For 6 I think they're referring to the entire picture?
#help-0
clever folio
idle minnow
Ohh yesss
clever folio
Also 3 and 4 are done?
idle minnow
no?
clever folio
Yeah the whole thing is the coordinate system
idle minnow
ye
clever folio
The axes/grid specifically I guess
idle minnow
I only have the answers for 5,6,1,2
clever folio
3 was just coordinates, they are pairs (x,y)
It's referring to the box next to A (3,2) which is a coordinate as far as I can tell.
clever folio
idk which german word in your list was line but it should be line
Then yeah 7 should be route because it's trying to illustrate how to GET to the point A (3,2)
clever folio
Okay, I need to go do hw and stuff but you can post them here and somebody will help.
clever folio
You can ping helpers after 15 mins if nobody sees your q too
idle minnow
Question: how do you measure an angle Arrange the substeps with numbers
1 answer: I move the triangle so that the center is at the apex
2 answer: I read the value on the other leg
3 answer: I put the set square with the long side on a leg
(I have to choose 1 of it for this question)
.close
zenith lichen
Why does the prime factorization method for finding the LCM between two numbers work? Whats the reason behind reducing the factors/only counting factors once if they appear twice?
prime badge
12267 is divisible by 87
or in prime factors, 3×3×29×47 is divisible by 3×29
and you get 3×47
you drop the prime factors in the denominator from the numerator, and that's division, and it's not divisible iff you can't do that
prime badge
Why does the prime factorization method for finding the LCM between two numbers ...
right?
zenith lichen
Im sorry Im having some trouble understanding what you mean, could you clarify please?
lone heartBOT
@zenith lichen Has your question been resolved?
lunar trail
I'm trying to come up with a formula, and would love to get help in working out how to go about it. I wrote up some sample data for what I'm trying to achieve in a code pen link which I can share. (not sure if I'm allowed to post links), or I can paste all the information straight into discord. I'd imagine someone with some Calculus knowledge would be able to wrap their heads around the problem fairly quickly.
abstract fractal
What do you need a formula for
lunar trail
For a program I'm trying to write.
abstract fractal
What does the formula need to do though
lunar trail
oh this is my own channel now right?
ok I'll paste everything here
/*
* Input Data
*
* Setup:
* fractions are allowed
* market: x (left) y (right)
* 1 unit price = x/y (or) y/x
* x * y = k (constant)
*
* (reversible)
* To determine the amount of x units needed to buy y, we must do
* x = k/(y - amount)
*
* (reversible)
* To determine how many units of y (z) an amount of x can buy, we must do
* z = k/(x + amount)
*
* k = (z-y) * (x + amount)
*/
const inputData = [
{
market: 'Apple-Banana',
x: 500,
y: 300,
fee: .05 %
},
{
market: 'Orange-Pear',
x: 100,
y: 600,
fee: .03 %
},
{
market: 'Potato-Apple',
x: 500,
y: 500,
fee: .01 %
},
{
market: 'Banana-Orange',
x: 500,
y: 900,
fee: .08 %
}
]
/*
* Desired Output Data
*
* priceFactor needs to be determined equal value comparison between all assets (is this even possible?)
* scalabilityFactor needs to be determined base on availability (k). The higher the availability, the less "price slippage"
*
*/
const outpuData = {
Apple: [
{ market: 'Apple-Banana', priceFactor: null, scalabilityFactor: null },
{ market: 'Potato-Apple', priceFactor: null, scalabilityFactor: null }
],
Banana: [
{ market: 'Apple-Banana', priceFactor: null, scalabilityFactor: null },
{ market: 'Banana-Orange', priceFactor: null, scalabilityFactor: null }
],
Orange: [
{ market: 'Orange-Pear', priceFactor: null, scalabilityFactor: null },
{ market: 'Banana-Orange', priceFactor: null, scalabilityFactor: null }
],
Pear: [
{ market: 'Orange-Pear', priceFactor: null, scalabilityFactor: null }
],
Potato: [
{ market: 'Potato-Apple', priceFactor: null, scalabilityFactor: null }
],
}
So in english, I'm trying to write a formula that can give me 1 measurable/comparable "price factor"
I'm not entirely sure if what I'm after is possible, but this formula would be the first step in balancing out this.. "farmer's market"
the complications come in the fact that there's not a common currency that can be used, as it's a market where you trade in produce only, so for example, if you want to buy bananas, you need to have either apples or oranges to trade with
lone heartBOT
@lunar trail Has your question been resolved?
lone heartBOT
@lunar trail Has your question been resolved?
blissful epoch
lost jungle
okay so you use rational root theorm right
white crown
solar maple
Check your formula
lone heartBOT
lone heartBOT
Available help channel!
fleet dragon
Hello! Can someone please help me figure out what I'm doing wrong in calculating the number of 3-of-a-kind poker hands?
fleet dragon
I know what the answer should be but I'm not sure where my logic is flawed
So let's say I want to first get my 3-of-a-kind, and then get my other two cards. There are 52 cards I can choose for my first card. Whichever I choose, there are 3 ways for my next card and 2 ways for the third card, for that to be 3 of a kind. But that was permutations, so to get combinations, I divide by 3!.
Then for the next two, since they can't share a suit, there are 48 options for the first and 44 for the second, and then I divide by 2! for order
and that would give me the correct number of 54912
and I don't get why I don't need to . oh
tribal haven
everything is correct, what are you confused about?
fleet dragon
I thought I needed to multiply by 4 choose 2
but I don't
I was trying to account for the fact I didn't have to draw them in that order
but I already had lol
.close
alpine sable
lone heartBOT
alpine sable
Given that a is true, how can I prove that b is true? I already know that the lim of cn goes to 0, but how can I approve that cn is a decreasing function?
worn fox
Are you not allowed to just use the comparison test?
worn fox
It will work for b too
alpine sable
since its alternating, i figured i would use the alternating series test. more appropriate i think?
worn fox
(-2)^n <= 2^n
alpine sable
alright
alpine sable
(-2)^n <= 2^n
but is this really enough proof for the DCT?
oh wait
hmm
yeah
itis
thanks!
.close
delicate lake
hi
last ether
Use L'Hopitals
last ether
Although actually
I don't think you need to
That's the same as $\lim_{x\to 0} \left(\frac{x}{\sin(x)}\right)^2$
ocean sealBOT
Umbraleviathan
last ether
Therefore it's the same as $\left(\lim_{x\to 0}\frac{x}{\sin(x)}\right)^2$
ocean sealBOT
Umbraleviathan
last ether
Use your sin(x)/x identity
lyric stream
0/0 isnt 0
delicate lake
wait it isn't?
last ether
0/0 is indeterminate
delicate lake
ok
delicate lake
last ether
Yeah
But just so you know
Save yourself the pain of doing 1/x / 1/x
You can also rewrite it as
$\left(\lim_{x\to 0} \frac{\sin(x)}{x}\right)^{-2}$
delicate lake
damn
delicate lake
that does make a lot of sense
lyric stream
you can l'hopital x/sin(x) pretty easily
ocean sealBOT
Umbraleviathan
worn fox
you can l'hopital x/sin(x) pretty easily
It's circular iirc
lyric stream
0/0 is not 0 its indeterminate
worn fox
You didn't particularly do anything wrong you just didn't do anything useful
delicate lake
oh
so why did i not get 1 as my answer
was it possible to get 1 using maybe some of the same steps i used?
worn fox
Because the steps you took did not enable you to yet arrive at an answer
delicate lake
oh
last ether
**Umbraleviathan**
Just this will suffice
Although I will admit I default to L'H because it's doo doo easy
delicate lake
yeh i want a backup plan if i forget the squaring it method
delicate lake
L'Hopital again
but how would i do l'hospital again?
last ether
Well you do L'H on the L'H
delicate lake
oooooooo
last ether
You can use L'H infinitely many times as long as the conditions allow it
delicate lake
so i do something to this?
multiply num and den by 1/x again?
this is what i get when i do that
worn fox
Are you sure you know what lhopital is
worn fox
delicate lake
it isn't?
worn fox
No lhopital involves derivatives
It is a method for finding limits of certain indeterminate forms
worn fox
Hi how can I get help
next fiber
Yeah but this is help -0
delicate lake
go away
worn fox
Just read
next fiber
Oh okay
delicate lake
@worn fox i think my teacher just taught us we should get it into a form similar to sinx/x because we just know that is 1
thats all he taught us
worn fox
Okay well then ignore all the talk about lhopital
delicate lake
nvm i def accidentally multiplied wrong here
worn fox
What umbral showed you
delicate lake
ok theres good news
i was actually doing it right 😌
so it works with both techniques
the one i did and the one umbral showed me
@last ether @worn fox thx for helping me guys
o wait
no
i messed up again
wait nvm
it was a false flag
worn fox
Nah it works, just very long way to do it
delicate lake
lmao
i thought if i plug in 0 for x/x then its actually 0
then i remembered u just simplify to 1 first
worn fox
Yeah its okay this time because cancels
delicate lake
alr thx
zenith lichen
no, i don't know what I'm supposed to say
What you do is you clarify
lone heartBOT
@delicate lake Has your question been resolved?
jolly spoke
can someone double check this for me
lone heartBOT
can someone double check this for me
jolly spoke
this is my last attempt
and i think it is 1 but can someone else double check with me
wary stream
Did you sketch the graph?
jolly spoke
yeah
something like this right @wary stream
<@&286206848099549185>
can someone else double check this i got ghosted
or <@&268886789983436800> idk which one to ping
next brook
Is there a moderation problem here?
jolly spoke
idk who am i supposed to ping when i get no help @next brook
i rememebr someone told me but i forgot
next brook
Helpers, as you already did.
next brook
It's up to luck whether any helpers are actually around to respond, though.
lone heartBOT
@jolly spoke Has your question been resolved?
jolly spoke
.close
torn night
How do I start this?
lone heartBOT
How do I start this?
torn night
Let $(x_n)$ be a sequence with $x_n\in{0,, 1,, \dots ,, 9}$. Then, $$x=\sum_{n=1}^{\infty}\frac{x_n}{10^n}$$
ocean sealBOT
KStarGamer
torn night
I was trying to split this into partial sums and equation partial sums based on when the kth terms agree
but doesn't seem to be helping me at the moment
tiny vigil
hah is that like a competition question? : p
torn night
Probably haha but it's actually from one of my example sheet questions
I don't know how to do it though
been searching online but can't find any hints 
tiny vigil
I don't know it seems like a silly question, if you multiply two real numbers you will get a real number
they HAVE to repeat, otherwise it'd be irrational
tiny vigil
@autumn kelp you need your own channel, see the ones in math help(available)
autumn kelp
can u type the channel where i should go?
tiny vigil
Ok no I'm wrong, because we need to consider the case where multiplying two repetetives would give a non-repetetive
torn night
they HAVE to repeat, otherwise it'd be irrational
not sure how that's true
autumn kelp
i joined this server a few minutes ago
tiny vigil
I don't think sums are the way to go though
you can't sum it up anyway, and conv/div doesn't matter
ok, maybe?? they are the answer? this is beyond what I know, I'm only about to start some more proof-oriented stuff
so all we can count on is maybe my rambling will inspire you? Lol
torn night
you can't sum it up anyway, and conv/div doesn't matter
convergence is trivial, it's bounded above by $\sum_{n=1}^{\infty}\frac{9}{10^n}=1$
ocean sealBOT
KStarGamer
torn night
also how do I get the undergrad role? 
tiny vigil
xD
go to #info and click the manage roles button
Every rational number is either a terminating or repeating decimal
Every repeating or terminating decimal is a rational number
torn night
Every rational number is either a terminating or repeating decimal
yes that's true
tiny vigil
torn night
go to <#525440994242461702> and click the manage roles button
ah cheers
torn night
but yeah it's not too hard to show rational <=> periodic
maybe hang on:
I'm gonna prove that and see if I think of something
tiny vigil
could be some sort of algebra solution
(i know, this is the exact same thing like in the task)
I'm trying to understand what that part means
torn night
but yeah it's not too hard to show rational <=> periodic
If $x\in\bQ$, then $x$ has a periodic expansion. To see this, write $x=\frac{p}{2^a 5^b q}$ where $a,b,p,q\in\bZ : a,b\geq 0$ and $q>0$, with $\gcd(q,10)=1$. Then $$10^{\max {a,b}} x = \frac{t}{q}=n+\frac{c}{q}$$ where $n,c\in\bZ$ and $0\leq c<q$. By Fermat-Euler, since $\gcd(q,10)=1$, $$10^{\varphi(q)} \equiv 1\pmod{q}$$ or equivalently, $$10^{\varphi(q)}-1=kq$$ for some $k\in\bN$. Hence, \begin{align*}\frac{c}{q}&=\frac{kc}{kq}\&=\frac{kc}{10^{\varphi(q)}-1}\&=kc\sum_{j=1}^{\infty}\frac{1}{\left(10^{\varphi(q)}\right)^j}\end{align*} Since $0\leq kc<kq$, we can write $kc$ as a $\varphi(q)$-digit number $d_1 d_2\dots d_{\varphi(q)}$. Then $\frac{c}{q}=0.d_1d_2\dots d_{\varphi(q)} d_1d_2\dots d_{\varphi(q)} \dots$ and so $x=10^{-\max{a,b}}\left(n+\frac{c}{q}\right)$ is periodic. $\square$
I'd be impressed if I made no latex error
wow I'm based
ok this proves that any rational is periodic
to prove the other way is easier but I can't be bothered lmao
ocean sealBOT
KStarGamer
torn night
unfortunately, it hasn't helped me 
tiny vigil
i'm trying to squeeze this into that series
if we could just square something inside that
and then show that the square is also periodic, it'd be fiesta
torn night
why do you know that series is 1?
torn night
oh ok
tiny vigil
torn night
😮 I got an idea
If $x$ is repetitive then we can write it as $0.\overline{x_1 x_2\dots x_k}$
ocean sealBOT
KStarGamer
torn night
alright then now notice
$10^k x=x_1 x_2\dots x_k.\overline{x_1 x_2\dots x_k}$
taking the difference
$(10^k-1)x = 0.x_1 x_2\dots x_k$
ocean sealBOT
KStarGamer
torn night
so $x=\frac{0.x_1 x_2\dots x_k}{10^k-1}$
ocean sealBOT
KStarGamer
torn night
alright now somehow the square of this is itself repetitive 
ocean sealBOT
KStarGamer
tiny vigil
hmm
ocean sealBOT
torn night
,w N[(12/(10^3-1))^2]
torn night
How do I start this?
if one let's m=1 and n=333
tiny vigil
can't you get a function for each decimal, and then square the function?
haha not sure if that makes sense, you are levels above me dude
torn night
lmao
torn night
**KStarGamer**
ok but we've gotten somewhere
I need to write x^2 explicitly in a similar way hang on
wait no no
I'm getting mixed up between a periodic number and a repetitive one
a periodic number is when there only exists one such k, namely the period number
but a repetitive has to be every k 
I can't even construct an example oh my
oh ok
we need a modular arithmetic argument
nope
ugh
torn night
How do I start this?
<@&286206848099549185> anyone know how to do this?
tiny vigil
ok I have no clue, I'd have to read the whole book on proof introduction, I will go try to help other people with something more on my level.
but, do ping me if you figure something out!! I'd highly appreciate it. good luck
torn night
thanks
lone heartBOT
@torn night Has your question been resolved?
torn night
.close
rocky pulsar
How do we solve for x in 25^x+10^x=4^x
lone heartBOT
How do we solve for x in `25^x+10^x=4^x`
weary wyvern
Divide both sides by 10^x
rocky pulsar
why exactly?
weary wyvern
You'll see
lone heartBOT
Commands:
clopen: .close, .reopen, .solved, .unsolved
consensus: .poll
factoids: .tag
help: .help
Type .help <command name> for more info on a command.
ocean sealBOT
rocky pulsar
,help
ocean sealBOT
A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!
rocky pulsar
You'll see
,tex so (25^x+10^x)/10^x=(4^x)/10^x
ocean sealBOT
heureux
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
weary wyvern
Simplify
marble panther
Can anyone tell me what im doing wrong here for this question
marble panther
sour dove
hi one second
ah I see
so your 2 integrals are correct as are your constants
but it's asking you to find f(1), you're doing f(-1) 🙂
marble panther
but it's asking you to find f(1), you're doing f(-1) 🙂
ah mother trucker
good catch
marble panther
yeah, i redid the problems 3 times couldn't see what i did wrong
thanks dude, just needed another pair of brain XD
.close
eternal yarrow
A swimmer can swim 10 laps in 15 minutes. One lap in the pool is 50 meters long. How fast is the swimmer going in miles per hour?
remote heron
A swimmer can swim 10 laps in 15 minutes. One lap in the pool is 50 meters long....
how far have you gotten?
or do you have any ideas of what to try
remote heron
these problems i think are all about organization, figuring out what you need to know
so working forwards from the given information, and backwards from the information you want, until you can find a place to connect them in the middle
remote heron
A swimmer can swim 10 laps in 15 minutes. One lap in the pool is 50 meters long....
my first thought would be the laps, right
10 laps in 15 minutes is almost a normal speed
eternal yarrow
Right
remote heron
but its in laps per minute, and not meters per minute, and not meters per hour
how can you relate laps to meters?
eternal yarrow
10 divided by 50?
eternal yarrow
5?
remote heron
One lap in the pool is 50 meters long
you can sorta think of it like fractions, idk if this will be helpful or massively confusing
eternal yarrow
So if i think about it with fractions would it be like 1/50? Since 1 lap is 50 meters
remote heron
$\frac{\text{10 laps}}{\text{15 minutes}} \cdot \frac{\text{50 meters}}{\text{1 lap}}$
ocean sealBOT
jan Niku
remote heron
the important part about the fraction is the units
eternal yarrow
Ohh ok
remote heron
i know to put that second fraction in that way
because i want the units to cancel
if you kinda squint and imagine them like theyre just factors
like how a 2 in the top and a 2 in the bottom cancel
laps just go away here
does that make sense?
the hard part is getting the fraction on the left set up correctly, so you have to sanity check yourself
remote heron
if you want, you can create a chain of these
leave some space, fill in as you go
$\frac{\text{10 laps}}{\text{15 minutes}} \cdot \frac{\text{50 meters}}{\text{1 lap}}\cdot \cdots = \frac{\text{??? miles }}{\text{1 hour}}$
ocean sealBOT
jan Niku
remote heron
or piece by piece is fine too 
remote heron
i can try
eternal yarrow
You work at a local print shop who does the printing for a Community College. You're in charge of ordering supplies for the next year. On average, the shop will print about 12,675 pages every term. One ink cartridge has enough ink to print about 1100 pages. One box of 10 ink cartridges costs the school $35. How much money will the print shop need to spend to have enough ink cartridges for the entire school year if there are three terms in each year?
remote heron
you can use a similar sort of method for this one
can you tell what fraction you want in the end?
what units over what
eternal yarrow
Let me check
remote heron
btw i guess i could say
this technique or w.e you wanna call it
its called dimensional analysis
in case u wanna look up vids or whatever
remote heron
You work at a local print shop who does the printing for a Community College. Yo...
well i think in the end, they want $\frac{\text{??? dollars}}{\text{1 term}}$
ocean sealBOT
jan Niku
remote heron
Alright :)
this is a start, it gets you to what, cartridge per year?
or per 3 terms
but you still need to introduce cost
which is gonna require you going through the box relationship
eternal yarrow
Yes
remote heron
but you have an additional relationship
number of cartridges in a box
so if its 35 bucks a box
and 10 cartridges in a box
i can see box in 2 places there
meaning if you arrange these right, you should be able to cancel out boxes , yea?
and leave just $ and cartridge
remote heron
$\frac{\text{dollars}}{\text{school year}} = \frac{\text{dollars}}{\text{box}} \cdot \frac{\text{box}}{\text{cartridge}} \cdot \frac{\text{cartridge}}{\dots} \cdot \cdots \cdot\frac{\text{3 terms}}{\text{school year}}$
hows this as a hint?
i think you have most of the pieces from here
oop, 1s
eternal yarrow
Ty! Let me do this
ocean sealBOT
jan Niku
eternal yarrow
Ok i think i filled them in right, would i put the year under the cartridge fraction?
remote heron
youre missing a tiny amount of pieces there
actually, maybe just one?
ah, no, two
youre missing info about pages
remote heron
Ok i think i filled them in right, would i put the year under the cartridge frac...
year already exists at the end
remote heron
well what you have left to add
that terms at the very end
that has to cancel somewhere
so youre missing a fraction with term at the bottom
then you have info about pages you havent used
but not pages on the left hand side of the equation
so that has to show up twice
once on the top and once on the bottom
lone heartBOT
@eternal yarrow Has your question been resolved?
eager plaza
hi
eager plaza
can i get some help on angle of inclination
and angle of refraction
A bird is sitting on top of a tree which is in front of a house. the angle of elevation and the depression of the bird from the bottom and top of a house are 60 and 40 resp. if the height of the tree is 24m, find height of house and distance between the house and tree
compact spindle
i always wonder why do the question producer always give a bunch of words but not draw it on the paper instead
lone heartBOT
@eager plaza Has your question been resolved?
lone heartBOT
@eager plaza Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
wanton falcon
What would be the smallest number for the function to have a pole, I cant figure it out somehow
wanton falcon
have to get "b"
vernal siren
Can someone explain to me how im meant to work this out?
lone heartBOT
Can someone explain to me how im meant to work this out?
vernal siren
So would it be 3x-5 x4?
alpine sable
So would it be 3x-5 x4?
(3x-5)x4
vernal siren
12x-20?
alpine sable
Square the side lol
heady tusk
(3x-5)^2
vernal siren
ohhh okay
vernal siren
so 9x^2 -25?
vernal siren
No?
alpine sable
oh okay
(a-b)^2 = a^2 + b^2 -2ab
this is the identity
So if a=3x
and b= 5
apply the identity and you will get the answer
vernal siren
so
a 9x^2 - 25 -30x
vernal siren
yes
alpine sable
remember the identity
vernal siren
so 9x^2 + 25 - 30x?
vernal siren
okay
alpine sable
so 9x^2 + 25 - 30x?
yep
lone heartBOT
alpine sable
ill write it down, thanks alot :)
cool
lone heartBOT
Available help channel!
rough yoke
any easy ways to identify an imaginary root in a quadratic formula? other than making sure b^2 is smaller than 4ac, ofc
little mulch
Using graph ig
primal berry
The only way that I know of that's easy...is that method.
Use the discriminant (b^2-4ac) and check from there really
little mulch
Using graph ig
If if first coeff is +ve it's an upward paraola
little mulch
If if first coeff is +ve it's an upward paraola
-D/4a gives u the vertex
alpine sable
any easy ways to identify an imaginary root in a quadratic formula? other than m...
You can deduce it from the vertex i guess
little mulch
-D/4a gives u the vertex
So you'll know whether it cuts the x axis or not
alpine sable
if u have a vertex at like x = 4 or something and it is pointing up, pretty good indicator it has imaginary roots only
little mulch
So you'll know whether it cuts the x axis or not
-a => downward parabola
little mulch
So you'll know whether it cuts the x axis or not
Whether the graph cuts or not...
jaunty onyx
lone heartBOT
jaunty onyx
Hi! I need help with this exercise in topology, I'm really having a problem answering this sorry
vale wigeon
do you know what the basic opens in a product space look like?
jaunty onyx
Yup! What I am doing now is finding the basis, which in my calculations is {null, (a,a), X}
vale wigeon
ah no not quite
there's some sets you've missed here
{aa, ab, ac} and {aa, ba, ca} are also basic opens
being the product of {a} with {a,b,c} in either order
jaunty onyx
Oh! Because I have to cross {a} x X
Thank you so much
My problem now is
How do I find the open sets now that I have the basic open sets?
I know that I have to get the union of elements, but I'm struggling
vale wigeon
your basic opens are:
- empty
- {aa}
- {aa,ab,ac}
- {aa,ba,ca}
- {aa,ab,ac,ba,bb,bc,ca,cb,cc} (everything)
you need to find the sets, if any, that can be obtained from these by means of unions and aren't already on your list.
i'm abbreviating pairs such as (a,b) -> ab, purely to reduce clutter
jaunty onyx
alright I understand the basic opens part, thank you so much for that
but I'm now struggling to understand how to find the union of two
so what I should do now is
for example, {aa} U {aa,ab,ac}
and then do this for all sets in the basis? is that right?
lone heartBOT
@jaunty onyx Has your question been resolved?
lone heartBOT
@jaunty onyx Has your question been resolved?
thick vault
May someone help me?
I have to know if my steps are right in linear equations/linear inequalities.
alpine sable
May someone help me?
I have to know if my steps are right in linear equations/li...
Sure
thick vault
Yes
Hold on
4x+12y>6
I will divide ax to c
And by to c too
And do some division.. There it is 6 over 4 plus 2
Or in 2nd:Ax+by=c will turn to y=mx+b
And so I do some solving.. There it is!
thick vault
Can you send me the question?
:)
Is it eq 1 or eq 2 that's right or are they both wrong
Cuz like.. I'm not sure
alpine sable
Ah i see
thick vault
I should prob ask my teacher tmrw too
alpine sable
I should prob ask my teacher tmrw too
You should im not a teacher
thick vault
Ye, do you see what's wrong and what's right?
alpine sable
I will divide ax to c
And by to c too
Seems good enough
thick vault
Should 6 over 4 be
4 over 6 instead?
alpine sable
We have to solve for x and y?
alpine sable
Ty <@456226577798135808>
Cool
thick vault
Have a NC day
alpine sable
Write the steps neatly tho lol
thick vault
Write the steps neatly tho lol
Why
alpine sable
We sure to write up what you are doing
alpine sable
Why
Because teachers dont have time to understand everyone’s handwritings and they judge based on your handwriting as well
thick vault
I will show u smth!
alpine sable
I will show u smth!
You are probably my senior lol
I think linear inequalities is in 11th grade
thick vault
I think linear inequalities is in 11th grade
Oh no no I'm g8 xd
alpine sable
Oh no no I'm g8 xd
Dayum
thick vault
That's true tho
Our teacher will also teach functions and relativity?? What relations? Yeah relations
Function and relations.. I forgor man☠️
alpine sable
Our teacher will also teach functions and relativity?? What relations? Yeah rela...
Dayum man
Thats 11t grade shit
thick vault
Why it's easy
alpine sable
Why it's easy
Cool then
thick vault
Oh damn
Wait lemme show u smth OK? :)
OK here
18x+9y<3
M=6
B=3
That's my answer :D
I divided as you said was right
I should learn division tricks so that I can get better at it
craggy idol
Hi, how can I get all the tangent lines that go through a certain point?
craggy idol
I tried using f(x)=f'(x_0)*(x-x_0)+f(x_0) and trying to plug the point (0,-2)
but that gave me an absurd
lone heartBOT
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craggy idol
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glacial pike
- What is the remainder when P(x) = x^5 – 3x^2 + 2x – 4 is divided by x+3?
Applying Reminaider Theorem or Factor theorem with complete solution
alpine sable
1. What is the remainder when P(x) = x^5 – 3x^2 + 2x – 4 is divided by x+3?
A...
do long divison i suppose
glacial pike
oh ok not synthethic?
alpine sable
i prefer long division in most situations
lone heartBOT
wary stream
oh ok not synthethic?
Synthetic division is a shortcut method to long division
lone heartBOT
Available help channel!
carmine copper
Can someone give me steps on how to achieve this result?
lone heartBOT
Can someone give me steps on how to achieve this result?
alpine sable
Can someone give me steps on how to achieve this result?
Sure bro
You know the identity (a-b)2?
carmine copper
Yeah
carmine copper
of course
carmine copper
yup
alpine sable
And we also know that 3 squared is 9
carmine copper
Yup
alpine sable
So √ 3^2 + √5^2 - 6√5 ?
carmine copper
hold on
carmine copper
somewhat
carmine copper
Maybe A2 -2AB + B2 sounds simpler
alpine sable
Maybe A2 -2AB + B2 sounds simpler
Okay if you wanna say that
carmine copper
Yeah
alpine sable
Square and square root cancel out?
carmine copper
yup
alpine sable
3-√5 is our answer
carmine copper
But like how does that 14 disappear
I get its 9+5
then it turns into sqrt3 + 5
or something
alpine sable
then it turns into sqrt3 + 5
No, its square of 3 + 5
carmine copper
yeah that's what i mean
alpine sable
where does the 6√5 dissappear
I wrote 6√5 as 3x2x√5
alpine sable
do i have dementia 😭
Lol no
carmine copper
Could you write down the steps on that board if possible?
alpine sable
Okay sure
carmine copper
Alright
alpine sable
I really appreciate your time
No problem bro
alpine sable
Thank you so much 😭
Nope
carmine copper
.close
lone heartBOT
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Available help channel!
minor osprey
does the rank of the image = the rank of the transformation matrix
blissful temple
rank of a linear transformation is the dimension of its image
minor osprey
so i find the basis for the mapped to transformation
and it is of size 2
does that tell me the dimension of the image
for example this, i found the basis for the second matrix, which was (1,1,0) (-1,0,1)
shy oasis
Hey
lone heartBOT
analog falcon
😐
shy oasis
.help
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Commands:
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help: .help
Type .help <command name> for more info on a command.
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quartz bloom
Hey
lone heartBOT
Available help channel!
neon smelt
how do i simplify my steps
hushed zephyr
In a model, the arc, shown in the picture below, can be described by a function f. The table shows some function values for f
hushed zephyr
here is the table
The function has a prescription of the type f(x)=ax^(2)+bx+c
a) Determine the constants a, b and c in quadratic regression.
I have no idea how to do this
But the teachers have told us the results, we just need to make the steps. Results are:
a=0.1512
b=0
c=20
lone heartBOT
@hushed zephyr Has your question been resolved?
hushed zephyr
<@&286206848099549185>
sonic kiln
You know that f(0)=20, that's in your table. And you know that f(0)=a×0²+b×0+c
so you immediately get c=20
you have 2 other equations, f(11.5)=0 and f(-11.5)=0. 2 equations, 2 unknowns, you can do it.
hushed zephyr
I did it
But the next one I don't get
b) How high is the arch and how wide is the arch at the bottom?
I don't know if theyre asking about this one
Or the function prescription from before
sonic kiln
Well, when does the arch hit its max ?
They look identical
It's probably the f from before, describing the arch
what's the value of f when the arch hits the ground?
hushed zephyr
Well with the values we have now the equation becomes: f(x)=0.1512x^(2)+0x+20
For some reason I can't make the graph in my cas program
sonic kiln
Just look at the table
sonic kiln
yes
hushed zephyr
so it's 20 tall
sonic kiln
yes
hushed zephyr
how do i found out how wide it is
sonic kiln
you know that it hits the ground at x=-11.5 and x=11.5
sonic kiln
sure, no problem
craggy idol
what would be a graphic representation with the trigonometric circle of lim x->-3/2 pi of 1/cos(x)?
craggy idol
if cos(-3/2pi)=cos(3/2pi), why wouldnt 1/cos(-3/2pi) be +oo
taking -3/2pi from the right
prime badge
if cos(-3/2pi)=cos(3/2pi), why wouldnt 1/cos(-3/2pi) be +oo
that makes sense what is it instead?
craggy idol
if you have $\lim_{x \to \frac{-3\pi }{2}^+} \frac{1}{cos(x)}$ that is equal to $-\infty$, but I dont really understand why, bc the same but 3/2pi positive, will tend to +oo
shouldnt 3/2pi and -3/2 pi be equal?
ocean sealBOT
Neo
hollow sparrow
$cos(\frac{-3\pi}{2}) = 0$
$cos(\frac{-3\pi}{2}^{+}) = 0^-$
$cos(\frac{-3\pi}{2}^{-}) = 0^+ $
teal roost
IIRC, In this case, because the function "cos" is continuous through the entire domain of possible angles. As a result, the limit of the function when taken through the angle of 2pi/3 is the same as when taken through the angle of 5pi/3. This limit is +oo. However, the function "1/cos" is discontinuous at its angle of 2pi/3 as the value of the function in that location is undefined. This makes it impossible to determine to what the limit of the function approaches as it is taken through the angle of 2pi/3.
My bad frownyfrog, you removed your message.
ocean sealBOT
Mehdi_Moulati
prime badge
teal roost
Polar angle?
prime badge
@craggy idol there, we're in the negative when we approach −3/2pi, we're in the positive when we approach 3/2pi, both from the right
left half is negative cos
lone heartBOT
@craggy idol Has your question been resolved?
craggy idol
Ill read in a mom, ty
craggy idol
but in that case, why isnt -3/2pi ^ + positive?
prime badge
but in that case, why isnt -3/2pi ^ + positive?
because we're in the left half of the circle?
cos(x) approaches 0 from the left while x is approaching -3/2 pi from the right
i guess that's the idea
like it says in mehdi's picture
$cos(\frac{-3\pi}{2}^{+}) = 0^-$
$cos(\frac{3\pi}{2}^{+}) = 0^+$
ocean sealBOT
frownyfrog
craggy idol
so the - and + would be wrong there?
prime badge
for the x, all four quadrants are negative
-3/2
-1 -2
-1/2
```i mean, it's like this isn't it?when you go clockwise, x is decreasing, so clockwise is from the right
prime badge
yeah that's wrong, if that's the direction
craggy idol
oh ok, I think I finally understood, ty
craggy idol
one more thing, I had to find for which x's, f'(x) exist
and I did this, but the problem is, is the procedure ok?
specially at the bottom, I can conclude that f'(x) exists for all x except 2 right?
or maybe, isnt it the way of solving this, using the definition of derivative?
like do $lim_{x \to -1} f'(-1)=\frac{f(x)+f(-1)}{x+1}$?
ocean sealBOT
Neo
craggy idol
oh its the same
lone heartBOT
@craggy idol Has your question been resolved?
lone heartBOT
@craggy idol Has your question been resolved?
craggy idol
.close
lone heartBOT
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Available help channel!
slate shore
can you guys explain to me uqadratics?
lone heartBOT
can you guys explain to me uqadratics?
tacit arch
can you guys explain to me uqadratics?
be more specific. otherwise just watch khan academy videos
slate shore
be more specific. otherwise just watch khan academy videos
7th grade quadratic equations
tacit arch
7th grade quadratic equations
even more specific
tacit arch
rose sigil
wise choice
lone heartBOT
@slate shore Has your question been resolved?
alpine sable
Hello
alpine sable
Is ln(x) here acting like a factor which is why its not turning into 1/x but staying the same instead ?
@desert fractal hello can you chat here maybe it was wrong in the other chat for me to post i opened this room
desert fractal
Yeah pretty close
Focus only on x lnx first
u is x and v is lnx
u doesn't have to be x, it could also have been lnx, but if we set u equal to x then v has to be equal to lnx
u' is then equal to x'
Which is 1
And v' is equal to (lnx)'
Which is 1/x
desert fractal
(uv)' = u' v + u v'
Plug this back into this formula
And you get $1\cdot lnx + x \cdot \frac{1}{x}$
ocean sealBOT
edwardborn
alpine sable
But why did u ignore the -x
😔
I thought v = lnx - x i thought you take the entire part after the • symbol as v ?
desert fractal
But why did u ignore the -x
Just so it would be easier to explain the product rule
desert fractal
**edwardborn**
Like does this make sense to you?
desert fractal
(uv)' = u' v + u v'
That is if you just take this formula for granted
alpine sable
I understand the product rule there i think if there wouldnt be the additional -x there , wcy did you not include the -x ? Just for demonstration purposes, or is it actually correct to ignore it in this example ?
desert fractal
I can just add it in later if i want to
Since the derivative of xlnx - x is (xlnx)' - (x)'
So then we just solve (xlnx)' first and afterwards we can do (x)'
So what did we figure out (xlnx)' was?
alpine sable
Is ln(x) here acting like a factor which is why its not turning into 1/x but sta...
But how did we get to ln(x) as a result here ?
alpine sable
So what did we figure out (xlnx)' was?
Isnt that 1 • 1/x ?
desert fractal
Isnt that 1 • 1/x ?
Think you forgot to apply the product rule here
Seems like what you did here was (uv)' = u' v'
But you should instead do this (uv)' = u' v + u v'
desert fractal
**edwardborn**
Then you'll eventually end up with this
alpine sable
Can you maybe point out my mistake here ?
I tried to follow the instruction
I tried showing what i did by writing the u' v and u v' below by the way
desert fractal
You only need to apply product rule on xlnx
alpine sable
Only the thing that directly follows the • ?
desert fractal
You can leave the -x outside of this alternative equation for now
You're pretty close tho
alpine sable
Ok so if I get rid of the -x or basically -1 then its correct?
alpine sable
desert fractal
Nice!
alpine sable
But how do we get from this to f'(x) = lnX lol
desert fractal
Well this is the derivative of x lnx right?
alpine sable
I guess so 😄
desert fractal
Since the derivative of xlnx - x is (xlnx)' - (x)'
Now we go back to the (-x)'
We've found (xlnx)'
Now we just need to find (-x)' and then just insert it all back into the equation
alpine sable
-1
desert fractal
Yup
desert fractal
So what do you need to add back to this equation?
alpine sable
May i ask why we didnt include the -x into the product rule? Is it really only the first thing that is directly connected to the • ?
Like in 2•3-1 you would ignore the 1 ?
alpine sable
How do i know whats necessary and whats not? I dont really know when a product rule is necessary to be honest
desert fractal
If it's something ugly that has an x in it multiplied with something else that also has an x in it then you'll use the product rule
That's why we use the product rule only on xlnx
Since it's x times lnx
alpine sable
What about x ln(x^2-4) for example?
desert fractal
But those are like the only two rules you really need to know
alpine sable
Is there an order in which you use them? Or both at once?
alpine sable
So what do you need to add back to this equation?
I guess a -1 at the end ? Or is it 2 times a -1 ?
desert fractal
Nah you got a lot of freedom when you're differentiating actually
Multiple techniques can lead to the same answer
desert fractal
Since the derivative of xlnx - x is (xlnx)' - (x)'
Because you want to insert the (-x)' back in which we found it out to be equal to -1
desert fractal
What does this turn into if you add -1?
alpine sable
just a -1 after the 1/x i assume
desert fractal
Gj!
alpine sable
Thank you 🙏🏻🙇