is twice the size of x, so y=2x

#

if you do the same for z, you're left with the width, height and length in terms of x

#

if you then use the formula to calculate volume and just insert your x'es and the number given for volume you should get an answer

undone sentinel Oct 31, 2023, 10:16 PM

#

Thanks

#

.close

obtuse pebbleBOT Oct 31, 2023, 10:16 PM

#

Channel closed

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obtuse pebbleBOT Oct 31, 2023, 10:47 PM

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lean dust Oct 31, 2023, 10:49 PM

#

help

obtuse pebbleBOT Oct 31, 2023, 10:49 PM

#

lean dust help

lean dust Oct 31, 2023, 10:49 PM

#

obtuse pebbleBOT Oct 31, 2023, 11:04 PM

#

@lean dust Has your question been resolved?

desert verge Oct 31, 2023, 11:04 PM

#

what should you say?

lean dust Oct 31, 2023, 11:16 PM

#

.close

obtuse pebbleBOT Oct 31, 2023, 11:16 PM

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grave crypt Oct 31, 2023, 11:19 PM

#

how would i sketch this?

obtuse pebbleBOT Oct 31, 2023, 11:19 PM

#

grave crypt how would i sketch this?

#

@grave crypt Has your question been resolved?

grave crypt Oct 31, 2023, 11:42 PM

#

Consider the function
a) Estimate the slope of the tangent line at
b) Using the slope and the point of tangency, find the equation
of the tangent line.
c) The tangent line intersects the original graph one more time.
Where? Graph both the original function and the tangent line
to illustrate this.

#

i found the iroc is about -1

#

so thats my slope

obtuse pebbleBOT Nov 1, 2023, 12:13 AM

#

@grave crypt Has your question been resolved?

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ember island Nov 1, 2023, 12:46 AM

#

why does 4-4sin^2 turn in 4(1-sin^2)

obtuse pebbleBOT Nov 1, 2023, 12:46 AM

#

ember island why does 4-4sin^2 turn in 4(1-sin^2)

ember island Nov 1, 2023, 12:46 AM

#

he said both of the terms have a common factor of 4

#

and said lets remove that common factor

#

but ion get it

stoic vale Nov 1, 2023, 12:48 AM

#

well both 4 and -4sin^2x can be divided by four

ember island Nov 1, 2023, 12:48 AM

#

yes

stoic vale Nov 1, 2023, 12:48 AM

#

so you factor it out

ember island Nov 1, 2023, 12:48 AM

#

4/4=1

stoic vale Nov 1, 2023, 12:49 AM

#

i imagine you split it into root 4 * root (1- sin^2x)

#

okay well think about it like this

ember island Nov 1, 2023, 12:49 AM

#

i dont get the 4 outside

stoic vale Nov 1, 2023, 12:49 AM

#

say you had

#

9x^2 + 6x + 3

#

would you agree that all of these are multiples of three

ember island Nov 1, 2023, 12:50 AM

#

yes

stoic vale Nov 1, 2023, 12:50 AM

#

that means that you can turn it into 3(3x^2 + 2x + 1)

ember island Nov 1, 2023, 12:50 AM

#

ye

stoic vale Nov 1, 2023, 12:50 AM

#

okay so

#

its the exact same even when you have sin^2x

#

4 - 4sin^2x

ember island Nov 1, 2023, 12:51 AM

#

so its like if i were to distrubute the 4

#

it would go to be 4-4sin^2

stoic vale Nov 1, 2023, 12:51 AM

#

ye

#

if u want u can think about it like this

ember island Nov 1, 2023, 12:51 AM

#

oh ok maybe im just having a slow moment

stoic vale Nov 1, 2023, 12:51 AM

#

i have those

ember island Nov 1, 2023, 12:51 AM

#

i can do factoring and stuff

stoic vale Nov 1, 2023, 12:51 AM

#

so i get it

#

i think ur just overthinking it

ember island Nov 1, 2023, 12:52 AM

#

but having to do everything wit sin cos and all that

#

struggling hard rn

stoic vale Nov 1, 2023, 12:52 AM

#

cuz if ur at the level to be using sin^2x and all that you definitely know how to do it

#

its just recognising it that can bet he problem

ember island Nov 1, 2023, 12:54 AM

#

and then he mentions how 1-sin^2x is equivalent to the identity sin^2x+cos^2x=1 which i get how but like ig its just confusing me cuz its just stuff u should know but i havent rememeber all this yet

stoic vale Nov 1, 2023, 12:54 AM

#

if u just remember sin^2x + cos^2x = 1

#

you can rearrange that

#

but ye these identities are stuff you eventually just remember

ember island Nov 1, 2023, 12:55 AM

#

would cos+1=sin

stoic vale Nov 1, 2023, 12:55 AM

#

no

ember island Nov 1, 2023, 12:55 AM

#

cos-1

#

...

stoic vale Nov 1, 2023, 12:55 AM

#

no

ember island Nov 1, 2023, 12:55 AM

#

damn

stoic vale Nov 1, 2023, 12:55 AM

#

you can figure that out using sin^2x + cos^2x = 1

#

if you think about it

#

sin^2x = 1 - cos^2x

#

sqr root both sides

#

sin = root(1 - cos^2x)

ember island Nov 1, 2023, 12:56 AM

#

so since 1-sin^2x is equivalent to cos

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u can simplify that to

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cos^2

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so iits 1/sqrt4cos^2x?

stoic vale Nov 1, 2023, 12:57 AM

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cos does not equal 1 - sin^2x

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cos^2x = 1 - sin^2x

ember island Nov 1, 2023, 12:57 AM

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oh

stoic vale Nov 1, 2023, 12:57 AM

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its a rearrangement of sin^2x + cos^2x = 1

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depending on ur country/exam board you may not need to memorise these

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but generally you should just know them after using them enough

ember island Nov 1, 2023, 12:59 AM

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for my exam i get a list of the trig identities

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its just using them correctly🥲

stoic vale Nov 1, 2023, 1:00 AM

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ahaha good luck

ember island Nov 1, 2023, 1:01 AM

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like the way this was explained i just understood that 1-sin^2x=cos^2x because sin^2x+cos^2x=1 and if you subtract sin^2x from the left and right then it looks like what he said

stoic vale Nov 1, 2023, 1:01 AM

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thats right

ember island Nov 1, 2023, 1:03 AM

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is there a time where it would be 1-cos^2x

stoic vale Nov 1, 2023, 1:06 AM

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what do you mean?

ember island Nov 1, 2023, 1:07 AM

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like does sin^2x=1-cos^2x make sense

stoic vale Nov 1, 2023, 1:07 AM

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yup

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again you just need to remember sin^2x + cos^2x = 1

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and rearrange it

ember island Nov 1, 2023, 1:08 AM

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okay

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and then he sqrts it

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so cos^2x is just cos(x)

stoic vale Nov 1, 2023, 1:09 AM

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yep

ember island Nov 1, 2023, 1:09 AM

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and ik sqrt4 is 2

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1/2cos(x)

stoic vale Nov 1, 2023, 1:09 AM

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because cos^2x is actually just (cosx)^2

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ye thats right

ember island Nov 1, 2023, 1:13 AM

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.close

obtuse pebbleBOT Nov 1, 2023, 1:13 AM

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lethal garnet Nov 1, 2023, 1:18 AM

#

Hi, if I attempt and have 50% chance of getting 1 point, and if I get it I have a 50% chance of it becoming 2 points, and if I get that I have a 50% chance of it becoming 3 points, what is the average points I get per attempt?

obtuse pebbleBOT Nov 1, 2023, 1:18 AM

#

lethal garnet Hi, if I attempt and have 50% chance of getting 1 point, and if I get it I have ...

#

@lethal garnet Has your question been resolved?

obtuse pebbleBOT Nov 1, 2023, 2:03 AM

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@lethal garnet Has your question been resolved?

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slim glen Nov 1, 2023, 2:40 AM

#

Hello. I am in pre algebra, and i have just a quick question. I am conevrting repeating decimals to rational numbers, and i multiply it by 100x etc. then i would subtract 10x. Why tf 10? And how does subtracting 10 make an irrational number rational 😭

obtuse pebbleBOT Nov 1, 2023, 2:40 AM

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slim glen Hello. I am in pre algebra, and i have just a quick question. I am conevrting re...

slim glen Nov 1, 2023, 2:42 AM

#

plain stag Nov 1, 2023, 2:44 AM

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You aren't subtracting 10x here

slim glen Nov 1, 2023, 2:53 AM

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Ik

slim glen Nov 1, 2023, 2:53 AM

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plain stag You aren't subtracting 10x here

But ik saying

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Sometimes its 10, 100 etc

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And why would it get rid of the decimal?

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And how do you know which number to use?

slim glen Nov 1, 2023, 2:54 AM

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slim glen But ik saying

*im

plain stag Nov 1, 2023, 2:54 AM

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Well you multiply by 10, 100 etc so that you have one iteration of the repetition on the left side of the decimal

slim glen Nov 1, 2023, 2:54 AM

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Yes

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I understand that

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But not the subtraction part

plain stag Nov 1, 2023, 2:55 AM

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So for 0.45 repeating, you need to move the decimal 2 digits to the right, which is multiplying by 100

slim glen Nov 1, 2023, 2:55 AM

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Yes

plain stag Nov 1, 2023, 2:55 AM

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Well you subtract the original number to remove the decimal point entirely

slim glen Nov 1, 2023, 2:55 AM

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Original number?

plain stag Nov 1, 2023, 2:56 AM

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These two numbers have the same decimal part (since the decimal is infinite), so subtracting them gives 0

slim glen Nov 1, 2023, 2:56 AM

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How would i know when to subtract 10, 1, 100 etc

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?

plain stag Nov 1, 2023, 2:57 AM

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Can you show a problem where you've subtracted anything other than 1?

slim glen Nov 1, 2023, 2:57 AM

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I was absent, i was looking over the slideshow and was confused, but i will provide what the slideshow gave me

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plain stag Nov 1, 2023, 3:00 AM

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Seems to me it's a matter of convenience

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You could do 1000x - x = 136, giving you x = 136/999 which is somewhat harder to reduce

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Oh wait no, oops

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You need to make the decimal parts match

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So you have an extra 1 before the repeating part, so you need to multiply by 10 to move that to the left side of the decimal

slim glen Nov 1, 2023, 3:04 AM

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Ok, thanks so much.

#

.close

obtuse pebbleBOT Nov 1, 2023, 3:04 AM

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harsh remnant Nov 1, 2023, 3:05 AM

#

Hello

obtuse pebbleBOT Nov 1, 2023, 3:05 AM

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harsh remnant Hello

harsh remnant Nov 1, 2023, 3:05 AM

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Can anyone explain what this means?

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I understand that the probability vector above

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But for the bottom, I am not sure why identity matrix is introduced

brave bramble Nov 1, 2023, 3:12 AM

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To get the result (P - I)s = 0

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Do you understand how that result was obtained?

harsh remnant Nov 1, 2023, 3:14 AM

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brave bramble Do you understand how that result was obtained?

Not really..

brave bramble Nov 1, 2023, 3:14 AM

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They factored s

harsh remnant Nov 1, 2023, 3:15 AM

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I mean like

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I understand Ps - s = 0

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But why is this equation

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The equivalent to

brave bramble Nov 1, 2023, 3:15 AM

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s = Is

harsh remnant Nov 1, 2023, 3:15 AM

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Ps - Is = 0

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How though

brave bramble Nov 1, 2023, 3:15 AM

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Take any vector. Multiply it by the identity matrix. You get that vector back.

harsh remnant Nov 1, 2023, 3:15 AM

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I is a stochastic matrix

brave bramble Nov 1, 2023, 3:16 AM

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Ia = a

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Ix = x

harsh remnant Nov 1, 2023, 3:16 AM

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Ohh

harsh remnant Nov 1, 2023, 3:23 AM

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brave bramble Ix = x

Can you also explain this part please?

brave bramble Nov 1, 2023, 3:28 AM

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Okay so we're at (P - I)s = 0

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This actually gives a method for determining s, given P.

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Compute P - I, then find the nullspace

harsh remnant Nov 1, 2023, 3:30 AM

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Why does s = [t/2, t]?

brave bramble Nov 1, 2023, 3:31 AM

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To get the nullspace of a matrix, we row reduce it, then look at the rows, as if they were equations

#

That top row says:
x - y/2 = 0

harsh remnant Nov 1, 2023, 3:32 AM

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But the matrix is not augmented

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?

brave bramble Nov 1, 2023, 3:32 AM

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That's one equation, but two variables. So, one of the variables is free. To show this, we set that free variable to t

harsh remnant Nov 1, 2023, 3:32 AM

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So wait

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x2 = t

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So x1 = t/2?

brave bramble Nov 1, 2023, 3:33 AM

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And that's the result

harsh remnant Nov 1, 2023, 3:33 AM

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Ohhhh

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Okay

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Oh

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nvm

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Now

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How do I go to the next step?

brave bramble Nov 1, 2023, 3:34 AM

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harsh remnant But the matrix is not augmented

We are finding the nullspace, so we care about the case where these rows are equal to 0

harsh remnant Nov 1, 2023, 3:34 AM

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How does t/2 and t become 1/3 and 2/3 respectively?

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Ohhh ic

brave bramble Nov 1, 2023, 3:34 AM

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Looks like the components have to sum to 1

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A probability thing

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So t + t/2 = 1
t = 2/3

harsh remnant Nov 1, 2023, 3:37 AM

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By the way

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Why is transpose also introduced?

#

.close

obtuse pebbleBOT Nov 1, 2023, 3:49 AM

#

Channel closed

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manic plover Nov 1, 2023, 4:26 AM

#

can anyone actually help me with whats wrong..

obtuse pebbleBOT Nov 1, 2023, 4:26 AM

#

manic plover can anyone actually help me with whats wrong..

plain stag Nov 1, 2023, 4:37 AM

#

Have you constructed your tangent line?

tardy epoch Nov 1, 2023, 4:40 AM

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plain stag Have you constructed your tangent line?

@manic plover

manic plover Nov 1, 2023, 4:40 AM

#

wym

plain stag Nov 1, 2023, 4:40 AM

#

I mean precisely what I said

tardy epoch Nov 1, 2023, 4:41 AM

#

plain stag Nov 1, 2023, 4:41 AM

#

The question asks you to use a tangent line near a "nice" point; have you figured out such a line?

manic plover Nov 1, 2023, 4:41 AM

#

-1(x-1)+1

#

no?

plain stag Nov 1, 2023, 4:43 AM

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Now evaluate that at x = 1.002

manic plover Nov 1, 2023, 4:43 AM

#

ok

#

1.001996

plain stag Nov 1, 2023, 4:44 AM

#

,calc -1*(1.002-1)+1

warm shaleBOT Nov 1, 2023, 4:44 AM

#

Result:

0.998

plain stag Nov 1, 2023, 4:44 AM

#

You sure?

manic plover Nov 1, 2023, 4:45 AM

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what

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you did 1.002

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not 1/1.002

plain stag Nov 1, 2023, 4:45 AM

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Knowing the shape of f(x) = 1/x, if x > 1, should f(x) > 1?

tardy epoch Nov 1, 2023, 4:46 AM

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manic plover not 1/1.002

x is not 1/1.002. x = 1.002

manic plover Nov 1, 2023, 4:48 AM

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bro what

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why is 1/1.002 in the problem then

obtuse pebbleBOT Nov 1, 2023, 5:03 AM

#

@manic plover Has your question been resolved?

obtuse pebbleBOT Nov 1, 2023, 5:18 AM

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undone sentinel Nov 1, 2023, 5:30 AM

#

If you click on the curve in 1950, 32.44 babies died in the first year of their lives. In 2020 there were 5.5 babies per 1000 live births. Using this to create points (1950, 32.44) and (2020, 5.5). Find the slope. What does this mean in the context of the problem

obtuse pebbleBOT Nov 1, 2023, 5:30 AM

#

undone sentinel If you click on the curve in 1950, 32.44 babies died in the first year of their ...

undone sentinel Nov 1, 2023, 5:30 AM

#

#

the slope is -0.39

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but idk what that means

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that the mortality rate decreased by 0.39 per year?

obtuse pebbleBOT Nov 1, 2023, 5:45 AM

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@undone sentinel Has your question been resolved?

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timid silo Nov 1, 2023, 6:03 AM

#

is there a limit? if there is what is solution? I calculated it as 1 but not sure

obtuse pebbleBOT Nov 1, 2023, 6:03 AM

#

timid silo is there a limit? if there is what is solution? I calculated it as 1 but not su...

royal basin Nov 1, 2023, 6:03 AM

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can you show how you calculated it as 1?

timid silo Nov 1, 2023, 6:04 AM

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royal basin can you show how you calculated it as 1?

i wrote also x as square root

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which is sqrt(x^2)

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then divide both of them by sqrt(x^2 ) in square root

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that made it sqrt(1/(1-0))

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and then sqrt(1)=1

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like this

royal basin Nov 1, 2023, 6:08 AM

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ok yeah that tracks

timid silo Nov 1, 2023, 6:09 AM

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royal basin ok yeah that tracks

is this correct

royal basin Nov 1, 2023, 6:13 AM

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yes, that's what i said.

timid silo Nov 1, 2023, 6:13 AM

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royal basin yes, that's what i said.

Also can you really check if limit exists in limits goes to infinity?

#

When it is something like 3,4 i learned that you could check it from left and right side and see if they are equal which causes problems in piecewise functions i guess.

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but can you do that really for infinities too?

brave bramble Nov 1, 2023, 6:15 AM

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Infinite limits are one-sided limits

timid silo Nov 1, 2023, 6:16 AM

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brave bramble Infinite limits are one-sided limits

yeah so would that make them naturally doesn't exist or something?

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that really confused me

brave bramble Nov 1, 2023, 6:16 AM

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So no, you can't check from the left and right, like you would with a two-sided limit

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None of this naturally exists. We made it all up!

timid silo Nov 1, 2023, 6:17 AM

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thats right

brave bramble Nov 1, 2023, 6:17 AM

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But infinite limits are "as legit" as other limits

timid silo Nov 1, 2023, 6:17 AM

#

oh okay thanks

obtuse pebbleBOT Nov 1, 2023, 6:32 AM

#

@timid silo Has your question been resolved?

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Channel closed

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obtuse pebbleBOT Nov 1, 2023, 7:34 AM

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kindred marten Nov 1, 2023, 7:41 AM

#

why is one infinity on the x part of the point while the other is on the y? ik one is negative and one isnt but i dont understand why one is on "x" and one is on "y"

obtuse pebbleBOT Nov 1, 2023, 7:41 AM

#

kindred marten why is one infinity on the x part of the point while the other is on the y? ik o...

cunning breach Nov 1, 2023, 7:45 AM

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That are the intervals, not the points.

kindred marten Nov 1, 2023, 7:45 AM

#

oh

humble solstice Nov 1, 2023, 7:45 AM

#

Calculate the angles of trapezium ABCD. Justify the answer!

zZeMaB2Da3V7rHRk8bndsuQ6hlMSwu3DLd8TNjpjNUHF3Ri_38ECiwrvUzwFk2jWI7EFzxruaBueQM8Gu4L-duJJ0bdyVEp5kvBWAfsFnk1bta0o243uoEWrpZ6pt-769gw309.png

kindred marten Nov 1, 2023, 7:45 AM

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what's the difference between the 2

#

..

cunning breach Nov 1, 2023, 7:46 AM

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Point is something defined in the coordinate system, and intervals restricts x-values.

kindred marten Nov 1, 2023, 7:46 AM

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ah i just remembered ty though

humble solstice Nov 1, 2023, 7:47 AM

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humble solstice Calculate the angles of trapezium ABCD. Justify the answer!

been tryna figure this out for 5 days now and im 1 day late for my test

kindred marten Nov 1, 2023, 7:47 AM

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humble solstice been tryna figure this out for 5 days now and im 1 day late for my test

there are unoccupied channels btw

humble solstice Nov 1, 2023, 7:47 AM

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i could just send it in how it is but i wanna get a good grade

kindred marten Nov 1, 2023, 7:47 AM

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ur supposed to

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use those

#

in the future

#

.close

obtuse pebbleBOT Nov 1, 2023, 7:47 AM

#

Channel closed

Closed by @kindred marten

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humble solstice Nov 1, 2023, 7:47 AM

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kindred marten there are unoccupied channels btw

what

#

how can i use one

kindred marten Nov 1, 2023, 7:47 AM

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see how there are ones under "occupied" and ones that arent

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the channels

humble solstice Nov 1, 2023, 7:48 AM

#

oh my bad

kindred marten Nov 1, 2023, 7:48 AM

#

ur fine

humble solstice Nov 1, 2023, 7:48 AM

#

what do i do now tho

#

do i occupy it or?

obtuse pebbleBOT Nov 1, 2023, 7:51 AM

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cunning breach Nov 1, 2023, 7:53 AM

#

humble solstice do i occupy it or?

You post your question in one of the available channels.

obtuse pebbleBOT Nov 1, 2023, 7:53 AM

#

cunning breach You post your question in one of the available channels.

cunning breach Nov 1, 2023, 7:53 AM

#

.close

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Channel closed

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#

brave bramble Nov 1, 2023, 8:14 AM

#

Yes