So the missing information we just fill in with what’s already given?
#help-39
vestal gust
coarse harbor
So the missing information we just fill in with what’s already given?
Sorry, which information are we missing?
vestal gust
I just mean it’s not a real value but I guess it’s just to illustrate the point
midnight haven
What is not a real value?
Just because they're unknown variables, doesn't mean they're not real values.
coarse harbor
I just mean it’s not a real value but I guess it’s just to illustrate the point
Think of it as of a parameter, idk
As if someone can come and suddenly write 42 instead of x0
Or 7 or any other number
vestal gust
Think of it as of a parameter, idk
just to show the form of the equation gotcha
but some of these questions are asking me to sketch it based on just looking at the graph with no value
so i guess in an equation it makes sense
i'm not sure how to incorporate this with graphing tho
or at the very least i'm not sure i understand what they're asking
coarse harbor
or at the very least i'm not sure i understand what they're asking
I assume they're asking you to draw a bunch of tangent lines on some given graph
vestal gust
This is the way it’s pictured in the book
pearl pondBOT
@vestal gust Has your question been resolved?
pearl pondBOT
pearl pondBOT
Available help channel!
azure flax
Whats ⁸√w⁴ transformed into Algebraic expression with rational exponents
foggy mason
Whats ⁸√w⁴ transformed into Algebraic expression with rational exponents
$\sqrt[a]{x}^b = x^{\frac{b}{a}}$
jolly parrotBOT
Herels
pearl pondBOT
@azure flax Has your question been resolved?
pearl pondBOT
pearl pondBOT
Available help channel!
north talon
Let p be prime, show that 7^p + 4p^2 is never a perfect square
north talon
all i can think of is 7^p = 1 (mod 4) but i dont think that helps
midnight haven
7 ≡ -1 (mod4)
7^p ≡ (-1)^p (mod4)
since p is odd, (-1)^p = -1?
midnight haven
ye
pearl pondBOT
north talon
all i can think of is 7^p = 1 (mod 4) but i dont think that helps
this came from 7^p + 4p^2 = k^2 (mod 4) btw
pearl pondBOT
Available help channel!
midnight haven
can anybody help me with this?
pearl pondBOT
can anybody help me with this?
compact ridge
can anybody help me with this?
do you have to use all 4 of the numbers?
midnight haven
Yeah
compact ridge
ah try 8 * 9/6 - 5
midnight haven
I can only use what’s in the number base
compact ridge
I know
midnight haven
Oh mb
compact ridge
basically you just have to keep trying
different combinations
make sure you don't end up with a fraction
midnight haven
yeah Ive been stuck for abt an hour
midnight haven
brother there’s no / or *
unborn abyss
3.0 5 ! 6 / 8 - 9 -
4 5 !! 6 + 8 - 9 -
5.0 5 6 8 9 * ! / +
7.0 5 !! 6 8 * + 9 /
8.0 5 6 !! 8 / - 9 +
close but didint work
compact ridge
close but didint work
,calc 8 * 9/6 - 5
jolly parrotBOT
Result:
7
keep trying lmao
unborn abyss
apparently my script gives up? hold on
compact ridge
I've played these games before and all should be possible
midnight haven
Yeh they are
compact ridge
broken calculator game lmao
midnight haven
8,5,4,3
compact ridge
oh I see how to make 3 also but when you're ready
midnight haven
ready
midnight haven
yeah?
compact ridge
from 5, 6, 8, 9 but we added 6 + 9
midnight haven
5,8 we can use
compact ridge
5,8 we can use
yeah we have 5, 8, 15
midnight haven
yeah
compact ridge
can you try dividing two of the numbers
midnight haven
which two?
compact ridge
yeah don’t work
if you use 5 and 15
how can you divide them to get a whole number?
compact ridge
I really don’t know bro that’s why I’m here
do you know your 5 times tables
or really times tables at all
midnight haven
or really times tables at all
no but ik my 5
compact ridge
no but ik my 5
okay what are the first three numbers in the 5 times table
midnight haven
5,10,15
unborn abyss
ok i fixed my script jeez that was really bad
midnight haven
ok i fixed my script jeez that was really bad
nice
compact ridge
5,10,15
great so that means 5 * 3 = 15
so divide both sides by 5
$\frac{\cancel{5} \cdot 3}{\cancel{5}} = \frac{15}{5}$
jolly parrotBOT
south's secret twin brother
compact ridge
$3 = 15 \div 5$
jolly parrotBOT
south's secret twin brother
midnight haven
huhhhh
compact ridge
huhhhh
if you want to get better at maths, first step is to understand numbers
understanding the relationships between numbers and operations
addition and subtraction undo each other
multiplication and division also undo each other
midnight haven
Bro I don’t care about math I want to just finish this all ten so tommorow at school I can say I instantly finished it
compact ridge
say if 5 + 2 = 7, then 7 - 2 = 5
compact ridge
Bro I don’t care about math I want to just finish this all ten so tommorow at sc...
you have to be honest with yourself, that you're missing something huge
midnight haven
yes I am
compact ridge
that if you don't understand this maths will keep getting harder and harder
compact ridge
https://www.youtube.com/watch?v=fc2zif8oKt8
like please just spend a bit of time on this
or in school in general
finding all 10 numbers is hard yeah, it's supposed to be hard
midnight haven
hm
compact ridge
but it's so much harder if you don't have the right foundations to start with
midnight haven
yeah ur right
compact ridge
thank you
midnight haven
I mean I honestly didn’t understand half of the things u said so I had to search them up but still yeah
compact ridge
I mean I honestly didn’t understand half of the things u said so I had to search...
cause at this level of maths you're going to struggle to manage your own money
midnight haven
Really
compact ridge
struggle with knowing if 3 bottles of soda for 5 bucks is a better deal than 10 bottles of soda at 30 bucks
poor numeracy, that's the word for number skills
a lot of maths is harder than numbers and yeah you probably aren't interested in those parts
midnight haven
struggle with knowing if 3 bottles of soda for 5 bucks is a better deal than 10 ...
Ur actually right cuz im having a hard time knowing which ones better rn
compact ridge
poor numeracy, that's the word for number skills
really holds people back in life, keeps them in poverty and shit
midnight haven
a lot of maths is harder than numbers and yeah you probably aren't interested in...
I’m a lazy guy that’s not interested in school hoping to just make a living off games
compact ridge
struggle with knowing if 3 bottles of soda for 5 bucks is a better deal than 10 ...
there's a trick we can use
3 bottles of soda = 5 bucks
multiply everything by 6
18 bottles of soda = 30 bucks
so wow, we can get 18 bottles of soda for the same 30 bucks
midnight haven
there's a trick we can use
3 bottles of soda = 5 bucks
multiply everything by ...
Probably would of never thought of that tbh
compact ridge
I’m a lazy guy that’s not interested in school hoping to just make a living off ...
oh yeah then you definitely need some level of maths to code, to build your own games and animations
midnight haven
u help me more than my teacher does bro ima be serious
compact ridge
stuff like trigonometry for instance, maths to do with triangles
midnight haven
oh yeah then you definitely need some level of maths to code, to build your own ...
No I ment like Fortnite
compact ridge
like functions also help, algebra 1 and 2 basically
compact ridge
No I ment like Fortnite
ah shit
I thought you meant a real programming language like JS
midnight haven
Im actually really good ngl
midnight haven
I thought you meant a real programming language like JS
I’m too lazy for that
compact ridge
no wonder you don't need maths to work as a game dev on Roblox
midnight haven
I wanna be a content creator too. But again too lazy
midnight haven
Are you going to be a teacher?
compact ridge
Are you going to be a teacher?
nah I'm going to be a researcher in the social sciences
midnight haven
Wow bro
compact ridge
I've done 1 1/2 years of maths at undergraduate level though
midnight haven
Wow
compact ridge
but right now I've switched to sociology, the study of society basically
midnight haven
I have no idea what that is but nice job
compact ridge
why is our society built the way it is
and I'm aiming to finish my undergrad so that I can get a step closer
midnight haven
Damn
compact ridge
you have many more options after you graduate HS for example
midnight haven
Im not tryna joke rn but sometimes if ppl explain stuff to me in Fortnite terms i understand better
compact ridge
but if you want to do something academic or a good white-collar job you need your undergraduate, I don't mind studying tbh
if you want to do a trade then forget uni haha
it's good money but I'm not good with my hands
midnight haven
if you want to do a trade then forget uni haha
can u be my teacher for a while
compact ridge
stuff like HVAC, aircon renovations, landscaping, welding etc
compact ridge
can u be my teacher for a while
nah I don't deserve it
there are other people who will be just as patient with you also
I'm not the only one like this
but yeah people like me aren't super common I agree
also lucky to be living somewhere where an undergraduate degree is 3 years instead of 4
1 less year spent mucking around I bet
compact ridge
the way education works is that unfortunately you have to climb a ladder to the top
midnight haven
could u still help me with the all ten
compact ridge
you have to graduate HS before you start uni most of the time, unless you have dual enrollment courses where you can go to college and HS at the same time
compact ridge
could u still help me with the all ten
okay
midnight haven
you have to graduate HS before you start uni most of the time, unless you have d...
Nice bro I don’t think I’ll be doing that
compact ridge
$5 = 8 - (9 + 6) \div 5$
jolly parrotBOT
south's secret twin brother
midnight haven
compact ridge
$3 = 6 - 9 \div (8 - 5)$
jolly parrotBOT
south's secret twin brother
midnight haven
It’s crazy how I’ve tried all ai bots to try solve all ten and they all failed
compact ridge
interesting let me try GPT
midnight haven
I tried gpt the most
compact ridge
I'm missing the solution for 4 but I swear I had it at one point
midnight haven
Always fails
compact ridge
,calc 8 * 9/6 - 5
7
unborn abyss
||```
0 = ((8 - 9) - 5) + 6
1 = ((8 - 9) * 5) + 6
2 = ((8 + 9) - 5) / 6
3 = (8 * 6) - (9 * 5)
4 = (8 / (5 - 9)) + 6
5 = 8 - ((9 + 6) / 5)
6 = ((8 + 9) - 5) - 6
7 = ((8 * 9) / 6) - 5
8 = (8 / (9 - 5)) + 6
9 = (8 - 5) * (9 - 6)
10 = ((8 - 9) + 5) + 6
solutions
midnight haven
||```
0 = ((8 - 9) - 5) + 6
1 = ((8 - 9) * 5) + 6
2 = ((8 + 9) - 5) / 6
...
It’s blank
unborn abyss
click on it, it's a spoiler tag
midnight haven
O
compact ridge
oh wait $4 = 6 - 8 \div (9 - 5)$
jolly parrotBOT
south's secret twin brother
midnight haven
your a legend omg
compact ridge
yeah Hayley knows how to code
unborn abyss
python
compact ridge
I could probably do it but I'm rusty
I'd need at least 30 minutes, no, scrap that, 1 hour
cause implementing parentheses is hard
midnight haven
I have to go now but thank you both, is it fine if I add you guys?
unborn abyss
the trick is to do the parentheses last
import operator
import math
import itertools
import time
import sys
import argparse
from collections import defaultdict
OPERS = {
'+': operator.add,
'-': operator.sub,
'*': operator.mul,
'/': lambda a,b: a/b,
#'^': lambda a,b: a**b if 0 < b < 100 and 0 <= a else 0/0,
}
NUMBERS = set([5, 6, 8, 9])
def tryit(stack=(), nums=None, journal=''):
if nums is None: nums = set(NUMBERS)
#print(f'{journal=!r}, {stack=!r}')
if len(stack) == 1 and not nums:
yield stack[0], journal
return
if len(stack) >= 2:
for oper in OPERS:
try:
op = OPERS[oper]
res = op(*stack[-2:])
if abs(res) > 10**1000:
continue
yield from tryit(
stack=stack[:-2] + (res,),
nums=nums,
journal=journal + ' ' + oper
)
except OverflowError:
pass
except ZeroDivisionError:
pass
for num in nums:
yield from tryit(
stack=stack + (num,),
nums=(nums - set([num])),
journal = journal + ' ' + str(num)
)
def post2in(s: str) -> str:
symStack = []
for tok in s.split():
if not tok: continue
if tok in OPERS:
symStack[-2:] = [f'({symStack[-2]} {tok} {symStack[-1]})']
else:
symStack.append(tok)
out = symStack[0]
if out.startswith('('):
out = out[1:-1]
return out
def main(args):
found = defaultdict(list)
for dest, path in tryit(nums=set(args.seeds) or None):
found[dest].append(path)
seen = set()
for dest in sorted(found):
if abs(dest) > 10**100:
continue
destI = round(dest, 2)
if destI % 1 == 0:
seen.add(int(destI))
postfix = found[dest][0]
if args.postfix:
expr = postfix
else:
expr = post2in(found[dest][0])
print(f'{int(destI):-3d} = {expr}')
for num in range(1, 300):
if num not in seen:
print(f'did not see {num}')
if __name__ == '__main__':
parser = argparse.ArgumentParser()
parser.add_argument('seeds', nargs='*', type=int)
parser.add_argument('--postfix', action='store_true')
args = parser.parse_args()
main(args)
also the last 10% takes the same time as the first 90%, common inside joke in programming
unborn abyss
i generate it as postfix first
compact ridge
the trick is to do the parentheses last
```python
import operator
import math
im...
yeah I can't code that in 30 minutes for sure
probably would take me hours
unborn abyss
neither can i, this was code that i had written but had to adapt
compact ridge
it's super challenging the more I think of it
unborn abyss
because the original problem was 4 numbers that you had to use in order
compact ridge
fuck yeah it's a good coding challenge
midnight haven
the trick is to do the parentheses last
```python
import operator
import math
im...
Is there a way I could get a hold of this and change the numbers every time I need to use it?
unborn abyss
yeah that's why i posted it lol
compact ridge
I was thinking you create like 4 arrays
1 array has all 4 of the the original numbers
the second array has only 3, since you combine 2 numbers to make another one
unborn abyss
when you run it it will dump out all the solutions
hayls@yavin ~/projects/12345 $ python 12345.py
-427 = 5 - ((8 * 9) * 6)
-402 = (5 - (8 * 9)) * 6
-392 = 8 * (5 - (9 * 6))
-387 = 9 * (5 - (8 * 6))
-354 = 6 - ((8 * 9) * 5)
-330 = 5 * (6 - (8 * 9))
-312 = 8 * (6 - (9 * 5))
-306 = 9 * (6 - (8 * 5))
-262 = 8 - ((9 * 5) * 6)
-231 = 9 - ((8 * 5) * 6)
-230 = (8 - (9 * 6)) * 5
you can pass seeds on the command line
hayls@yavin ~/projects/12345 $ python 12345.py 3 4 7
-25 = 3 - (4 * 7)
-17 = 4 - (3 * 7)
-16 = (3 - 7) * 4
-9 = 3 * (4 - 7)
-8 = (3 - 4) - 7
-7 = (3 - 4) * 7
-6 = (4 - 3) - 7
-5 = 7 - (3 * 4)
-1 = 3 / (4 - 7)
0 = (3 + 4) - 7
1 = (3 + 4) / 7
5 = (3 * 4) - 7
the third array has only 2
the fourth array is the answer
put all the arrays in a loop
then iterate over like all possible combinations
so that you don't have to think about implementing brackets
Loaded maybe I'll send you the code if I even manage to do it
wait then there will be like (4 * 3 * 4) * (3 * 2 * 4) * (2 * 4) possible answers
,w (4 * 3 * 4) * (3 * 2 * 4) * (2 * 4)
jolly parrotBOT
compact ridge
a computer can do it though
midnight haven
I’m back sorry I had to go for a sec
compact ridge
for a computer it can spit out numbers from 1 to 10,000 in under 1 sec
jeez yeah this is actually fairly challenging to code
I'd be quicker with my brain
midnight haven
So do I just run the command in a channel or sum?
compact ridge
there would be a million loops
midnight haven
Is python what I need to run it on
unborn abyss
yes
compact ridge
yeah search up python online
midnight haven
I went on the website and it won’t really let me do anything
Ok I found the right website
This is what it said
clear moon
you've included the discord comment as code. only use what's in the code block
midnight haven
could u paste that for me
clear moon
on desktop for me you can click the top right of the text block to copy to clipboard
it's too long for me too paste lol
midnight haven
Bruh
midnight haven
Alg
clear moon
just don't include the part of the message
the trick is to do the parentheses last
that's not python code
midnight haven
I just won’t use it bruh
clear moon
i ran it successfully here https://www.online-python.com/g14HJtCAN0
unborn abyss
i ran it successfully here <https://www.online-python.com/g14HJtCAN0>
ah thanks
clear moon
all you hehe
midnight haven
ah thanks
I appreciate you so much, you’re one of the best people I have ever met. Thank you
pearl pondBOT
@midnight haven Has your question been resolved?
polar steppe
Which integration is the diagram of in the top right?
pearl pondBOT
Which integration is the diagram of in the top right?
sharp vigil
those should be equivalent
pearl pondBOT
Available help channel!
dense plover
pearl pondBOT
dense plover
Can someone explain what the first 2 points are trying to say
since i got no clue
what does i and j mean?
merry carbon
The i'th row of the vector/matrix (and j'th column for a matrix)
e.g. if you take $n = 3$ and $\mathbf{a} = \pmqty{4 \ 20 \ 69}$ then $a_1 = 4, a_2 = 20, a_3 = 69$
jolly parrotBOT
@merry carbon
merry carbon
if you also took $\mathbf{b} = \pmqty{4 \ 5 \ 9}$ then the dot product $\mathbf{a} \cdot \mathbf{b} = 4(4) + 20(5) + 69(9)$, but then $\mathbf{a}\mathbf{b}^T = \pmqty{4(4) & 4(5) & 4(9) \ 20(4) & 20(5) & 20(9) \ 69(4) & 69(5) & 69(9)}$
jolly parrotBOT
@merry carbon
pearl pondBOT
@dense plover Has your question been resolved?
pearl pondBOT
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Available help channel!
runic finch
can someone help with this, i dont even know where to start
pearl pondBOT
can someone help with this, i dont even know where to start
runic finch
its suppost tpo be an exercise of finite projective planes
pearl pondBOT
@runic finch Has your question been resolved?
robust cedar
I just assumed because the question says to use bracket notation. i could see the answer being a scalar or a vector depending on how you solve it. i tried solving it by plugging (3,1,2) into F and G and adding them and then multiplying by f(3,1,2) which gives a vector but i could also see it as plugging the x y and z values of F + G into f and then plugging in 3,1,2 which would give a scalar
pearl pondBOT
robust cedar
@plush bramble heres what i get when doing it the vector way
plush bramble
i don't know how you're getting any of that. repost the question here
plush bramble
i still have no idea where you're getting this from
should show your entire steps so people can follow your work
robust cedar
sorry ill rewrite that. i tried to make this scalar method more clear
vector method
pearl pondBOT
@robust cedar Has your question been resolved?
pearl pondBOT
@robust cedar Has your question been resolved?
plush bramble
vector method
this is not what the question is asking for
$f(F+G) \neq f \cdot (F+G)$
jolly parrotBOT
riemann
plush bramble
This is function composition
plush bramble
vector method
this is multiplication
robust cedar
so is the top way correct
plush bramble
yea
robust cedar
alright that makes sense to me the question just made me think it was supposed to be a vector 😭
thanks
.close
pearl pondBOT
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Available help channel!
novel rose
Im not sure if im doing this correctly
a) 3x = 9 mod 10
=> x = 3 mod 10
and the solution is [3]?
b) 5x + 2 = 27 mod 15
=> 5x = 25 mod 15
=> x = 5 mod 3
[5] = {...., -4, -1, 2, 5, 8, 11, 14....}
But we need it in terms of mod 15 idk what to do...
c) -11x - 3 = 30 mod 7
=> -11x = 33 mod 7
=> -x = 3 mod 7
and the solution is [3]?
west sapphire
for (b) you'll have multiple solutions, just list all of them that are between 0 and 14
novel rose
for (b) you'll have multiple solutions, just list all of them that are between 0...
so x = z mod 15 where z \in {2, 5, 8, 11, 14}?
west sapphire
your answer for (c) is wrong, you didn't deal with the - sign
west sapphire
so x = z mod 15 where z \in {2, 5, 8, 11, 14}?
mod 15 but yea
novel rose
your answer for (c) is wrong, you didn't deal with the - sign
how would I deal with that. I havent really done anything like this in class before
novel rose
mod 15 but yea
and why do we ignore the negatives? (-4, -1 etc)
west sapphire
add 7 to that and you get x=4
west sapphire
and why do we ignore the negatives? (-4, -1 etc)
they're also valid, but for example -1 = 14 (mod 15)
west sapphire
yw, cheers
novel rose
.close
pearl pondBOT
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Available help channel!
naive cypress
I have question about proofs. If we have "If p and r and s then q, and I want to use contraposition. Would it be fine to do if (not q) and r and s, then not p?
potent birch
yo can any1 help me review for amc 10b
naive cypress
I'm using this channel already lol
sick adder
I have question about proofs. If we have "If p and r and s then q, and I want to...
It's definitely on the right track, your statement if not q, and r and s, then not p (Meaning -q, r, and s are all true and thus p is not) is true but not quite the contrapositive
naive cypress
Right
but I was wondering because
um
So if I only assume not q, then I would have to show
3 different cases, which at least one of them fails
but then if I have some way to assume r and s or something
then I would have more tools followed from proposition, theorem, etc
maybe contradiction is the best way
sick adder
Yeah if not q is true, then at least one of p, s, and r must be false
I think the full contraposition would be if not q, then not (p and r and s)
Which can be expanded to if not q, then not p or not r or not s
naive cypress
yea that's what I was saying
because
if p and s and r, then q
I am not sure if we can reformulate
s and r holds first, and if p then q
for example,
for all x > 0, x^2 > 0
contraposition of this is if x^2 <=0, then x <= 0
however notice that we already have that x is real number
so if I think differently, then
if x^2 <=0, then x <= 0 or x is not a real number
sick adder
If x^2 <= 0 then the only real x can be is 0 if I'm not mistaken
naive cypress
right
sick adder
For any x^2<0, x is complex
naive cypress
right
but if you see the original statement
"if x^2 <=0, then x <= 0"
This was sufficient
or something like this
I am not communicating this well i guess
sick adder
I'm not either lol I dipped my toes into a subject I'm not good at lol
naive cypress
lmao
pearl pondBOT
@naive cypress Has your question been resolved?
naive cypress
.close
pearl pondBOT
pearl pondBOT
Available help channel!
sharp smelt
pearl pondBOT
sharp smelt
shouldnt it be till n
I think this notation is right too?
sick adder
Your reimann sum is 124/3 and the integral is equal to 21 so something's off
sharp smelt
It shouldn't ., should it
dusty flame
sharp smelt
How'd you construct it?
so we move the origin one unit to the right, and then sum between 1 and 3n, because we're now effectuvely finding teh area between 1 and 3
*0 and 3
dusty flame
why 3n
dusty flame
sick adder
Where did the six come from in the first place?
Also I never shifted the limits in my class so I'm not sure if it's a method I'm unaware of but I imagine the nature of functions like this suggest that the integral from 0 to 3 will be a different area as that from 1 to 4
sharp smelt
huh
sick adder
For this particular integral, evaluated from 1 to 4 is equal to 21, but from 0 to 3 is 3, so I don't see why the Riemann sum would follow a different pattern
sharp smelt
I'm trying to figure out why the -5 remains -5
sick adder
In what way?
sharp smelt
nvm, makes sense
sick adder
Riemann sum includes f(stuff) so naturally it would be there
sharp smelt
I was overthinking it
oops
This is a digression, but where can I find problems on upper and lower sums
stewart doesn't seem to have any
I do have spivak, but not\ sure if that's the right choice 3 weeks before my exam
sick adder
I always used Wolfram's problem generator but I don't think they have series
sharp smelt
yeah, doesn't seem to have any
I think my library does have lang
I think that has upper and lower sum problems
thanks!
.close
pearl pondBOT
pearl pondBOT
Available help channel!
inland moon
I’m on a and the answer is B
pearl pondBOT
I’m on a and the answer is B
feral leaf
I’m very confused on what the arrows mean
Are you referring to the < and > signs?
That's inequality symbols
inland moon
yeah but my teacher says it tells which way they are shading but I forgot
Like he doesn’t have notes
shrewd mist
Solid line means less/greater than or equal to, dotted line means exclusively less/greater than. That’s why the answer is b over a- which is what you circled (?)
inland moon
oh so when it’s solid it’s >
shrewd mist
Other way around
shrewd mist
Yup
inland moon
okay valid but how do you tell which way it’s shading using the symbol
feral leaf
You can plug in a value from the shaded region to check
inland moon
Like take a point from where they overlap?
feral leaf
Yes
inland moon
okay so if I wanted to test 1,4 I would plug 1 for x and 4 for y?
and then if it symbol is correct then it’s right?
feral leaf
Yes
inland moon
We plug it in for both right
Linear and parabola?
okay bet I just got understand jy
feral leaf
Yes, if you've given the graph and want to find out what choice it is, you can plug in a value from the overlap region to check
inland moon
Imma try these next problems
But if you know a way I can tell which equation goes to the graph without having to plug from the overlap please lemme know
feral leaf
With process of elimination and knowing that solid line is great/less than or equal to and dotted is less/greater than, then you can eliminate to 2 choices then just plug in a value for just those two rather than 4 choices
inland moon
thanks bro imma try that I did process of elimination for the next problem and it rlly helped
Do you want to help me with number 5 if you have time @feral leaf
feral leaf
I don't see a 5?
inland moon
oh sorry imma send it it’s a different problem
Wait hold on
don’t we just draw lines through where the equal sign is
feral leaf
Not sure what you mean by draw a line where the equal sign is
inland moon
Like for example the first one equal 12
so wouldn’t we draw a line thru 12 on the graph like
That
Or am I wrong cause ngl I forgot 😂
feral leaf
That's right
inland moon
I’m on fire
feral leaf
Then you just find the x values that intersect it
tiny sequoia
i need help with 3b, struggling to get started, would appreciate anything
pearl pondBOT
i need help with 3b, struggling to get started, would appreciate anything
@tiny sequoia Has your question been resolved?
pearl pondBOT
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novel rose
The way it reduced 21 and 35 modulo 19 and then subbed in 2 and 16 for 21 and 35 ... is something like this legal? The reason im asking this is because I havent really seen anything like this in class before
novel rose
oooh tysm
spiral pivot
It is legal whenever the mod is prime, you can just do algebra
You need to be careful with multiplication when the mod is composite though.
novel rose
You need to be careful with multiplication when the mod is composite though.
Im kinda confused by this
can you show me a case pls
spiral pivot
Sure, take mod 12 as an example.
4 * 3 = 0 mod 12
Which means 3 and 4 are divisors of 0 in mod 12.
This winds up breaking stuff a little bit
3x + 4 = 4 mod 12 gives x = 0 mod 12. But you are missing cases, because x could be 4 and 8 as well
novel rose
3x + 4 = 4 mod 12 gives x = 0 mod 12. But you are missing cases, because x could...
sorry but how did u get x = 0 mod 12 here
3x = 0 mod 12
whats the next step
oh wait
im slow
divide by 3
spiral pivot
Yes exactly.
novel rose
I thought u divide mod 12 by gcd(3, 12)
spiral pivot
Yes.
pearl pondBOT
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olive crystal
given a function, i can find the inflection points like this:, right?
set f''(x)=0, plug the found x value(s) into f(x),
(x,(fx)) is an inflectionpoint
am i correct
versed mica
sign needs to change
versed mica
well it isn’t enough for f’’ to be zero
we need to ensure f’’ changes sign
f’’ = 0 is a necessary but not sufficient condition
well
i guess f’’ could also technically not exist
so technically not necessary
olive crystal
wait youre right
versed mica
think of points of inflection as the relative extrema of f’
olive crystal
i missed the part where inflection=change in concavity
versed mica
yep
olive crystal
so was my initial method of findingt POI correct or no
i assumed f''=0 meant sign change
versed mica
think of points of inflection as the relative extrema of f’
^
versed mica
yes that’s one condition
key word is can
the other condition is that f’’ must change sign
olive crystal
example: f''=o at x=1 and x=2
from this i have 3 intervals: (-inf,1)(1,2)(2,inf)
then
i choose numbers from each interval, plug into f'', and see if the output changes sign on each interval?
like uhhhhhh if f''(0) and f"(1.5) are both positive, there would be NO POI on any of the first 2 intervals?
i hope that was clear sorry
versed mica
i choose numbers from each interval, plug into f'', and see if the output change...
well you’re checking to see if the sign changes from before those critical points to after
versed mica
like uhhhhhh if f''(0) and f"(1.5) are both positive, there would be NO POI on ...
yea
well POI at the point x = 1
no POI there you mean
pearl pondBOT
@olive crystal Has your question been resolved?
vagrant wave
im getting a diff answer from the solution is there a mistake??
unkempt yacht
im getting a diff answer from the solution is there a mistake??
i havent read the thing yet but your most critical mistake is not having a differential
vagrant wave
i did differentiate it
jolly parrotBOT
unkempt yacht
this is what an integral look like
you are missing the dx, called the differential
vagrant wave
oho
pearl pondBOT
@vagrant wave Has your question been resolved?
vagrant wave
.close
rigid night
Hi I'm an architecture student. I want to make a wall system consisting of movable panels, I designed the columns so the panels could rotate around them. Column should look like the image below ( L shaped part is piece of + shaped column). In order for the panel to rotate smoothly while moving on the blue rail line; What should be the minimum rail-column distance (x), the length of the rail (y), the length of the column part (z)?
pearl pondBOT
Hi I'm an architecture student. I want to make a wall system consisting of movab...
@rigid night Has your question been resolved?
rigid night
<@&286206848099549185>
pearl pondBOT
@rigid night Has your question been resolved?
pearl pondBOT
@rigid night Has your question been resolved?
midnight haven
I have a question.
pearl pondBOT
I have a question.
vocal lark
I have a question.
you don't say?
floral ember
hello
midnight haven
Suppose I have rope. It's length is L.
Suppose it hangs from the edge of a table. The rope is by mass uniformly distributed over the length.
The gravitational acceleration is g.
What is the G.P.E of the whole rope?
vocal lark
gravitational potential energy
midnight haven
Or, in other words, what will be the work done to pull it wholly to the table.
Yes.
midnight haven
Of course not
floral ember
complete derivation and answer
vocal lark
direct formula or
Hi Yoobie, are you doing this problem now?
floral ember
yes
midnight haven
I know that GPE of a point of mass m at a height h is mgh.
floral ember
actually we are from the same country
midnight haven
But the height of different point varies.
floral ember
that is a common problem from JEE i have already given that exam before
and solved the problem too
vocal lark
Alright Yoobie, let me get out of your way then
floral ember
i dont mean to intrude either.. sorry if i dusturbed you
vocal lark
i dont mean to intrude either.. sorry if i dusturbed you
Of course you do
go ahead though
floral ember
hey anjali how much part of rope is hanging from the edge of the table
midnight haven
The GPE of a small part of the rope ∝ the height of that part from the lower end of the rope.
floral ember
so the entire rope is
oak quiver
Is friction there?
midnight haven
No
oak quiver
Use CM
midnight haven
Disconsider every other factor
oak quiver
Center of mass
floral ember
i mean she should ideally use centre of mass.. if she has learnt that chapter
if not then she has to integrate it completely and solve
oak quiver
I don't think she knows integration
floral ember
a basic level of integration for physics is taught in class 11
for solving these types of problems
oak quiver
Center of mass also in 11th
floral ember
that is the standard solution in every textbook
midnight haven
This integration is linear
That GPE ∝ height
So there must be a simple way to do it
floral ember
Center of mass also in 11th
that chapter is after Work Power Energy, if she wants to solve the question using solely work power energy concepts she will have to use integration
floral ember
So there must be a simple way to do it
yess that is the case here
you should actually learn it step by step
because learning this integration will be very helpful for further physics in JEE
floral ember
you dont learn this type of integration in maths in class 12
so L part of the rope is hanging down from the edge right?
midnight haven
yes
oak quiver
that chapter is after Work Power Energy, if she wants to solve the question usin...
Yeah but the WPE in this is class 9 and she has done it
floral ember
Yeah but the WPE in this is class 9 and she has done it
in class 9 the level is very low compared to JEE level
its just basic
oak quiver
Yup
midnight haven
ok
floral ember
you can try going x distance down from the edge
and select a small portion of rope dx
can you write dU? (gravitational potential for the small portion of rope)
oak quiver
I don't think she does
floral ember
lets see if she can
if not i should try to teach that
this is a very common type of problem for JEE
midnight haven
uhm, what is dx
oak quiver
Lol
midnight haven
Sort of
oak quiver
Hmm
midnight haven
I just know the def
floral ember
oh
listen so
dx is the small lenght of rope you selected after going x distance down
oak quiver
Center of mass is basically a point where we can concentrate all the mass of a body for the purposes of NLM, GPE only
midnight haven
oh
oak quiver
You will learn why in chapter centre of mass and rotational dynamics
midnight haven
can't we use graphs
oak quiver
I don't think so
floral ember
well if you want to there is a short trick
oak quiver
Graph of what?
midnight haven
yes
floral ember
since the integration is linear
midnight haven
it will be a triangle
floral ember
you can just take the mean
midnight haven
mhm
floral ember
so in this case MgL/2
sinful nebula
gpe = mgh
floral ember
but like its not the ideal,, its fast but you should know the fundamentals
floral ember
that is what i was talking about..
oak quiver
!nosols
pearl pondBOT
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.
floral ember
oops
midnight haven
oops
floral ember
my bad
oak quiver
I hope to do so too
floral ember
dont worry its for the better just try your best thats all that matters
midnight haven
Ok Anjali by CM you can concentrate all the mass in the middle of the rod
yes
yes
oak quiver
Ok Anjali by CM you can concentrate all the mass in the middle of the rod
So m mass will be at a depth of l/2
oak quiver
dont worry its for the better just try your best thats all that matters
Ohh thanksss
midnight haven
what about the average power on a block if the acceleration of the block is constant in a horizontal plane
floral ember
what is the question?
midnight haven
A force 'F' accelerates a block of mass 'm' along a straight line to velocity 'v' from rest adn displace it through a distance of 's'. What is the average power developed?
oak quiver
What's the formula for avg power?
midnight haven
I think I get it
we would again take the mean of the initla power and the final power
Ok thanks
.close
pearl pondBOT
pearl pondBOT
✅
oak quiver
Because a is constant the answer would be correct
But the correct method would be
Average power = total work done / total time
midnight haven
Average power = total work done / total time
yup
lethal vigil
Did I setup the integral correctly?
pearl pondBOT
Did I setup the integral correctly?
@lethal vigil Has your question been resolved?
lethal vigil
.close
pearl pondBOT
pearl pondBOT
Available help channel!
pearl pondBOT
spiral pivot
!show
pearl pondBOT
Show your work, and if possible, explain where you are stuck.
wind moss
Question iii
plush bramble
Question iii
did you see this message #help-39 message
plush bramble
pearl pondBOT
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Available help channel!
restive wedge
SHRIMPLE QUESTION
pearl pondBOT
SHRIMPLE QUESTION
restive wedge
sorry for caps
is this just
0 and 1 integral + | 1 and 2 integral|
1/2?
or is it
0 untill 2 inegral
clear moon
regular integral is signed area
so it would cancel out
so yes you'd want to break it up and abs value the integrand from P to Q
pearl pondBOT
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Available help channel!
chilly imp
Anyone know what I do to get an answer for this? V and p are throwing me of a bit
plush bramble
,rotate
ocean hornet
You should get a value for p and a value for k
jolly parrotBOT
ocean hornet
Use the fact that if a+bi=c+di then a=c and b=d
pearl pondBOT
@chilly imp Has your question been resolved?
chilly imp
Use the fact that if a+bi=c+di then a=c and b=d
Oh so
Its
Yeah but where does a=c and b=d come from?
Oh wait
I understand now so its a+bi but instead you have c+di as well?
The only issue is how do you remove the ki and pi? I dont see a way to do it through addition or subbing since they cant get rid of each other w different symbols
I got
-7-3pi=+1-6ki
If anyones interested 😭
ocean hornet
The only issue is how do you remove the ki and pi? I dont see a way to do it thr...
You can factor out the i
Also wait how did you get that
You should combine all the real terms and all the imaginary terms
pearl pondBOT
@chilly imp Has your question been resolved?
chilly imp
You should combine all the real terms and all the imaginary terms
Yeah that's what I tried but I got stuck again on with ki and pi
I wasnt sure how to get rid of them to combine the real and imaginary numbers
chilly imp
You can factor out the i
Oh is that cause i=1? So it just goes away?
ocean hornet
Yeah that's what I tried but I got stuck again on with ki and pi
I wasnt sure ho...
,, 2-3pi - 9 -ki = 4k+1-i
jolly parrotBOT
Bair
ocean hornet
,, -7+(-3p-k)i = (4k+1)-i
jolly parrotBOT
Bair
ocean hornet
,,-7 = 4k+1, (-3p-k)=-1
jolly parrotBOT
Bair
chilly imp
Ah ok I get you now
@ocean hornet thanks a million
I got exams for maths in 2 days, that helped a lot
Now I wont be cooked completely..
ocean hornet
<@367838036647608323> thanks a million
I got exams for maths in 2 days, that hel...
Np, type .close
pearl pondBOT
@chilly imp Has your question been resolved?
steady brook
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Available help channel!
torn lodge
what does a "unique solution" mean in matrices?
pearl pondBOT
what does a "unique solution" mean in matrices?
merry carbon
"There are no others, and if you find another solution, it's actually the same" 
torn lodge
"There are no others, and if you find another solution, it's actually the same" ...
could u give an example of what u mean?
merry carbon
If $A$ is an invertible square matrix then the \emph{only} solution to $A\mathbf{x} = \mathbf{b}$ is $\mathbf{x} = A^{-1}\mathbf{b}$, in which case that's a unique solution as there are no others
jolly parrotBOT
@merry carbon
merry carbon
Whereas e.g. if I take the matrix $A = \pmqty{1 & 0 \ 0 & 0}$ then both $\mathbf{x} = \pmqty{0 \ 1}$ and $\mathbf{x} = \pmqty{0 \ 69420}$ are solutions to $A\mathbf{x} = \pmqty{0 \ 0}$, so there is not a unique solution in that case
jolly parrotBOT
@merry carbon
merry carbon
third time lucky 
torn lodge
ohhh btw the x values can be found by inversing A or?
merry carbon
if A is invertible, you can, but if it isn't, no 
torn lodge
if A isnt invertible then how are the x values found?
merry carbon
e.g. Gaussian elimination
torn lodge
e.g. Gaussian elimination
hmm i dont think ive learnt how to do that but ill keep it in mind, tysmm tho!
.close
pearl pondBOT
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undone pond
I’m trying to answer part b however I’m getting a wrong answer. I don’t know where im making the mistake
pure rapids
hi
pure rapids
so u completed the square alr
undone pond
As to where I’m making the mistake
pure rapids
hmm
undone pond
Yeah I completed the square to find the equation of the circle in order to substitute the equation of l inside of it and find point p and w
Q
And to find the tangents of point p and q I just done the normal formula but I’m getting the wrong answer according to my text book I tried this multiple times but I don’t know what I’m doing wrong
pure rapids
And to find the tangents of point p and q I just done the normal formula but I’m...
idk what formula is
i just do math without memorising too much frfr
aiyo
undone pond
Ohh okay bro it’s y2-y1 divided by x2-x1 to find the gradient
pure rapids
Ohh okay bro it’s y2-y1 divided by x2-x1 to find the gradient
i know
undone pond
Yeahh
pure rapids
fr just sub it in
then 2 sols
one negative one pos
we have the grid axis as the reference
pearl pondBOT
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Available help channel!
gusty thorn
who here has chegg premium
pearl pondBOT
who here has chegg premium
pure rapids
what
gusty thorn
gusty thorn
yo
pure rapids
tf chegg premium
gusty thorn
i dont got that bro
pure rapids
💀
gusty thorn
chegg premium got the answer
versed mica
tf chegg premium
you pay for homework answers
pure rapids
you pay for homework answers
ah
gusty thorn
i can but i dont want to buy it
since theres this server here
i am asking for someone cuz this server isnt helping out
pure rapids
you could just send the question
versed mica
i can but i dont want to buy it
it’s all good man everyone’s in different positions
pure rapids
ppl would answer if you did first time
gusty thorn
i bought too many coc passes
pure rapids
other than 'chegg premium'
gusty thorn
i cant afford chegg
versed mica
i bought too many coc passes
gold pass fire though
versed mica
ahh damn don’t tell me you bought the hammer jam packs
versed mica
i’m th16 bruh
versed mica
you would not
pure rapids
very related to math
versed mica
bro you edrag spam
gusty thorn
once m yqueen gets upgraded though
nah i am like albert estien on that
fr though how u do this
i been procastrinating my chem exam studying with this
for last 3 hours
versed mica
you’re in calc yea?
gusty thorn
i dont even really need this either but icant
yea
i dont wanna skip it without knowing how to do it
gusty thorn
chatgpt but i can give u the formulas
ik how to do it but the problem is one isnt bigger than the other
and one of them is negative
and i havent seen any of these kinds of problems before
what we doing @versed mica whats the game plan
versed mica
is this what your teacher gave you?
static latch
I’m trying to prove (3)
pearl pondBOT
I’m trying to prove (3)
static latch
No matter what I do they all equal to 0, but I can’t prove the limit does exist either
I only learned to prove it dne
😭
I’m looking at 3 by the way
question 3
sharp vigil
how did you get that for the limit with x = 0?
wait nvm i was looking at q4
have you tried any other paths than x = 0, y = 0?
static latch
Ya I tried other paths. But sin(whatever) always equal to 0
Because both x and y is 0
sharp vigil
i would recommend trying some path that would allow you to simplify the denominator
static latch
Even if I simplify detonator if sin keeps going to 0 the final limit still results in 0
static latch
i would recommend trying some path that would allow you to simplify the denomina...
Please expand on that 😭
sharp vigil
you can pick any path going through (0,0)
for example x = f(y) or y = g(x) for any function f, g which pass through the origin
static latch
Yes I tried many😭
sharp vigil
such as?
sharp vigil
remember that 0/0 is an indeterminate form
sharp vigil
so you can get a limit in the form 0/0 which is not 0
sharp vigil
well 0/0 is indeterminate meaning we haven't solved it yet, not that we can't solve it
sharp vigil
if we can show this path limit exists and is not 0, then that would show the overall 2D limit DNE
static latch
Yes
That’s what I’m trying to do, but can’t
Please, no more puzzles, what can I plug in so it’s not 0?😭😭😭
sharp vigil
so we are considering [ \lim_{x \to 0} \frac{x^2\sin^2(x)}{2x^4}]
jolly parrotBOT
cloud
static latch
Ya
sharp vigil
this is a one variable limit so you can use all of the techniques you have used for one variable limits before
static latch
Even if I cancel it out, sin(0) is still 0
I would still get 0
Which doesn’t prove it dne since other substitutions also gets me 0
sharp vigil
ok so what simplification can we perform?
sharp vigil
does the limit [ \lim_{x \to 0}\frac{\sin^2 x}{2x^2} ] remind you of any famous limits?
jolly parrotBOT
cloud
static latch
Not in my knowledge 🥸
sharp vigil
what if we rewrote it as [ \frac 12 \lim_{x \to 0}\ab(\frac{\sin x}x)^2 ]
jolly parrotBOT
cloud
