#help-13

plucky pawn Jun 16, 2022, 9:08 PM

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this is calc 2????

unkempt aspen Jun 16, 2022, 9:08 PM

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I only ruled it out because it doesn't really make sense

unkempt aspen Jun 16, 2022, 9:08 PM

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plucky pawn this is calc 2????

yes

plucky pawn Jun 16, 2022, 9:08 PM

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OOOOOOOOOOOOOOO

unkempt aspen Jun 16, 2022, 9:08 PM

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relative rates of growth is in our cal 2 class for some reason

plucky pawn Jun 16, 2022, 9:08 PM

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I thought calc 2 was integration

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not this but idk

unkempt aspen Jun 16, 2022, 9:08 PM

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it is mostly

plucky pawn Jun 16, 2022, 9:09 PM

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get ready integration is a whole new ball game compared to diff

unkempt aspen Jun 16, 2022, 9:09 PM

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i have to finish out this section then do integration by parts by tomorrow

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oh we're already well into integration

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they just have an ungodly scheme for this class

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satan made out syllabus

plucky pawn Jun 16, 2022, 9:10 PM

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sounds like my calc 1

unkempt aspen Jun 16, 2022, 9:10 PM

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you de facto have to have a 100% on every homework to do the quiz, and without doing the previous quiz you can't look or see what the next topic is

plucky pawn Jun 16, 2022, 9:10 PM

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I swear proff covering calc 2 in calc 1

unkempt aspen Jun 16, 2022, 9:10 PM

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i wouldn't have minded 1 semester for the entirety of single variable calc

plucky pawn Jun 16, 2022, 9:11 PM

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I couldn't care for it much... just gotta take em as a preque

unkempt aspen Jun 16, 2022, 9:12 PM

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alright so according to symbolab which I'm now learning has a limit function (a funky tool which will help with tomorrow's exam) this evaluates to infinity

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which i knew had to be the answer due to nlnx being slow as hell from comp sci

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mystery solved boys

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.close

cedar kilnBOT Jun 16, 2022, 9:12 PM

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Channel closed

Closed by @unkempt aspen

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unkempt aspen Jun 16, 2022, 9:13 PM

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.reopen

cedar kilnBOT Jun 16, 2022, 9:13 PM

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✅

unkempt aspen Jun 16, 2022, 9:13 PM

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actually let me explain WHY, work-wise this is the answer

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constant multiple rule makes it 4/3 * the limit

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x^2/xlnx

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x^2/xlnx = x/lnx

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1/1/x

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4/3*inf = inf

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hence the function is slower

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.close

cedar kilnBOT Jun 16, 2022, 9:15 PM

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Channel closed

Closed by @unkempt aspen

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cedar kilnBOT Jun 17, 2022, 12:33 AM

#

Available help channel!

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mental summit Jun 17, 2022, 12:49 AM

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Hello so i'm trying to reduce a fraction (i'm not sure that's the correct term)
but the fraction is:
x^2-2xy

2y^2-xy
The answer i got is:
x

y
The correct answer is:
-x

-y
The way i solved:
x(x-2y) x
--------- = ---
y(2y-x) y

-Probably missed an important step or rule but i'm lost to why it's minus and not plus

cedar kilnBOT Jun 17, 2022, 12:49 AM

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mental summit Hello so i'm trying to reduce a fraction (i'm not sure that's the correct term) ...

cerulean star Jun 17, 2022, 12:51 AM

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mental summit Hello so i'm trying to reduce a fraction (i'm not sure that's the correct term) ...

The correct answer cannot possibly be

mental summit Jun 17, 2022, 12:51 AM

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Sorry my bad

cerulean star Jun 17, 2022, 12:51 AM

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$\frac{-x}{-y}$

wraith daggerBOT Jun 17, 2022, 12:51 AM

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Disorganized

mental summit Jun 17, 2022, 12:51 AM

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it's just - x/y

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That's the correct answer (according to the answers in the book i'm learning)

cerulean star Jun 17, 2022, 12:53 AM

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Ok whats the issue

mental summit Jun 17, 2022, 12:53 AM

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i got x/y without the minus

cerulean star Jun 17, 2022, 12:53 AM

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You just didn't show one step

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Under "way I solved"

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2y-x is the negative of what you need

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So

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Mutliply the denominator by two factors of -1

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And distribute one of them INTO the parentheses

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This will let you write the parenthesized part backwards

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And it will match the factor in the numerator

mental summit Jun 17, 2022, 12:56 AM

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oh i can't substract what's in the parentheses before i match them to look alike? (bad english sorry)

cerulean star Jun 17, 2022, 12:56 AM

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mental summit oh i can't substract what's in the parentheses before i match them to look alike...

You didn't try at all in your working out

mental summit Jun 17, 2022, 12:57 AM

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i didn't know it's not possible if it's not the same

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i thought i could just substract what's in the parentheses

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i'm sorry if i sound stupid, but what is the way to make (x-2y) into (2y-x)

cerulean star Jun 17, 2022, 12:58 AM

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First multiply through by -1

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(Do it, write it)

mental summit Jun 17, 2022, 12:59 AM

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-1(-2y+x)

cerulean star Jun 17, 2022, 12:59 AM

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Uh uh and that becomes?

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Wait no

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You are doing it all at once

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This is correct

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So it's fine

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Moving fast then, lol

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What you have done

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Is multiplied by (-1)(-1)

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...which is just 1

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But one of those -1's

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...

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Wait

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No.

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Let's go slower

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Start here

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(-1)(x-2y)

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Distribute the -1

mental summit Jun 17, 2022, 1:02 AM

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-x+2y

cerulean star Jun 17, 2022, 1:02 AM

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Now commute the terms

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(Commutative property)

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@mental summit

mental summit Jun 17, 2022, 1:03 AM

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commute as to explain what i did ?

cerulean star Jun 17, 2022, 1:03 AM

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No, "commutative property", Google it

mental summit Jun 17, 2022, 1:04 AM

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-1x+(-1)-2y

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ughhhh i hope that's what u meant

cerulean star Jun 17, 2022, 1:05 AM

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No, Google "commutative property" so you remember what it is

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You need to know it

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$a+b = b+ a$

wraith daggerBOT Jun 17, 2022, 1:07 AM

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Disorganized

cerulean star Jun 17, 2022, 1:07 AM

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Commutative property (of addition)

cerulean star Jun 17, 2022, 1:07 AM

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mental summit -x+2y

Apply this to this

mental summit Jun 17, 2022, 1:08 AM

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so -x+2y=2y-x

cerulean star Jun 17, 2022, 1:08 AM

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Yes

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And this is the factor you needed

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BUT

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We have changed what we started with

mental summit Jun 17, 2022, 1:09 AM

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no no you right that was important for me in general

cerulean star Jun 17, 2022, 1:09 AM

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Because we multiplied by -1 in the denominator only

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We can fix this

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Just by multiplying by another factor of -1

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It won't matter if we do it in the numerator or denominator

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That will make the net result the same as if we had multiplied by 1 in the first place (since (-1)(-1)=1)

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So your denominator could look like

-y(x-2y)

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Now you can cancel stuff

mental summit Jun 17, 2022, 1:13 AM

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i kinda understood what you said, but by what you've said to me about commutative property

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isn't y(x-2y) would be the same ?

shut reef Jun 17, 2022, 1:13 AM

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man I was confused

mental summit Jun 17, 2022, 1:16 AM

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i just having hard time to realise why it's not x/y and it's - x/y

past orbit Jun 17, 2022, 1:21 AM

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mental summit Hello so i'm trying to reduce a fraction (i'm not sure that's the correct term) ...

how did u get x/y

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u had
x(x-2y)

y(2y-x)

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x-2y <> 2y-x

mental summit Jun 17, 2022, 1:22 AM

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Yes and just substracted

past orbit Jun 17, 2022, 1:22 AM

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x-2y = -1* (2y-x)

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when u cancel those 2 out, ur left with a negative sign

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so it becomes -x/y

mental summit Jun 17, 2022, 1:23 AM

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past orbit x-2y <> 2y-x

alright i got confused with the commutative property i thought that's equal

past orbit Jun 17, 2022, 1:24 AM

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nope

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a-b is not the same as b-a unless both are 0 or the same value

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so the reason it doesnt work

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is because the commutive property states that a+b=b+a

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but a stands for ANY number

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that means u have to bring the negative sign into it

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so if a is negative thats fine

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u would just have (-3)+(4)=4+(-3)

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not 3-4 which is what u did

mental summit Jun 17, 2022, 1:28 AM

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Thank you very much for the explanation

cedar kilnBOT Jun 17, 2022, 1:43 AM

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@mental summit Has your question been resolved?

mental summit Jun 17, 2022, 1:44 AM

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past orbit is because the commutive property states that a+b=b+a

so x(x-2y) = -x(2y-x), right because x^2-2xy=-2xy+x^2

cedar kilnBOT Jun 17, 2022, 1:45 AM

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Channel closed

Closed by @mental summit

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past orbit Jun 17, 2022, 1:46 AM

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yes exactly

cedar kilnBOT Jun 17, 2022, 1:46 AM

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mental summit Jun 17, 2022, 1:47 AM

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that's why @cerulean star brought up commutive property, sorry for not understanding what u meant, thanks both !

cedar kilnBOT Jun 17, 2022, 1:47 AM

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mental summit that's why <@598041720583618605> brought up commutive property, sorry for not un...

worthy path Jun 17, 2022, 2:00 AM

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u have no question @mental summit

cedar kilnBOT Jun 17, 2022, 2:05 AM

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@mental summit Has your question been resolved?

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Channel closed

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cedar kilnBOT Jun 17, 2022, 3:42 AM

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cedar kilnBOT Jun 17, 2022, 5:51 AM

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tropic oxide Jun 17, 2022, 6:03 AM

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the top one is in REF and the bottom one is in RREF, yes.

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does your textbook forbid non-1 leading coefficients?

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show me the definition of REF as given in your textbook.

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row echelon form, yes.

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orifyoulikeomittingspacesbetweenwordsit'srowechelonformyes

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you can and should check it yourself lol

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okay then let's walk through the definition step by step

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_Recall that a matrix is in row-echelon form if:

Rows of all zeroes are at the bottom.
The first entry of any nonzero row is a 1.
All leading 1's are to the right of the leading 1's in the rows above it._

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is it true that in your matrix all rows consisting of nothing but zeros are at the bottom? Y/N

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@plain bridge are you still here?

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actually you're wrong

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it is true that all rows of zeros are at the bottom

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precisely because there are no rows of zeros

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just to be clear, what you're wrong about is your assessment of the first criterion as false.

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the first criterion is true; it's the second which fails, for a reason you have already mentioned.

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no, wrong again

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how is the top one in ref when there's a leading 5
in the third row

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we've been talking about the first one all along.

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yes, it is neither.

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yes, you were wrong about the reason.

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yes

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what's wrong with them?

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oh, they made a typo

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you made it seem like there was something wrong with it fundamentally

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there's a typo in either the rref or the parameterized solution

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ok then there's a typo in the solutions

cedar kilnBOT Jun 17, 2022, 6:49 AM

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@plain bridge Has your question been resolved?

#

Channel closed

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cedar kilnBOT Jun 17, 2022, 12:11 PM

#

Available help channel!

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Remember:
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crimson obsidian Jun 17, 2022, 12:23 PM

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cedar kilnBOT Jun 17, 2022, 12:23 PM

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crimson obsidian

crimson obsidian Jun 17, 2022, 12:23 PM

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Which one of the above 2 images is the correct version?

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First one or second.

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I just learned this determinant and properties so I'm not confident

random shale Jun 17, 2022, 12:32 PM

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crimson obsidian

this is the correct form for 2A

crimson obsidian Jun 17, 2022, 12:33 PM

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random shale this is the correct form for 2A

But if take value

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It doesn't match

random shale Jun 17, 2022, 12:33 PM

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Yes

crimson obsidian Jun 17, 2022, 12:33 PM

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Is not the double

random shale Jun 17, 2022, 12:33 PM

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$det(2A) = 2^ndet(A)$

wraith daggerBOT Jun 17, 2022, 12:33 PM

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Max..

random shale Jun 17, 2022, 12:33 PM

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Where n is the dimension of A

crimson obsidian Jun 17, 2022, 12:34 PM

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What is dimension?

random shale Jun 17, 2022, 12:34 PM

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It is a 2 by 2 matrix

crimson obsidian Jun 17, 2022, 12:34 PM

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Ohh

random shale Jun 17, 2022, 12:34 PM

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So dimension is 2 in this case

crimson obsidian Jun 17, 2022, 12:34 PM

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I see

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Which is 4 delta A

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Right?

random shale Jun 17, 2022, 12:35 PM

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Yea

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but not delta

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Det(A)

crimson obsidian Jun 17, 2022, 12:35 PM

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That triangle is delta right?

random shale Jun 17, 2022, 12:35 PM

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You can prove this for any number lambda using the fact $det(A\times B)= detA \times detB$

wraith daggerBOT Jun 17, 2022, 12:35 PM

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Max..

crimson obsidian Jun 17, 2022, 12:36 PM

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I see

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Its kind of not taught yet

random shale Jun 17, 2022, 12:36 PM

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$det(\lambda A) = det((\lambda I) A) = det(\lambda I) \times det(A)$

wraith daggerBOT Jun 17, 2022, 12:36 PM

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Max..

crimson obsidian Jun 17, 2022, 12:36 PM

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So I was having trouble but thanks

random shale Jun 17, 2022, 12:37 PM

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And the determinant of I is the product of the diagonal and the product of the diagonal is just $\lambda^n$ and the result follows

wraith daggerBOT Jun 17, 2022, 12:37 PM

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Max..

crimson obsidian Jun 17, 2022, 12:37 PM

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wraith dagger **Max..**

There is I as well there it seems

random shale Jun 17, 2022, 12:37 PM

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crimson obsidian So I was having trouble but thanks

Yes I = Identity Matrix

crimson obsidian Jun 17, 2022, 12:37 PM

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I didn't learn them but thanks

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.close

cedar kilnBOT Jun 17, 2022, 12:37 PM

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Channel closed

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crimson sedge Jun 17, 2022, 12:43 PM

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do i just have to plug the numbers in or is a different?

Screen_Shot_2022-06-17_at_8.40.46_AM.png

cedar kilnBOT Jun 17, 2022, 12:43 PM

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crimson sedge do i just have to plug the numbers in or is a different?

elder pewter Jun 17, 2022, 12:45 PM

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wdym plug numbers in?

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your mass defect is when the LHS is not equal to the RHS

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you get a difference in mass

crimson sedge Jun 17, 2022, 12:46 PM

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oh

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Then how would i do this

crimson sedge Jun 17, 2022, 12:48 PM

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elder pewter your mass defect is when the LHS is not equal to the RHS

wym

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im a bit lost

elder pewter Jun 17, 2022, 12:51 PM

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first calculate the total mass on the left

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in terms of u

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then calculate the total mass on the right in terms of u

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find difference

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that is your mass defect

crimson sedge Jun 17, 2022, 12:52 PM

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Oh okay

crimson sedge Jun 17, 2022, 12:58 PM

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elder pewter first calculate the total mass on the left

how would I do that? Sorry I just wasn't here on this day so I'm clueless

elder pewter Jun 17, 2022, 12:59 PM

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you have been given mass of everything

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so just add them up

crimson sedge Jun 17, 2022, 1:00 PM

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oh okay

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well i got 1.25 x 10^-1

elder pewter Jun 17, 2022, 1:14 PM

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u?

crimson sedge Jun 17, 2022, 1:14 PM

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elder pewter u?

yea

crimson sedge Jun 17, 2022, 1:14 PM

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elder pewter u?

wait no

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the mass defect

elder pewter Jun 17, 2022, 1:15 PM

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I got that too

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as in the units is u

crimson sedge Jun 17, 2022, 1:15 PM

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Ohh okay

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now for the yield am i suppose to (1.25 x 10^-1) (

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what am i suppose to be multiplying it by?

elder pewter Jun 17, 2022, 1:18 PM

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do you know the energy mass equation

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famous one by einstein?

crimson sedge Jun 17, 2022, 1:20 PM

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Yea

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I got it

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I got 1.17045 x 10^16

elder pewter Jun 17, 2022, 1:21 PM

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that doesn't look quite right

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did you convert to kilograms first?

crimson sedge Jun 17, 2022, 1:22 PM

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elder pewter did you convert to kilograms first?

Oh no

elder pewter Jun 17, 2022, 1:23 PM

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need to do that first

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mass must be in kilograms first

crimson sedge Jun 17, 2022, 1:24 PM

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elder pewter mass must be in kilograms first

1.25 x 10^-1 so i would have to conver this ino kg?

elder pewter Jun 17, 2022, 1:24 PM

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yes

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because that is currently in units of u

crimson sedge Jun 17, 2022, 1:27 PM

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ohh okay

cedar kilnBOT Jun 17, 2022, 1:42 PM

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@crimson sedge Has your question been resolved?

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Channel closed

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gritty mulch Jun 17, 2022, 2:01 PM

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how many sides has a regular polygon whose number of sides increases by 2 when its angle increases by 9 degrees

cedar kilnBOT Jun 17, 2022, 2:01 PM

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gritty mulch how many sides has a regular polygon whose number of sides increases by 2 when i...

gritty mulch Jun 17, 2022, 2:04 PM

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I'll be back in a few minutes

crimson sedge Jun 17, 2022, 2:05 PM

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write it out as an equation

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will help

gritty mulch Jun 17, 2022, 2:19 PM

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sorry but how?

livid hound Jun 17, 2022, 2:20 PM

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no

cedar kilnBOT Jun 17, 2022, 2:37 PM

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@gritty mulch Has your question been resolved?

livid hound Jun 17, 2022, 2:42 PM

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its a little more convenient to work with exterior angles rather than interior as the angle sums of those is constant

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also don't just hang in the background otherwise i'm gonna assume you're not there

gritty mulch Jun 17, 2022, 2:45 PM

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the answer is 8

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if anyone can find that solution

livid hound Jun 17, 2022, 2:47 PM

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start by introducing a variable to denote the number of sides in your original polygon

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or don't...

gritty mulch Jun 17, 2022, 2:51 PM

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livid hound or don't...

why?

livid hound Jun 17, 2022, 2:51 PM

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sarcasm

gritty mulch Jun 17, 2022, 2:51 PM

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ok

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heh

livid hound Jun 17, 2022, 2:51 PM

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i'm attempting to guide you through the problem

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and that takes effort and responses from you

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otherwise i'm potentially gonna bail and do other things

gritty mulch Jun 17, 2022, 2:52 PM

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livid hound start by introducing a variable to denote the number of sides in your original p...

ok thank you but i don't know how to write this

livid hound Jun 17, 2022, 2:52 PM

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pick a letter/symbol or whatever

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and use that to represent the number of sides of the original polygon

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let "insert choice here" be the number of sides of the original regular polygon

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at this point all i really want from you is to pick an appropriate letter/symbol

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which is pretty much standard for all questions where you're trying to find an unknown and no variable has been given to you (so you introduce one yourself for ease of calculations)

gritty mulch Jun 17, 2022, 3:12 PM

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.close

cedar kilnBOT Jun 17, 2022, 3:12 PM

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Channel closed

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bright sorrel Jun 17, 2022, 3:21 PM

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very quick q: is (5-x)^2=(x-5)^2

cedar kilnBOT Jun 17, 2022, 3:21 PM

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bright sorrel very quick q: is (5-x)^2=(x-5)^2

bright sorrel Jun 17, 2022, 3:21 PM

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it is right?

sacred stone Jun 17, 2022, 3:22 PM

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yes

bright sorrel Jun 17, 2022, 3:22 PM

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ok ty

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.close

cedar kilnBOT Jun 17, 2022, 3:22 PM

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Channel closed

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cedar kilnBOT Jun 17, 2022, 4:17 PM

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#

knotty tartan Jun 17, 2022, 4:30 PM

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.close

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regal fog Jun 17, 2022, 4:49 PM

#

I know (a^b)^x is (a)^b×c but what about

cedar kilnBOT Jun 17, 2022, 4:49 PM

#

regal fog I know (a^b)^x is (a)^b×c but what about

regal fog Jun 17, 2022, 4:50 PM

#

(a^b×k^r)^x

crimson sedge Jun 17, 2022, 4:52 PM

#

use the product of power rule to move the power of x in, then use power of power rule

cedar kilnBOT Jun 17, 2022, 5:05 PM

#

@regal fog Has your question been resolved?

regal fog Jun 17, 2022, 5:07 PM

#

Thanks.

cedar kilnBOT Jun 17, 2022, 5:20 PM

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fossil thorn Jun 17, 2022, 5:36 PM

#

cedar kilnBOT Jun 17, 2022, 5:36 PM

#

fossil thorn

fossil thorn Jun 17, 2022, 5:36 PM

#

Can someone help me understand why this is incorrect

still hare Jun 17, 2022, 5:40 PM

#

You multiplied with positive number 3 ... No need to change the inequality sign.

#

In 2nd last step

fossil thorn Jun 17, 2022, 5:40 PM

#

But aren't we multiplying (-3*3)?

#

So there is a negative number

still hare Jun 17, 2022, 5:42 PM

#

Basically you are multiying +3 on both sides. So the inequality doesn't change

fossil thorn Jun 17, 2022, 5:42 PM

#

Oh okay so if it was X/-3 then we would change signs

cold briar Jun 17, 2022, 5:43 PM

#

fossil thorn Oh okay so if it was X/-3 then we would change signs

if you multiply both sides with -3, yes

fossil thorn Jun 17, 2022, 5:43 PM

#

Kk tysm

#

.close

cedar kilnBOT Jun 17, 2022, 5:43 PM

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late halo Jun 17, 2022, 6:34 PM

#

Can anyone tell how it was solved that x,y,z was obtained?

cedar kilnBOT Jun 17, 2022, 6:34 PM

#

late halo Can anyone tell how it was solved that x,y,z was obtained?

dire geode Jun 17, 2022, 6:38 PM

#

late halo Can anyone tell how it was solved that x,y,z was obtained?

need more information

late halo Jun 17, 2022, 6:43 PM

#

dire geode need more information

Never mind, I solved it

dire geode Jun 17, 2022, 6:43 PM

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.close

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urban plover Jun 17, 2022, 6:53 PM

#

hello can anyone check my answer

cedar kilnBOT Jun 17, 2022, 6:53 PM

#

urban plover hello can anyone check my answer

urban plover Jun 17, 2022, 6:53 PM

#

balmy apex Jun 17, 2022, 6:54 PM

#

$\bar{z}$ denotes the complex conjugate of z?

wraith daggerBOT Jun 17, 2022, 6:54 PM

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illuminator3

urban plover Jun 17, 2022, 6:59 PM

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you can see under the second picture

crystal raptor Jun 17, 2022, 7:01 PM

#

urban plover Jun 17, 2022, 7:08 PM

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so nothing?

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<@&286206848099549185> ?

vernal shell Jun 17, 2022, 7:21 PM

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urban plover

It looks correct to me 🤔, last line is 4abi + 2a-b = 8i, right?

urban plover Jun 17, 2022, 7:22 PM

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yeah

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but I have no clue what should I do next because the instructions say define every complex number of z for which is true:

vernal shell Jun 17, 2022, 7:26 PM

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vernal shell It looks correct to me 🤔, last line is `4abi + 2a-b = 8i`, right?

Right side and left side must be equal, considering a and b are real numbers

#

The real part of 8i is 0

#

What's the real part of the left-hand side of the equation?

urban plover Jun 17, 2022, 7:28 PM

#

Umm

#

I don't know honestly

cedar kilnBOT Jun 17, 2022, 7:45 PM

#

@urban plover Has your question been resolved?

cedar kilnBOT Jun 17, 2022, 8:15 PM

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@urban plover Has your question been resolved?

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round magnet Jun 17, 2022, 8:37 PM

#

i need to get A valor & B valor

cedar kilnBOT Jun 17, 2022, 8:37 PM

#

round magnet i need to get A valor & B valor

shut reef Jun 17, 2022, 8:38 PM

#

no way ..

hazy minnow Jun 17, 2022, 8:38 PM

#

Multiply both side by x^2 - 1.

#

Recall x^2 - 1 = (x+1)(x-1).

#

The rest follows easily since your dealing with two polynomials that are equal.

round magnet Jun 17, 2022, 8:40 PM

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I need to solve smth like this?

hazy minnow Jun 17, 2022, 8:41 PM

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Yep, try expanding stuff out.

#

In standard form.

round magnet Jun 17, 2022, 8:41 PM

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Oh

hazy minnow Jun 17, 2022, 8:42 PM

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We have two polynomials over R that are equal.

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What should that tell you?

round magnet Jun 17, 2022, 8:46 PM

#

um?

urban plover Jun 17, 2022, 8:56 PM

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yeah exactly why are people here answering in fingquestions

cedar kilnBOT Jun 17, 2022, 9:01 PM

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@round magnet Has your question been resolved?

cedar kilnBOT Jun 17, 2022, 9:16 PM

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Channel closed

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cedar kilnBOT Jun 18, 2022, 1:11 AM

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#

torpid fulcrum Jun 18, 2022, 1:22 AM

#

can you get x+2z=0 and y+z=0?

hazy minnow Jun 18, 2022, 1:22 AM

#

This ^ is it.

#

z is the free variable.

#

So write x = -2z and y = -z.

#

The solution space is (-2c, -c, c) for any scalar c.

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That is one solution.

#

Did you mean c(-2,-1,1)?

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@plain bridge

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Yes.

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“free non leading variable” trying to parse this.

#

If the system you have has no solution then it’s not true. But if a solution exist your statement is false.

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False I meant.

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Yep.

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Sure.

#

rank means number of linear independent columns, which is the columns that have pivot entries, so yes we have one free variable.

#

Remembering my past LA course, I am kinda of rusty. Currently relearning.

#

(c,c,c,c,c) yes.

#

Not sure what you mean by “making our answer just 1”.

#

Ok then yes.

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Are we talking about the same matrix but doing two different elementary operation on them?

#

If not then yes the system of equation are not the same.

#

If so then it will have the same solution space not matter what elementary operation you do.

#

But it possible the two matrix might be row equivalent.

hazy minnow Jun 18, 2022, 1:55 AM

#

hazy minnow But it possible the two matrix might be row equivalent.

In this case I will refer to my first answer.

#

Yep.

#

Unless we know the two different system are row equivalent.

#

Which we can check by row reducing.

hazy minnow Jun 18, 2022, 2:03 AM

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hazy minnow In this case I will refer to my first answer.

Second I meant.

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A solution exist.

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@plain bridge

#

Yep.

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x = 1, y = 0, z = 0.

#

Yep.

cosmic steppe Jun 18, 2022, 2:06 AM

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x = 1, y = 0, z = 0 if you're using x y and z

hazy minnow Jun 18, 2022, 2:06 AM

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Why’s did you think a solution did not exist?

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Yes.

cosmic steppe Jun 18, 2022, 2:06 AM

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I guess it works

hazy minnow Jun 18, 2022, 2:07 AM

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Even if we had 1 on the last rows of the last column we still have a solution.

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Can you explain why you still think for this case that a solution does not exist?

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If we had that.

#

If the last row was (0,0,0,1) then we have no solution.

#

Is that what you meant?

#

np.

cedar kilnBOT Jun 18, 2022, 2:36 AM

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@plain bridge Has your question been resolved?

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restive tapir Jun 18, 2022, 3:03 AM

#

quick question, how do i transform a multiplication to a fraction form?

cedar kilnBOT Jun 18, 2022, 3:03 AM

#

restive tapir quick question, how do i transform a multiplication to a fraction form?

restive tapir Jun 18, 2022, 3:04 AM

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id like to transform sin(x)*ln(x) to a fraction so i can apply the hospital rule

dire geode Jun 18, 2022, 3:05 AM

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$y = 1/(1/y))$ where $y=sin(x)$ or $\log(x)$

wraith daggerBOT Jun 18, 2022, 3:05 AM

#

riemann

dire geode Jun 18, 2022, 3:05 AM

#

Probably the former

#

Since $1/\sin(x)=\csc(x)$

wraith daggerBOT Jun 18, 2022, 3:05 AM

#

riemann

restive tapir Jun 18, 2022, 3:09 AM

#

just to confirm that i got it right because i felt lost for a good minute, transform sinx to 1/cscx, multiply by lnx = lnx/csx then put back the sin or just keep as is correct?

#

basically ln(x)/csc(x) or ln(x)/1/sin(x)

cedar kilnBOT Jun 18, 2022, 3:25 AM

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@restive tapir Has your question been resolved?

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vast wolf Jun 18, 2022, 3:48 AM

#

The letters of promise are arranged randomly in a row. Find how many solutions there are if the letter p and r are seperated by at least three letters

cedar kilnBOT Jun 18, 2022, 3:48 AM

#

vast wolf The letters of promise are arranged randomly in a row. Find how many solutions t...

vast wolf Jun 18, 2022, 3:48 AM

#

Anyone able to help

#

It's a permutation since it has order to it

#

Should I somehow find out when p and r are in 2 letters or less in proximity then subtract that from 7!

#

🤷‍♂️

cedar kilnBOT Jun 18, 2022, 4:06 AM

#

@vast wolf Has your question been resolved?

cedar kilnBOT Jun 18, 2022, 4:41 AM

#

@vast wolf Has your question been resolved?

sick ruin Jun 18, 2022, 5:21 AM

#

@vast wolf I think you should go for the complement here

#

Take the number of rearrangements that have p and r separated by exactly 0, 1, or 2 letters, and subtract that from all possible rearrangements

#

Hmm

#

Maybe there’s something better here

vast wolf Jun 18, 2022, 5:32 AM

#

Yeah

#

It's okay haha

#

I've given up on it and just asked my teacher

#

.close

cedar kilnBOT Jun 18, 2022, 5:32 AM

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Channel closed

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balmy beacon Jun 18, 2022, 5:46 AM

#

Hi. I want to prove that a + b = a' + b' mod d.

Please tell me if this is correct:

So let be:
a, b, a', b' in Z and d in Z+
with (a = a mod d) and (b = b' mod d).

Then let be k, k', k'' in Z
(a = a' mod d) <=> (a = a' + kd)
(b = b' mod d) <=> (b = b' + k'd)

So
a+b = a' mod d + b' mod d
= a' + kd + b' + k'd
= a' + b' + kd + k'd
= (a' + b' + k''d)
= a' + b' mod d

Is thiss proof correct?

cedar kilnBOT Jun 18, 2022, 5:46 AM

#

balmy beacon Hi. I want to prove that a + b = a' + b' mod d. Please tell me if this is corre...

#

@balmy beacon Has your question been resolved?

torpid fulcrum Jun 18, 2022, 6:09 AM

#

assuming that k''=k+k', the proof looks good

#

just as a side note, the "a' mod d + b' mod d" isn't strictly necessary

#

a+b = a' + kd + b' + k'd is sufficient

balmy beacon Jun 18, 2022, 6:17 AM

#

thank you @torpid fulcrum !

#

I'll close this then

#

.close

cedar kilnBOT Jun 18, 2022, 6:17 AM

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craggy anchor Jun 18, 2022, 6:42 AM

#

cedar kilnBOT Jun 18, 2022, 6:42 AM

#

craggy anchor

crimson sedge Jun 18, 2022, 6:46 AM

#

Ooo fancy question

#

I like it

#

Build systems of 180-a

#

180-b

#

Bla bla

#

And you will get it

craggy anchor Jun 18, 2022, 6:52 AM

#

cant i just use exterior angles of polygon add to 360? i know that if i can get to x-180 + a + b + c = 360 then x= 540-(a+b+c) but i dont know what that last angle is

#

your method does work tho so ill just use that ig

#

.close

cedar kilnBOT Jun 18, 2022, 6:57 AM

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Channel closed

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cedar kilnBOT Jun 18, 2022, 8:58 AM

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crimson sedge Jun 18, 2022, 9:00 AM

#

How to increase your chances of winning at games of chance?

cedar kilnBOT Jun 18, 2022, 9:00 AM

#

crimson sedge How to increase your chances of winning at games of chance?

balmy apex Jun 18, 2022, 9:00 AM

#

crimson sedge How to increase your chances of winning at games of chance?

you don't

crimson sedge Jun 18, 2022, 9:01 AM

#

balmy apex you don't

LMFAOO

crimson sedge Jun 18, 2022, 9:01 AM

#

balmy apex you don't

But like, be sure to get a gain at least

fair geyser Jun 18, 2022, 9:02 AM

#

not every game is gameable, and it wouldn't be the same strategy anyway

crimson sedge Jun 18, 2022, 9:03 AM

#

I know I'm going to have to calculate the probability of winning the games and see if it's over 50% etc but I don't know where to start

crimson sedge Jun 18, 2022, 9:03 AM

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fair geyser not every game is gameable, and it wouldn't be the same strategy anyway

It's fine I think, cuz i can choose the game

balmy apex Jun 18, 2022, 9:03 AM

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choose coin flip

#

ez

crimson sedge Jun 18, 2022, 9:03 AM

#

Coin flip game I see

fair geyser Jun 18, 2022, 9:03 AM

#

it doesn't make sense to do that no

crimson sedge Jun 18, 2022, 9:04 AM

#

Do what?

fair geyser Jun 18, 2022, 9:05 AM

#

oh you mean you are going to calculate it before choosing the game and then just play it?

crimson sedge Jun 18, 2022, 9:05 AM

#

Yes, it can be a benefit over a certain number of rounds or in general

crimson sedge Jun 18, 2022, 9:06 AM

#

balmy apex choose coin flip

U got another game to compare?

fair geyser Jun 18, 2022, 9:06 AM

#

i meant like, it doesn't matter if your chance to win is 58% if you pay x to win 1.75x

#

something like that

crimson sedge Jun 18, 2022, 9:07 AM

#

But, if the winrate is 58% if I play a lot of times I'm sure to make a profit

fair geyser Jun 18, 2022, 9:08 AM

#

no, that depends on what the prize is and what you pay to play

crimson sedge Jun 18, 2022, 9:08 AM

#

Ye but in most of game u pay less than the profit right

fair geyser Jun 18, 2022, 9:09 AM

#

of course you pay less than the prize, it's not enough

crimson sedge Jun 18, 2022, 9:11 AM

#

The probability of winning is 53% and we pay 2€ we can win 3€ if we play 1000 times we are sure to make a profit I mean

fair geyser Jun 18, 2022, 9:12 AM

#

yeah that's what i think you mean

#

that loses you money big time

crimson sedge Jun 18, 2022, 9:13 AM

#

So, u make profit right

fair geyser Jun 18, 2022, 9:14 AM

#

you lose

#

what do you mean

#

why would i use words "that loses you money big time"

crimson sedge Jun 18, 2022, 9:15 AM

#

How u lose money

fair geyser Jun 18, 2022, 9:15 AM

#

are you used to people saying the opposite of what they want to say lmao

crimson sedge Jun 18, 2022, 9:15 AM

#

english not my native language haha

balmy apex Jun 18, 2022, 9:15 AM

#

fair geyser are you used to people saying the opposite of what they want to say lmao

your lawyer in court wouldn't be too happy about that

fair geyser Jun 18, 2022, 9:17 AM

#

crimson sedge How u lose money

just count it

#

you pay 2€ 1000 times

#

you win 530 times, -2000 paid, 1590 won

crimson sedge Jun 18, 2022, 9:18 AM

#

wtf am i that dumb

#

Ye i mean ur right

#

forgot that the gain must be above x2 at least

fair geyser Jun 18, 2022, 9:21 AM

#

slightly below x2

#

50% and x2 means you can play for fun, it's free

#

53% and x2 means you make profit, and it can be a bit below x2, still profitable

crimson sedge Jun 18, 2022, 9:28 AM

#

Oh ye

#

depend of the winrate

#

so how can u know the profit u need to make with the winrate

fair geyser Jun 18, 2022, 9:40 AM

#

when you win you gain (prize − cost), this happens 53% of the time, rest of the time you lose the money, you can write an equation
0.53((multiplier * x) - x) = 0.47x

#

#

when it's that, you don't lose

#

1.89x is below 2x

#

so you want the multiplier to be 1 / winrate

#

,w 1/0.53

wraith daggerBOT Jun 18, 2022, 9:46 AM

#

Results provided by WolframAlpha

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

cedar kilnBOT Jun 18, 2022, 9:51 AM

#

@crimson sedge Has your question been resolved?

cedar kilnBOT Jun 18, 2022, 10:06 AM

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Channel closed

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craggy anchor Jun 18, 2022, 10:09 AM

#

cedar kilnBOT Jun 18, 2022, 10:09 AM

#

craggy anchor

rotund vine Jun 18, 2022, 10:09 AM

#

what have you done

#

any thoughts or work

craggy anchor Jun 18, 2022, 10:10 AM

#

well i constructed line CA thats literally it but im pretty sure i cant say its parallel to qp cause it wants me to prove that so im not sure

cedar kilnBOT Jun 18, 2022, 10:25 AM

#

@craggy anchor Has your question been resolved?

craggy anchor Jun 18, 2022, 10:27 AM

#

<@&286206848099549185>

elder pewter Jun 18, 2022, 10:29 AM

#

do you know the requirements for proving similar triangles

craggy anchor Jun 18, 2022, 10:31 AM

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well i usually just use equiangular

craggy anchor Jun 18, 2022, 10:48 AM

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<@&286206848099549185>

velvet mortar Jun 18, 2022, 10:55 AM

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BQ/BC = BP/BA = 1/2

craggy anchor Jun 18, 2022, 10:58 AM

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does that prove that the triangles are similar?

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that doesnt prove that pq is similar to ca does it?

craggy anchor Jun 18, 2022, 11:24 AM

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can anyone confirm

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<@&286206848099549185>

cedar kilnBOT Jun 18, 2022, 12:04 PM

#

@craggy anchor Has your question been resolved?

craggy anchor Jun 18, 2022, 12:17 PM

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.close

cedar kilnBOT Jun 18, 2022, 12:17 PM

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vagrant current Jun 18, 2022, 12:26 PM

#

cedar kilnBOT Jun 18, 2022, 12:26 PM

#

vagrant current

vagrant current Jun 18, 2022, 12:26 PM

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will i have to find the distance between every point

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or the gradient

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since 2 sides

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need to be equal

tropic oxide Jun 18, 2022, 12:27 PM

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you can either find the gradients of your lines and show that they're equal or you can find the distances and show those are equal

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it's entirey up to you

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you can do both if you're really paranoid

vagrant current Jun 18, 2022, 12:29 PM

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Ohh right , since if the gradients are the same it gotta be parallel and parallelograms have parallel opposite sides

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didnt think i could use the gradient for that tbh

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ty for help

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.close

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cedar kilnBOT Jun 18, 2022, 1:20 PM

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lusty tiger Jun 18, 2022, 1:20 PM

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Yes

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balmy apex Jun 18, 2022, 1:21 PM

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yes

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lusty tiger Jun 18, 2022, 1:22 PM

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https://www.wolframalpha.com/input?i2d=true&i={{1%2C2%2C3}%2C{3%2C2%2C1}%2C{2%2C1%2C3}}

{{1,2,3},{3,2,1},{2,1,3}} - Wolfram|Alpha

Wolfram|Alpha brings expert-level knowledge and capabilities to the broadest possible range of people—spanning all professions and education levels.

cedar kilnBOT Jun 18, 2022, 1:37 PM

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@plain bridge Has your question been resolved?

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cedar kilnBOT Jun 18, 2022, 3:27 PM

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bold snow Jun 18, 2022, 3:34 PM

#

how do I prove that OBB' is congruent to AXX'?

cedar kilnBOT Jun 18, 2022, 3:34 PM

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bold snow how do I prove that OBB' is congruent to AXX'?

bold snow Jun 18, 2022, 3:36 PM

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OABX is the original parallelogram, with a shear applied to it by some multiple of OA

silent yew Jun 18, 2022, 3:37 PM

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@bold snow can u prove that the 2 triangles are similar?

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U can easily prove congruency after proving the similarity

bold snow Jun 18, 2022, 3:41 PM

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silent yew U can easily prove congruency after proving the similarity

I need to prove that BB' is the same as XX' to check the similarity

silent yew Jun 18, 2022, 3:42 PM

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bold snow I need to prove that BB' is the same as XX' to check the similarity

No u dont

silent yew Jun 18, 2022, 3:43 PM

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bold snow how do I prove that OBB' is congruent to AXX'?

So angle BOB' = XAX' , because a shear was applied and the incline should be equal

silent yew Jun 18, 2022, 3:44 PM

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bold snow how do I prove that OBB' is congruent to AXX'?

Since OB is Parallel to AX , and BX is the transversal, we can say that angle OBB' = angle AXX'

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So from AA property, the two triangles OBB' and AXX' are similar

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Now since it's a parallelogram, OB = AX

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So the respective sides are in a ratio 1:1

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Therefore triangle AXX' is congruent to triangle OBB'

cedar kilnBOT Jun 18, 2022, 3:56 PM

#

@bold snow Has your question been resolved?

bold snow Jun 18, 2022, 3:59 PM

#

silent yew So angle BOB' = XAX' , because a shear was applied and the incline should be equ...

can you phrase this more formally?

cedar kilnBOT Jun 18, 2022, 4:11 PM

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cedar kilnBOT Jun 18, 2022, 5:05 PM

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low rose Jun 18, 2022, 5:34 PM

#

Hi, I am not sure how to solve these problems, but i attempted and got 6591 for the second one. Can someone check it?

cedar kilnBOT Jun 18, 2022, 5:34 PM

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low rose Hi, I am not sure how to solve these problems, but i attempted and got 6591 for ...

crimson sedge Jun 18, 2022, 5:35 PM

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Do you know

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The properties of powers

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@low rose

low rose Jun 18, 2022, 5:36 PM

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ye

crimson sedge Jun 18, 2022, 5:37 PM

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Try to write them in base forms first

#

Do you know how to write square root as a power

low rose Jun 18, 2022, 5:37 PM

#

i got the answer now

#

.close

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cedar kilnBOT Jun 18, 2022, 6:19 PM

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crimson sedge Jun 18, 2022, 6:39 PM

#

What exactly is he doing here, what does he mean by "taking x * h^(n-1) n times" and "selecting h from atleast two factors"

cedar kilnBOT Jun 18, 2022, 6:39 PM

#

crimson sedge What exactly is he doing here, what does he mean by "taking x * h^(n-1) n times"...

crimson sedge Jun 18, 2022, 6:40 PM

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This seems like another simple thing worded confusingly which is what always gives me the most headaches

sage forge Jun 18, 2022, 6:47 PM

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crimson sedge Jun 18, 2022, 6:48 PM

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Oh, it's that thing again

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Ok i think i know what i need to reread

sage forge Jun 18, 2022, 6:48 PM

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Are you familiar with it?

crimson sedge Jun 18, 2022, 6:49 PM

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Well, i forgot what the two numbers ontop of eachother mean but i know what the sigma means

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Maybe that's a sign i should reread the previous book

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It'll be easier to retain everything

sage forge Jun 18, 2022, 6:50 PM

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Those are binomial coeffizients

crimson sedge Jun 18, 2022, 6:51 PM

#

.close

cedar kilnBOT Jun 18, 2022, 6:51 PM

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sand sedge Jun 18, 2022, 7:10 PM

#

Can I get some help with this

cedar kilnBOT Jun 18, 2022, 7:10 PM

#

sand sedge Can I get some help with this

sand sedge Jun 18, 2022, 7:10 PM

#

fierce shard Jun 18, 2022, 7:15 PM

#

Find the y intercept and the gradient

velvet mortar Jun 18, 2022, 7:15 PM

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Do you know y=mx+b?

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What is m and b ?

sand sedge Jun 18, 2022, 7:16 PM

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I actually go through it thank you ☺️

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Now I’m struggling with another one

#

velvet mortar Jun 18, 2022, 7:20 PM

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What have you tried

cedar kilnBOT Jun 18, 2022, 7:32 PM

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@sand sedge Has your question been resolved?

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cedar kilnBOT Jun 18, 2022, 9:17 PM

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cinder sierra Jun 18, 2022, 9:26 PM

#

I'm writing a short paper where I analytically prove a few theorems of elementary arithmetic about the divisibility relation n | m \↔️ ∃p(m = np), prior to introducing division with remainder and/or its related algorithms, as a proof of concept for a friend. right now I'm trying to prove a lemma of Euclid's lemma, to in turn prove the uniqueness part of the fundamental theorem of arithmetic

the lemma is that, given nonzero integers m,n,p,q where p,q are coprime and mq = np (i.e. m/n = p/q), there is an integer k such that m = pk and n = qp (i.e. m,n are multiples of p,q by the same integer). I know that, if q | n, then the theorem follows (because then n = qk for some k, in which case mq = pkq, and so m = pk), so in turn I just have to prove that q | n, but I don't know where do I even begin

so far I've proven that divisibility is a pre-order over the nonzero integers having 1 as a minimal element over the positive integers, that every composite number is a product of primes (though not the uniqueness of this product, of course), and that the integers resulting from the division of m,n by their gcd are coprime (i.e. that if m,n are nonzero, and if m = gcd(m, n)p and n = gcd(m, n)q, then gcd(p, q) = 1)

cedar kilnBOT Jun 18, 2022, 9:26 PM

#

cinder sierra I'm writing a short paper where I analytically prove a few theorems of elementar...

mighty drift Jun 18, 2022, 9:29 PM

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To prove q|n, use mq=np. This means q|np, but since q and p are coprime, it means (Gauss's lemma) that q | n

cinder sierra Jun 18, 2022, 9:30 PM

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mighty drift To prove q|n, use mq=np. This means q|np, but since q and p are coprime, it mean...

note that I'm trying to prove this lemma in order to prove Euclid's (Gauss') lemma

mighty drift Jun 18, 2022, 9:30 PM

#

Oh

cinder sierra Jun 18, 2022, 9:30 PM

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so that would be circular

cedar kilnBOT Jun 18, 2022, 9:45 PM

#

@cinder sierra Has your question been resolved?

cinder sierra Jun 18, 2022, 9:45 PM

#

<@&286206848099549185>

cedar kilnBOT Jun 18, 2022, 10:15 PM

#

@cinder sierra Has your question been resolved?

cinder sierra Jun 18, 2022, 10:16 PM

#

asking the question once more

#

.close

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bold shadow Jun 18, 2022, 10:35 PM

#

Hi guys, what equation should I use to build the following graph? The second screenshot is the closest I found so far

cedar kilnBOT Jun 18, 2022, 10:35 PM

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bold shadow Hi guys, what equation should I use to build the following graph? The second scr...

balmy apex Jun 18, 2022, 10:38 PM

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bold shadow Hi guys, what equation should I use to build the following graph? The second scr...

you need a fourier series there I think

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nvm

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you can use something like

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$y = -\frac{2a}{\pi}\arctan(\cot\frac{\pi x}{p})$

wraith daggerBOT Jun 18, 2022, 10:40 PM

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illuminator3

balmy apex Jun 18, 2022, 10:40 PM

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with a being the amplitude and p being the period

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such things are called sawtooth waves

crystal raptor Jun 18, 2022, 10:43 PM

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also messing with $a\cdot\text{arctan}(\tan(b(x-c)) + d$ will get you there

wraith daggerBOT Jun 18, 2022, 10:44 PM

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ΣAC

bold shadow Jun 18, 2022, 10:46 PM

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crystal raptor also messing with $a\cdot\text{arctan}(\tan(b(x-c)) + d$ will get you there

well, I think I can work with that

#

.close

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rugged palm Jun 18, 2022, 10:47 PM

#

They gave you two great answers
you can also use the floor() function, but I'm pretty sure that's not what you are meant to use

cedar kilnBOT Jun 19, 2022, 1:58 AM

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odd seal Jun 19, 2022, 2:19 AM

#

Am I doing this right?

cedar kilnBOT Jun 19, 2022, 2:19 AM

#

odd seal Am I doing this right?

odd seal Jun 19, 2022, 2:20 AM

#

?

#

whoops

#

.close

cedar kilnBOT Jun 19, 2022, 2:30 AM

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crimson sedge Jun 19, 2022, 2:39 AM

#

i have one that makes no sense to me, and yes its math not science

cedar kilnBOT Jun 19, 2022, 2:39 AM

#

crimson sedge i have one that makes no sense to me, and yes its math not science

crimson sedge Jun 19, 2022, 2:40 AM

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a radioactive material has a half-life of 20 Years

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how radioactive is the material after 80 years, if the value is set to 1 at the year 0?

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<@&286206848099549185> idk if the question is broken or im dumb

gaunt hamlet Jun 19, 2022, 2:58 AM

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What have you tried?

crimson sedge Jun 19, 2022, 3:04 AM

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Just different ways of trying to understand it

gaunt hamlet Jun 19, 2022, 3:06 AM

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Well, how radioactive is the material after 20 years?

crimson sedge Jun 19, 2022, 3:06 AM

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Literely no idea

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I dont know where to subtract from

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Like halflife

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It doesent tell me how much there is, it just says that the value is 1 at year 0

gaunt hamlet Jun 19, 2022, 3:10 AM

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What does halflife mean?

crimson sedge Jun 19, 2022, 3:14 AM

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That it looses its radioactive power

gaunt hamlet Jun 19, 2022, 3:16 AM

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By how much?

cedar kilnBOT Jun 19, 2022, 3:29 AM

#

@crimson sedge Has your question been resolved?

cedar kilnBOT Jun 19, 2022, 3:44 AM

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quiet shadow Jun 19, 2022, 4:31 AM

#

cedar kilnBOT Jun 19, 2022, 4:31 AM

#

quiet shadow

quiet shadow Jun 19, 2022, 4:31 AM

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How could I continue this?

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Don't know how to make it meet l'hopital conditions

dire geode Jun 19, 2022, 4:32 AM

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log(x^2) = 2log(x)

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But also it does meet l'hopital conditions

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Recheck what those are in your notes or textbook

quiet shadow Jun 19, 2022, 4:33 AM

#

I thought log of infinity was undefined

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I thought incorrectly I suppose lmao

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its inf/inf

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nevermind, thanks @dire geode

#

.close

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frozen tendon Jun 19, 2022, 5:01 AM

#

guys can anyone telll me how is (b,c) = (b,-c)?

cedar kilnBOT Jun 19, 2022, 5:01 AM

#

frozen tendon guys can anyone telll me how is (b,c) = (b,-c)?

vernal palm Jun 19, 2022, 5:01 AM

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we need context

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what's the theorem

frozen tendon Jun 19, 2022, 5:03 AM

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@vernal palm

vernal palm Jun 19, 2022, 5:03 AM

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oh damn

frozen tendon Jun 19, 2022, 5:03 AM

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the euclidean algorithm

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its proof is like a nightmare

vernal palm Jun 19, 2022, 5:04 AM

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yeah

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idk if I can help u here

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sorry

frozen tendon Jun 19, 2022, 5:04 AM

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@vernal palm btw one remark is also given

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idk if its related to it

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@vernal palm^

vernal palm Jun 19, 2022, 5:05 AM

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idk lol sorry

frozen tendon Jun 19, 2022, 5:05 AM

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oh np

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@tropic oxide sry for the ping

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ig i need help again

frozen tendon Jun 19, 2022, 5:06 AM

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frozen tendon guys can anyone telll me how is (b,c) = (b,-c)?

can u plz help me with this

tropic oxide Jun 19, 2022, 5:06 AM

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any common divisor of b and c is also a common divisor of b and -c, and vice versa

frozen tendon Jun 19, 2022, 5:07 AM

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so it meant that the gcd is always the same

#

?

tropic oxide Jun 19, 2022, 5:07 AM

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"the gcd is always the same" is too vague

frozen tendon Jun 19, 2022, 5:08 AM

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tropic oxide "the gcd is always the same" is too vague

then what's the most appropriate statement for it?

dusty hazel Jun 19, 2022, 5:08 AM

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The absolute value of gcd is always the same?

tropic oxide Jun 19, 2022, 5:09 AM

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perhaps "multiplying either argument of gcd by -1 doesn't change the value"

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or "gcd doesn't depend on the sign of its inputs"

frozen tendon Jun 19, 2022, 5:09 AM

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tropic oxide or "gcd doesn't depend on the sign of its inputs"

oh

#

#

Guys is it the general form of gcd in which the largen number will always be in the first place and be considered as the value of b in b=aq+r ?

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@tropic oxide

tropic oxide Jun 19, 2022, 5:23 AM

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???

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"general form"?

frozen tendon Jun 19, 2022, 5:25 AM

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I mean why is it that 4840 = b and 1512 = to a like yea it's quite common to divide the bigger number with the smaller one but still I should have some statement or prove in order to make it true right?

tropic oxide Jun 19, 2022, 5:26 AM

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......

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what do you mean?

#

are you looking for a theorem that says "The evaluation of a gcd MUST proceed with the bigger number first and the smaller number second, and in NO OTHER WAY"?

frozen tendon Jun 19, 2022, 5:27 AM

#

Kinda

tropic oxide Jun 19, 2022, 5:27 AM

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well there is no such theorem because such imperatives are very very rare in math

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i think you're confusing the gcd function itself with the Euclidean algorithm that evaluates it in a certain way.

frozen tendon Jun 19, 2022, 5:28 AM

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My question is that why in b=aq+r, b=4840 and a=1512

tropic oxide Jun 19, 2022, 5:28 AM

#

what "lemme"?

frozen tendon Jun 19, 2022, 5:28 AM

#

tropic oxide i think you're confusing the gcd function itself with _the Euclidean algorithm_ ...

Tbh yea I am kind of confused with gcd and Euclidean algorithm

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Division algorithm or like what bruuhhhhhh

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Now it's freaking confusing

tropic oxide Jun 19, 2022, 5:30 AM

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there should be a clear difference between "what gcd is" and "how to find gcd"

frozen tendon Jun 19, 2022, 5:30 AM

#

Ok

tropic oxide Jun 19, 2022, 5:31 AM

#

one method of finding the gcd of two numbers is to run the euclidean algorithm on them, recursively doing division-with-remainder until the remainder turns to zero at some point

frozen tendon Jun 19, 2022, 5:32 AM

#

To find gcd I can use the Euclidean algorithm, using b=aq+r where the gcd of a and b can be represented as ax+by also which is Stated in thee bézouts theorem, right?

tropic oxide Jun 19, 2022, 5:33 AM

#

...no, i never mentioned bézout's theorem...

#

again you are confusing two things that are very different: finding the gcd itself vs. representing gcd(a,b) as a linear combination of a and b

frozen tendon Jun 19, 2022, 5:34 AM

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No I mean there is a part of the question that requires the bezouts theorem

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It's just the half question

tropic oxide Jun 19, 2022, 5:34 AM

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im trying to take you through the underlying theory

frozen tendon Jun 19, 2022, 5:35 AM

#

tropic oxide again you are confusing two things that are very different: finding the gcd itse...

Ok so u mean bézouts theorem help us to represent the gcd of A and B in a linear combination of a and b?

tropic oxide Jun 19, 2022, 5:35 AM

#

bézout's theorem states that such a representation EXISTS

#

but it does not "help" us beyond that

#

the theorem itself gives us no method of computing it

frozen tendon Jun 19, 2022, 5:35 AM

#

And you Euclidean algorithm helps us to find the gcd of two number say a and b

frozen tendon Jun 19, 2022, 5:35 AM

#

tropic oxide the theorem itself gives us no method of computing it

True

frozen tendon Jun 19, 2022, 5:38 AM

#

tropic oxide bézout's theorem states that such a representation EXISTS

Hmm

cedar kilnBOT Jun 19, 2022, 5:53 AM

#

@frozen tendon Has your question been resolved?

cedar kilnBOT Jun 19, 2022, 6:08 AM

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frozen tendon Jun 19, 2022, 6:15 AM

#

Guys can anyone explain me what are the definitions for bézouts theorem, division algorithm and eucliding algorithm and what is the use of gcd in all of them

cedar kilnBOT Jun 19, 2022, 6:15 AM

#

frozen tendon Guys can anyone explain me what are the definitions for bézouts theorem, divisio...

torpid fulcrum Jun 19, 2022, 6:19 AM

#

do you mean bezouts identity?

frozen tendon Jun 19, 2022, 6:20 AM

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torpid fulcrum do you mean bezouts identity?

Yep

#

Like I am a bit confused as all of this uses the gcd

torpid fulcrum Jun 19, 2022, 6:21 AM

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if we're just considering integers: if gcd(a,b)=c then there exists numbers x and y such that ax+by=c

#

and assuming you're referring to the Euclidean algorithm

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the euclidean algorithm is used for finding the GCD

frozen tendon Jun 19, 2022, 6:22 AM

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frozen tendon

Well one more question why in this question the lhs is 4840 and not 1512?

torpid fulcrum Jun 19, 2022, 6:23 AM

#

#

(just posting it so i dont have to scroll)

frozen tendon Jun 19, 2022, 6:23 AM

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Haha sure

torpid fulcrum Jun 19, 2022, 6:23 AM

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that is part of bezouts identity

frozen tendon Jun 19, 2022, 6:23 AM

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No I mean in the part where the Euclidean algorithm is used

torpid fulcrum Jun 19, 2022, 6:24 AM

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we are trying to find the remainder when 4840 is divided by 1512

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i.e. 4840 mod 1512

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since the remainder is 304

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next, we do 1512 mod 304

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and so on

frozen tendon Jun 19, 2022, 6:26 AM

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No like I mean that

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here it's in the form of b=aq+r

torpid fulcrum Jun 19, 2022, 6:26 AM

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yes

frozen tendon Jun 19, 2022, 6:26 AM

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So why is 4840 = b and a= 1512

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This is what I am a bit confused about

torpid fulcrum Jun 19, 2022, 6:27 AM

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that is the process of the euclidean algorithm

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4840=3(1512)+304

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so 4840 mod 1512 gives 304

frozen tendon Jun 19, 2022, 6:28 AM

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torpid fulcrum that is the process of the euclidean algorithm

Oh

cedar kilnBOT Jun 19, 2022, 6:43 AM

#

@frozen tendon Has your question been resolved?

torpid fulcrum Jun 19, 2022, 6:49 AM

#

did you have another question?

frozen tendon Jun 19, 2022, 6:52 AM

#

torpid fulcrum did you have another question?

Nope

#

But just one thing

#

The larger number is always supposed to be on the left side right?

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@torpid fulcrum

cedar kilnBOT Jun 19, 2022, 7:23 AM

#

@frozen tendon Has your question been resolved?

torpid fulcrum Jun 19, 2022, 7:37 AM

#

sorry, was away for a bit

#

the order doesn't matter

#

but if you start with the smaller number on the left

#

the next step will swap the two numbers

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for example if we had 425 and 623

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425 mod 623 = 425

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so in the next step we do 623 mod 425

#

@frozen tendon

cedar kilnBOT Jun 19, 2022, 8:23 AM

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@frozen tendon Has your question been resolved?

cedar kilnBOT Jun 19, 2022, 9:23 AM

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cedar kilnBOT Jun 19, 2022, 11:31 AM

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fast turret Jun 19, 2022, 11:39 AM

#

cedar kilnBOT Jun 19, 2022, 11:39 AM

#

fast turret

fast turret Jun 19, 2022, 11:40 AM

#

hello, for this problem i have all inequalities set up for exponents of base 3 and 4, but cannot think of a way to compare exponents of base 3 and 4.

#

i will show you my reasoning so far:

#

3^3^4 > 3^4^3, because 3^4^3 = 3^64 and 3^3^4 = 3^81

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3^4^4 > 3^3^4 just by looking as it as both are the same, except that for 3^4^4 its exponents are greater

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so we have the inequality 3^4^4 > 3^3^4 > 3^4^3

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4^3^4 > 4^3^3 because 4^3^4 has greater exponents

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4^3^4 > 3^3^4 because 4^3^4 is of a greater base

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now i know i must change bases of these exponents because there appears to be no other way to figure this problem out

#

i have done a bit of research but cannot find anything conclusive about how to change the bases of these exponents

elder pewter Jun 19, 2022, 11:46 AM

#

#

Of thats really what you want to use

#

But you could just intuitively look at the numbers

fast turret Jun 19, 2022, 11:47 AM

#

elder pewter But you could just intuitively look at the numbers

yeah, but that only got me so far

cedar kilnBOT Jun 19, 2022, 12:02 PM

#

@fast turret Has your question been resolved?

ember python Jun 19, 2022, 12:27 PM

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fast turret

Oh this is a bmo1 problem I’ve literally done this before

fast turret Jun 19, 2022, 12:32 PM

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ember python Oh this is a bmo1 problem I’ve literally done this before

hey, thanks for chiming in. could you explain the remaining part of the solution please?

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i understand that to prove 3^256 is greater than 4^81 (without using a calculator) i would have to either find a common base or use some exponential/logarithmic rule which i do not know of

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imma try and figure it out using a logarithmic rule rq

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one sec

ember python Jun 19, 2022, 12:37 PM

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fast turret i understand that to prove 3^256 is greater than 4^81 (without using a calculato...

No no this isn’t necessary

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We don’t need bases or exponents to be the same to make comparisons

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We could have both the exponent and the base of a number be less than another

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4^81 = 2^162 and clearly 2^162 > 3^256

fast turret Jun 19, 2022, 12:38 PM

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ember python We could have both the exponent and the base of a number be less than another

very true actually

ember python Jun 19, 2022, 12:39 PM

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You can do a similar thing to fit the remaining numbers together

fast turret Jun 19, 2022, 12:39 PM

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yeah like with 4^3^3

ember python Jun 19, 2022, 12:40 PM

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Yea

fast turret Jun 19, 2022, 12:41 PM

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do you come from the uk then?

ember python Jun 19, 2022, 12:41 PM

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Yeah I do

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I did this problem last December

fast turret Jun 19, 2022, 12:41 PM

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ah cool me too

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where in the uk?

ember python Jun 19, 2022, 12:42 PM

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Surrey

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What about you?

fast turret Jun 19, 2022, 12:46 PM

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im from the north west

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what year are you in?

ember python Jun 19, 2022, 1:00 PM

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fast turret what year are you in?

I’m in year 12

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So first year of college

fast turret Jun 19, 2022, 1:00 PM

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ahh right im in y11

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i really should be studying for science and history but this is way more fun lol

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besides after this week exams will be done

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ill have 3 months to do just competitive maths

ember python Jun 19, 2022, 1:01 PM

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Lmao yea you’ve got gcses I guess

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What got you starting to do bmo1 problems

fast turret Jun 19, 2022, 1:06 PM

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well i really like the subject so it’s fun but there’s also the advantage that it will look really good for maths related degree courses and jobs and such

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but it’s mostly recreational for me

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do you do the olympiads or do you just look at the questions?

ember python Jun 19, 2022, 1:11 PM

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That’s cool, I did the most recent bmo1 although I only started preparing like a week in advance

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2016/17 had some pretty doable problems imo

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Q1 - Q3

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It’s decent to pick up skills tbf

#

I didn’t even know about this stuff in year 11 so I just did a level stuff instead, I kinda wish I did tbh

cedar kilnBOT Jun 19, 2022, 1:37 PM

#

@fast turret Has your question been resolved?

fast turret Jun 19, 2022, 1:44 PM

#

ember python I didn’t even know about this stuff in year 11 so I just did a level stuff inste...

yeah i can’t wait for college personally, but this is rlly fun and will be really beneficial for solving questions at college

cedar kilnBOT Jun 19, 2022, 2:44 PM

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@fast turret Has your question been resolved?

elder pewter Jun 19, 2022, 2:54 PM

#

@fast turret college is fun. I became heavily interested in maths whilst at college

#

I found further maths so much more interesting than normal A level maths

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cedar kilnBOT Jun 19, 2022, 4:09 PM

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crimson sedge Jun 19, 2022, 4:10 PM

#

f(x)=x²-4x+8
g(x)=-|-x-2t|+9
h(x)=f(x) (f(x)<g(x))
g(x) (f(x)>=g(x))
for some t y=2k and h(x) has 3 different intersection points
find every integer k

cedar kilnBOT Jun 19, 2022, 4:10 PM

#

crimson sedge f(x)=x²-4x+8 g(x)=-|-x-2t|+9 h(x)=f(x) (f(x)<g(x)) g(x) (f(x)>=g(x)) ...

elder pewter Jun 19, 2022, 4:16 PM

#

$f(x) = x^2-4x+8$

wraith daggerBOT Jun 19, 2022, 4:16 PM

#

IntelligentCake

elder pewter Jun 19, 2022, 4:16 PM

#

$g(x) = -|-x-2t|+9$

wraith daggerBOT Jun 19, 2022, 4:16 PM

#

IntelligentCake

elder pewter Jun 19, 2022, 4:17 PM

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what is t

#

just a parameter?

crimson sedge Jun 19, 2022, 4:22 PM

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constant

elder pewter Jun 19, 2022, 4:23 PM

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value of constant??

crimson sedge Jun 19, 2022, 4:24 PM

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idk

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i edited the question

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idk what to call t

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maybe its not called constant

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<@&286206848099549185>

crimson sedge Jun 19, 2022, 4:35 PM

#

elder pewter just a parameter?

ur prob right

cedar kilnBOT Jun 19, 2022, 4:50 PM

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@crimson sedge Has your question been resolved?

cedar kilnBOT Jun 19, 2022, 5:05 PM

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crude scroll Jun 19, 2022, 5:43 PM

#

Screen_Shot_2022-06-18_at_11.03.10_PM.png

cedar kilnBOT Jun 19, 2022, 5:43 PM

#

crude scroll

shell lance Jun 19, 2022, 5:43 PM

#

420 hah

wraith daggerBOT Jun 19, 2022, 5:44 PM

#

Kurama

crude scroll Jun 19, 2022, 5:44 PM

#

Im trying to generate some contradiction here

#

Not sure what the next step should be

cedar kilnBOT Jun 19, 2022, 6:00 PM

#

@crude scroll Has your question been resolved?

crude scroll Jun 19, 2022, 6:00 PM

#

<@&286206848099549185>

cedar kilnBOT Jun 19, 2022, 6:30 PM

#

@crude scroll Has your question been resolved?

tough aurora Jun 19, 2022, 7:01 PM

#

You will need to provide more information

crude scroll Jun 19, 2022, 7:02 PM

#

Z(An) is the center of the alternating group

#

epsilon is the identity here

cedar kilnBOT Jun 19, 2022, 8:02 PM

#

@crude scroll Has your question been resolved?

dire geode Jun 19, 2022, 10:02 PM

#

.close

cedar kilnBOT Jun 19, 2022, 10:02 PM

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cedar kilnBOT Jun 19, 2022, 11:09 PM

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lethal moat Jun 20, 2022, 12:33 AM

#

”Circle: (x+2)² + (y-3)² = 20 Line: y = -⅓x + 3. Give me the coordinates of the points were they intersect”

cedar kilnBOT Jun 20, 2022, 12:33 AM

#

lethal moat ”Circle: (x+2)² + (y-3)² = 20 Line: y = -⅓x + 3. Give me the coordinates of the ...

lethal moat Jun 20, 2022, 12:33 AM

#

what do you get if you substitute y = -⅓x + 3 into (x+2)² + (y-3)² = 20

cedar kilnBOT Jun 20, 2022, 12:48 AM

#

@lethal moat Has your question been resolved?

gleaming cloud Jun 20, 2022, 12:50 AM

#

lethal moat what do you get if you substitute y = -⅓x + 3 into (x+2)² + (y-3)² = 20

just substitute it

lethal moat Jun 20, 2022, 12:55 AM

#

Help me w it

#

<@&286206848099549185>

dire geode Jun 20, 2022, 1:01 AM

#

lethal moat Help me w it

What do you need help with

gleaming cloud Jun 20, 2022, 1:01 AM

#

he just wants the answer

dire geode Jun 20, 2022, 1:02 AM

#

Oh psh

cedar kilnBOT Jun 20, 2022, 1:03 AM

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lethal moat Jun 20, 2022, 1:05 AM

#

.reopen

cedar kilnBOT Jun 20, 2022, 1:05 AM

#

✅

lethal moat Jun 20, 2022, 1:05 AM

#

dire geode Oh psh

Answer + wanna learn how to do it

dire geode Jun 20, 2022, 1:12 AM

#

gleaming cloud just substitute it

. That's how you do it

cedar kilnBOT Jun 20, 2022, 1:20 AM

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@lethal moat Has your question been resolved?

cedar kilnBOT Jun 20, 2022, 1:35 AM

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delicate ember Jun 20, 2022, 3:22 AM

#

this calculation seems wrong, shouldn't the power of 10 be -1

cedar kilnBOT Jun 20, 2022, 3:22 AM

#

delicate ember this calculation seems wrong, shouldn't the power of 10 be -1

gaunt hamlet Jun 20, 2022, 3:36 AM

#

It shouldn't be -5, but it shouldn't be -1 either

cedar kilnBOT Jun 20, 2022, 3:41 AM

#

@delicate ember Has your question been resolved?

tropic oxide Jun 20, 2022, 3:42 AM

#

,calc 1.7 * 5/14.9

wraith daggerBOT Jun 20, 2022, 3:42 AM

#

Result:

0.57046979865772

tropic oxide Jun 20, 2022, 3:42 AM

#

should be 5.7 * 10^-2 surely

delicate ember Jun 20, 2022, 3:43 AM

#

Ah yes its 10^-2

#

alright

#

thanks

#

.close

cedar kilnBOT Jun 20, 2022, 3:43 AM

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crimson sedge Jun 20, 2022, 4:04 AM

#

cedar kilnBOT Jun 20, 2022, 4:04 AM

#

crimson sedge

crimson sedge Jun 20, 2022, 4:04 AM

#

Would this be present value formula what formula would I use to solve this

cedar kilnBOT Jun 20, 2022, 4:19 AM

#

@crimson sedge Has your question been resolved?

crimson sedge Jun 20, 2022, 4:21 AM

#

<@&286206848099549185>

sick ruin Jun 20, 2022, 4:46 AM

#

Let’s just figure it out @crimson sedge

cedar kilnBOT Jun 20, 2022, 4:56 AM

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@crimson sedge Has your question been resolved?

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cedar kilnBOT Jun 20, 2022, 8:05 AM

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pastel sonnet Jun 20, 2022, 8:49 AM

#

cedar kilnBOT Jun 20, 2022, 8:50 AM

#

pastel sonnet

pastel sonnet Jun 20, 2022, 8:50 AM

#

can I find the gradient for both first

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then use m1 m2=-1

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then I can use simultaneous eqn to check parallel?

oblique loom Jun 20, 2022, 8:52 AM

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ok so the gradient for this first like

#

is -3 as shown

pastel sonnet Jun 20, 2022, 8:52 AM

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yea

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well no

oblique loom Jun 20, 2022, 8:52 AM

#

and are you aware of the formula for finding gradient with two points

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no

pastel sonnet Jun 20, 2022, 8:52 AM

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cuz u want it to become a mx+c

oblique loom Jun 20, 2022, 8:52 AM

#

it must be in y = mx plus b form

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mb

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put it into y = mx + c form

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and then

#

use this formula

elder pewter Jun 20, 2022, 8:53 AM

#

first what is gradient for l1

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tell use that first

oblique loom Jun 20, 2022, 8:53 AM

#

y2 - y1/ x2-x1

pastel sonnet Jun 20, 2022, 8:53 AM

#

3/4

elder pewter Jun 20, 2022, 8:53 AM

#

ok good

oblique loom Jun 20, 2022, 8:53 AM

#

if the gradients are the same than they are parralel

elder pewter Jun 20, 2022, 8:53 AM

#

now for l2

pastel sonnet Jun 20, 2022, 8:53 AM

#

and then its 9/6

elder pewter Jun 20, 2022, 8:53 AM

#

what is gradient

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no

pastel sonnet Jun 20, 2022, 8:54 AM

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-9/6

elder pewter Jun 20, 2022, 8:54 AM

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yes

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or -3/2

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is -3/2 the same as 3/4

pastel sonnet Jun 20, 2022, 8:54 AM

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No

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so its neither?

elder pewter Jun 20, 2022, 8:54 AM

#

so therefore they are not parallel

pastel sonnet Jun 20, 2022, 8:54 AM

#

cuz using m1 m2=-1

oblique loom Jun 20, 2022, 8:54 AM

#

no

elder pewter Jun 20, 2022, 8:54 AM

#

now to check for perpendicular, m1m2 =-1

pastel sonnet Jun 20, 2022, 8:54 AM

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its not true as well

oblique loom Jun 20, 2022, 8:55 AM

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thats for perpendicular lines

elder pewter Jun 20, 2022, 8:55 AM

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ok good

#

so therefore it is neither

oblique loom Jun 20, 2022, 8:55 AM

#

didnt read the question

elder pewter Jun 20, 2022, 8:55 AM

#

so you are correct @pastel sonnet

pastel sonnet Jun 20, 2022, 8:55 AM

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okok

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thx

#

I was over complicating stuff earlier

#

thats why I was a little confused

#

I thought about inplict differentiate the first one

#

implicit*

#

but I didn’t see I could just change sides lol

#

.close

cedar kilnBOT Jun 20, 2022, 8:56 AM

#

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cedar kilnBOT Jun 20, 2022, 1:08 PM

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wide light Jun 20, 2022, 1:17 PM

#

cedar kilnBOT Jun 20, 2022, 1:17 PM

#

wide light

wide light Jun 20, 2022, 1:17 PM

#

#

i dont understand this at all

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on its own the question is weak tbf, what im asking

#

but consider this following question:

#

#

#

so in this question

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its first order because ratios are 0.1

#

but in that question 7 with sarah, its between 1 and 2 because its 0.35?? i dont understand

Hello so i'm trying to reduce a fraction (i'm not sure that's the correct term) but the fraction is: x^2-2xy

2y^2-xy The answer i got is: x

y The correct answer is: -x

u had x(x-2y)

Hello so i'm trying to reduce a fraction (i'm not sure that's the correct term)
but the fraction is:
x^2-2xy

2y^2-xy
The answer i got is:
x

y
The correct answer is:
-x

u had
x(x-2y)