#help-10

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wooden axle
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obtuse pebbleBOT
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zinc scaffold
#

. The function f(x) satisfies the equation f(x)=f(x−1)+f(x+1) for all values of x.
Define f(1)=1 and f(3)=3; then, f(2)=1+3=4. Determine the value of f(1867).

rotund vector
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How would I find the final velocities for A and B?

rotund vector
obtuse pebbleBOT
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@rotund vector Has your question been resolved?

rotund vector
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<@&286206848099549185>

somber spear
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I haven't checked every step but it looks lke you have equations 1 and 2

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just solve for Va or Vb and substitute that expression into the other equation

obtuse pebbleBOT
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@rotund vector Has your question been resolved?

rotund vector
somber spear
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show your work an I'll check it

rotund vector
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Okay so after substitution I get Va = 1.28m/s

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and Vb = 1.5936m/s

somber spear
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u got it

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i actually rounded up to 1.60

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for Vb

rotund vector
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thanks man

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long hedge
obtuse pebbleBOT
long hedge
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so the angle of 7pi/6

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is 210 degrees

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since cos is negative and its the inverse of sine we need it to be in quarter 4

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the corresponding angle to 210 degrees in quarter 4 is

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330 degrees

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or -30 degrees

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-30 degrees is pi/6 away from 0

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and 3/pi away from -90 degrees

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is this all right ?

ionic summit
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firstly o7 for using pearson

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The first thing I saw was that the refrence angle for 7pi/6 is in the 3rd quadrant, cosine is negative

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and then i was like okay ima draw my special triangles too see

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what cosine evaluates too at that refrence angle

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and then with that angle i just did the same sorta thing except what angle has those side lengths for sin

long hedge
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so are you measing the angle from -90 to the angle

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or from 0 to the angle

ionic summit
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sorry are u referring to refrence angle

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this is a diff approach from what you did i like special triangles if u dont know them then it will probs be more work

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also like what the heck is the point of that problem i always found it so redundent thats 100% a calculator problem

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i dont really know what you mean by the 3/pi away from -90 degrees bit tho

long hedge
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if you measure the angle from -90 to -30 degrees it -pi/3

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if you measure the angle from 0 to -30 degrees its -pi/6

ionic summit
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ahhh there she is

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your a unit circle enjoyer

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yeah you will be just fine then

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looks good mate

long hedge
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so which one is it

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are you measuring the angle from -90 or from 0

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270 degrees = -90

ionic summit
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uhhh i honestly dont know what ur reffering to

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like well the refrence angle was measured from 180 degrees

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for 7pi/6

south oracle
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-π/2 in radians is -90° in degrees, and π/2 in radians is 90° in degrees.

long hedge
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we know its -30 degrees

south oracle
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What do you mean by where you "start"

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-30° is just -π/6 in radians

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No?

long hedge
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30 degrees = pi/6

long hedge
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which means it would be measuring from 90degrees not 0

south oracle
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Then you messed up on the part where you're finding cos(7π/6)

south oracle
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It's supposed to be -√3/2

ionic summit
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indeed

long hedge
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we're finding an angle not a value

south oracle
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And sin (-60°) is -√3/2

ionic summit
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yuppers

south oracle
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Not sin(-30°)

ionic summit
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hooly bazed

long hedge
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the values are meaningless beyond determining negative or positive here

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we're not evaluating for a point

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we're evaluating for an angle THATS WHAT INVERSE DOES

south oracle
ionic summit
south oracle
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Because sine is a function where you take an angle ang give a value

long hedge
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ok where is cos 7pi/7 ?

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210 degrees -root3/2

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But we need it in quadrant 4 because its negative and inverse of sine is in Q1 and Q4

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ok so now we are at -30 degrees

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NEGATIVE FKING 30

south oracle
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No we aren!t

long hedge
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?????

south oracle
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DO GET YOUR SIN VALUES CORRECT

glossy basalt
ionic summit
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why is everyone malding

glossy basalt
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hi turtle~

south oracle
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Ok I got angry sorry

long hedge
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you are LOST

ionic summit
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😮

south oracle
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On where

long hedge
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Inverse of sine allows you to find an angle with a value

south oracle
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Yes

long hedge
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WE HAVE THE VALUE ITS NEGATIVE ROOT OVER 2

south oracle
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YES

ionic summit
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most sane trig enjoyer

long hedge
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WHICH IS IN ONLY 2 PLACES Q3 and Q4

south oracle
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YES

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-60° IS ALSO IN Q4

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NOT ONLY -30°

long hedge
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WE NEED IT IN Q4 BECAUSE INVERSE SINE THAT MAKES IT NEGATIVE 30 DEGREES

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THE ADJACENT ANGLE OF 210 DEGREES IN Q4 IS 330

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OR -30

glossy basalt
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hmmm I better read the question 😛

south oracle
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sin(-30°)=-1/2 so arcsin(-1/2)= -π/6

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where is my logic wrong

south oracle
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sin(-60°)= -√3/2 so arcsin(-√3/2)= -π/3

glossy basalt
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interesting

south oracle
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I just used the definition of the inverse function

long hedge
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the answer is -pi/3

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where are you getting to -60 from

south oracle
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Fine
arcsin(cos(7π/6))= arcsin(-√3/2)

south oracle
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So the answer is -π/3

ionic summit
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maybe drawing special triangles will help

long hedge
south oracle
long hedge
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arcsin(-root3/2)= -30 degrees

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magically pulling -60 out of his ass

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THERE IS NO SINE

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THERE IS ONLY ARCSINE

glossy basalt
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,w sin(-60°)

ionic summit
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ima put this here and then we can all smile

south oracle
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I have no words

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THE DEFINITION OF Y=ARCSIN X IS THAT X=SINY WHEN (-π/2<X<π/2)

south oracle
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Yeah keep coping

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I'm out

long hedge
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there is no -60 degrees

ionic summit
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did you guys see the downhill cheese race

south oracle
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Nah

long hedge
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arcsin(-root3/2)= -30 degrees

ionic summit
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that was less chaotic then this

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a few people got concussions surely

long hedge
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so we are supposed to take the sine of -30 because ???/

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there is no sine

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how are you able to take the sine of -30

south oracle
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Yeah you win

long hedge
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you just took the inverse sine of -root3/2 to get there

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you're done

south oracle
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The answer is -π/6

long hedge
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so this garbage program is broken

south oracle
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Your teacher is wrong

long hedge
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I FUCKING NEW IT

south oracle
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Good luck with your exams

long hedge
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wait you're being sarcastic

ionic summit
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pearson is one of the homework helpers of all time

long hedge
south oracle
ionic summit
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hes probably trolling

long hedge
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daddy leonard is going to teach me

ionic summit
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hoooly chad

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papa leonard

long hedge
ionic summit
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😍

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OMG

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look at him

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his jawline extends past his face

south oracle
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He's hot and I need to eat lunch

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I'm out

long hedge
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if only his production quality and video organization was as good as the organic chem tutor

ionic summit
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real

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do u really think its -pi/6 tho

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between you and me

long hedge
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"what angle gives you this coordinate in the appropriate Quarter"

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its sine( -60) degrees

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or -pi/3

ionic summit
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good man

long hedge
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@south oracle you hear that

ionic summit
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i understand

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that you did not get our explination

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we are meer mortals in comparison to papa leonard

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not even the most expereinced math person here has the jawline or knowladge as him (surely)

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alrighty anyways im glad u got it

dusk elk
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is $$\prod_{n=4}^{6}{(3n-1)}$$ 2,618

warm shaleBOT
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ericcartman6900

is $$\prod_{n=4}^{6}{(3n-1)}$$ 2,618
dusk elk
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i am just asking

glossy basalt
south oracle
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And also, next time

obtuse pebbleBOT
dusk elk
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okay

south oracle
obtuse pebbleBOT
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@long hedge Has your question been resolved?

obtuse pebbleBOT
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astral mural
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Hello I got B but the answer guide says it is C can someone help explain please:

warm shaleBOT
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uncreeperble

royal basin
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your answer is correct

astral mural
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I know it is C because the marking criteria says so though so are we missing something bigger

royal basin
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are you required by law to view the marking criteria as infallible, under threat of a grave penalty?

astral mural
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the marking criteria has to be correct because it is from the state exam last year unless the whole state was marked wrong (which I hope not)

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royal basin
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well it's not

astral mural
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Yeah i found the answer

royal basin
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this question in particular is given the wrong answer in the answer key

astral mural
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its weird because every other answer lined up exactly lol

obtuse pebbleBOT
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hardy robin
#

bp'+ap=32
a+b=4
p'+p=8
ap=11; bp'=21
(a,b,p,p'>0)
Find p and p'

unkempt bramble
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p' is derivative wrt to ehat

royal basin
hardy robin
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It's a chemistry problem

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i have solve 2/3

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the problem

unkempt bramble
royal basin
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nibberge, i don't think p' is meant as the deriative of p...

unkempt bramble
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Oh shhh

hardy robin
royal basin
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anyway ok so you have what

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5 equations?

hardy robin
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...

unkempt bramble
royal basin
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4 equations

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a + b = 4
p + p' = 8
ap = 11
bp' = 21

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in 4 unknowns

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have you made any progress thus far

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this feels vaguely quadratic

unkempt bramble
hardy robin
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it's still possible tho?

royal basin
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have you made any progress thus far?

unkempt bramble
hardy robin
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i think i need a integer number

unkempt bramble
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I mean try finding a solution

hardy robin
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i don't think so

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i'm stuck with it

unkempt bramble
royal basin
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right ok

unkempt bramble
hardy robin
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if you want to know st more, ask me then

royal basin
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well nibberge did give a good-sounding suggestion

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but yes, i would like to know more

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i'd like to know the original problem

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in full

hardy robin
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okay, but it's kinda intricate

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wait

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can you use google translate?

royal basin
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... what language is it in

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maybe i can figure it out without

hardy robin
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Vietnamese

royal basin
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oh vietnamese

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don't speak that :X

hardy robin
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yes, so i did ask you about using google translate

unkempt bramble
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Compound A is made up of 2 elements M and X with the formula MaX% where X makes up 64.615% by mass. In the nucleus of an M atom, the number of charged particles is 1 less than the uncharged particles. In the nucleus of atom X, the number of particles of both types is equal. Given a + b=4, a molecule of substance A has 32 protons, the atomic mass is assumed to be equal to the total number of protons and neutrons in the atom. Calculate the number of protons in each atom of M and X.

hardy robin
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nice

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@unkempt bramble thank you

unkempt bramble
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Check pic for translation mistakes

royal basin
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so an M atom has one less proton than it does neutrons, and X has an equal amount of each

hardy robin
unkempt bramble
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MaXb*

royal basin
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i think it would be easier to just brute-force the three cases for a and b here

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a=3, b=1
a=2, b=2
a=1, b=3

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than to come up with something clever

hardy robin
royal basin
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?

hardy robin
unkempt bramble
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Also a+b=4

unkempt bramble
royal basin
hardy robin
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oh

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wait

hardy robin
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but it didn't make sense, nvm

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cuz a+b=4

hardy robin
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ap + bp'=32

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(a+b) (p+p') = 32

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4 (p +p') = 32

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p + p' =8??

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is it right?

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@royal basin

obtuse pebbleBOT
#

@hardy robin Has your question been resolved?

obtuse pebbleBOT
#

@hardy robin Has your question been resolved?

hardy robin
#

.close

obtuse pebbleBOT
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ivory coral
#

How can a • become a :

obtuse pebbleBOT
ivory coral
royal basin
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are you asking about part b?

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or c?

normal oracle
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He is talking about c.

normal oracle
# ivory coral

You just have to solve the equation. What have you tried so far?

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Remember the LHS is raised to n, that's why.

obtuse pebbleBOT
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@ivory coral Has your question been resolved?

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granite eagle
#

How to do ^3sqrt27 ONCE again

obtuse pebbleBOT
warm shaleBOT
#

northsteve

teal turret
#

@granite eagle

mellow glacier
high lily
#

please don't ghost us again

vapid blaze
#

hi

obtuse pebbleBOT
#

@granite eagle Has your question been resolved?

granite eagle
#

Prime the drink?

mellow glacier
mellow glacier
granite eagle
#

Older than you

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Oh

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So it’s

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27:3
9:3
3:3
1

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3^3

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Ok and then what @mellow glacier

mellow glacier
mellow glacier
#

do you know how powers work?

granite eagle
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Woah

granite eagle
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I did its 3^3

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3 * 3 *3

mellow glacier
#

$3^{3 \cdot \frac{1}{3}}$

warm shaleBOT
#

shockshwat

granite eagle
#

I don’t understand this

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Why

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??

mellow glacier
granite eagle
#

How is ^3 = 1/3?

mellow glacier
clear condor
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3^3 = 27

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the cube root is ^ (1/3)

granite eagle
#

I don’t understand this

clear condor
#

what don't you understand

obtuse pebbleBOT
#

@granite eagle Has your question been resolved?

obtuse pebbleBOT
#

@granite eagle Has your question been resolved?

granite eagle
timid silo
#

the nth root of a number is the same thing as that number to ^1/n

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5throot(32) = (32)^(1/5) = 2

obtuse pebbleBOT
#

@granite eagle Has your question been resolved?

timid silo
#

@granite eagle was ur question answered?

obtuse pebbleBOT
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obtuse pebbleBOT
#

@plain gust Has your question been resolved?

jade hornet
#

Can you please send a picture that doesn't cut off the question?

obtuse pebbleBOT
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misty kindle
#

I don't know how to start this

obtuse pebbleBOT
misty kindle
#

i dont know the first step

grizzled shore
#

Try factorise 3x + 3

misty kindle
#

not sure what you mean

polar fossil
#

Frosst's question was an example of a simpler problem that you should be able to do; it was not directly related to your question

misty kindle
#

3(x+1)

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i dont know how to write it

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for this problem

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7(x-7)(x+1)(x+1)-8(x-7)^2(x+1)?

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why isn't it 7(x-7)(x+1)(x+1)-8(x-7)(x-7)(x+1)?

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why is only one of them kept squared

obtuse pebbleBOT
#

@misty kindle Has your question been resolved?

polar fossil
misty kindle
#

I figured it out thank you

#

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rotund vector
#

could someone help me out with this problem

candid yarrow
rotund vector
#

How would I find the velocity of the 5kg ball?

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I have found the vertical and horizontal components of the 10kg and 5kg ball although I don't know how to find V

limpid sandal
#

Is there an equation that goes with this?

rotund vector
#

well I know that the 5kg ball has not vertical component initially

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therefore 0 = 10 * 2sin30 + 5 * Vsin(theta)

limpid sandal
#

What math class is this for?

rotund vector
#

trigonometry

limpid sandal
#

Just making sure

candid yarrow
rotund vector
#

I got 30 = 10 * 2cos30 + 5 * Vcos(theta)

candid yarrow
#

How did you get 30 on the left side

rotund vector
#

the initial horizontal momentum is only 30

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since the 5kg ball is not moving intially

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P = MV

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10 * 3 = 30

candid yarrow
#

Yes

rotund vector
#

30 = 17.3 + 5 * Vcos(theta)

candid yarrow
#

So now you can calculate V sin theta and V cos theta

rotund vector
#

alright and since I know that Pi(5kg) = Pf(5kg) + Pf(10kg)

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30 = 17.3 + Pf(5kg)

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hence pf(5kg) in the horizontal direction = 12.7

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and now for the pf(5kg) in the vertical direction

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I know that Pf(10kg) + Pf(5kg) = 0 in the vertical direction

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hence 10 + Pf(5kg) = 0

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and Pf(5kg) = -10

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what would I do now?

obtuse pebbleBOT
#

@rotund vector Has your question been resolved?

candid yarrow
#

you already had expressions for them

candid yarrow
#

so you can combine the components using pythagoras's theorem to get V

obtuse pebbleBOT
#

@rotund vector Has your question been resolved?

obtuse pebbleBOT
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azure anchor
#

can someone clarify this? what does K represent here? the maximum possible value of f(x) or f''(x)? why is 1/x <= 1 relevant here?

azure anchor
#

okay so i think its the maximum value of f''(x)?

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how would i find the maximum value if this is the second derivative in question? given 0 <= x <= 2

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the original function has local min at -1 and local max at 1

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i found the third derivative to find the max of the second derivative but its a 4th degree polynomial devastation

obtuse pebbleBOT
#

@azure anchor Has your question been resolved?

azure anchor
#

i found out i didnt have to find the maximum of the second derivative, but maybe of the original function. which in my case was 1/2. still didn't get the book answer for the error bound though.

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even cheating and using desmos to find the max of the second derivative, i got an error bound that was more off than using 1/2. idk man

#

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timid silo
obtuse pebbleBOT
timid silo
#

i have no clue where to even start

rich plume
#

divide 652 by 16 and write the remainder aside

#

and write the quotient also

timid silo
#

??

rich plume
#

Do you know the process of conversion?

timid silo
#

no

#

40 r 12

rich plume
#

Okay

#

Now divide 40 by 16

#

and do the same thing

#

write quotient and remainder

timid silo
#

2 r 8

rich plume
#

now do it again

timid silo
#

?

rich plume
#

q=0 r=2

timid silo
#

oh

rich plume
#

Do you know how to write 12 in hexadecimal?

timid silo
#

idek wtf a hexadecimal is

#

idek how to convert bases

#

should prob figure that out first huh

rich plume
#

12 is denoted by C

frosty spoke
#

if you don't know what it means, you should investigate what it actually means to write a number in another base

timid silo
#

yeah im gna learn bases before doing this

#

wait

#

man fuck this question

#

.close

obtuse pebbleBOT
#
Channel closed

Closed by @acoustic topaz

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rich plume
#

interesting

timid silo
#

i have to learn bases before this anyway

#

bc i have zero clue abt em

obtuse pebbleBOT
#
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timid silo
#

i dont understand why 30.6 doesnt work

obtuse pebbleBOT
timid silo
#

i got a 1/5 on this question and i think its because i got the answer wrong

#

30.6 what

#

?

#

@timid silo

#

inches

#

how’d you get there

#

show

#

i changed it to 31 now

#

but last time idk why 30.6 doesnt work

#

i shouldve gotten at least half the ooints

#

Howd you get T^2(g)

#

How did you rearrange the equation again

#

?

#

From this

#

g shouldn’t be in the brackets ima tell u that one

#

Where’d blud go 💀

#

probably a missclick

#

no i put g in the brackets

#

why

#

so i can divide all of it with 4pi^2

#

Ok rearrange the equation rn to isolate for L

#

i wanna see how u did it

#

how i isolated L

#

he

#

ye

#

lemme go do the math again

#

what’d you get

#

did you want the answer i got or me showing my work

#

right now im figuring it out

#

my work

#

show ur work

#

cuz u made error somehwere

#

T^2 *G

#

4pi^2

#

wait

#

no

#

U can’t multiply anything by g when g is still in a square root

#

its in an equation

#

Ok you gotta divide both sides by 2pi first

#

thats the 1st step, not squaring anything

#

whats next

#

square everything

#

to get rid of the sqrt on right side

#

how do i use texit

#

0 clue but when distributing an exponent, use brackets

lyric vale
timid silo
#

,T=2piSQRT(L/G)

#

oh

#

das the starting equario

#

equation

#

right

#

T=1

#

G is 32 feet

#

32ft/s^2

#

alright so before u did

#

(T^2) = (2pi)^2(sqrt(L/g))^2 and got

#

T^2 = 4pi^2 * L/g

#

(T^2)/(4*pi^2) * g = L?

#

This is actually correct because I wasn’t seeing properly, but usually you gotta follow order of operations

#

whats correct?

#

i dont know what the question mark means

#

Thas what u just did.

#

30.6 is correct?

#

No

#

oh

#

.flip

#

.rotate

#

,flip

#

bruh

#

,rotate

warm shaleBOT
timid silo
#

Have u gotten here @timid silo Thats what im tryna ask

timid silo
# warm shale

im really slow and it takes me at least a minute and a half to read this

#

i dont think i did that

#

i dont remember

#

most likely i didnt

#

oh wait

#

i think i do remember something like that

#

but i put the g next to it

#

you CANNOT put the g next to it here, you must square both sides

#

true

#

my bad

#

what do i do next from there

#

U squared both sides?

#

ok wait lemme do that

#

T^2/(4pi^2)=L/G

#

and the right side…

#

ok now how do you get rid of the /G to isolate L

#

divide both sides by g

#

No

#

oh

#

multiply both sides by g

#

thats what i meant

#

lol

#

Ight sick now do that and plug in ur nums

#

(T^2/(4pi^2))G=L

#

plug the numbers

#

(1/(4pi^2))32=L

#

and solve right

#

oui

#

Yes

#

1/4pi^2 is 0.03

#

*32 is 0.875

#

no

#

1/(4pi^2) = 0.02533

#

don’t round up while actively calculating

#

0.8865

#

10.64 inches?

#

Very close

#

1/(4pi^2) is not 0.03

#

11 inches

timid silo
#

and multiplied by 32?

#

yes

#

and then converted it to inches

#

(0.02533) * 32 = 0.8106

#

feet

#

THEN convert to inches

#

ohh

#

10ft

#

U mean 10 inches?

#

yes that

#

Correct

#

W

#

thank you cheeson

#

.close

obtuse pebbleBOT
#
Channel closed

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timid silo
#

np

obtuse pebbleBOT
#
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dire fable
#

Hi i can do ab and c but my answer for d is soo off I cant get it thanks

obtuse pebbleBOT
#

@dire fable Has your question been resolved?

dire fable
#

<@&286206848099549185>

#

pls

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lyric totem
#

$Would e^{ln(ln(x))} simply to just ln(x)?$

obtuse pebbleBOT
warm shaleBOT
#

dopediscorduser

wooden cipher
#

Indeed

royal basin
#

Would $e^{\ln(\ln(x))}$ simplify to just $\ln(x)$? yes

warm shaleBOT
lyric totem
#

Okay thanks

#

Yeah I’m not exactly a latex wizard

#

.close

obtuse pebbleBOT
#
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native fern
obtuse pebbleBOT
#
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echo gazelle
#

how is the derivative of (x^3-x+7) 3x^2-1 . I understand how x^3 goes to 3x^2 bc of the power rule and +7 goes to +0 but why does -x go to -1?

royal basin
#

as in "what the fuck is going on here?" or "i think -x should differentiate to sth else"?

echo gazelle
#

i just dont think ive seen x with no exponent be derivated before

#

so idk why it goes to -1

royal basin
#

so it's a "what the fuck is going on"

#

okay

echo gazelle
#

yeah

royal basin
#

consider that lone x is the same thing as x^1.

#

consider also that -x is (-1)x

echo gazelle
#

yeah

#

so u do the product rule and the x goes away?

royal basin
#

i mean you could but it's overkill

echo gazelle
#

true

royal basin
#

$\dv{x} (c f(x)) = c \cdot \dv{x} f(x)$

warm shaleBOT
royal basin
#

constant multipliers pull out

echo gazelle
#

huh

royal basin
#

not what i wrote there.

royal basin
# echo gazelle huh

if i gave you the function 100x^3 and asked you to take its derivative would you be able to do it?

echo gazelle
#

yeah

royal basin
#

i was talking about the constant multiple rule.

echo gazelle
#

300x^2

royal basin
#

ok great

#

so you see how it's 100 * [3x^2]'

#

yes?

echo gazelle
#

yeah

#

ah so for -1x its -1 * x

#

then when u do power rule x^1 goes to x^0 which is 1 and ur multiplying 1* -1

#

right?

#

so it just stays -1

#

yeah

#

yes

#

3x^2-1

urban patrol
#

.

echo gazelle
#

typo 😅

urban patrol
#

lmao

echo gazelle
#

haha

#

so same thing for any num before x if it was 8x it would be 8 etc

#

alr i think i understand now ty guys

#

ty! u2

#

.close

obtuse pebbleBOT
#
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royal basin
#

late but yes you're correct

obtuse pebbleBOT
#
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vital pilot
#

Hello, I am unsure how to solve the question: x^2 y dv E solid below z =x+1 above the xy plane between cylinder x^2+y^2=4 and x^2 +y^2 =9

so is z 0 to x+1
theta 0 to 2pi
r 2 to 3?

obtuse pebbleBOT
#

@vital pilot Has your question been resolved?

obtuse pebbleBOT
#

@vital pilot Has your question been resolved?

vital pilot
#

Please help

thick fog
#

I'm not sure why your integrand x^2 became a x^2y but that image doesn't look that bad other than that the final calculation kind of sucks to do for something as lazy as I am.

vital pilot
#

sorry about that, i wrote the question wrong. its x^2y

#

ok so im on the right track

#

i'll try to complete it, i also have another question if u dont mind

thick fog
#

Normally you would learn from another course that those integrals you are calculating are orthogonal and save a lot of time, but if you don't have it you just need to grind out the reduction formulas or whatever

vital pilot
#

the question states that I need to look at the fourth quadrant. what will be the limits for theta?

thick fog
#

It doesn't really matter, either would work

#

oh sorry that second one is just wrong

#

Well, it'll probably end up being equivalent, but it's bad practice. You can do 3pi/4 to 2pi, or -pi/2 to 0, but -pi/2 to 2pi wraps around the circle once and you should avoid that

vital pilot
#

ok thanks, i will try solving it with -pi/2 to 0

polar fossil
#

you definitely don't want to do -pi/2 to 2pi you'll get the wrong answer
personally I'd do -pi/2 to 0 since 0 in the bounds tends to make the algebra easier

vital pilot
#

Did I go wrong somewhere?

polar fossil
#

how did r^2 become r^4 eeveeThink

thick fog
#

I expected the answer to be 0 by an orthogonality argument but I'm not going to check that

#

Also there is an r^2 from the cos, an r from the sin, and an r from the jacobian, so r^4.

vital pilot
#

i distributed the r

thick fog
#

The "easy" way to do that integral without a theorem is to just look at the picture of a plot of sin(x) and cos(x) between 0 and 2pi.

vital pilot
#

oh okay

thick fog
#

You can see that cos(x) is an even function and sin(x) is an odd function. So cos^3(x) is even and sin(x) is odd so the first integral is 0

vital pilot
#

thank u so much

thick fog
#

Similarly, cos^2(x) is even because cos(x) is even, and sin(x) is odd, so the integral of cos^2(x)sin(x) is also 0

vital pilot
#

got it

#

i remember hearing about this before

#

ty:)

#

.close

obtuse pebbleBOT
#
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verbal lava
#

Hello guys I'm considering the following solution to a stochastic process by using Ito's Calculus

verbal lava
#

I haven't studied yet at school integrals with respect to a Brownian motion

#

but I would like to know what is the result of the second integral in order to simulate the dynamics of this solution with python

#

in the case where the sigma function is given by

#

If anyone can provide some help it would be wonderful

#

I am asking for some help and the result here because I don't have the time today to dig into a stochastic integration course...

#

<@&286206848099549185>

#

It’s a Wiener integral I found

obtuse pebbleBOT
#

@verbal lava Has your question been resolved?

verbal lava
#

Nope

verbal lava
#

I copied my question in there

#

I will therefore close here

#

.close

obtuse pebbleBOT
#
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fierce geyser
#

Question 2 am I on the right track? Is that how you do it

#

<@&286206848099549185>

timid silo
#

Division is the inverse operation of multiplication

#

$a \div b = a \times \frac{1}{b}$

warm shaleBOT
#

breathe88rising

royal basin
timid silo
#

OH, my bad

royal basin
fierce geyser
#

.close

obtuse pebbleBOT
#
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warm nebula
#

<@&286206848099549185>

obtuse pebbleBOT
#
Channel closed

Closed due to the original message being deleted

warm nebula
#

Mb

timber island
#

open another channel

#

this one will close

warm nebula
#

Ok

timber island
warm nebula
#

Close

#

.close

timber island
#

it will close leave it

obtuse pebbleBOT
#
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oak aurora
obtuse pebbleBOT
oak aurora
oak aurora
# oak aurora

this is telling me that every piecewise continuous function that has period 2pi will have a unique fourier expansion

oak aurora
# oak aurora

this seems to be tellingm e that sin^2t which is of period 2pi will have two different fourier expansion depending on whether I treat it as having pi or 2pi as a period

#

But don't this two kind of contradict each other since if I treat it as having period pi, it will still have period 2pi?

obtuse pebbleBOT
#

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#
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solid pawn
#

If my vector field is defined by F(x,y) = x*i - y^3 *j
how to get a parametrization of the streamline of F passing through the point (3, -4).
and if F is a velocity field and a particle in this field is at the point (3, -4) at time t = 0 do i find the place it is at t=2 by using the gradient ?

obtuse pebbleBOT
#

@solid pawn Has your question been resolved?

obtuse pebbleBOT
#

@solid pawn Has your question been resolved?

obtuse pebbleBOT
#

@solid pawn Has your question been resolved?

obtuse pebbleBOT
#

@solid pawn Has your question been resolved?

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hollow cradle
#

how do i do this

obtuse pebbleBOT
normal oracle
#

u-sub

#

7-2x

hollow cradle
#

i brought the denominator to the top and made the power negative

#

so then i got 20(7-2x)ˆ-5

normal oracle
#

use u-sub

hollow cradle
#

???

normal oracle
#

u = 7-2x

obtuse pebbleBOT
#

@hollow cradle Has your question been resolved?

obtuse pebbleBOT
#
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obtuse pebbleBOT
#
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next basalt
#

can someone tell me how they joined these?

obtuse pebbleBOT
next basalt
#

is it a rule? what is it?

#

cuz i thought they were just moving the 2 from the denom in 7x^5/2 to the num

sour lance
#

first express sqrt(x) in exponential form

#

then they find a common denominator, multiplying the numerators as needed

next basalt
#

wait id understand, the common denom in this example is it 1/2? cuz they add 1/2 to the exponet of 7x

sour lance
#

well the common denominator is the denominator in the result

#

2x^(1/2)

next basalt
#

wait lemme write this out

#

yeah id get it, how is 2x^1/2 the common denom?

#

its not int he 2nd fraction

high lily
#

2x^(1/2) is the lcm of 2 and 2sqrt(x)

#

second fraction was manipulated to get that denominator, before fractions were combined

#

similar to how you'd simplify
1/6 - 1/2

next basalt
#

but isnt 2x^1/2 the same as 2sqrt(x)

high lily
#

2x^(1/2), but yes

next basalt
#

ok i was mult the other 2 in the 2sqrtx for the lcm

next basalt
high lily
#

no

next basalt
#

but 6*2 is 3?

high lily
#

no

next basalt
#

oh wait lmao

#

i was thinknig of division

#

its 12 right?

high lily
#

no

#

12 is a common multiple, but its not the lowest

next basalt
#

the lowest being 6

high lily
#

yes

next basalt
#

alr gimme a sec, i wana see if i get this right

#

wait the way i learned to do lcm is to mult the denoms together, then divide the answer by the denom of each fraction

high lily
#

huh?

#

that doesn't sound right

next basalt
#

like the finding the lcm for 1/6-1/2 would be to mult the 2 and divide by 6 and 2

#

maybe im remembering wrong lemm see if that gets me an answer

#

ok nvm i had my way all the way messed up

#

lemme try and solve the original problem now

high lily
#

you don't really want the lcm of the whole fractions

#

but rather the lcm of only the denominators

#

which allows you to combine through addition/subtraction

next basalt
#

👉 Learn how to add and subtract fractions whose denominators are not the same. Recall that when we want to add or subtract fractions having the same denominator, we add the numerators and retain the (common) denominator. This is different when the fractions have different denominators. When adding fractions with different denominators, we conver...

▶ Play video
#

sorry it took so long i found the right vid

high lily
#

note that you don't necessarily need to use the lowest, any common denominator will suffice,
its just using the lowest will be less tedious

next basalt
#

also the answe to the example is -1/3 right?

next basalt
#

also this is my way

#

i got the same answe but i wana know if this way is fine @high lily

high lily
#

note that you don't necessarily need to use the lowest, any common denominator will suffice,
its just using the lowest will be less tedious
yes

next basalt
#

gotcha, well thx

high lily
#

i.e. you could've just multiplied the fraction on the right by sqrt(x)/sqrt(x)

#

and you'll get a denominator of 2sqrt(x) for both fractions

next basalt
#

oh right thats much easier

#

but what happened to the 2's?

#

did they cancel each outher out?

#

or is it because the 2sqrtx is the same as the one on the left that it doesnt matter to include it

#

either way u have jogged my memory a lot thank you

#

.close

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#
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broken hare
#

I'm not sure how to solve this

obtuse pebbleBOT
fluid holly
fathom flicker
#

!nosols

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

fluid holly
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and the answer is the derivative of that function at the point t=0

broken hare
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I'm not getting any of the given answers

brave bramble
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Recheck your derivative on dV/dt

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Notably, the derivative of r² is not dr/dt

broken hare
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but that's given, so wouldn't I use it?

brave bramble
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Hmm?

broken hare
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the word problem says what dr/dt is, that it's 1

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so using product rule, it should be h * r' + r * h'

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8 * 1 + 5 * -4

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but that doesn't give an answer either so I was trying other stuff

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Does that make sense?

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maybe I'm confused

brave bramble
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You'll use a dr/dt somewhere, yeah

But your derivative implies that dr²/dt = dr/dt

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You might have missed the square when taking the derivative

broken hare
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okay let me try something 1 sec

broken hare
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.close

obtuse pebbleBOT
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Channel closed

Closed by @broken hare

Use .reopen if this was a mistake.

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sweet sparrow
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I need help

obtuse pebbleBOT
sweet sparrow
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it's a bit tedious

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I've got to sleep got hw due tmrw

tired sierra
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Dont ask to help just ask

sweet sparrow
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Find the exact value of the expression in terms of x with the help of a reference triangle

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I'm confused because of the x-1

tired sierra
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Oh boy

sweet sparrow
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what?

tired sierra
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I can't remember how to explicity do this but it uses the domain of sin^-1

fathom flicker
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There is a general identity for the tangent of the sine inverse

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you can make the reference triangle, or just learn the identity

sweet sparrow
high lily
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draw a right triangle where sin(theta) = x-1

sweet sparrow
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how tf do you do that

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what's the length of the opposite and hypotenuse

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with a fraction like 1/3 it's obvious but x-1? That's an expression

fathom flicker
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SOHCAHTOA

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sine=opp/hyp

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pick an angle

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make the opposite side length x-1

sweet sparrow
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is it just just x-1/1

sweet sparrow
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I'm really confused

sweet sparrow
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.close

obtuse pebbleBOT
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Channel closed

Closed by @sweet sparrow

Use .reopen if this was a mistake.

obtuse pebbleBOT
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Available help channel!

Send your question here to claim the channel.

Remember:
Ask your math question in a clear, concise manner.
Show your work, and if possible, explain where you are stuck.
After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

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

uneven otter
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Im honestly confused as to whgat this question rlly wants

uneven otter
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Previous parts related to this question:

sour lance
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basically the same as the first part but with an arbitrary number of ninjas

uneven otter
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do like rough work for the first 5-6 ninjas

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to see what the pattern is

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and divide into two cases ofc

sour lance
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hmm i wouldnt do too much work like that

uneven otter
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where 1) 1 ninja is the strongest and then 2) everyone wins and loses one fight

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oh

sour lance
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just to save time

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try to think in generalizations. what happens if a ninja loses to everyone?

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what if they beat everyone?

uneven otter
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hes at the end

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if the beat

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everyone

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hes at the front

sour lance
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try to build up an argument from that kind of thinking

uneven otter
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mhm but now im confused abt one more thing

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how is induction used here

sour lance
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if i had to guess, youll pretty much be constructing the line based on a couple of cases at each value of n

uneven otter
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i dont get it

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so like

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first x ninjas

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then first y ninjas

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then first z ninjas

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out of n ninjas

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wait can i start with 2 ninjas 1 strong n one weak

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and then keep adding another strong ninja to front and then another weak to the end

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and keep repeating that

sour lance
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that wont work in general bc you dont know if the ninjas are strong or weak in actuality

uneven otter
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oh

brisk matrix
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you can do this by induction

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probably why they asked you to prove the base case

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the inductive hypothesis is that you can arrange n ninjas in this manner

uneven otter
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base case being n = 3?

brisk matrix
uneven otter
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mhm

brisk matrix
sour lance
brisk matrix
uneven otter
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wait wth

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so

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like

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can i assume that the new ninja is either

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the strongest

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or the weakest

brisk matrix
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start by assuming they are the weakest

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it’s a case thing

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if they lost to everybody

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there’s a clear position they can go in

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specifically

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if they lost to the first person in the queue

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then there’s a clear position they can go in

sour lance
uneven otter
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wait

brisk matrix
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no

uneven otter
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so is this correct

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this is what I did

brisk matrix
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i’m suggesting they go at the start of the queue

uneven otter
brisk matrix
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oh i think i had it backwards

uneven otter
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i did 3 cases

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strongest, weakest, neither

brisk matrix
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but the same thing applies

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don’t use this “weakest ninja” notion

uneven otter
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oh should i change it to loses to everyone ?

brisk matrix
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like just assume they lost to the last ninja

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no that’s the thing

uneven otter
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oh

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oh so strongest = beat the first ninja in the queue

brisk matrix
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no

uneven otter
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whattttt

brisk matrix
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get away from the generalization to all ninjas

uneven otter
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ok my fault

brisk matrix
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just think about winning/losing 1 match at a time

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so assume the ninja lost to the first person in line

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where can you put them?

uneven otter
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right so they should be placed right after them

brisk matrix
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right behind them

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oh wait

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when you say “behind”

uneven otter
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yes my fault same thing

brisk matrix
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what do you mean

uneven otter
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yeye

brisk matrix
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nah you’re good

uneven otter
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behind

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ok so

brisk matrix
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just so we’re clear

uneven otter
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i get it

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so basicallty

brisk matrix
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like i want to make sure we’re saying the same things, can you clarify what you mean by “behind” and “in front”

uneven otter
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i think about each fight

if they lose to someone in the queue then they are to be put behind them and if they win againt someone they are to be put ahead of them

uneven otter
brisk matrix
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i see

uneven otter
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and infront means y is first in queue

brisk matrix
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ok gotcha

brisk matrix
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well that’s the goal