So for both c and f, you are on the right track, by using conjugates
#help-13
pliant wedge
You just need to cancel out the sqrts and get to your answers
Now, for g, make 1 into y/y and cancel.
I can explain further if needed
swift fossil
ohhhh that makes sense for g, thanks. Let me try them all again I will send again in channel either that I completed them or if I am still confused
pliant wedge
Gotcha
swift fossil
where would I go from here
pliant wedge
Okay lets backtrack to your initial substitution.
swift fossil
alright
pliant wedge
Let us multiply by complex fraction by y/y (as to make it a simpler fraction, however, it is possible to do it without this step)
pliant wedge
Correct
pliant wedge
It's better to leave the denominator as a factored form, but do you see where we might be able to cancel a factor on the numerator and denominator?
pliant wedge
is there a way you can make it y-2?
the coefficients of both the constant and the y are the same
But it's just one thing that's different...
swift fossil
if we flip it it will be -y+2
pliant wedge
correct.
swift fossil
should i multiply by -1 or something
pliant wedge
Yup
swift fossil
ok
swift fossil
is this correct
pliant wedge
Yep
swift fossil
so the answer would just be 0?
pliant wedge
Mhmm
swift fossil
oh so it would be 1/2
pliant wedge
that's right.
swift fossil
thank you so much that was helpful
pliant wedge
No problem!
swift fossil
/solved
pliant wedge
use .close
slate lintel
.close
lofty granite
cedar kilnBOT
lofty granite
im confused on what are the first steps
tight garden
ooh i loved these types of questions
lofty granite
thats good
tight garden
so are you aware of the ASTC rule?
lofty granite
no ive never heard of it
tight garden
in Quadrant II only sine and cosec are positive, which means the other 4 trigonometric function will be negative
tight garden
are you able to calculate what sin(t) will be, knowing that csc(t) = 3 ?
tight garden
yes but it's value
lofty granite
oh no i dont know how to
tight garden
will be 1/3
sin(t) = 1/3
are you aware sin(t) = 1/csc(t)
lofty granite
no
tight garden
you will be working with the reciprocal and pythagoream identities
to find all six trig functions
first step was to know which are postive and negative. (we now know by the ASTC rule that only sin and csc are positive)
next....
we apply the first identity to find sin(t)
which is simply the reciprocal of csc(t)
lofty granite
yeah
tight garden
and csc(t) = 3 according to the question. so sin(t) = 1/3
lofty granite
oh okay
tight garden
next we will find cos(t)
we will use the first pythagoran identity
we now know that sin(t) = 1/3 so we will use this info to find cos(t)
lofty granite
gotchu
lofty granite
sqrt(2)?
lofty granite
oh okay yeah
lofty granite
the second pythagorean equation
tight garden
But for that you need the value of tan(t)
You will use the second reciprocal identity
Because you already know cos(t)
You will use it to get sec(t)
lofty granite
oh
tight garden
And then use the second Pythagorean equation to get tan(t) using sec(t)
Then the last step: use tan(t) to get cot(t) using the final reciprocal identity
lofty granite
okay thank you unfortunately i had to leave my homework to drop somone off but i will keep a picture of the convo
tight garden
I have a sample question somewhere let me get that
I will DM you the sample/example question
@lofty granite
lofty granite
okay thank you
cedar kilnBOT
@lofty granite Has your question been resolved?
glad dagger
Hi. Best learning apps.
For math.
13-15 year old math.
Especially algebra
And creating algebra equation
Example like this
The price of a theater ticket is 64$ more than a cinema ticket. A total of 400$ was paid for 4 theater tickets and 5 cinema tickets
Calculate the price of one theater ticket. Save calculations.
I wanna learn how to do these
I suck at these
cinder venture
x = 64 + y
400 = 4x + 5y
Simplify
Yk how to do this?
@glad dagger
substitute the x in 4x with “64+y”
400 = 4(64+y) + y
400 = 256 + 4y + y
400 = 256 + 5y
I think I have made a mistake
Anyway this is pretty much the process
crimson sedge
Hi. Best learning apps.
For math.
13-15 year old math.
Especially algebra
And cr...
Have you heard of khan academy?
crimson sedge
Hi. Best learning apps.
For math.
13-15 year old math.
Especially algebra
And cr...
This book is a good for pre-algebra.
https://batch.libretexts.org/print/Letter/Finished/math-22458/Full.pdf
This book is good for basic algebra
https://batch.libretexts.org/print/Letter/Finished/math-19848/Full.pdf
glad dagger
Have you heard of khan academy?
No
glad dagger
What’s this
crimson sedge
click on it and see
cedar kilnBOT
@glad dagger Has your question been resolved?
cedar kilnBOT
@glad dagger Has your question been resolved?
crimson sedge
Hi. Best learning apps.
For math.
13-15 year old math.
Especially algebra
And cr...
i watched a lot of black pen red pen on youtube he does stuff like that
unreal spear
how do i do this? where do i start? am trying to simplify
cedar kilnBOT
how do i do this? where do i start? am trying to simplify
slate lintel
i would replace the bases with their prime factorizations
unreal spear
after that this is what i got: (8)^12 x (3)^30 / 1^46
unreal spear
i would replace the bases with their prime factorizations
what do i do from here? plz ping me next time so i get a notif
slate lintel
after that this is what i got: (8)^12 x (3)^30 / 1^46
doesn't seem right, did you skip some steps?
slate lintel
ok well first of all you misread a 5 as a 6 but beyond that
you can't cancel factors like that when they're inside a power
slate lintel
$(2.2.2.2)^{12} = 2^{12}.2^{12}.2^{12}.2^{12} = 2^{48}$
wraith daggerBOT
hayley!
wraith daggerBOT
hayley!
unreal spear
ok well first of all you misread a 5 as a 6 but beyond that
5?
slate lintel
**hayley!**
do something like this to the factors
unreal spear
the 45 in the denominator became 46 somehow
oh whoops its my handwriting sry
slate lintel
yep
slate lintel
i haven't done the math myself but what did you do with the 18^45 on the bottom?
unreal spear
yeah i split it up to 3x3x2
slate lintel
oh ok cool
ocean garnet
cedar kilnBOT
ocean garnet
I have a small question
for part a how do I know what to differentiate with respect to?
when it says if k is a constant does that mean I differentiate with respect to k?
cedar kilnBOT
@ocean garnet Has your question been resolved?
stark kiln
hey so there is this game on a discord bot where it's essentially a sort of gambling. basically you can "buy a chicken" for 100 coins and send it to fight and bet that it will win for however much money as long as it's >= 100 coins. in the first round, it has a 50% chance of winning. each time you win, you gain 1% chance (so 51%, 52%, etc). if it dies, you have to buy a new chicken for 100 coins.
I find this game very interesting because it feels like there's a decent amt of probability and decision making
SO, I'm trying to make a program that can play in the most "accurate" way and gain money. i know this sounds dumb, it's virtual money after all, but I am more interested in the math behind it and how (or if) this can even be done?
finite lion
winpercentage = min(0.5+0.01*wincount, 100)
flint plinth
virtual chickenfighting, what will they think of next
stark kiln
virtual chickenfighting, what will they think of next
LOL
finite lion
virtual chickenfighting, what will they think of next
have you seen that problem where 2019 penguins waddle to their favourite rewstaurant
slate lintel
lootBWAKses
slate lintel
how much do you get if you win?
stark kiln
random?
stark kiln
how much do you get if you win?
however much you betted
and you lose that same amount too
finite lion
can you just bet very little every time, until the percentage goes higher then you roll in the big bucks
stark kiln
yeah but you often lose by like round 2 or 3
but yeah i was actually trying that
coding some weird exponential function where it begins to spend more in later rounds
it seemed like it just performed worse
slate lintel
so the first round is always 100 and then after that you get to pick?
slate lintel
confused
you buy it for 100 coins - exactly?
and then what you send it in with some amount of coins stuffed up its butt? that also has to be at least 100?
finite lion
yeah but you often lose by like round 2 or 3
yeah which is why dont bet in the early percents
wait until you’re pretty confident it aint gonna die
wait is it theroeiteically possible for the chicken to hit 100%
cuz if that’s the case then ya could just keep doin it until a chick
stark kiln
you buy it for 100 coins - exactly?
yeah, so like for example
- you start a game (buy a chicken) for 100
- you play round 1 by betting any amount you want
- if you win, you go to round 2 with a higher chance, still betting how much u want.
If you lose, you go back to step 1
stark kiln
wait is it theroeiteically possible for the chicken to hit 100%
well unfortunately the devs were smart and capped it at 70% xd
slate lintel
wait is it theroeiteically possible for the chicken to hit 100%
,w 100!/(100^50*50!)
stark kiln
but I don't think I've seen it reach round 20 even (prob the chance is so low)
wraith daggerBOT
slate lintel
good luck hitting 100%
finite lion
well unfortunately the devs were smart and capped it at 70% xd
ah fuck
slate lintel
feels like the first actual bet you do should be a large amount
finite lion
i think if you bet a constant amount, the expected value will go up
stark kiln
i was thinking, is there a bigger chance of winning after you lose a lot of games?
stark kiln
oh
finite lion
but even if so, because of the winning percentage going up, the expected value should be a profit
could we be a bit more greedy and bet more on the higher percentages to abuse it
how much money in the game do you have
slate lintel
but even if so, because of the winning percentage going up, the expected value s...
actually that 50% chance of losing 100 coins (at least) right away seems like a lot
stark kiln
how much money in the game do you have
technically like 5000 rn but if you gamble right with other games it won't take long to reach like 50000
finite lion
actually that 50% chance of losing 100 coins (at least) right away seems like a ...
depends on what the game
finite lion
technically like 5000 rn but if you gamble right with other games it won't take ...
are there any better games
is it dank memer
what game
stark kiln
unbelievaboat
stark kiln
i think if you bet a constant amount, the expected value will go up
constant amount failed according to my program
like i lost a lot of money 💀
slate lintel
even if the chance were always 70% there would be some minimum bet that you need to use or you lose money on chickens
finite lion
try telling it to bet 100 every time
and try running it for 1000 games or however many your pc can handle within a second
stark kiln
yeah i did that and it lost so much lol
finite lion
woah what the hell;
stark kiln
even if the chance were always 70% there would be some minimum bet that you need...
right
finite lion
why would it happen tho
stark kiln
probably because you are buying chickens in the first place
stark kiln
😭
finite lion
SO IF I LOSE, I NEEDA BUY ANOTHER CHICKEN AGAIN
stark kiln
yes
finite lion
so when you lose you’re not only losing your bet, but losing another 100 on top of that
well fuck dont play this game it’s guarantee lose
stark kiln
BRUH
slate lintel
i feel like the max EV here is going to be bet nothing on the 50 then bet everything on the 51% chance
stark kiln
yeah..
it's even more scammy that you must bet at least 100 each round so you can't bet nothing
im starting to think there is no solution
it's just pure luck
slate lintel
so i mean
it shouldn't be
the entry fee doesn't really matter
if you have a big enough bank
finite lion
wait i agree with hayley
slate lintel
and the game is otherwise positive EV
finite lion
buy 100, bet 200 on the 51%
yeah
so bet as little as possible on the 50%
and bet 200 for everything >50%
can ya try running a 1000 games or sth on tht
stark kiln
hmm okay i will try
slate lintel
i think with a finite bank you're probably guaranteed to go bust at some point? not sure
some kind of martingale otherwise
but yeah like without the entry fee it's positive EV
stark kiln
finite lion
ok that was not the best run
slate lintel
-100,000
did it lose every game???
stark kiln
but yeah like without the entry fee it's positive EV
very true i just tested it
stark kiln
-100,000
did it lose every game???
uhh
yeah this is kinda alarming
let me look into it
slate lintel
sometimes you can analyze these problems from absurdism
imagine you had a bank of 101 coins
cedar kilnBOT
@stark kiln Has your question been resolved?
stark kiln
imagine you had a bank of 101 coins
well you couldn't quite afford a round with that
but what is your point? i am curious
slate lintel
well you couldn't quite afford a round with that
oh wait yeah you need to bet at least 100 on top of the chicken?
stark kiln
yeah
slate lintel
ohhhh okay
a good test for a method like this is to do it over and over with some starting bank
and see whether you go bust first or double your starting cash first
stark kiln
ah thats a good idea
so i started with around 10k and it busts first, anywhere from game 60 to 200
stark kiln
im gonna head out, i honestly dont think there's really a way to play this game accurately lol
thank you everyone for the help
.close
deft trench
Been stuck on number 4 for a while. I have an inkling idea of what it means but no idea how to actually rewrite it
celest ledge
x is in at least one of P(A), meaning x is a subset of A, where A is a member of F
deft trench
That makes sense
So there exists an x that is a subset of A?
Where A is in F
Is that how I’d write it?
This?
celest ledge
I simply explained what it means. I don’t know what form of answer it requires since it’s your assignment.
What you sent looks perfectly correct to me, I just don’t know whether it’s the form your assignment requires
celest ledge
Np
deft trench
.close
crimson sedge
hello
crimson sedge
can anyone help me
gaunt trench
crimson sedge
sorry its a lot
^
yes
these are all new attempts
second to last question, i put :
[-7,-7] U [7,7]
but it was wrong
wraith daggerBOT
cedar kilnBOT
@crimson sedge Has your question been resolved?
hearty arch
have you tried just [-7,7]? the only values y can hold lie in that interval, even though y is only either -7 or 7
since it's only asking for one set, that's what my first thought would be
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
@crimson sedge Has your question been resolved?
cosmic steppe
have you tried just [-7,7]? the only values y can hold lie in that interval, eve...
Well no because f doesn't take all values between -7 and 7 between x in [-5, 5]
hybrid light
cedar kilnBOT
hybrid light
why was sinxdx set to dv and not v?
celest ledge
(-cos(x))’=sin(x)
hybrid light
so when solving integrals by parts, you set u to the first part and derive it and then set the next part to dv instead of v?
and then derive it?
also according to the formula for integration by parts, don't you subtract
celest ledge
It’s simply d(f(x))=f’(x)dx
cedar kilnBOT
@hybrid light Has your question been resolved?
regal peak
If one performs a singular value decomposition on some demeaned data, (n,m) matrix X where n and m are the number of features and observations accordingly, we will get USV = X. From here we can recover the covariance matrix $V^{T}SV$. This will be the equivalent of a maximum likelihood estimator for the covariance under a Gaussian distribution. How is the Gaussian distribution related to the SVD? Is there a normality assumption here somewhere?
wraith daggerBOT
LetečiDebjule
cedar kilnBOT
@regal peak Has your question been resolved?
cedar kilnBOT
@regal peak Has your question been resolved?
signal vault
cedar kilnBOT
signal vault
can someone explain a
dreamy sleet
can someone explain a
What are you confused about?
signal vault
i triedf expanding lhs
so i got
$\frac{1}{\cos(\theta)} + \frac{1}{\sin(\theta)} \times \frac{\cos(\theta)}{\sin(\theta)}
how does this work
\frac{1}{\cos(\theta)} + \frac{1}{\sin(\theta)} \times \frac{\cos(\theta)}{\sin(\theta)}
dreamy sleet
$\frac{1}{\cos(\theta)} + \frac{1}{\sin(\theta)} \times \frac{\cos(\theta)}{\sin(\theta)}$
wraith daggerBOT
rysrobrgldvoelroep>vneae=u
signal vault
yep
dreamy sleet
you missed a dollar sign on the end
dreamy sleet
You could try expanding the right side as well
signal vault
i did
signal vault
$\frac{1}{\cos(\theta)} \times \frac{1}{\sin^2(\theta)}$
wraith daggerBOT
kevvv
dreamy sleet
And then you could multiply both expressions for the left and right sides by (cos theta)(sin theta)^2
so that it’s easier to identify them
crimson estuary
how should i do this?
cedar kilnBOT
how should i do this?
tropic oxide
ok
can you write out what a generic polynomial of degree 2 looks like
no other information known about it yet
crimson estuary
ax^2 + bx + c?
tropic oxide
yes of course. what room is there for second guessing?
crimson estuary
wait
tropic oxide
now make it monic. do you know what it means for a polynomial to be monic?
crimson estuary
so a = 1
crimson estuary
2 + bx
tropic oxide
❌
tropic oxide
yes of course
again this is all simple if you put some thought in it
now make the constant term 1
crimson estuary
so x^2 + bx +1
crimson estuary
if i subbed in p(-1) just 2 -b = 7
tropic oxide
❌
crimson estuary
-5
crimson estuary
not really
crimson estuary
how to do b and c
crimson estuary
what does quartic mean?
tropic oxide
degree 4.
crimson estuary
so it the first term would be 2ax^4
tropic oxide
don't try to kill two birds with one stone unless you know exactly what you are doing.
crimson estuary
ok
tropic oxide
write me a generic 4th-degree polynomial
do nothing else with it until i say otherwise
crimson estuary
ax^4+ bx^3 + cx^2 + dx + e
tropic oxide
now make its leading coefficient 2.
crimson estuary
2x^4+bx^3+cx^2+dx+e
tropic oxide
the other terms do not vanish
crimson estuary
2x^4 + bx^3+cx^2+dx+0
crimson estuary
i think ill just keep it there to make sure i do everythig=ng
tropic oxide
anyway, now write what it means that Q(-2) = 12
tropic oxide
why would you not keep "the b and stuff"
why's your default to throw them away like they are junk to rid yourself of
tropic oxide
better would have been to put it in a new message.
but yes, the equation is 32 - 8b + 4c - 2d = 12
tropic oxide
do you see how to proceed?
crimson estuary
-8b +4c - 2d = -20
tropic oxide
i think you are overthinking it.
observe that all of the information from the problem has already been incorporated
and the problem asks only for an example of a polynomial with the properties it gives you
you have 3 variables and 1 equation relating them
pick two of your three variables (b, c, d) and set them to any values you want.
there are no wrong answers here, but if you are having trouble deciding, then say "I am Buridan's ass!" and i will pick some for you.
tropic oxide
indeed.
crimson estuary
so is it just 2x^4 + 10x?
tropic oxide
you yourself set b to 1 and c to 2
but now you have struck them down entirely
as if they were trash to rid yourself of
crimson estuary
fhoauisfj
tropic oxide
you need to not forget things that you yourself have done
crimson estuary
oh ok
tropic oxide
are you able to do part c?
cedar kilnBOT
@crimson estuary Has your question been resolved?
still raft
Hello how do I solve this?
cedar kilnBOT
Hello how do I solve this?
still raft
do I just 0=x-cos(x) and then solve for x?
untold torrent
No, there's no good way of isolating x.
You just need to show a solution exists somewhere.
jaunty mural
do I just 0=x-cos(x) and then solve for x?
you don't have the tools to do it this way?
I mean - what's your idea to try if u wanna do this
still raft
You just need to show a solution exists somewhere.
like the intemediate value theorem?
or something
still raft
I mean - what's your idea to try if u wanna do this
something to do with continuity is what I think I should be doing
gleaming cloud
yes
jaunty mural
No - I was saying if you wanted to solve the equation
what did you wanna do
(im just checking - because nothing should really work)
still raft
what did you wanna do
put it in wolframalpha lol, I dont really know
jaunty mural
yeah no, you cant
gleaming cloud
put it in wolframalpha lol, I dont really know
kid named wolf:
jaunty mural
All you have is a theorem that can show the existence of solutions given certain conditions
twilit nest
Hey, i am unsure if this is correct. Could someone have a look?
cedar kilnBOT
Hey, i am unsure if this is correct. Could someone have a look?
@twilit nest Has your question been resolved?
hollow beacon
can someone help me understand: https://www.geeksforgeeks.org/find-the-largest-possible-value-of-k-such-that-k-modulo-x-is-y/
namely this observation: to maximize the answer, we need to consider only two integers:
n−nmodx+y
n−nmodx−(x−y)
.
cedar kilnBOT
@hollow beacon Has your question been resolved?
cedar kilnBOT
@hollow beacon Has your question been resolved?
cedar kilnBOT
@hollow beacon Has your question been resolved?
cedar kilnBOT
@hollow beacon Has your question been resolved?
cedar kilnBOT
@hollow beacon Has your question been resolved?
sacred stone
hwo do i find m<IJK
cedar kilnBOT
hwo do i find m<IJK
crimson sedge
Well we know that IJL is 92°
sacred stone
yess
crimson sedge
And LJK is 65°
Is there any relationship between these two angles and the angle we want to get?
sacred stone
nope
crimson sedge
There isn’t?
sacred stone
no because
crimson sedge
There is.
crimson sedge
What angles does the angle IJK consist of?
sacred stone
isnt a relationship like when theyre intersecting
sacred stone
What angles does the angle IJK consist of?
I j k
sacred stone
IJK consists of angles IJL + LJK
?
surreal cave
m∠IJK = m∠IJL + m∠LJK
cedar kilnBOT
sacred stone
.reopen
cedar kilnBOT
✅
cedar kilnBOT
cedar kilnBOT
Available help channel!
fervent depot
cedar kilnBOT
fervent depot
help pls
surreal cave
use $a_{n}=a_{1}+(n-1)d$ to solve for $a_{1}$ :)
wraith daggerBOT
MrFancy
cedar kilnBOT
@fervent depot Has your question been resolved?
warm bone
hello, i would like some help in solving this limit
cedar kilnBOT
hello, i would like some help in solving this limit
warm bone
i need to determine the limit as x approaches inf and -inf
however i'm not sure what exactly i should do. i'd like to first divide every term by x^2/3
celest ledge
Divide by x^(4/3) both above and below
warm bone
says to divide every term by the highest power of x that appears in the denominator, so how did we get x^4/3 from 4x^2/3
vestal bear
highest power in the denominator
celest ledge
…
vestal bear
youre trying to get rid of x in the denominator
celest ledge
Let him
vestal bear
says to divide every term by the highest power of x that appears in the denomina...
bro
scarlet star
Hello I need help with all four questions. I do not understand anything in this question.
nimble mulch
Are you familiar with integrals
scarlet star
No
nimble mulch
but you were introduced to calculating area under a curve
scarlet star
Not really
nimble mulch
even if not, here you only need to calculate the area of triangles and rectangles
eg consider the first graph
scarlet star
Ok
scarlet star
Ok
nimble mulch
meaning you know the length and the height of the triangle which forms the shape under the graph relative to the x-axis
can you thereby calculate that area?
scarlet star
I don’t know how to calculate it
scarlet star
can you thereby calculate that area?
Yes, but I am not sure how to do it
nimble mulch
well if I tell you a right triangle
has length 0.09
and height 3
can you tell me the area of that right triangle
scarlet star
0.135
scarlet star
Ok
nimble mulch
that's the area for A
once you see the relation between the area under the graphs and the according triangles/rectangles it's easy
you can apply the same for the other tasks
just keep in mind that area under the x-axis is considered negative
scarlet star
Can I try them and tell you the answer to tell me if it’s correct
nimble mulch
sure I may not be here but others can check as well :)
scarlet star
Ok
For the first one I got 0.135
Not to doubt you or anything but when I searched it up they all used a itegrals formula starting with an s symbol
I that the same thing on the paper I am doing or something completely different?
nimble mulch
I that the same thing on the paper I am doing or something completely different?
Given that you mentioned you haven't yet done integrals you can ignore that for now
generally you solve them with integrals
Eg if I gave you a sine curve
And you want to know the area
you can't use triangles
scarlet star
so what i am doing right now is correct?
do you want me to show you the previous pages i worked on?
for b i got 20
and a i got 0.135
nimble mulch
for b i got 20
How is it 20
I think you may have gotten the rectangle wrongly
which is just length * height
8 for the left triangle
scarlet star
so just 40?
scarlet star
i am confused what triangles?
scarlet star
oh the drawing makes 2 triangles
scarlet star
i honostly think this may be wanting the definite integral formula
would that be possible?
nimble mulch
Sure but I thought you didn't have intwgrals
scarlet star
yea i didnt learn them yet its my summer packet so it may want me to do it for the first time
i am going into physics this year
lets do it using that
the page before it was talking about best fit lines and scatter plots, and slope intercept form
nimble mulch
lets do it using that
k a sec
scarlet star
ok
nimble mulch
are you fully unfamiliar with the integral notation
scarlet star
yes
nimble mulch
because if so I may have trouble writing it out on phone, would be better if someone else may take over as I'm not on my setup
but the interpretation of the symbol is fairly straightforward
you have two values at the top and bottom of the S
scarlet star
ok
nimble mulch
and then a function inside
the values describe the interval for the integral
eg in your first image a)
you'd take the integral for the interval 0 to 0.09
and the function would be 100x/3 which you get by retrieving the linear function for the line
so you actually calculate the integral from 0 to 0.09 of 100x/3
which is the same as the area under curve
scarlet star
can u get me a picture of this formula
nimble mulch
the key aspect is that the value of the integral always refers to the signed area
nimble mulch
can u get me a picture of this formula
I would but on phone it becomes quite annoying, I'll hope someone else comes by though :)
nimble mulch
yes
bottom a for the lower interval bound
upper a for the higher interval bound
usually
in case no one comes along I'll be able to write to you tomorrow as well
scarlet star
ok, thank u
dire geode
.close
serene badge
I'm stuck on number 20, I'm having problem starting the problem and haven't continued after that.
weary vessel
spare dome
how do you find the oblique asymptotes to this?
cedar kilnBOT
how do you find the oblique asymptotes to this?
@spare dome Has your question been resolved?
south tundra
Do you know how to find oblique asymptotes for a function in general?
spare dome
Do you know how to find oblique asymptotes for a function in general?
yeah, top divided by bottom. how would you divide a square root in this case?
south tundra
You need to find a and b s.t. lim (f(x) - (ax + b)) = 0 as x -> inf or x -> -inf
So here you can make the denominators common for x^4/sqrt(x^6 + 1) - ax and then use the conjugate
cosmic steppe
how do you find the oblique asymptotes to this?
Think about this in terms of end behavior. In other words, focus only on the leading terms
So you can just omit the 1
cedar kilnBOT
@spare dome Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
meager sonnet
Hi anybody here
cedar kilnBOT
Hi anybody here
cedar kilnBOT
@meager sonnet Has your question been resolved?
cedar kilnBOT
@meager sonnet Has your question been resolved?
cedar kilnBOT
@meager sonnet Has your question been resolved?
civic meteor
cedar kilnBOT
civic meteor
x'=3x+5y
y'=x+2y
x=(x'-5y)/3
y=(y'-x)/2
i plugin these expressions into y=2-3x
(y-x)/2=2-3((x-5y)/3)
y-x=2(2-(x-5y))
y-x=4-2x+10y
9y=x-4
y=(x-4)/9
did i do it it right?
civic meteor
wdym?
the x' and y' are only to indicate that the old equation will be used to plugged into
as they are the new x and y after the tranformation has taken place
wraith daggerBOT
jstn.
cedar kilnBOT
@civic meteor Has your question been resolved?
civic meteor
<@&286206848099549185>
cedar kilnBOT
@civic meteor Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
dim tiger
@celest ledge dw you can respond when you want in #help-21｜아리스킨충1 you said that A is index of $\alpha$ wdym by that
wraith daggerBOT
calculus is fun
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
dim tiger
so A is indexing set
but then what does this set have to do with what we were talking about
celest ledge
It’s just that p-1 elements of x is replaced
|A|-(p-1) many x remaining
I just didn’t see any reason I express the number |A|-(p-1) differently
dim tiger
ohh yea i get your idea now
celest ledge
Okay
dim tiger
tysm for your time sorry if you dont like to get pinged i wont do that again
i just pinged this time because it was something you wrote so you are the best to clarify what you wrote
.close
azure citrus
Hi guys! just started abstract math. i definitely didnt do this right i think..
My understandings is that true implies true, false implies false, and false implies true. but not sure i did this right, or even understand what the question was asking.
tropic oxide
your column for $\neg Q$ looks wrong.
azure citrus
like im not sure if the column is saying "This statement is true" and i plug it in
wraith daggerBOT
Ann
azure citrus
or would it be then like:
F
F
T
T
F
F
T
T
cause i feel like it wants me to plug -q into the truth table statement
tropic oxide
idk what "plug -q into the truth table statement" means
azure citrus
yeah sorry okay lemme try again
tropic oxide
or would it be then like:
F
F
T
T
F
F
T
T
yes that is exactly what it would be
tropic oxide
that is the most likely cause of your confusion, yes.
azure citrus
can you help me with this one then? i’m not sure at all how to start.
tropic oxide
construct one big truth table with columns for !P, !Q, P=>Q, !Q=>!P and !P OR Q.
azure citrus
! being not right?
cedar kilnBOT
@azure citrus Has your question been resolved?
onyx owl
Hello, how can I get dot product out of the degrees between the two vectors?
nimble mulch
Hello, how can I get dot product out of the degrees between the two vectors?
cos(angle) = dot(A,B)/(|A|*|B|)
therefore if you have the angle, you get the dot product via
cos(angle)*(|A|*|B|)
where A, B are the vectors
onyx owl
Oh, yeah, forgot about that formula, yeah, sounds brilliant, thank you 😄
nimble mulch
and |...| would be the magnitude
nimble mulch
Oh, yeah, forgot about that formula, yeah, sounds brilliant, thank you 😄
np 🦇
the same applies for sin btw
sin(angle) = det(A,B)/(|A|*|B|)
really neat equations for linear algebra
as they're quite fundamental
onyx owl
but there is not actual reason to use sin instead of cos I suppose?
I mean, they give the same result
nimble mulch
but there is not actual reason to use sin instead of cos I suppose?
for sin you have the determinant instead of the dot product
nimble mulch
sin(angle) = det(A,B)/(|A|*|B|)
so if you had the angle but instead wanted the determinant, then you'd get it this way :)
onyx owl
alright, thank you so much 🙏
nimble mulch
seh jz erst das München, selten dass hier Deutsche sind :3
onyx owl
I'm not actually German
onyx owl
hehe, it's just a local meme 😛
nimble mulch
kk cya
cedar kilnBOT
@onyx owl Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
limpid bane
Is a liter = dm^3 for both solids, liquids and gases? Or only for water?
limpid bane
Oki
Oh nevermind i just remembered that a liter of water weights 1kg
I confused the things
tropic oxide
yes, that's one of the original defining features of metric.
limpid bane
Also if I’m doing some operations in chemistry should I use liters or dm^3?
I know I should use pascals instead of bars
Or kelvins instead of celsius
But with the volume?
vagrant elbow
litres are pretty standard
but it depends on what the question you're working on uses
limpid bane
Sometimes they give me the wrong measuring unit to confuse me
But idk if I should use liters or dm^3 (the question uses dm^3 but idk if it’s accepted in the standard National measuring thing)
limpid bane
Thanks 🙏
cedar kilnBOT
dire geode
better suited for#discussion
graceful island
cedar kilnBOT
graceful island
i’m kinda confused with this bc i did everything to not solve it
but all i could do is process of elimination to determine that it’s the first two that aren’t crossed out
ik it’s these two bc i accidentally solved them lol, but can’t seem to figure out how to do it without solving
<@&286206848099549185> ?
fallow steppe
sorry if something important got purged, but autodelete on ban failed
graceful island
nw
repost?
so i narrowed it down to the first two that aren’t crossed out mainly bc i accidentally solved the integral. Going back, i kinda bs’ed it using process of elimination, but i’m still unsure if there’s another way of going about this. Any clue how to go about solving it?
tranquil drift
I think method of elimination works fine. You correctly deduced that it cannot be bottom left because the integral would be negative.
tranquil drift
I am not so sure myself what they want for the other one but i assume its because of the large values on the y axis
graceful island
gotcha
stiff totem
fwiw, it asks about the area of the shaded regions, so I think you'd take the absolute value of the lower left integral anyway
the area is still too small in this case, but just because the integral spits out a negative doesn't mean the shaded area is necessarily different
graceful island
Ahh i see
tranquil drift
ah true
graceful island
how could i justify the bottom left?
i mean tbf, i don’t think i even did the bottom right justification correctly
stiff totem
the curve doesn't go below -1 I guess
so it's constrained within a really small box, so you know the area will be small
graceful island
so it's constrained within a really small box, so you know the area will be smal...
ahh i see
stiff totem
oh, I just read the title; it says "using the substitution rule"
there's probably a neater way of doing this
graceful island
definitely
that’s where i’m kinda confused lol
stiff totem
try transform them all into the form ae^x or something using u-substitution
graceful island
alr alr
tranquil drift
oh, I just read the title; it says "using the substitution rule"
ah yeah reading helps 😅
graceful island
for the first graph
using u=-x^2
i would also have to adjust the bounds accordingly
correct?
stiff totem
yes, always adjust the bounds
tranquil drift
i would do u=x^2 without the -
graceful island
smart
uh
itd be the same thing lol
when u integrate
the negative will come down regardless
graceful island
oh i see what u mean
matching the integral
bro i ended up solving it again 🤦🏽♂️😭
i think i got it! tysm 🙂
.close
crimson sedge
cedar kilnBOT
tropic oxide
image incoming?
cedar kilnBOT
crimson sedge
.reopen
cedar kilnBOT
✅
crimson sedge
crimson sedge
This is the method i used
crimson sedge
image incoming?
look^
tropic oxide
ok so
crimson sedge
My ans is 1512
tropic oxide
36 = 2 * 2 * 3 * 7?
crimson sedge
Which is wrong
tropic oxide
where did 7 come from in the factorization of 36?
crimson sedge
O:
tropic oxide
for that matter, why is 84 written as 2 * 2 * 3 * 3...
did you switch 84 and 36 around, or what
tropic oxide
120 = 2 * 2 * 2 * 3 * 5
84 = 2 * 2 * 3 * 7
36 = 2 * 2 * 3 * 3
your answer curiously doesn't include any fives even though 120 has one.
how come?
cedar kilnBOT
cedar kilnBOT
Available help channel!
tawdry thunder
how do I solve this?
crimson sedge
how do I solve this?
need help?
tawdry thunder
yup
crimson sedge
the domain is rappresented in the x axes and the range in the y axes
so in this case the function is between 2 and 6 in the x right?
tawdry thunder
I think ye
crimson sedge
while in the y axes what is the interval?
tawdry thunder
?
crimson sedge
in the y axes what are the point where there is th funcion?
the funcion is between -2 and -6
so domain [2;6] and range [-6;-2]
tawdry thunder
ohhh makes sense what about this one?
This one looks completely different to me
Then how I was taught a bit
cedar kilnBOT
@tawdry thunder Has your question been resolved?
tawdry thunder
.close
cedar kilnBOT
Can someone tell me what i did wrong to 3 and 4
shrewd blaze
Can someone tell me what i did wrong to 3 and 4
I cant get the square roott
crimson sedge
what are your steps for 3 first
shrewd blaze
what are your steps for 3 first
I put 80 to 0,Then change it's sign, Then i divided 4,to cancel it, and make it to y²
I swear im right, But i cant Make square root
crimson sedge
no number 3 not number 4 we'll do number 4 second
shrewd blaze
Oh okay
Basically i did the parentisis first, So 2y will be 4y² since it is squared, then 3x3=9, then i transfer it to -49 and change its sign, Then it would be -49 - -9=40
Then i find the root square
crimson sedge
Well
shrewd blaze
I Divided with 2 first to cancel it
shrewd blaze
because 49 is a perfect square
Ahh, so what do ido😭😭😭
crimson sedge
so you can just find the square root of both sides at the start
and get 2y-3=+-7
then
2y-3=7
2y-3=-7
you should be able to solve from there
crimson sedge
squarte root of 49
square
is + or - 7
because (-7) squared and 7 squared are both 49
shrewd blaze
So y=+-7?