#help-49

1 messages · Page 88 of 1

proud island
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f(x) = 1/x?

grand pondBOT
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f(why am i here )= I don't know

twilit field
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h(x)=x

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but this feels like cheating

proud island
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lol

twilit field
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I mean it's technically correct.

proud island
#

I would suggest to call a function g(y)

twilit field
#

But yk.

proud island
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g(y) = sqrt(x + y)

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and h(x) = sqrt(x)

wary trail
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sqrt(x)+x, sqrt(x), 1/x

proud island
#

I think that's more likely resonable

proud island
twilit field
#

Thanks both of you.

proud island
#

np

twilit field
#

But my example would be wrong, right?

wary trail
#

no that's fine

twilit field
#

Cool

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thanks

#

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#
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faint loom
#

The radius is squareroot 34 how do I write it in gen equation

faint loom
#

I know I have to cancel the squareroot but idk how to input it

proud island
#

x2/a2 + y2/b2 = 1

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u want to have this?

midnight plankBOT
#

@faint loom Has your question been resolved?

faint loom
#

Idon’t understand that help

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I have to write in general equation

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Nvm

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Is my gen equation right

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Nvm I got it

#

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worthy kestrel
#

we get homology groups by taking the boundary maps between n skeletons and taking ker n/im n+1 right. and it kinda means n holes in a space?

cohomology is similar but instead we look at boundary maps between maps from a n skeleton to a graded ring? not sure what it means help please

last slate
#

I guess it keeps on going

worthy kestrel
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well

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i actually had a question

last slate
#

yeah I get it

runic hamlet
#

to the advanced section with you

midnight plankBOT
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worthy kestrel
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last slate
#

if i was given y = x(x+1) how do i get back x from y ?
im thinking like x = y / sqrt(y-1) or something but that doesnt work

small jasper
#

Now, notice that this can be rearranged as a quadratic in x

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Btw, it would be better to say “isolate x/solve for x in terms of y”

last slate
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oh

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x^2+x = y

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wait i really need the quadratic formula for this then?

olive matrix
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or completing the square (which is the same thing)

last slate
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uhhm

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is there no other way?

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welp

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drifting root
midnight plankBOT
drifting root
#

what does it mean by from parameters to points?

fierce karma
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ie what makes the numerator and denominator 0

drifting root
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ummmmm

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how do we tell that

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from the eq

fierce karma
#

wait, that doesnt make sense cause the denominator has only imaginary roots

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hmm

drifting root
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oH WAIT

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SORRY

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I JUST DIFF IT AND SAY ITS MONOTONIC INCREASING DONT I

fierce karma
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unless its just dumb grammar

drifting root
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for like

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the one to one

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sorry i should have been more clear

fierce karma
#

ur gud LUL

drifting root
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this is a pain to diff and put together lmao

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how can i do this more cleanly

fierce karma
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im failing to understand why proving its monotonic increasing helps u on whethers it one to one or not

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all that tells you is the curvature of the function

drifting root
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cause then it just

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increases

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like

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theres no turning points

fierce karma
#

oh shit I think I understand whats going on

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man thats a weird af function

drifting root
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yeyeye

fierce karma
drifting root
#

yea

fierce karma
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ye that should work

drifting root
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if i do that and say theyre both pos, then its one to one right?

fierce karma
#

yep

drifting root
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you kinda saved me

fierce karma
#

i dont think you gotta find the concavity tho

drifting root
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i was gonna do taht then put them back together

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like that

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not needed tho

fierce karma
# drifting root

nah jus differentiate the parameterized functions individually

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you only need to differentiate once not twice

drifting root
#

thanks for the help

fierce karma
#

ofc

drifting root
#

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frigid turret
#

if the 6th term of an a.p. is equal to four times its first team, and the sum of its first 6 terms is 75 , find the first term and the common difference

frigid turret
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i got my answer as first term as 5

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and common difference as 3

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can someone cross check it

fallen aurora
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manic bison
midnight plankBOT
manic bison
#

idk how to start

midnight plankBOT
#

@manic bison Has your question been resolved?

gray flume
#

use the trignometric relations

manic bison
#

how?

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<@&286206848099549185>

robust forge
manic bison
#

ohh

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tysm

robust forge
manic bison
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ye

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robust forge
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fallen aurora
#

How should I approach this problem?
any hint is fine...

grim vector
#

Use identity that sin2x = 2tanx/(1+tan^2)

robust forge
fallen aurora
robust forge
fallen aurora
robust forge
fallen aurora
#

thank you anyway

#

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last slate
#

Can someone talk in french here?

gray flume
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non

grim vector
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Oui mais parcontre ouvre un nouveau canal d'aide

last slate
#

Non?

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Okeey

gray flume
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anyone can

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using translate

last slate
#

Sorry

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Idk how to send my question

midnight plankBOT
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blissful drum
midnight plankBOT
blissful drum
#

can someone tell what i did wrong for this question?

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36 b part

modern sapphire
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B is in 1st quadrant, so -B has to be in 3rd Q

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you seem to be calculating with -80deg, which makes it in 4th Q

midnight plankBOT
#

@blissful drum Has your question been resolved?

blissful drum
#

i was supposed to do 80+180

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260

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feral barn
#

21c

midnight plankBOT
midnight plankBOT
noble vapor
#

You should be able to solve it by proving that ASO and ATP are similar triangles and then finding the similarity constant

midnight plankBOT
#

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manic bison
midnight plankBOT
manic bison
#

locus of this point

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needs to be found

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im clueless

hearty rune
#

sounds like a circle

manic bison
#

isnt a circle probably

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because both x and y can vary individually idk tho

midnight plankBOT
#

@manic bison Has your question been resolved?

manic bison
#

<@&286206848099549185>

radiant matrix
manic bison
#

alr

noble vapor
#

it is a circle

grand pondBOT
#

VincentBH

midnight plankBOT
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untold oyster
midnight plankBOT
untold oyster
#

Is this right?,

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The book says it's -2 but i don't know why

gaunt imp
#

Could you explain what you're doing?

untold oyster
#

Its integral u substitution

gaunt imp
untold oyster
#

My u is (1-e^t)^1/2 and i end up with 2(√1-e^t)^1/2

gaunt imp
#

That should be where the - comes from?

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And btw, if you want some advice: I'd recommend choosing what's inside the root as u instead of the entire root

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It's much easier to differentiate and will make things cancel out pretty neatly in this case

untold oyster
#

Can i try to write it?

gaunt imp
untold oyster
#

Hang on

gaunt imp
#

Without that 1/2

gaunt imp
untold oyster
gaunt imp
untold oyster
#

i got confuse how did we get it,

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bacause ist exponential

gaunt imp
#

That 1/2 is a mistake you made differentiating

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The derivative of (1-e^x) is -e^x

untold oyster
#

yes

gaunt imp
#

Go on from there, integrating with respect to u

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And you should get to the right answer without too much difficulty

untold oyster
#

du is negative right?

gaunt imp
untold oyster
#

so integral of u

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(u)^1/2

gaunt imp
#

The square root is still there

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And it's still dividing

untold oyster
#

ohh yea

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should i do the 1/2? and bring it to numerator?

gaunt imp
#

Else it'll get too confusing

untold oyster
untold oyster
#

.close

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timid verge
#

hey i need help

midnight plankBOT
timid verge
#

in middle school cant understand this

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i try something and my teacher says its wrong

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im confused

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please help

fair kayak
#

i would use logarithms to solve that

timid verge
#

what is that

midnight plankBOT
timid verge
formal palm
timid verge
#

yes

formal palm
#

so compare the powers

timid verge
#

as in?

tacit rose
#

If the bases are the same, then you can set the exponents equal to each other

timid verge
#

oh

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yes

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so what would y equal?

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and how would i find that

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i just want to understand the working of this atm

tacit rose
#

Apply what was stated

timid verge
#

ok

tacit rose
#

Make 9^y have the same base as 3^12

timid verge
#

yes

tacit rose
#

Then set the exponents equal to each other

timid verge
#

so to make the same base

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it would be

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3^2y

tacit rose
#

Yes

timid verge
#

and then i reverse calculate?

timid verge
#

yes

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after that the equation equals to

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3^2y=3^12

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which would be

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y=6

tacit rose
#

Yes

timid verge
#

ok thanks for helping

#

my doubt is solved

midnight plankBOT
timid verge
#

.close

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woeful escarp
#

guys help

midnight plankBOT
woeful escarp
#

is it 44?

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18x3?

fallen aurora
woeful escarp
#

o yea

fallen aurora
#

that "basketballs" thing

woeful escarp
#

.

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💀

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whats answer?

fallen aurora
#

is it the complete question?

woeful escarp
#

yes

fallen aurora
#

basketball means 1 ball right?

woeful escarp
#

ys

fallen aurora
#

and basketballs means more than 1

woeful escarp
#

yes

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idk why-_-

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they use balls

merry skiff
#

what grade are you in

woeful escarp
#

LOL"

fallen aurora
#

Probably question setters did a mistake there i suppose

woeful escarp
#

its my summer hw

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incoming 8 grade

fallen aurora
woeful escarp
#

full question

merry skiff
woeful escarp
#

whats blank table for?

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broskis help

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😭

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😭

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😭

last slate
merry skiff
#

ohh wait

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its like

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help for the multiplication algorithm thing

last slate
#

Help for 18 x 3?

woeful escarp
#

no

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its 54

slender walrus
#

i think they expect you to do it via addition

woeful escarp
#

bruh

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im js comfused

slender walrus
#

column for number of bballs, and cost

last slate
#

Long day for u

woeful escarp
#

bballls

slender walrus
#

n cost
1 18
2 36
etc

last slate
woeful escarp
#

LOL

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3 54

slender walrus
#

or just be malicious and write
$18 x 3 = $54
over all the lines in the "table"

woeful escarp
#

i only just write numbers that all

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so 54?

slender walrus
#

yes

woeful escarp
#

OK

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how do i write y=3x in numbers

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HELPPPPPPPPPPP

merry skiff
#

oh so basically

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do you remember what direct proportion is

woeful escarp
#

i do know

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wait

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wdym?

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u mean lines?

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x and y?

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axis

#

.close

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midnight plankBOT
misty carbon
#

first statement implies that B is a subset of A

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ok then youre done

grand pondBOT
#

Pupu&Bubu

#

Pupu&Bubu

misty carbon
#

just say

#

first statement implies B is a subset of A

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second statement implies A is a subset of B

#

therefore A = B

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last slate
#

how do you know whether the number of primes between 0 to 1000 is more than the number of primes between 10^8 and 10^8 + 1000?

robust forge
last slate
#

tbh idk if that works well

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and that was my first thought too

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but consider something like

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primes between 7001 and 8000 and primes between 9000 - 10000

last slate
#

if u use your approximation

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you get the wrong answer in this case

last slate
#

💀 at least that's what i found out

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u easily show x < 45 and y < 45 from geometry with no construction except with the fact that larger angle -> larger side

last slate
#

if 90 - x = a and x well = x

then a > x because one side was 3s and the other one was s? and so a > 45 and x < 45 💀

#

same idea but smth like that

robust forge
last slate
#

nah i doubt the approximation has any merits

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tbh

last slate
#

cuz of the counterexample i provided

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isn't he suggesting to use an approximation to count the number of primes between 10^8 and 10^8 +1000

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acknowledging that it is indeed an approximation

robust forge
last slate
#

The only way I can think of doing it would be using a computer program

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it was on my test lol

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😭

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Really?

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Maybe I'm missing something obvious then

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i think tbh their argument was probably

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primes get sparser the further you go

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but like that argument doesn't hold for a finite length interval

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maybe?

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That's not a correct argument

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cuz of my counterexample above

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yeah exactly (byut i'm guessing they're oging for that)

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or well smth else idk tbh

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i have no ideas other than using the approximation just like display said (that was my hunch too)

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There could be stronger more concrete approximations that gives you some bounds on the error

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Something like that could maybe be used to prove this

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But idk

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do you suppose i should go to the adv number theory channel or something then?

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i don't want them to think i'm trolling lol

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Yes, I think that channel fits this question

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If I'm mistaken and this is somehow trivial, blame me

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alright thanks

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i'm a pending postgraduate for a bit now

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💀

#

You don't have access to that channel?

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not with my initial roles yeah

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You don't need postgraduate role for it

#

Undergraduate is enough

#

it's an undergrad+ channel

robust forge
#

Btw is the answer 0 - 1000

last slate
#

u can check w WA

vital sinew
last slate
#

,w number of primes between 0 to 1000

last slate
#

,w number of primes between 10^8 and 10^8 + 1000

last slate
vital sinew
#

You know it's basically certain that it's true by the prime number theorem

last slate
#

hold on

vital sinew
robust forge
last slate
#

but.... the approximation fails for the case where you count the number of primes between 7001 to 8000

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and number of primes between 9k - 10k

vital sinew
#

It's an approximation

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That as n goes to infinity gets closer to the actual value

last slate
#

yeah but it gives me a wrong conclusion, i need a definitive conclusion on which closed interval with fixed length has a higher prime number count

#

i don't have to count them

vital sinew
robust forge
last slate
#

well that was the question, i'm dubious whether we're missing something trivial or this question is just pretty hard for the average elem number theory student

robust forge
last slate
#

💀

robust forge
#

I do have a person in mind but he's just to rude on answering easy ques wut

robust forge
midnight plankBOT
#

@last slate Has your question been resolved?

midnight plankBOT
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ruby pivot
midnight plankBOT
ruby pivot
#

Wait

#

.close

midnight plankBOT
#
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prime hornet
robust forge
# ruby pivot ??

No of primes ko count karne ka koi exact method hai
Ya fir distribution dekhne ka koi method?

#

wut waise sooya nahi tu ab tak

midnight plankBOT
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novel nexus
#

Can someone coach me normal precalc?

midnight plankBOT
novel nexus
#

plz

steep hinge
#

how much do you offer=

#

?

surreal moon
#

Normally you ask specific questions and we help you with those

surreal moon
steep hinge
#

it's another thing

novel nexus
subtle blaze
midnight plankBOT
subtle blaze
#

Just ask a question and if someone finds an interest in it they’ll help you

steep hinge
novel nexus
novel nexus
steep hinge
novel nexus
steep hinge
#

i am not interested anymore...additionally we are not supposed to speak about that here

grim vector
#

How 100 of it cant even be represented in euros, even with cents

novel nexus
#

Don't convert it to usd currency.

grim vector
#

Its like 0.004 usd

last slate
novel nexus
grim vector
#

Anyway, try to have a look into khan academy and online stuff, many are free and well construct courses

grim vector
#

Here are questions answering/ exercices checking, its not learning about full topic

novel nexus
#

.close

midnight plankBOT
#
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formal blade
#

.reopen

midnight plankBOT
#

formal blade
#

@novel nexus since you are claiming that your offer was only a cent I'm gonna assume you were kidding. In general please don't use the server to arrange paid tutoring. We can't deal with the complications that come with that. Please only use these help channels for asking actual math questions. You can ask whatever precalc qs you like in them. There is also #precalculus as well.

#

Precalc level stuff also tends to have a broad range of people ready/able to address too.

novel nexus
#

ok

#

.close

midnight plankBOT
#
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formal blade
#

.reopen

midnight plankBOT
#

formal blade
# steep hinge i ain't teaching shit

The same goes for you. If you suspect somebody is breaking a rule or toeing the line please try to just point out the rule conflict and ping mods if you feel it needs addressed by mods.

#

Sorry dezpa I know you're trying to close this.

#

.close

midnight plankBOT
#
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molten moth
#

wtf happened here

midnight plankBOT
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twin anvil
#

How is this 1/5

midnight plankBOT
twin anvil
#

sin (0) / (0)

should be undefined right

viral dagger
#

$\lim_{x\to0}\frac{sin(x)}{x}=1$

grand pondBOT
#

Skill_Issue

twin anvil
#

How

#

how is it 1

#

i thought it would be undefined

#

sub x =0

viral dagger
#

you cant just do that

#

with your logic x/x is undefined as x approaches 0

twin anvil
#

Yes

#

thats how i evaluated it algebraically

#

how do u evaluate it to become 1

viral dagger
#

this was from my textbook

twin anvil
#

i cant read that

#

so do i really know why it equals 1 or do i just memorize it

vague seal
#

the logic goes as follows

#

instead of looking at the value at that location

#

like sin(x)/x

#

at x = 0

#

because that becomes 0/0 and that is undefined

#

we look at a value close to x = 0

#

for example x = 0.1

#

and then x = 0.01

#

and so on and so forth

#

and you look at the limit of that as x goes closer and closer to 0 without ever getting to 0

#

and it results in 1

#

you can calculate it yourself

subtle blaze
#

you can use our favourite calculus trick, lhopital's rule if you forget

vague seal
#

the important message here is

#

$\lim_{x \rightarrow 0} \frac{\sin(x)}{x} \neq \frac{\sin(0)}{0}$

grand pondBOT
#

Katharine

vague seal
#

and so we say that sin(x)/x is not continuous at x = 0

subtle blaze
#

well it's not even defined there so it can't possibly be continuous

vague seal
#

yes but even if it was defined

#

if the limit isn't equal to the value then it is not continuous

subtle blaze
#

but $f(x)=\begin{cases}\frac{\sin(x)}{x} & x\neq 0 \ 1 & x = 0\end{cases}$ is continuous everywhere

vague seal
#

this is all unrelated to the question though just some info on what that inequality says

grand pondBOT
#

frosst

vague seal
#

in that case the limit of f(x) x -> 0 = f(0)

subtle blaze
grand pondBOT
#

frosst

midnight plankBOT
#

@twin anvil Has your question been resolved?

midnight plankBOT
#
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midnight plankBOT
#

Please don't occupy multiple help channels.

#

@gritty badger Has your question been resolved?

nova yoke
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.close

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midnight plankBOT
astral garnet
#

yeah but C contains every element of D

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twilit coyote
#

Let A and B be two different points from the plane. what are the set of points M from the plane that satisfy AM + MB = AB

blissful pier
#

do you know what AM, MB, and AB mean?

twilit coyote
#

lengthes

blissful pier
#

so AB is the length from point A to point B?

twilit coyote
#

yes

#

isnt it how it is written

#

thats how to symbolize lengthes in geometry

blissful pier
#

now suppose instead of going right from A to B, we stop at point M somewhere between. So it's like saying we went from A to M, stopped at M then went from M to B

twilit coyote
blissful pier
#

so then M lies somewhere between A and B

twilit coyote
#

so whats the set of points M

#

in mathematical notation

plain osprey
#

am i allowed to do sothx for those dislikes brothers

#

go for it

#

?

lavish venture
#

pajamamamallama is helping

violet storm
#

!noans

midnight plankBOT
#

The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.

twilit coyote
#

i mean i would understand it if i get the answer

#

i dont require explanation

lavish venture
#

so what is it a test

twilit coyote
#

well no i would understand how to think as well

#

understand the method

#

the way of thinking

#

not learn it by heart

blissful pier
#

alright here's a diagram of what I mean. Notice how we could've just traveled AB, but instead we took a stop at M right?

twilit coyote
#

i already understood u ty

#

but the mathematical notation

blissful pier
#

There's not mathematical notation for this that I'm aware of panda_think unless knief knows of some

harsh badger
#

Barycentric?

twilit coyote
plain osprey
#

there is a notation

#

but idk if yk it

#

depending on where u live

twilit coyote
#

js send it

plain osprey
#

kinda paralyzed to do anything after ive received 3 dislikes

#

from unknown people 😦

#

so idk

twilit coyote
#

bruh

lavish venture
plain osprey
#

alr thanks

plain osprey
twilit coyote
#

so segment AB privated from A and B?

plain osprey
#

yep

twilit coyote
#

why is A and B removed

plain osprey
#

A and B are two different points from the plane

#

so they cant be on top of each other

#

and if u sub A and B in ur equation

#

AA + BB = AB

#

thats wrong

twilit coyote
#

makes sense i guess

#

yea

#

ty @plain osprey @blissful pier

plain osprey
#

np

twilit coyote
#

.close

midnight plankBOT
#
Channel closed

Closed by @twilit coyote

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blissful pier
#

just don't give answers to people

twilit coyote
#

u heard that donia

#

even tho

#

i wanted the answer

plain osprey
midnight plankBOT
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twin anvil
#

i completely forgot how to do this someone help

midnight plankBOT
#

@twin anvil Has your question been resolved?

vagrant marlin
#

Then plug thr x value in it

#

I'm telling u how because u forgot how to do it, and it's not ur first time learning

midnight plankBOT
#

@twin anvil Has your question been resolved?

burnt flame
proven portal
#

Can u help me

twin anvil
#

is that an insult or

#

idk what thats supposed to mean

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obtuse pivot
#

My Question is: Let $a_{n}$ be a sequence of positive integers and define $U_n$ and $V_n$ by the recursion $$f_{n + 2} = a_{n + 2}f_{n + 1} + f_{n}, ~~ f = U, V$$, with initial conditions $U_{0} = a_{0}$, $U_{1} = a_{0}a_{1} + 1$, and $V_{0} = 1$, $V_{1} = a_{1}$. Prove that $\gcd(U_n, V_n) = 1$ using Bezout's Identity.

What I've Tried:
So, firstly I know that it's trivial to say that $\gcd(U_0, V_0) = 1$, since I can write $0 \cdot U_{0} + 1 \cdot V_{0} = 1$. Then I tried to work out a general pattern, noticing that $V_{0} U_{1} - U_{0}V_{1} = 1$, which would imply that $\gcd(U_1, V_1) = 1$. However a problem immediately arose when I found that, upon indexing all of terms in $V_{0} U_{1} - U_{0}V_{1}$ by 1, I came across an issue:
$V_{1}U_{2} - U_{1}V_{2} = a_{1}(a_{0}a_{1}a_{2} + a_{2} + a_{0}) - (a_{0}a_{1} + 1)(a_{1}a_{2} + 1) = -1$.

Now I'm almost certain that this pattern is too similar for it to not be a coincidence, and I'm wondering that if I have perhaps structured my steps in such a way that my choice of Bezout Coeffiecents doesn't work for the case where $n = 2$. Or if I've just completely misunderstood the problem entirely. Any help at all would be very appreciated

grand pondBOT
#

Ammardian

midnight plankBOT
#

@obtuse pivot Has your question been resolved?

obtuse pivot
#

<@&286206848099549185>

mint mauve
#

yes

mint mauve
grand pondBOT
#

dhani (Vorqid)

fervent ember
obtuse pivot
# fervent ember have you tried a proof by induction?

The plan has been proof by induction, the trouble is that I get $V_{n}U_{n + 1} - U_{n}V_{n + 1} = -1$ for $n = 1, 3, ..., 2k + 1$. It feels like it goes in circles, with it working for $n = 0, 2, 4, ..., 2k$ and then being so close to working with the odd cases

grand pondBOT
#

Ammardian

obtuse pivot
#

I'm not sure if there is some case to be made where I use strong induction, with two base cases of $n = 0$ and $n = 1$, then I get to specify two different sets of bezout coefficients in my inductive hypothesis.

grand pondBOT
#

Ammardian

frank wolf
obtuse pivot
grand pondBOT
#

Ammardian

obtuse pivot
#

If my choice of coefficients is such that $xU_{n + 1} + yV_{n + 1} = -1$ idk if that still implies that $\gcd(U_n, V_n) = 1$

grand pondBOT
#

Ammardian

fervent ember
frank wolf
obtuse pivot
#

and then have my inductive hypothesis specify two different sets of coefficients for odd and even cases?

midnight plankBOT
#

@obtuse pivot Has your question been resolved?

midnight plankBOT
#
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midnight plankBOT
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chilly cobalt
#

hey, how do i approach number 7? (i dont think i have to translate anything since all the information is given)

chilly cobalt
#

i know that |z| is 1

#

also the question wants theta in degress for some reason

#

<@&286206848099549185>

fallen aurora
chilly cobalt
#

oh

#

hi

#

could you help?

fallen aurora
#

without plugging those values directly in the equation

#

?

chilly cobalt
#

there must be right?

fallen aurora
#

but not sure

chilly cobalt
#

this is an olympiad problem n most questions do that

fallen aurora
#

lemme see

chilly cobalt
#

maybe 1 - az could be manipulated

fallen aurora
#

I can't think of any other than Trig identities

chilly cobalt
#

i think i found it

chilly cobalt
#

|z| is 1 and 1/z is conjugate of z

#

then the two things are equal to eachother no?

#

so cos x = 0

#

x = pi/2 + 2(pi)n

#

(2n + 1)90 in degrees

chilly cobalt
fallen aurora
#

wait

#

yeah seems right

chilly cobalt
#

hooray

#

.close

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#
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midnight plankBOT
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alpine gyro
#

How do I show this is true? $$2abcd\leq (ad)^2+(bc)^2$$

grand pondBOT
alpine gyro
#

I derived it from $$
|z+w|\leq|z|+|w|
$$

grand pondBOT
alpine gyro
#

Assuming z = a +bi, w = c+di

olive matrix
#

if you derived it then that seems pretty good to me

last slate
#

as hayley said, if you derived something from a formula that is true, then the derived formula will also be true.

alpine gyro
#

But how could I be sure that 2abcd is less or equal than (ad)^2 + (bc)^2?

#

Or how do I show it?

last slate
#

use AM-GM

alpine gyro
#

Alright, I'll look at into that. Thanks:)

#

.close

last slate
#

np:)

midnight plankBOT
#
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last slate
midnight plankBOT
last slate
#

i dont know where to start

fallen aurora
#

or without them?

last slate
#

i have no restriction

modern sapphire
#

you can always convert some sin into cos

fallen aurora
last slate
#

oh

fallen aurora
#

similarly 2 and 88 and so on

last slate
#

sin(x) =cos(pi/2-x)?

modern sapphire
fallen aurora
# last slate

you can also convert it to linear cosines and use formula too

#

but that will be inefficient

fallen aurora
flat veldt
modern sapphire
flat veldt
#

Then do (1st+last)+(2nd+penultimate) and use the trig identity sin²x+cos²x=1

last slate
#

okay yeah that was smart

#

i didnt thought of that

flat veldt
last slate
#

ok so answer is 45

modern sapphire
#

what did you do with sin^2(45)?

last slate
#

ohh

#

that's 1/2

#

mb

#

but wait

#

i dont understand this

#

so sin^2(1) => cos^2(89)

#

right?

modern sapphire
#

yes

flat veldt
modern sapphire
flat veldt
last slate
#

no

#

its

#

the answer is D

#

45 * 1/2

modern sapphire
flat veldt
last slate
last slate
#

wait

#

something is wrong

#

?

flat veldt
modern sapphire
#

45 * 1/2 = 22.5

slender walrus
#

$45\frac12$ is a mixed fraction representing the value $45 + \frac12$ \
it is not the product of $45$ and $\frac12$

grand pondBOT
#

ℝαμΩℕωⅤ

flat veldt
last slate
#

well thank you guys

#

all of you

flat veldt
last slate
#

really appreciate it

#

.CLOSE

#

.close

midnight plankBOT
#
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midnight plankBOT
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dim crane
midnight plankBOT
dim crane
#

anyone can help me with (b)?

midnight plankBOT
#

@dim crane Has your question been resolved?

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twilit field
#

13 is just a buch of horizontal line segments, right?

twilit field
#

at x= 1, 1.5 and 2

#

right

subtle blaze
#

How

#

Those 2 sets look mighty finite

#

The Cartesian product will also still be finite

twilit field
#

[1,2] is an interval IMO

subtle blaze
#

Lines are not finite

#

Oh

#

I misread

#

You’re right

twilit field
#

Cool. Thanks!

polar mortar
#

not horizontal

#

?

subtle blaze
#

Well I mean just draw them

twilit field
#

vertical

#

typo

#

yeah

subtle blaze
#

The x are fixed at whatever the first set has

#

Then slide it around with the 1, 2 interval

twilit field
#

Got it

#

.close

midnight plankBOT
#
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twilit field
#

Thanks

midnight plankBOT
#
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vagrant marlin
midnight plankBOT
vagrant marlin
#

Just so u know why I told u how

#

.close

midnight plankBOT
#
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robust pier
#

okay now i do need help with these two😭

midnight plankBOT
robust pier
#

the first one i got stuck after getting to them over 6

valid veldt
#

Send your work

robust pier
last slate
#

where did 3x come from

#

where did 16 come from

valid veldt
last slate
#

at this point what does anything come from

valid veldt
summer ravine
#

bro inventing his own methods

last slate
valid veldt
#

Fr

last slate
#

he s so cooked that he started inventing his own formulas

robust pier
last slate
#

hm

#

look up on youtube

#

how to add fractions

#

and get common denominator

valid veldt
robust pier
last slate
hearty isle
#

come on guys

#

don’t shit on him

hearty isle
#

do this

#

actually step by step

#

don’t do anything in ur head

#

and send that

robust pier
#

kay

#

like this??? or am I still doing it wrong-

valid veldt
robust pier
#

multiplying it?

#

or is it 3x?

royal dune
valid veldt
royal dune
#

when you combined the denomintors on the left

robust pier
#

oh

royal dune
#

i think that tripped you up

#

cuz you have the right idea

#

like this, then you can add them together

robust pier
#

oh right

#

its the same as i first send it-

#

okay not the same

#

only the 8 changed to 3

#

so,,

valid veldt
robust pier
#

well, yeah

valid veldt
# robust pier

Get x terms on LHS and non x on RHS for easier calculations

robust pier
#

shouldnt i need to eliminate the 6s first?

valid veldt
royal dune
robust pier
#

ah

midnight plankBOT
#

@robust pier Has your question been resolved?

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#
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fallen aurora
#

If a,b,c and d are four distinct numbers chosen from the set {1, 2, 3, 4, ... ,9}, then the minimum value of (a/b) + (c/d) is:-

A) 3/8
B) 1/3
C) 13/36
D) 25/72

fallen aurora
#

it is supposed to be a really simple problem

#

but how to do it?

dreamy lichen
#

the numerators must be as small as possible, the denominators as large as possible

#

so it's obvious which 4 numbers to choose, although it might not be yet obvious in which order

fallen aurora
#

I was lacking the thought of order

#

thank you so much

dreamy lichen
#

np

fallen aurora
#

.close

midnight plankBOT
#
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midnight plankBOT
#
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Show your work, and if possible, explain where you are stuck.
After 15 minutes, feel free to ping <@&286206848099549185>.
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lyric dust
midnight plankBOT
lyric dust
#

help no 3

delicate sage
#

It simply says you to

#

How many possible combinations are possible out of 9 numbers

#

It's simply 9c3

#

,calc 987/(6)

grand pondBOT
#

Result:

84
midnight plankBOT
#

@lyric dust Has your question been resolved?

lyric dust
#

wait can it be solved using fcp?

delicate sage
#

They r asking for combinations

#

The answer possibly would be 9³

#

Or if numbers are distinct it will be 9×8×7

#

It's better you check the answer key , it's not clear what actually they want

lyric dust
#

true

#

my teacher doesnt really teach that well

#

ill go with 9C3

#

assuming that numbers could repeat

#

right?

delicate sage
#

When we take 9c3 it's all distinct numbers and order doesn't matter

lyric dust
#

ohhh

delicate sage
#

If it's 9p3 numbers are distinct but order matters

lyric dust
#

i think order doesnt matter for a lock code

delicate sage
#

Yeah maybe they asking for combinations

lyric dust
#

it also said combinations, ill go with 84

#

thank u

delicate sage
#

So just go with it

lyric dust
#

wait last

#

how about 9

#

am confused also by that

#

combination right?

#

because when u order food u dont really have it in order?

delicate sage
#

It's 7c5

delicate sage
#

,calc 7c2

grand pondBOT
#

The following error occured while calculating:
Error: Undefined symbol c2

delicate sage
#

7*6/2 = 21

#

It will be combinations

lyric dust
#

thank u so much xor

#

ur the first one who like helped me right away

#

hey

#

can u help with one question in science?

#

its about physics

#

what determines the accuracy with which you can make measurements using the vernier caliper and micrometer

midnight plankBOT
#

@lyric dust Has your question been resolved?

midnight plankBOT
#
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quasi zenith
#

help with factoring out lowest power factors

midnight plankBOT
quasi zenith
#

would i be able to make x = x-6

#

and factor out ^3/2

#

i don't know im im on the right track or completely off

viral dagger
#

im pretty sure it wants you to factor the ^3/2 out yeah

quasi zenith
#

looks good?

#

i forgot a line

#

x^3/2(x) -36(x)

#

and then i plug the x for x?

#

well x-6

#

and simplify

#

?

#

doesnt look right

#

it cant be x+/- 0 can it?

viral dagger
#

hm

#

if you plug x=x-6 youll get
x^7/2-36x^3/2

#

factor x^3/2 you get x^3/2(x^2-36)

quasi zenith
#

i was thinking i could js make the parenthesis x

#

instead of havign the whole thing of (x-6)7^7/2

#

which explains the x=x-6

#

it wasnt given in the example so to speak

viral dagger
quasi zenith
#

FOR EXAMPLE

viral dagger
#

oh that was your tryna do

#

nvm sorry

quasi zenith
#

o

#

yaknow

viral dagger
viral dagger
quasi zenith
#

like dis?

#

i got lost

midnight plankBOT
#

@quasi zenith Has your question been resolved?

#
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midnight plankBOT
#
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sudden harbor
midnight plankBOT
sudden harbor
#

I don't understand how to derive rev and profit from the formulae above

midnight plankBOT
#

@sudden harbor Has your question been resolved?