What advice☠️
#help-23
spiral crescent
final loom
btw for the "what's wrong" part, I'd say you probably fucked up the 
part
flat frigateBOT
Arya
final loom
or $(x + 4)(2x + 17) > 0$
flat frigateBOT
Arya
final loom
Ah, I see.. 👀 I wonder how you went from [ 2x² + 25x + 68 > 0 ] to [2x² - 8x - 17x + 68 > 0 ] 👀
what's with the sudden sign change?
final loom
👀
spiral crescent
I was trying to speedrun a lot of these
final loom
What advice☠️
oh that's ... from the start, the question says: $$2(x + 4) > \sqrt{(x + 4)(2x - 1)}$$ but you clearly know that $\sqrt{\text{anything}} > 0$ so you're given that $x + 4 > 0$ so, $2x - 1 > 0$ should also be true
flat frigateBOT
Arya
final loom
and so, $x > 0.5$ must be true
flat frigateBOT
Arya
spiral crescent
with exceptions of x = -4 / 0.5
WHat is this
final loom
👀 trivial solutions to the inequality if the inequality sign was ≥
but the question only asks for >, so the solution set will be concurrent only with x > 0.5
spiral crescent
👀 trivial solutions to the inequality if the inequality sign was ≥
Can you speak in easier terms, i dont remember what trivial solutions were, we only learnt them while doing determinants and that was like 2 months ago☠️
spiral crescent
but the question only asks for >, so the solution set will be concurrent only wi...
Are u saying why i took greater than equal to and not greater than
final loom
$2(x + 4) > \sqrt{(x+4)(2x-1)}$ and not $$2(x + 4) \geq \sqrt{(x+4)(2x-1)}$$
flat frigateBOT
Arya
final loom
so, the solution set won't contain $x = {-4, \frac{1}{2}}$
spiral crescent
Yes
flat frigateBOT
Arya
spiral crescent
Yes
final loom
can you do the question again now?
spiral crescent
Why would i do the question again what
final loom
Why would i do the question again what
lmao, didn't you get the answers wrong? you won't do it again?
spiral crescent
lmao, didn't you get the answers wrong? you won't do it again?
Im doing the part where i messed up the signs
Not completely from fresh
final loom
oh great !! good luck !!
spiral crescent
that were your only two mistakes in the solution
Wait
Why 2 mistakes👿
Wont those not come in the solution with the intersection eventually?
final loom
one was the sign change from plus to minus, and the other was including {-4} and {1/2} in the solution
spiral crescent
one was the sign change from plus to minus, and the other was including {-4} and...
But that{-4,1/2} only came cuz of the wrong calculation on the left part
Wait let me do it
spiral crescent
one was the sign change from plus to minus, and the other was including {-4} and...
Also 1/2 is there in the solution ☠️
According to the solution answers for the excercise at least
Yes whats wrong with 1/2 if we put it we have
2(1/2+4)> 0
👿
spiral crescent
Thanks i didnt have to do a through checking of these
Also finished 3 days of hw in one day
Thanks
.close
safe radishBOT
final loom
Also finished 3 days of hw in one day
that was all coz of me? 🙀 geniusu me 
safe radishBOT
Available help channel!
iron lintel
what could be another formula to write on these figures?
i have:
iron lintel
woeful plume
That's it! That's the formula for the triangular numbers
iron lintel
ahh but for my practice task it says i have to find another way too :(
i was thinking if it was possible to simplify or change it so it would still work
n^2
or something
woeful plume
Another way to get the formula, or another formula in itself?
iron lintel
another formula i guess that would work for the triangular numbers figures
wintry musk
well
woeful plume
I guess you could write it as a sum...? But that's the same thing as the above equation
wintry musk
i can see 1 way if u want to use like $a_{n +1} = a_{n} + \text{something}$
flat frigateBOT
madlor
stoic dust
safe radishBOT
quasi bison
inscribed angle theorem
an angle inscribed in a circle equals half the arc upon which it rests
and here your angle rests on an arc that is half the circle
safe radishBOT
@stoic dust Has your question been resolved?
stoic dust
and here your angle rests on an arc that is half the circle
wdym by half the circle?
could u show visually?
stoic dust
yes ik thats what im trying to understand tho
how to tell whether it is 90 deg or not
lean otter
idk how to word it but like
ok wait
so we learnt
angle formed at center is 2x the angle at circumference
so u see the angle formed at the center is 180
thus 90 at the circumference
stoic dust
thus 90 at the circumference
isnt symmetry relevantr?
@quasi bison so is it 90 degrees?
.close
safe radishBOT
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Available help channel!
abstract kayak
so for the first question, am i meant to sub in 1000cm^3 and 8 into the equation V= LWH?
safe radishBOT
so for the first question, am i meant to sub in 1000cm^3 and 8 into the equation...
abstract kayak
safe radishBOT
@abstract kayak Has your question been resolved?
abstract kayak
<@&286206848099549185>
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@lean otter Has your question been resolved?
raw tusk
Jack is going to cut an A4 paper so that it becomes a rectangular prism. He want's the rectangular prism to have the biggest surface area as possible. What will the lenghts of that rectangular prism?
safe radishBOT
Jack is going to cut an A4 paper so that it becomes a rectangular prism. He want...
raw tusk
Btw, we want to lengths to be integers and not fractions
This is a difficult approach to me, since there are endless way you could find lengths to an A4 paper, which has the lengths of 210 x 297 mm, aka 62 370 mm^2
What I know is that you should factor out 62370 into 3 factors, but this is again a pain to do, considerin the amount of possible factors you have
safe radishBOT
@raw tusk Has your question been resolved?
valid crow
having evaluated the following limit using the epsilon delta definition: $lim_{x \to 0} x^2=0$ is this evaluation correct? I'm afraid I missed up something in the absolute values.
I started with: $|x^2| \le \epsilon \implies x^2\le \epsilon \implies x \le \sqrt{\epsilon}$ choose $\delta(\epsilon)=\sqrt{\epsilon} \ |x| \le \sqrt{\epsilon} \implies -\sqrt{\epsilon} \le x \le \sqrt{\epsilon} \implies \epsilon \le x^2 \le \epsilon$ but here I got $x^2=\epsilon$ not $|x^2| \le \epsilon$ Any ideas?
safe radishBOT
having evaluated the following limit using the epsilon delta definition: $lim_{x...
flat frigateBOT
planeboi
shy temple
having evaluated the following limit using the epsilon delta definition: $lim_{x...
-sqrt(eps) <= x <= sqrt(eps) does not imply eps <= x^2 <= eps. It implies 0 <= x^2 <= epsilon.
Anyway, you don't need all that. Just square the original |x|<sqrt(epsilon)
fleet chasm
I have
D1:(x,y) = (-1,3) + t(2,1)
D2:(x,y)= (1,a) +k(1,b)
I need to find the a,b values so D2 so it is the same as D1 and also, the intersection point and of the x axis
fleet chasm
I have found that d(D1,O) = 7/sqrt(5)
so D1 is also: x-2y+7=0 in cartesian form
but I am lost for the rest
sharp island
What do you mean that D1 is the same as D2?
fleet chasm
the answer is a=4 and b=1/2 so I think it is asking for the a,b values where both equations are equal
sorry it is french so I am trying to translate it at the same time
sharp island
That's alright
Yeah, that seems reasonable, so would you like an explanation of how they got that?
fleet chasm
yes that I am lost when they asked the a,b value then to find the intersection point
sharp island
Oke, so to get the values of a and b, what I would get first is the position vector (1,a). So we know that this must give a point on D1, therefore we should find what value of t gives the point with an x coordinate of 1. So -1 +2t = 1, this gives t=1
Now we can find the value of a by calculating the y coordinate of this point again from D1, 3+ 1×1 =4, therefore the y coordinate is 4 of the point with x coordinate 1
Now we have the position vector of D2, we just need to get a vector in the same direction as D1, for this we need a vector which is some scaled version of (2,1) which has an x coordinate of 1, this must mean (2,1) has been scaled down by a half, so b must be 1/2
Is that alright?
sharp island
So the second row of D1, the row corresponding to y coordinate is
fleet chasm
y=3+t?
sharp island
Yes
And we found that t is 1 so y is 4
The 1×1 is just the value of t times the 1 in the vector
sharp island
Well if they are the same line, then they share every single point so this confuses me a bit
Does it mean where they intersect with the x or y axis?
fleet chasm
I think I translated it poorly
Let me rephrase
Find a point of intersection of the D1 and the x axis
sharp island
So if it intersects the x axis, what will the y coordinate be?
sharp island
Not quite sure why you are finding a distance here. Basically the point of intersection with the x axis must have a y coordinate of 0, therefore, we can find the value of t for which this occurs (we can use D1 or D2, they are the same), and then use that value of t to get the x coordinate
fleet chasm
so in the example of D1, I would say D1: x-2y=-7 and replace y by 0?
sharp island
Oh, have you converted it to just a normal straight line equation without the parameter t? That works too, and you can get the value of x directly by doing that
fleet chasm
Well I didn't understand with the t unfortunetly so I thought of this way
sharp island
That's no problem, you are actually doing the exact same thing, but the y=0 gets substituted at a later point in your method
fleet chasm
alright thank you so much 🙂
sharp island
No problem at all!
fleet chasm
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pastel abyss
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Available help channel!
spiral crescent
safe radishBOT
spiral crescent
are the answers- no, yes, no?
spiral crescent
how would you justify your answers?
for the first answer if a-b=c and a,b are natural numbers, if b is greater than or equal to a, then we get a zero or negative number, so not a natural number
merry sleet
yes
spiral crescent
for the second i just cudnt find any contradictions💀
merry sleet
just a tip for counter examples just take a concrete example
in this case
1-2 =-1
which is not a natural number
spiral crescent
for the third, i just wrote 9/12 is not natural number
merry sleet
for the second i just cudnt find any contradictions💀
thats not a proof, here its harder because you have to prove that its right for any two natural numbers that their product is also one
first what is the definition of a natural number?
spiral crescent
first what is the definition of a natural number?
numbers 1,2,3,4,... numbers which can be used to count objects and people etc.?
merry sleet
in what grade are you?
spiral crescent
in what grade are you?
12th, this wass the definition given in the book💀
merry sleet
ok
yeah i would have expected a better definition att this level tbh
i guess then you dont have to justify that much and just state your answers
spiral crescent
i guess then you dont have to justify that much and just state your answers
if you are talking about the maths chapter involving proofs and those stuff, that isnt done in school or tuitions here
merry sleet
oh yeah ok
spiral crescent
even this chapter that ive started today is only in one of the entrance exams here, not in most
merry sleet
just say no yes no then
spiral crescent
just say no yes no then
if you want to tell me the in depth proof im ready to listen
merry sleet
well how you usually define a natural number is this way:
you state that 0 is a natural number
and then yopu have an operation called "successor"
and for each natural number
the successor of this number exists and is a natural number
so
natural numbers are:
0
S(0) (successor of 0)
S(S(0))
S(S(S(0)))
but for simplicity's sake
we call them
0
1
2
3
.....
spiral crescent
where does the part come where u say 0 is not a natural number
merry sleet
it is a natural number tho in most definitions
but you could do the same and start at 1
spiral crescent
it is a natural number tho in most definitions
really in most books that ive seen, it comes into whole numbers?
spiral crescent
but you could do the same and start at 1
makes sense
spiral crescent
and so what would be the indepth proofs for b and c?
merry sleet
so a natural number is essentially something that can be expressed as the successor of 0 enough times
for c, your proof is good you gave a counter example
so if you have the product of a and b to natural numbers
a*b = a+a+ ...... +a (b times)
and adding a is doing the successor operation a times
spiral crescent
b times?
spiral crescent
2*3 = 2 + 2 + 2
we can also write this as 3+3 right? i am aware that it is read 2 times 3 so we are writing 2+2+2
merry sleet
yeah
spiral crescent
and adding a is doing the successor operation a times
i mean here should be b times
merry sleet
oh
hgere i'm talking about
a+a
or c+a
to do c+a
you take c
and do the successor operation a times
so c+a is still something of the form S(S(S(......S(0).....)))
so a*b can be expressed as an addition
and any addition of two natural numbers is of the form S(S(S(......S(0).....)))
so a*b is of the form S(S(S(......S(0).....)))
so its also a natural number
spiral crescent
to do c+a
here a is written as the successor operator a times?
just the a part i mean
merry sleet
a is a natural number
so you can write it using digits
or you can use the successor operation
to describe it
spiral crescent
so if 1 is a natural number, and if 0 is ur starting value for natural numbers, isnt 1 the successor operator 1 time?
spiral crescent
but if 1 was the starting value wudnt it be the successor operator 0 times?
merry sleet
you state that 0 is a natural number
as i did here for 0
spiral crescent
but wudnt we need to state
0 is the first natural number?
or 1 is the first natural number
merry sleet
its already stated in a way
0 is the only one that is the successor of no natural number
that means its the first
in a certain way
you can compare natural numbers using successors
like a>b
if a= S(S(....(S(b))....))
spiral crescent
0 is the only one that is the successor of no natural number
but that is if u define -1 to be the predecessor non natural number which is true, but what about the people who say 0 is the first non natural number, for them wudnt 1 be the only one that is the succesor of no natural natural?
natural number*
merry sleet
the limit is that we dont define negative numbers this way
you can notice that i only defined natural numbers
and not other numbers
to get whole numbers its another construction that stems from this one
to state it simply: any set of numbers that follows the rules i stated
is "like" the natural numbers
but you can add other definitions
to add other numbers
here i just did the basics
spiral crescent
so a*b is of the form S(S(S(......S(0).....)))
alright
merry sleet
to make the proof about
multiplication
if you want to dig deeper
what i talkied bout is called peano arithmetic
or peano axioms
spiral crescent
or peano axioms
ok ill search probably by the end of tomorrow
i have another question btw
merry sleet
go ahead
spiral crescent
here its said power has to be greater than equal to two, but is it talking only abt integer values, or can it also be fractions greater than two like 4^5/2 as long as we have an integer as the final value?
merry sleet
well for some advanced reasons if n is a natural number, and a is not
n^a is not a natural number
unless n i s0
or 1
spiral crescent
well for some advanced reasons if n is a natural number, and a is not
what advanced reason
merry sleet
well i would have to explain to you what is the definition of a power of a real number
like do you know what 2^3.7 means?
or 2^pi
?
spiral crescent
like do you know what 2^3.7 means?
2^(37/10)?💀
spiral crescent
yes
merry sleet
but you cant do this definition with non natural numbers
you cant multiply 2 by itself 3.7 times or pi times
spiral crescent
but you cant do this definition with non natural numbers
without exceptions?
merry sleet
without exceptions
spiral crescent
ok can you explain why the example 4^(5/2) wont be a natural number
is it something to do with a given statement?
spiral crescent
so do you know what the exponential is?
i can solve inequations and equations involving them, i know the graphs for it as well, but we havent started functions yet as we are doing a final revision of the pre requisites before going in
merry sleet
i'm sorry its too deep then,
i dont want to do a lecture on this
https://en.wikipedia.org/wiki/Exponentiation try to look at this
spiral crescent
here its said power has to be greater than equal to two, but is it talking only ...
so then its only for natural number powers greater than equal to 2?
merry sleet
yeah
like anyways
only natural number powers make sense
at the level of your class
spiral crescent
alright thanks, ill look into those two things when im free
spiral crescent
at the level of your class
we have negative powers and fractional powers as well
but that is something any high school student has
merry sleet
oh ok
spiral crescent
.close
orchid rapids
@lean otter come here
safe radishBOT
<@456226577798135808> come here
tall bough
<@456226577798135808> come here
show your work
fading raft
oh this should be interesting
orchid rapids
show your work
tall bough
ever heard of helmholtz decomposition?
orchid rapids
ok so, here, u want to find the area of the triangle and multiply it with the length of the pyramid
orchid rapids
some jee advanced topper stuff
tall bough
ys
undone umbra
Cool question
orchid rapids
?
tall bough
nice triangle
orchid rapids
im not sure how this helps
tall bough
you solved it?
fading raft
bro this is cheat
tall bough
whats the answer
lean otter
some jee advanced topper stuff
Where
tall bough
you sur
you sure
it was 2?
how can the volume be lower than the base, height and length
whats the formula of the area of a traignle
gogole it
undone umbra
I like to think of it like this, we got the height of the triangle, we got the base of it, so we got the face of the front of triangle
But we want to find the volume so like in the 3D image we drag the face of the triangle along which is the (10 x 9) then multiply by how long it is (10 x 9) x 8.
And the volume would be the answer
Oh we’re long past that stage
Y not?
It’s really simple when you understand it
That’s fair
tall bough
ur going to have an exam about it right?
lean otter
I like to think of it like this, we got the height of the triangle, we got the b...
The area of triangle face won't be 10×9 but half of it
undone umbra
The area of triangle face won't be 10×9 but half of it
No that would be 10 x 9/2
No?
lean otter
Yes ok right I was wrong
undone umbra
I swear that was a thing
tall bough
Still we dont give answer away
undone umbra
If you get the concept it’s easier to remember
lean otter
Grades won't give you anything
Math will give you a lot
undone umbra
Year 8?
tall bough
When asking for help, do not insist on getting just the answer; we are here to help you learn, not do the work for you. Likewise, if you are providing help to others, try your best to explain and elaborate instead of simply giving away the answer.
lean otter
You're in 8th you definitely need Math
undone umbra
What’s 8th?
Even construction workers use math
Math is basically a requirement for everything
Bro it’s volume
tall bough
architecture? engineering?
undone umbra
I feel like engineering would use volume a lot
tall bough
tbh if u just spend 10 minutes studying that topic, u will be easily be able to do it
fading raft
this is important math you need to learn before your jee exams bro
lean otter
You will use it
It's just that you don't see common people using it outside of their profession beacause they simply never understood it and rote learned it
undone umbra
😶
tall bough
@lean otter Do you want to get help or you just want the answer?
Then sorry, we can't.
No, you may close the channel if you don't want help.
undone umbra
You learn from the process not from the results
Volume = width x length x height
Use the formula triangle from science to rearrange if ur stuck
The height
tall bough
height
lean otter
No
lean otter
Bruh the area of triangle
tall bough
^
lean otter
Not units
tall bough
wbh is for 3d rectangle
tall bough
yess
undone umbra
Wtf
flat frigateBOT
tall bough
lol
undone umbra
its (b*h*l)/2
I’m ashamed of myself
tall bough
its not 21.5 fella
well you get it, it seems all th questions are about the volume of the same object
lean otter
I thought this channel was only for above 13 y/o's
safe radishBOT
@orchid rapids Has your question been resolved?
south moat
I'm trying to calculate the probability of winning 7 games in a row with a 50% win rate while being able to lose one game for free (mercy).
I understand that to calculate it without a mercy game is simply .5^7 or 0.78%. But I don't know where to start when trying to include the free game. I think it has something to do with 8 games instead of 7 games and thought maybe I would just multiply the the base probability by 8/7 but I'm not sure if that's correct.
Thanks 🙂
safe radishBOT
I'm trying to calculate the probability of winning 7 games in a row with a 50% w...
@south moat Has your question been resolved?
south moat
<@&286206848099549185>
safe pelican
im not a helper but these are my thoughts. You must play 7 total games (not eight) but you only have to win 6 of the seven games because you are allowed to lose one game…
south moat
im not a helper but these are my thoughts. You must play 7 total games (not eigh...
No, 7 games must be won, but you're allowed one loss
so it's at least 7/8
safe pelican
Gotcha, I haven’t taken statistics so im lost now lol... Is this a problem from a textbook? If it is, I can try to find a step by step solution on quizlet
south moat
Gotcha, I haven’t taken statistics so im lost now lol... Is this a problem from ...
no 😭
safe pelican
darn. i wish i coulda helped more. best of luck to you tho!!! 🙌🏻
safe radishBOT
@south moat Has your question been resolved?
south moat
darn. i wish i coulda helped more. best of luck to you tho!!! 🙌🏻
thanks anyway I appreciate it!
safe radishBOT
@south moat Has your question been resolved?
fiery merlin
I'm trying to calculate the probability of winning 7 games in a row with a 50% w...
There's one instance where you have 7 wins in a row and also seven instances for which of the 7 wins the loss is before.
You add the probabilities of all eight instances together.
south moat
ooh
fiery merlin
Sorry, 7 wins in a row with no losses.
Or you can do it a simpler way.
There are 9 relevant outcomes for the first 8 plays: ```
WWWWWWWW
WWWWWWWL
WWWWWWLW
WWWWWLWW
WWWWLWWW
WWWLWWWW
WWLWWWWW
WLWWWWWW
LWWWWWWW
And there are 2⁸ total outcomes.
So, 9/2⁸.
This only works when each outcome is equally likely, which is the case here, since both wins and losses are 50%.
south moat
I'm trying to wrap my brain around this so I can do 5 wins on my own lol
south moat
So 3 wins would be, WWWW, LWWW, WLWW, WWLW, WWWL
so 5/2^8
oh 1 win would be W or L or 1/1^1
south moat
oh
delicate aspen
sorry
for 3 wins
you could WWW (succeed)
WWLW
WLWW
LWWW
those are the possible successes
what are the possible failurs?
WWLL
WLWL
WLL
south moat
oooh
south moat
so 2^X where X is the number of games played (aka target consecutive wins+1)
and the numerator would be how many combinations that succeed
so 5 would be WWWWW, LWWWW, WLWWW, WWLWW, WWWLW, WWWWL
or 6/2^6
does that look right?
nope it doesn't
hang on
lol
WWWWWW, LWWWWW, WLWWWW, WWLWWW, WWWLWW, WWWWLW, WWWWWL
7/2^6 would be 5 in a row
or 10.9%
delicate aspen
what is the probability of winning 1 game with a mercy?
south moat
that would WW, WL, LW
so 3/2^2
75%?
delicate aspen
i disagree
1 game with a mercy
either you win the first
W
lose the 1st, win the 2nd
LW
or fail, LL
delicate aspen
so 2^X where X is the number of games played (aka target consecutive wins+1)
you are failing to take into account the possibilities that get cut short because you lost twice early
delicate aspen
i highly recommend that you start with smaller numbers and build up until you see the patter
*pattern
mint bloom
I need to simplify these, would love some help!!
safe radishBOT
I need to simplify these, would love some help!!
lilac patio
I need to simplify these, would love some help!!
General rule, $$x^a+b=x^a*x^b$$
flat frigateBOT
Arctic
lilac patio
yes
mint bloom
that’s the answer right?
lilac patio
yea
mint bloom
How did you apply the rule
lilac patio
What rule
mint bloom
The general rule
mint bloom
General rule, $$x^a+b=x^a*x^b$$
This one
mint bloom
Aha, sorry
lilac patio
if there's two terms in an exponent
You can split it
any amount of terms in the exponent you can split it
mint bloom
Yes and then?
lilac patio
then you have a negative exponent
Have to simplify that
x^-5 is 1/x^5
oh wait
I just realized that whole thing is a
mint bloom
I mean there’s more to it rather than only x^2k-5
mint bloom
Ohh LOL
mint bloom
but its the same two rules to do the whole problem
Mhm I get it!
I just apply those rules to it
Thank you
.close
mint flax
would $\dv x \iint f(x)^2\mathrm dx\mathrm dx= \int f(x)^2\mathrm dx$?
flat frigateBOT
gmod
delicate aspen
i think you are missing a chain rule
mint flax
oh really
delicate aspen
i may be mistaken
mint flax
so I would then multiply by 2f(x)f'(x)??
delicate aspen
i have to write it down
final halo
You're correct gmod
mint flax
You're correct gmod
originally?
delicate aspen
you have all the assumptions of continuity and differentiability right?
mint flax
yeah
final halo
originally?
Yes
mint flax
alright so im trying to write $\int f(x)^2\mathrm dx$ in terms of $f(x)$ and $\int f(x)\mathrm dx$ and I keep running into trouble: I started by stating that $$\left(\int f(x)\mathrm dx\right)^2=\iint f(x)^2 \mathrm dx \mathrm dx$$ and then I took the derivative of both sides to achieve $$2f(x)\int f(x)\mathrm dx = \int f(x)^2 \mathrm dx$$ but when I try the example $f(x)=x$ it doesn't work soooooo im assuming I made a mistake somewhere but I cant find it
safe radishBOT
alright so im trying to write $\int f(x)^2\mathrm dx$ in terms of $f(x)$ and $\i...
flat frigateBOT
gmod
mint flax
I dont see why not
lemme show u
$\left(\int f(x)\mathrm dx\right)^2=\int f(x)\mathrm dx\int f(x)\mathrm dx=\iint f(x)^2\mathrm dx\mathrm dx$
stone oasis
that cant be right
mint flax
do u know multivariable calc
stone oasis
yes
flat frigateBOT
gmod
stone oasis
wat?
final halo
You're taking a double integral over the same variable twice
true ingot
Anyone have any idea how to do this?
safe radishBOT
Anyone have any idea how to do this?
true ingot
my brother got this for 7th grade math homework and in my opinion if the teacher actually expects them to be able to solve it she's on something
but it's mandatory
young zinc
largest group? isn't that infinity
true ingot
I would imagine like
true ingot
13 is a prime number lol
that's a bad example
uhh
but yeah
intuitively it makes sense there's a largest number
cause I would assume anything past 10^100 (idk) would have to be some combination of 7,13,25
young zinc
why would that be 💀
true ingot
idk
but like
well if I knew the answer I wouldn't have posted here
but
idk intuitively the premise of the question sounds like there's an answer
young zinc
we need to analyze 7a + 13b + 25c
true ingot
wait
young zinc
and somehow prove that every number after a certain number can be divided by that
true ingot
I found the question
this mf took a grade 12 challenge problem
and made it grade 7 mandatory homework
LOL
young zinc
yeah this doesn't look like grade 7
young zinc
i have no idea either
true ingot
.close
delicate aspen
trying again:
safe radishBOT
trying again:
delicate aspen
is the reasoning here circular? was I supposed to substitute the polynomial expression of f into the uniform norm?
plucky elk
Did you learn Lebesgue's dominated convergence theorem?
I think uniform convergence works too
delicate aspen
Did you learn Lebesgue's dominated convergence theorem?
that has definitely been referenced before in the proofs in lecture
i will look it up
plucky elk
You're essentially swapping the derivative operator and the summation.
delicate aspen
right, or at least trying to say why it makes sense to do so
safe radishBOT
@delicate aspen Has your question been resolved?
sullen jetty
sudden harbor
Hi, i’m in an intro to calculus course and need some help evaluating this graph. the topic is limits.
if x is approaching -2 from both sides, does that mean that the limit is 3 because the limit is defined there? or is it just DNE since the two sides don’t meet? wasn’t getting it when my prof explained.
safe radishBOT
Hi, i’m in an intro to calculus course and need some help evaluating this graph....
quasi bison
or is it just DNE since the two sides don’t meet?
yes
if you want to look at the one-sided limits, from the left it's 3 but from the right it's +∞
sudden harbor
Alright i think i got it. using the graph i sent..if x was approaching 10 it would also be DNE as well?
quasi bison
no
sullen jetty
A simple thing to remember is a function should not have two diff values for one input
quasi bison
the limit of your function at 10 does exist.
sullen jetty
Functions cannot show many to many relationships
sudden harbor
will try to remember that!!
thank you, i’m prepping for a quiz and trying to do some review questions.
sullen jetty
Np ✌️
violet sundial
i think the answer is +/- sqr(3i)
safe radishBOT
i think the answer is +/- sqr(3i)
violet sundial
safe radishBOT
violet sundial
The answer is A right?
@limber patio
this topic is complex numbers
or anyone else else
there is my working
just 1
limber patio
x²=-9
So answer should be complex
trim trench
yes
trim trench
is this your alt?
trim trench
ah sorry
violet sundial
lmao
trim trench
would it be +/- 3i
yes
flat frigateBOT
||𝓚𝓪𝓼𝓹𝓮𝓻||
violet sundial
when i expand it
it is x^2 -9
wait
nv,
nvm
i understand
thank you everyone for the help
i also don't understnad this question
nvm got it
thanks
.close
quaint needle
vapid wasp
What does $z \in i \mathbb{R}$ mean?
safe radishBOT
What does $z \in i \mathbb{R}$ mean?
flat frigateBOT
vapid wasp
is this same thing as Complex set?
regal girder
I assume maybe $i\mathbb R = {ir | r \in \mathbb R}$?
regal girder
only the imaginary parts
C would be in the form a + bi
but again, this was just a guess
quaint needle
Hello
quaint needle
inner nest
.close
safe radishBOT
inner nest
@quaint needle don't use multiple channels
safe radishBOT
Available help channel!
glad frost
Hi guys can anyone help me with my homework, thanks in advance
safe radishBOT
Hi guys can anyone help me with my homework, thanks in advance
@glad frost Has your question been resolved?
glad frost
<@&286206848099549185> sorry for pinging you guys but can anyone help me solve these questions, thanks a bunch
safe radishBOT
@glad frost Has your question been resolved?
cinder viper
@glad frost For the first one, you can try multiplying/dividing by the conjugate $\sqrt{4x^2 - 4x + 2} + (3x + 1)$
flat frigateBOT
Sup?
cinder viper
Second one try factoring
glad frost
<@343905888488390656> For the first one, you can try multiplying/dividing by th...
but then i was left with a spare -x^2 so i ended up with -x * (a bunch of stuff that ends up being 0) so i was wondering is that wrong
glad frost
Second one try factoring
got it, thanks
glad frost
Second one try factoring
with the second is the lim the whole thing or just the (x^2 - x - 6) though?
cinder viper
Whole
glad frost
oh that makes sense
thanks a bunch
also how about turning the (x^2 - 6x +9) into a 1/(x-3)^2, will that also work?
glad frost
what will the factoring result be, though, im having a tough time with it
cinder viper
$\frac{-5x^2 - 10x + 1}{\sqrt{4x^2 - 4x + 2} + 3x + 1}$ is what you should get after rationalizing the first question
flat frigateBOT
Sup?
cinder viper
x^2 - x - 6 = (x + 2)(x - 3)
glad frost
ohhh yeah, thanks
glad frost
$\frac{-5x^2 - 10x + 1}{\sqrt{4x^2 - 4x + 2} + 3x + 1}$ is what you should get a...
wait then after this, should I take away the x^2 from the above and the x from below?
wraith root
Nowadays restaurants throw away a lot of excess food while other people can’t afford it.
This type of app will allow the restaurant to call on the charities that surround their area to donate excess food everyday to homeless
safe radishBOT
Nowadays restaurants throw away a lot of excess food while other people can’t af...
wraith root
anyone can help lol
safe radishBOT
@wraith root Has your question been resolved?
potent roost
Nowadays restaurants throw away a lot of excess food while other people can’t af...
ok?
what is the question
wraith root
How the product solves the problem:
With our application we collect all the remaining and edible food in restaurants rearrange it, pack it and send it to people in need.This app helps people in need to get food and also helps restaurants dispose remaining food, most importantly it decreases the damage done to the environment by all the leftovers restaurants throw away .
It also helps people who need food, they get the food packed from the restaurants for free,and it reduces hunger,which improves the relations between residents.
i have to write 2 questions to ask the person who made the app
potent roost
how does this relate to math?
lean otter
do you have a question even?
what are you gonna do about the legal part? Much of the food is thrown away because of strict goverment's standarts. What if a person gets sick and dies from eating it? Will you or the restaurant be responsible?
how are you gonna pack and send everything fast enough so the food doesn't become spoiled?
wraith root
do you have more ?
i will send you what i wrote
so you dont think iam just taking from others xd
-
How will the app distinguish people who need food?
-
How is that app different from normal packing the food and give it to the people who wants?
3.What if the excessive food can cause disease transmission by the people who ate it to others?
4.Why does the restaurants have to pay some money since the main goal is charitable work?
if you have more pls give
i only need 2 but i want the best 2
@lean otter sorry for mention 😅
lean otter
<@456226577798135808> sorry for mention 😅
idk more and dont really have time to think
haughty sapphire
Hi there, I have a stochastics problem I'm unable to solve
Following scenario:
Imagine a bowl of 10 different kind of balls labeled from 'A' to 'J'. In total, there are 100 balls in the bowl in the following constellation:
25 balls labeled 'A'
22 balls labeled 'B'
13 balls labeled 'C'
12 balls labeled 'D'
10 balls labeled 'E'
6 balls labeled 'F'
4 balls labeled 'G'
3 balls labeled 'H'
3 balls labeled 'I'
2 balls labeled 'J'
Now, we will draw 5 balls, but between every draw, all balls from the respective category that has been drawn will get removed. For example, if a ball labeled 'A' gets drawn in the first round, all balls labeled 'A' will get removed from the bowl. The bowl now only contains 75 balls for the second draw.
The question now is: How do I calculate the probability of each ball actually being picked after 5 draws? How would I go about this?
I think I could bruteforce my way through this by building a stochastics tree diagram; however this quickly gets out of hand considering the amount of possibilities. I don't really know if this would be the way to go, but it seems there must be a better way to get there.
Some help is greatly appreciated 🙂
safe radishBOT
Hi there, I have a stochastics problem I'm unable to solve
Following scenario:
...
@haughty sapphire Has your question been resolved?
haughty sapphire
<@&286206848099549185> Could really need some help on this statistics problem here, thanks so much
safe radishBOT
@haughty sapphire Has your question been resolved?
safe radishBOT
@haughty sapphire Has your question been resolved?
safe radishBOT
@haughty sapphire Has your question been resolved?
young osprey
Hi there, I have a stochastics problem I'm unable to solve
Following scenario:
...
the draw number 5 is based on the other 4 draw you have already done and there are 5040 probability for the the 4 draws if the balls were with the same number
5040x4!
safe radishBOT
safe radishBOT
Available help channel!
viral gate
HELP ME PLS
safe radishBOT
HELP ME PLS
drowsy moss
add up the area of each side
viral gate
so 7x8
drowsy moss
that's the area of one side
viral gate
so how do i get the surface area
drowsy moss
add up the area of each side
you can see 3 rectangles in the image. What is the area of each rectangle?
viral gate
56?
worthy hemlock
The area of each rectangle
drowsy moss
56 is the area of rectangle 1. What is the area of rectangle 2?
viral gate
28?
viral gate
im not sure
safe radishBOT
@viral gate Has your question been resolved?
safe radishBOT
Available help channel!
storm vine
Can someone explain to me how I can get a and b please
safe radishBOT
Can someone explain to me how I can get a and b please
@storm vine Has your question been resolved?
safe radishBOT
@storm vine Has your question been resolved?
storm vine
<@&286206848099549185>
safe radishBOT
@storm vine Has your question been resolved?
storm vine
<@&286206848099549185>
safe radishBOT
@storm vine Has your question been resolved?
marsh walrus
<@&286206848099549185>
were you able to make progress on this?
storm vine
nah
marsh walrus
what have you tried?
storm vine
bro ive been waiting for help man😭😭
marsh walrus
bro ive been waiting for help man😭😭
this may help at least get an idea of whats going on
can you tell which two points we need to go through?
storm vine
well we have the limits pi/6 and pi/3
storm vine
so what i was assuming is that
the trapezium is a result of a revolution so could u say that acos^2(pi/6)=1
storm vine
i think we should ignore the curves icl
i think since the handle has been revolved around, that 2cm distance PQ is actually a diameter idk if im making sence
so i think we can halve it and say that acos^2(pi/3) is equal to it
marsh walrus
oh, i see what you mean, i think
so the beginning x coordinate must be 1
this corresponds to the lowest value of theta plugged into that function
let me see
marsh walrus
the trapezium is a result of a revolution so could u say that acos^2(pi/6)=1
i believe that cos^2 theta is decreasing over the given interval
then we want the latter bound
as long as we let a>0 this should be true
so the point "starts at" R and goes to Q along the parameterization
storm vine
oh i think i was assuming that this trapezium was on a polar graph
wait no nvm ignore what i typed
storm vine
this is what i was thinking
marsh walrus
ok
storm vine
if we were to plot this on a graph
and make a half line at pi/3
hmm wait i dont think we can do this can we
marsh walrus
i dont think this is the way that the parameterization is being done
theta is a parameter, its not passed directly to the graph
it moves through functions
well, the point moves through theta
but on a cartesian graph
thats my impression
storm vine
ahh man
marsh walrus
i am explaining it poorly and making it sound more complicated
storm vine
the thing is we are given the theta limits but this question is worded hella weird lowkey
marsh walrus
try to imagine instead of theta
its t for time
so instead of being given a segment of a graph
you are being given a start point, an end point, and the direction you draw the curve in
so instead of just having a range of values, instead you have like
a mapping that defines how the point of the pencil moves on the plane
idk if that helps 
your idea for solving this is very good
i think it will lead us to the solution 
cos^2 t at p/3 is 1/4
cos^2 t at p/6 is 3/4
so it seems to me that we want the pi/3 one to be making that radius 1
like you said
meaning a would be 4
seem reasonable?
storm vine
yeah
marsh walrus
im just trying to extrapolate ur suggestion
storm vine
if we use pi/6 we get four too so i think what i was saying might be leading to smthn
marsh walrus
so a looks good 
it goes from 1 to 3 along x
which tracks with our two radii
of 1 and 3
we just need to repeat this process for b
storm vine
i dont think we do it the same for b right
since the height isnt being revolved we cant just set it up like that i think it should be smthn like
btan(pi/3)-btan(pi/6)=2
marsh walrus
sure, that works
i think alternatively since you only have one degree of freedom
either way works
unless the problem has no solution
but a geometric way of approaching it is maybe better
oh, wait, i see what youre saying
yea youre right
marsh walrus
come to think
you could probably have done this in a system
if youre into those
since all the functions collapse into constants
it would have just been a matter of arranging it correctly
then RREF and pow
anyways, you think youre set?
or ping if u want more help
storm vine
yhh im chilling now
marsh walrus
storm vine
how do i close this
marsh walrus
.close
safe radishBOT
marsh walrus
np 😊
safe radishBOT
Available help channel!
mild mulch
Hey
mild mulch
Here’s what I did
i dont understand how u got dy/dx = (-sin(sqrtx)) / 2sqrtx
because if y = cos(sqrtx) then dy/dx is just -sin(sqrtx) no?
safe radishBOT
@mild mulch Has your question been resolved?
lean otter
Is this the basis of a diagonal matrix nxn?:
safe radishBOT
Is this the basis of a diagonal matrix nxn?:
lean otter
.close
safe radishBOT
timber schooner
before i ask my question ill send an image to tell u what im working on
safe radishBOT
Available help channel!
timber schooner
here is the image
safe radishBOT
here is the image
timber schooner
basically i am trying to find a better way to represent that number in the bottom maybe as a fraction connected to some other mathematical constant
how do I do that?
supple ore
basically i am trying to find a better way to represent that number in the botto...
What accuracy?
timber schooner
exact
timber schooner
What accuracy?
exact accuracy
supple ore
exact accuracy
I feel like that requires being able to find the indefinite integral
timber schooner
the number on the bottom w is the limit of the lower bound that still allows the integral in the middle to have a definite answer, it is a decimal expansive number
the bottom number does not include all of the possible digits
safe radishBOT
@timber schooner Has your question been resolved?