1/2?
#help-26
untold cypress
echo siren
is that area over there
untold cypress
probably overthinking this
echo siren
dont worry, dont be harsh with yourself you are close to the answer
In the other hand this integral $\int_{0}^{1} x/2 $ represents the value of this area
so basically when you integrate $\int_{0}^{1} \frac{1}{1+x^{2}} - \frac{x}{2}$ you are calculating this area
thorny flameBOT
BillyElKid
echo siren
untold cypress
pi/4-1/4 should be it if it's under the curve
untold cypress
so pi/2-1/2
echo siren
exactly, because it's symmetrical respect the y axis
minor owl
(y+4)^(2)=-3(x+1)
topaz sinewBOT
(y+4)^(2)=-3(x+1)
minor owl
i managed to solve for the vertex and x-int but i got the y-int wrong
<@&286206848099549185>
topaz sinewBOT
@minor owl Has your question been resolved?
river pendant
How am I supposed to answer this? :<. I tried my method of answering it earlier and my tutor said it was all wrong
topaz sinewBOT
How am I supposed to answer this? :<. I tried my method of answering it earlier ...
drifting swift
@river pendant what was your method?
maybe there's a mistake in it that can be corrected to make it all right
river pendant
I tried doing this calculation my tutor gave us for question #2, my answers were long leg = 4 and hypo = 2 √3
I did the first one right so that's a plus. I just don't know what i can do for question #2
and all the questions
nvm, i know what to do know. thanks though
.close
pliant leaf
Was wondering how this equals 1
topaz sinewBOT
Was wondering how this equals 1
drifting swift
do you mean "how do we get to x=1 from this equation?" or "i think x=1 isn't a solution of this equation"
topaz sinewBOT
@pliant leaf Has your question been resolved?
pliant leaf
@drifting swift I meant, that I know the solution of the equation is one since my calculator tells me so, however I'm not sure algebraically how that happened.
I would have divided both sides by 2 and been left with
drifting swift
you would divide 2 by 2 to get 0?
drifting swift
there we go
drifting swift
there are several different things you could do
for example you could rewrite the left hand side as x^(-1/3)
drifting swift
how would you get rid of the exponent in an equation like z^7 = 128?
pliant leaf
I would root it
In this situation could I multiply both sides by the exponent of 3?
and 1^3 is =1
1/3*3=1
pliant leaf
how would you get rid of the exponent in an equation like `z^7 = 128`?
x=1? maybe?
Not sure if I can use exponents like that that works
drifting swift
In this situation could I multiply both sides by the exponent of 3?
no
you would raise both sides to the power of 3.
or -3, to get to x directly.
pliant leaf
Then what would I do?
drifting swift
after what
drifting swift
you would **raise both sides** to the power of 3.
.
drifting swift
or -3, to get to x directly.
.
pliant leaf
ah I was confused because I think thats what I was talking about
thanks I think I get it
.close
weary walrus
Better way to write this?
weary walrus
<@&286206848099549185>
huh
interesting
How would you set boundaries?
Cheers
.close
vocal nymph
what is an example of a real life problem that is a quadratic which only has one real answer (discriminant=0)
topaz sinewBOT
what is an example of a real life problem that is a quadratic which only has one...
drifting swift
are you asking this out of your own curiosity, or were you assigned this as a homework problem?
vocal nymph
ive been doing them but i dont understand when its useful in rl
like my homework is doing just number problems
drifting swift
okay, so you're asking this out of your own curiosity.
vocal nymph
yes
drifting swift
let's see
there are many ways to make such a problem
You have 12 meters of fencing and wish to make a rectangular enclosure of area 9 m^2. What should its dimensions be?
i believe this will fit the bill
vocal nymph
```
You have 12 meters of fencing and wish to make a rectangular enclosure of ar...
:OOOOOOOOOOOOO
wait let me try
also i know this may be a bit harder to answer but when would a discriminant of <0 be useful, i asked this before but the examples were too complicated for me
drifting swift
..."when would a discriminant less than zero be useful" is a bit of a weird question
it's like asking "when would the letters Q through Z be useful"
vocal nymph
i mean what is a rl problem that could use a quadratic which has a parabola that doesnt cross the x-axis
idk its my previous question but for imaginary numbers cuz all the examples i can find are always two solutions
drifting swift
i guess if you were to change the 9 m^2 in my problem to something like 10 m^2 you would find that the quadratic you end up with has a negative discriminant
from which you could conclude that the problem would be impossible
vocal nymph
wait i just found something but i dont completely understand it
its about bungee jumping
drifting swift
oh, you have a problem you'd like to share?
vocal nymph
yes but i dont understand it, if u could maybe help
i dont have to answer it btw, its just a random website
wait no
this
what is 9.2
im confused
drifting swift
9.2 is 9.2
it's just a number
it has some physical significance, but it's mostly irrelevant to solving this problem
vocal nymph
lol i dont get what the problem exactly is, is it saying that a quadratic can be used to find how long the rope should be?
mannnnn
drifting swift
no
the problem says,
we have control over how high the jumpers start from
(i.e. the value of k)
and we also don't want jumpers to hit the ground
because we're not maniacs and we don't want a pile of corpses on the ground right below our jumping platform
do you understand this? @vocal nymph
vocal nymph
yes but is there anything to solve?
vocal nymph
because we're not maniacs and we don't want a pile of corpses on the ground righ...
we?
drifting swift
we as in the company that makes the bungee jump
we want to know how high to build our platform
vocal nymph
we want to know how high to build our platform
YES
ok so the quadratic helps the company find how high the platform needs to be right?
drifting swift
you could say it like that i guess...
vocal nymph
but how would u write it as a question
like a quadratic to be solved
like ax^2+bx+c
but what are the a, b and c
0/y= is the height of the platform
the rest im not so sure
drifting swift
no
we aren't solving a quadratic equation
we are on a higher level of abstraction here
we have the quadratic equation x^2 - 9.2x + k = 0, and we want to ensure it doesn't have any roots
vocal nymph
oh so basically this situation mainly focuses on the discriminant, the company is just making sure the equation has no roots?
drifting swift
....you could say that
topaz sinewBOT
@vocal nymph Has your question been resolved?
topaz sinewBOT
topaz sinewBOT
Available help channel!
torpid fog
Two overlapping circles (with 2 intersection points), like in the diagram, with a know radius r1, r2 each (if it cant be solved for independent radii, same radius is fine). The centers of each circle lie on a line of length d. Perpendicular to this line is the line that joins the intersection points, of length a. What would be a way to calculate a as a function of d, r1, and r2; and if it isnt trivial, d as a function of a, r1, and r2 as well.
topaz sinewBOT
Two overlapping circles (with 2 intersection points), like in the diagram, with ...
torpid fog
Ive tried to play with trigonometry and it led me nowhere, theres something im missing
topaz sinewBOT
@torpid fog Has your question been resolved?
stark thicket
https://math.stackexchange.com/questions/689665/common-chord-of-two-circles
this is wat you're looking for
torpid fog
heron's is what i was missing
topaz sinewBOT
Available help channel!
dusty crane
topaz sinewBOT
dusty crane
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topaz sinewBOT
dusty crane
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topaz sinewBOT
Available help channel!
neon iron
Hello, I’m not very good at math, and I can't find calculator that work properly with big numbers. I just have a basic question. If we have 1 billion dollars, and 4.46 million people, how much money would each person get.
topaz sinewBOT
Hello, I’m not very good at math, and I can't find calculator that work properly...
silver trench
,w 1000000000 / 4460000
thorny flameBOT
silver trench
assuming u meant each person gets the same amount ^
neon iron
Yes I did, thank you!
silver trench
np happy to help!
neon iron
.close
next helm
why is the number of functions from $[n] \to [n]$ equal to $n^n$ and not $n!?$
thorny flameBOT
TheToadSage
topaz sinewBOT
@next helm Has your question been resolved?
next helm
<@&286206848099549185>
long stirrup
what does [] mean
anyway n! is for bijective functions
if every output must be achieveble
if a function always gives 0 it's also considered to have full range
i guess
long stirrup
why is the number of functions from $[n] \to [n]$ equal to $n^n$ and not $n!?$
i wanna figure it out, what's [] mean
next helm
i wanna figure it out, what's [] mean
$[n]={1,2,3,\dots,n}$
thorny flameBOT
TheToadSage
long stirrup
ok
warm hinge
Can anybody explain the stars and bars theorem to me?
topaz sinewBOT
Can anybody explain the stars and bars theorem to me?
long stirrup
there are 2
there's one where you have slots for "fences"
-
-
-
-
-
- ← 6 stars
to separate into 3 non empty groups choose 2 positions to fill out of 5
- ← 6 stars
-
-
-
-
and there's one where you can have empty groups, so you choose from sum of 6+2
long stirrup
you have 6+2 symbols, you choose which of them is a bar
it covers every order
|| * * * * * *
empty, empty, 6
- | * * * * * |
1, 5, empty
warm hinge
why am i choosing from the sum of 6 + 2 tho?
long stirrup
you don't think of slots to fill, it doesn;t make sense anymore if you can put several bars together
but you can still enumerate every permutation
of the whole thing
you always have 2+6 things at the end arranged in some order
you could do (2+6)! / (2!) / (6!)
it's equivalent to (2+6)c2
distinct permutation of 2 sorts of things = choose which things are the second sort
it's some visual thing
oh wow you can't be pinged
warm hinge
hmm
i'm really not getting how it's a valid concept tbh...
hold on
let's say we have k indistinguishable particles that can be distributed among n cells, and each cell can hold any number of particles, how can i really show that the number of possibilities to distribute those particles is n+k-1 choose k
warm hinge
shouldnt it be the concept of stars and bars?
long stirrup
you do the stars thing and it's absolutely convincing
warm hinge
let's say we have k indistinguishable particles that can be distributed among n ...
but how would i explain this then
with stars?
and bars
long stirrup
yes
warm hinge
is that even valid
long stirrup
if the cells are distinguishable
warm hinge
isn't stars and bars theorem supposed to be about indistinguishable stars and bars?
which is why you remove the permutations
long stirrup
only stars are indistinguishable
the cells are enumerated, the first one is the one that goes first
|| * * * is not the same as | * * * |
warm hinge
how tho
we still have 3 cells
and 3 particles
and if you say so, then |*|** would be the same as | * * * |
long stirrup
you can see which cell has the stars
bars are indistinguishble
cells are not bars they emerge from the thing
you gotta see the cells in the picture
contained between bars
it sounds like you skip the imagination part and it all becomes indecipherable
long stirrup
let's say we have k indistinguishable particles that can be distributed among n ...
n+k-1 choose (k-1) btw
warm hinge
wouldn’t it be n+k-1 choose n-1
topaz sinewBOT
Available help channel!
hollow swift
I understand the concepts involved and everything, I'm just struggling to come up with an example that does this. Any good places to start? This is homework so i can't have people just give me answers, thanks 🙂
topaz sinewBOT
I understand the concepts involved and everything, I'm just struggling to come u...
hollow swift
topaz sinewBOT
@hollow swift Has your question been resolved?
hollow swift
Currently trying to do something with the indicator function chi
Because it can be approximated with polynomials and such
But not really getting anywhere
<@&286206848099549185>
Im thinking since they are supposed to be differentiable everywhere on R that it must be some kind of well behaved rational function with n as an exponent, uniformly converging to a continuous function with a discontinuous derivative?
I found an example of a differentiable function with a discontinuous derivative online to base my work on, right now i'm working with the function $g(x) = \begin{cases} x^2\sin(\frac{1}{x}) & x \neq 0 \ 0 & x=0 \end{cases}$
thorny flameBOT
united9jackson
hollow swift
t see where it takes me
topaz sinewBOT
@hollow swift Has your question been resolved?
last quarry
which example do you want?
hollow swift
one that has all three
last quarry
You can't have all three at once
if $f'$ converges uniformly and $f$ converges for atleast one point, then $f$ also converges uniformly and $ \lim (f'_n) = (\lim f_n)'$
thorny flameBOT
Ryuzaki
hollow swift
That's if the interval they are defined on is bounded
f_n is guarenteed to converge pointwise though
I took the problem to mean the domain is R
last quarry
ok say what you are saying is right. then for a function in R to R has all those properties. now you can take any bounded interval [a, b] and look at the restriction of the function. since now the theorem must hold, it contradicts that the function has those properties.
hollow swift
Posting this from my professors notes so that we are on the same page
I think there is a fault in that logic somewhere because why would it specify this statement at the end
clearly the contrapositive means if it isnt uniform then it has to be an unbounded interval, which is what im working with (-infty, infty)
maybe like the lim at infinity doesnt converge correctly or something
last quarry
oh ok I think I get your point, the fault in my argument was that the convergence could be uniform for any bdd interval even though it's not uniform for entire R
hollow swift
Yeah
last quarry
it's a local property, one example is local integrability, the function 1/x in (0, infty) is locally integrable (means interable in every compact subset) but not globally integrable
last quarry
some thing similar phenomenon is at play probably
hollow swift
Maybe something based on $\sqrt(x)$ would work
thorny flameBOT
united9jackson
thorny flameBOT
Ryuzaki
last quarry
f'_n converges to 1/x and f_n to log(x)
last quarry
but |log(x+1/n)-log(x)| = log(1+1/(nx)| \to 1 not 0
hollow swift
Interesting
last quarry
interval is (0, infty) not [0, infty)
hollow swift
Mmm yeah
Do you think this would qualify since the problem says differentiable on R
last quarry
it may not work, check it and try to modify it to something that actually works
last quarry
Do you think this would qualify since the problem says differentiable on R
well for R you can change the variable to something that maps (0, infty) to R and replace x with it
hollow swift
Oh yeah
last quarry
I think this one works but check
$f_n = log(x)+log(1+\frac{x}{n})$ and we have $f'_n = \frac{1}{x} + \frac{1}{n+x}$. in the interval $[1, \infty)$. you can show with $M_n$ test that $f'_n$ converges uniformly to $\frac{1}{x}$ and $f_n$ converges to $log(x)$. Now $|log(x)+log(1+\frac{x}{n}-log(x)| = log(1+\frac{x}{n})$ since x is unbounded you take $x=n$ and show that the abs dist never goes to zero as sup is atleast log(2). So the convergence is not uniform but it is PW.
thorny flameBOT
Ryuzaki
last quarry
@hollow swift
note tho that it is uniform in any compact interval showing that it's an local property. That's where I messed up
for R to [1, infty) you can the simple modification u=1+|x|^2
hollow swift
Ah this sounds good
Before looking here i was trying to work it with just using what we talked about before, and i came so close to the solution that you just suggested
So i feel good about the amount of effort put into this on my part lol
I'm testing this further right now
last quarry
hollow swift
@last quarry a problem with your example might be that if you make n ridiculously large it begins to tend towards -infinity
at least when i replace x for 1+x^2
nvm give me more time lmao
fluid needle
I got to f(x) = 4 (x^2) (x-2)^3 + (x-2)^4 (2x)
topaz sinewBOT
I got to f(x) = 4 (x^2) (x-2)^3 + (x-2)^4 (2x)
sour bloom
what's this, expand? plot? find the derivative?
fluid needle
Sorry forgot to mention, find the derivitive
topaz sinewBOT
@fluid needle Has your question been resolved?
inner oracle
You took the derivative in first step itself then why is left side not f'
fluid needle
where does the x^2 on the left go when i simplify
inner oracle
4 (x²)(x-2)³ + 2x(x-2)⁴ = 2(x-2)³ (2x²+x(x-2))
fluid needle
inner oracle
4 (x²)(x-2)³ + 2x(x-2)⁴ = 2(x-2)³ (2x²+x(x-2))
.
fluid needle
oh you took a 2 out from the coefficients?
inner oracle
Yes idk how you misplaced it
fluid needle
yeah i can see that now
inner oracle
Finally you should get 2x(x-2)³(3x-2)
inner oracle
been looking at this ting for a while
Close the channel
fluid needle
.close
runic sail
topaz sinewBOT
fervent coyote
runic sail
What's t there??
fervent coyote
A natural number
Since a is a natural number and it is a fourth power .. I took it it to be t^4
runic sail
But a is fifth power. a⁵
fervent coyote
a is the form of a fourth power (since it's a natural number) . When you raise it to power 5, it becomes (t^4) ^5=t^20. So does b, it becomes (t^5) ^4= t^20
Side note: Actually, Even if "a" weren't a natural number i can take it to be t^4 for some t, simply because it is positive.
runic sail
a is the form of a fourth power (since it's a natural number) . When you raise i...
So we can write all natural numbers in the form of fourth power of some other natural number..?
fervent coyote
No.
We can write as the fourth power of some real number
In this case however it is a natural number
runic sail
We can write as the fourth power of some real number
Ok so you mean if we let a=3, then (some real number)⁴=3 then that real number will be 3¼ ?
runic sail
If we consider t⁴=a , then how is it sure then that same t⁵ will make b??
fervent coyote
Using that condition a^5= b^4
fervent coyote
Using that condition a^5= b^4
It's a given condition
runic sail
Now what should i do?
fervent coyote
Take the fourth root
fervent coyote
No, i mean take fourth root of b^4... Similarly on the other side of the equality
You end up with b=t^5
runic sail
How???
fervent coyote
(b^4)^(1/4)= (t^20)^(1/4) .... b = t^(20/4) = t^5...I suggest you clear up your basics
topaz sinewBOT
@runic sail Has your question been resolved?
topaz sinewBOT
topaz sinewBOT
Available help channel!
bright tendon
#9
sick vapor
n-th root of x is simply $x^{\frac{1}{n}}$
thorny flameBOT
Schrödinger's cat
sick vapor
So the first one would be $x^{25×\frac{1}{5}}$
thorny flameBOT
Schrödinger's cat
sick vapor
which is $x^5$
thorny flameBOT
Schrödinger's cat
outer jolt
Does anyone know why the equation of the sum of interior angles of a polygon is 180(n-2)
topaz sinewBOT
Does anyone know why the equation of the sum of interior angles of a polygon is ...
tiny marsh
I think the proof had something to do with how many triangles you can break the polygon down to
vague sapphire
topaz sinewBOT
vague sapphire
I have tried a few things but I am unsure
main mauve
expand the numerator
vague sapphire
Also I have a few questions, does 6sqrt(x) = 6 + x^1/2 or 6x^1/2
vague sapphire
Ok thanks
vague sapphire
(9-6sqrtx+x)/sqrtx
Like in my second to last calculation
rustic sapphire
help what do i pick
topaz sinewBOT
@rustic sapphire Has your question been resolved?
languid helm
topaz sinewBOT
languid helm
Why is there no loss of generality here?
topaz sinewBOT
@languid helm Has your question been resolved?
topaz sinewBOT
@languid helm Has your question been resolved?
somber osprey
Because you can assume any number as he just use 100 as example to help intuition. And don't even uses it on the calculations
vernal vale
hey tim
vernal vale
Why is there no loss of generality here?
100 is an arbitrary number, just like mahousenshi said
you could replace that with any number that leaves you without fractions of students
languid helm
Yeah I know
vernal vale
oh
languid helm
I solved it with arbitrary T
But what is the reason intuitively
Something to do with percentages right?
Could you formulate this thought
pls
vernal vale
you could just like
replace the number with percent
although maybe the statement let there be 100% students isnt super intuitive
its just like
say there are 50 students
then all the numbers are half
if its 200 then its double
maybe you get that too
languid helm
Oh right
languid helm
Whatever it is you can factor it out of top and bottom
vernal vale
say it was 200 instead of 100
languid helm
and you get multiplied by 1
vernal vale
i mean percents work this way since theyre unitless
but you may be thinking of normalized
like instead of saying colorado has X covid cases and new york has Y
youd probably say per 100k residents or something
alternatively unitless things are nice
but it wouldnt really matter here
like you did it generally right
vernal vale
so you have a bunch of stuff like K = 0.3*T
languid helm
that's a good word
vernal vale
they all come from T
languid helm
Right right
vernal vale
or whatever general universal collection you have
they all scale with T
that dependency just tracks though
languid helm
that dependency just tracks though
I get it I giet it
thanks janm
Will you graduate soon @vernal vale
just wondering
languid helm
Oh wow
That must be exciting
I want to take complex analysis
Maybe you can teach me some cool stuff if you ever have free time
languid helm
Will you become a teacher?
vernal vale
idk hopefully not since its not super great paying
but maybe
i feel like i could be good at it
but i might have a lot of loans
vernal vale
languid helm
.close
topaz sinewBOT
vernal vale
u too permastudybuddy
languid helm
,iamstudying
thorny flameBOT
topaz sinewBOT
Available help channel!
inland tapir
does fully simplifying a rational expression include expanding every factor in the end?
topaz sinewBOT
does fully simplifying a rational expression include expanding every factor in t...
inland tapir
like is it correct to say that this is fully simplified
or do i have to expand the denominator
and put it in standard form
damn why did i take the last help channel
topaz sinewBOT
@inland tapir Has your question been resolved?
topaz sinewBOT
@inland tapir Has your question been resolved?
inland tapir
.close
gilded summit
topaz sinewBOT
gilded summit
i need to find the area of the shaded side
btw not academic dishonesty this is a question i got on a math olympiad earlier today just wanted to find the solution bc its the only one i couldnt solve
topaz sinewBOT
@gilded summit Has your question been resolved?
final rock
sharp tapir
Are you supposed to prove this?
Have you gotten anywhere?
Do you have any idea what to do or no
topaz sinewBOT
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topaz sinewBOT
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Available help channel!
swift zephyr
I need help with this problem, I made the function f(x)=((-1(x-5)(x+4))/(5/3)(x+3)(x-4)) I know I need to reduce it but when I try I get
((-3(x-5)(x+4))/(5(x+3)(x-4))) Idk where I am incorrect
topaz sinewBOT
I need help with this problem, I made the function f(x)=((-1(x-5)(x...
@swift zephyr Has your question been resolved?
topaz sinewBOT
@swift zephyr Has your question been resolved?
leaden tusk
I need help with this problem, I made the function f(x)=((-1(x-5)(x...
that would not get you a horizontal asymptote ay y=-1
swift zephyr
For my Y asymptote I thought thats what the -1 was in f(x)=((-1(x-5)(x+4))/(5/3)(x+3)(x-4))
leaden tusk
$f(x)=\frac{-(x-5)(x+4)}{\frac53(x+3)(x-3)}$
thorny flameBOT
a disappointing son
leaden tusk
the numerator and denominator share the same power, so to get your horizontal asymptote, what do you do?
(note that none of your x terms have coefficients)
swift zephyr
I got a question on what function displayed I thought it would be $f(x)=\frac{-(x-5)(x+4)}{\frac53(x+3)(x-4)}$
thorny flameBOT
Weld🪒
swift zephyr
you put +3, -3, And I have +3 ,-4 because i thought it was x asymptote of x-3 and x4
leaden tusk
oh, that was just a typo
leaden tusk
the numerator and denominator share the same power, so to get your horizontal as...
this still applies
swift zephyr
Idk what todo since they have the same power
leaden tusk
did you not learn about horizontal asymptotes?
swift zephyr
Im new to doing them
leaden tusk
for a function $f(x)=\frac{ax+c}{bx+d}$, the horizontal asymptote(s) are equal to $\frac{a}{b}$
thorny flameBOT
a disappointing son
leaden tusk
and this goes for any polynomial with the same highest order power
seeing as the highest power will, at an infinitely high x value, take control of the function
none of the other terms will matter
swift zephyr
Aint that same for finding the y cord of a hole?
leaden tusk
so it will approach a value $\frac{ax}{bx}$, which is just $\frac{a}{b}$
thorny flameBOT
a disappointing son
leaden tusk
uhh
leaden tusk
i'm again not quite sure what you mean
if you want to find the y coordinate of a hole, just find the x coordinate where the hole occurs and plug that into the original function
leaden tusk
since all your x terms have coefficients of 1, expanding it out would also result in coefficients of 1, so yes, a is -1 and b is 5/3
this is just to tell you why your equation is wrong by the way lol
swift zephyr
ok
leaden tusk
your equation would have a horizontal asymptote at $\frac{a}{b}$, where $a=-1, b=\frac53$
thorny flameBOT
a disappointing son
leaden tusk
which is -3/5
so your equation gives a HA at y=-3/5
and your question wants one at y=-1
swift zephyr
where do I Plug in my Y intercept into my equation then? Because I dont want it to interfear with the -1 HA
leaden tusk
your equation doesn't have a HA at -1
that's your issue
it also doesn't have a y int of -5/3 because of that issue
you want your HA at y=1, therefore $\frac{a}{b}=-1$
thorny flameBOT
a disappointing son
leaden tusk
which means $a=\pm b$
thorny flameBOT
a disappointing son
swift zephyr
y-intercept is marked with a point located at (0,−5/3). ?
leaden tusk
yes, but your current equation doesn't have a y int at -5/3
swift zephyr
I just dont know where to put -5/3 into my equation
leaden tusk
just putting the number into the equation will not make it a y intercept
don't think about the intercept quite yet though
fix your asymptote problem
swift zephyr
Well to fix my asymptoe problem I just take out the 5/3
thorny flameBOT
a disappointing son
swift zephyr
yes
leaden tusk
what happens when you find your y intercept of that?
swift zephyr
So I just plug in -5/3?
swift zephyr
x is 0
swift zephyr
equals -5/3
leaden tusk
exactly
swift zephyr
and that would be my formula?
leaden tusk
well... $f(x)=\frac{-(x-5)(x+4)}{(x+3)(x-4)}$ has a y intercept of (0, -5/3), a horizontal asymptote at y=-1, vertical asymptotes as x=-3 and x=-4, and x intercepts at (5,0) and (-4,0)
thorny flameBOT
a disappointing son
leaden tusk
and that seems to meet your criteria
swift zephyr
Thank you
mild hearth
swift zephyr
When I try and graph this one the function I made the opposite of what I want? Do Do i change that?
I made f(x)= (x-0)/((x+6)(x-5))
When I graph it looks similar but is mirrored.
topaz sinewBOT
@swift zephyr Has your question been resolved?
swift zephyr
nothing much just trying to see where I messed up on this function
long time no see
swift zephyr
yes
thorny flameBOT
swift zephyr
how come it was the other way a second ago
swift zephyr
so if its mirrored the wrong way just put a negative in front?
vernal vale
well it depends on which way its mirrored
swift zephyr
well thank you for helping me out like always
swift zephyr
what the heck is that
swift zephyr
yes
vernal vale
you may be curious what line -f(-x) reflects across 
exercise for the reader
so your general shape matches
but youre still not hitting that point, i think?
,w -.5/( (.5+6)(.5-5))
thorny flameBOT
thorny flameBOT
Result:
0.5
so -f(-x) is backwards?
vernal vale
not backwards
its a reflection
you dont need it for this problem but if youre curious
swift zephyr
it just does x and y then?
vernal vale
well it takes something to the other side of the x axis
then to the other side of the y axis
which is a reflection about a line
but the line isnt either axis
swift zephyr
Thank you
vernal vale
so in the problem you posted
its still not going through that point
its off by about
0.48
or so
swift zephyr
the -x/((x+6)(x-5)) was good for the problem posted
vernal vale
oh, okay
vernal vale
hmm maybe its not about a line
i could just be dumb
i have to be careful about helping late at night
swift zephyr
idk you help me finish my hw so im thankfull, and i learned some new things
topaz sinewBOT
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violet glacier
$(46/148)/(46/148+51/152∙152/300)
topaz sinewBOT
$(46/148)/(46/148+51/152∙152/300)
thorny flameBOT
MrMadium
violet glacier
I know that this is supposed to simplify down to 46/97 to prove a Bayes application.
I just don't know how you go about simplifying the equation.
It was originally:
(46/97=(46/148∙148/300)/(46/148∙148/300+51/152∙152/300))
thorny flameBOT
MrMadium
topaz sinewBOT
@violet glacier Has your question been resolved?
topaz sinewBOT
@violet glacier Has your question been resolved?
topaz sinewBOT
@violet glacier Has your question been resolved?
pulsar falcon
I know that this is supposed to simplify down to 46/97 to prove a Bayes applicat...
,w (46/148148/300)/(46/148148/300+51/152*152/300)
thorny flameBOT
violet glacier
Thank you @pulsar falcon - I tried it in Symbolab and it didn't help. Many thanks again!
.close
sharp dew
topaz sinewBOT
sharp dew
Can I say 3x is the coefficient of y
drifting swift
if you're considering 3xy as a polynomial in y, then sure
topaz sinewBOT
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sharp dew
got it thank you so much ann
hazy crown
Hello! I need help with these problems.. If you can help me solve for the answer instead of giving me the actual answer, that would be nice ^_^//
topaz sinewBOT
Hello! I need help with these problems.. If you can help me solve for the answer...
@hazy crown Has your question been resolved?
hazy crown
Hello! I need help with these problems.. If you can help me solve for the answer...
<@&286206848099549185>
gusty estuary
what question are you stuck on, and what have you tried so far?
hazy crown
all of them- and i don't really know how to solve for them either,,
gusty estuary
well, in the first question you really dont need to solve for x
my bad those arent points
are you familiar with the quadratic formula?
hazy crown
yes
spare idol
I need some help
gusty estuary
I need some help
This channel is taken
Zeroes occour when the graph intersects the x axis, aka. When we let y=0
that you can do is let y=0 in all of those equations, and then plug in -4 and 5 for x too see if the right and left side are equal to eachother
If they are, then the zeros -4 and 5 match for that equation
hazy crown
so make y=0 and plug x= -4 & 5?
gusty estuary
yes
neon iron
@gusty estuary (x-a)(x-b) was more efficient no?
hazy crown
okay, same goes for question 12?
gusty estuary
On question 12 i think its actually more efficient if you use the quadratic formiula on the equation given
hazy crown
alright,, what about question 13?
gusty estuary
Its shifted 5 units up and 2 units to the right
hazy crown
wha-
gusty estuary
5 units up means it now will intersect the y axis at y=5
Thus you get a constant term +5
hazy crown
ohh
gusty estuary
2 units to the right means we just substitute x with x-2 (its - when its to the right, and + when its to the left)
hazy crown
last, question 14
gusty estuary
That the rectangular field can be enclosed by 80m of fencing basically means its perimeter must be =80
We can write the perimeter of a rectangle as 2L+2W
Then you can set 2L+2W=80, and then see which of the numbers in A-D match with the equation
hazy crown
oh i thought it was L×W at first but i got 3 digit numbers ajvdgd
anyways, thanks for helping! 17 & 18 is all good
gusty estuary
ightt np
hazy crown
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keen fulcrum
P and Q are two points 50 km apart, with Q due east of P. A third town R, to the north of the line joining P and Q, is 70 km from P and 30 km from Q. Find the bearing of R from Q and P.
topaz sinewBOT
P and Q are two points 50 km apart, with Q due east of P. A third town R, to the...
worthy lake
i would advise u drawing it
keen fulcrum
i need help findingr from q
yeah i did
and i used cosine rule
and got an angle but the angle i got was 120
which is wrong
so idk
worthy lake
u sure u put the right numbers?
keen fulcrum
yup
keen fulcrum
cosC = ((30)^2+(50)^2-(70))^2)/2(30)(50)
and then cosC = -1/2
C = cos inverse -1/2
= 120
keen fulcrum
wdym
worthy lake
read carefully
keen fulcrum
is it not meant to be -(70)^2
cos the number in c should be opposite the angle
which is 70
worthy lake
the numbers are right
worthy lake
keen fulcrum
so what did i input wrong?
worthy lake
so 50^2=70^2+30^2-2(30)(70)cos R
topaz sinewBOT
@keen fulcrum Has your question been resolved?
worthy lake
u need to find r and q
cause the question says find r from p and q
or u could find pand q
keen fulcrum
question 12
topaz sinewBOT
question 12
topaz sinewBOT
@keen fulcrum Has your question been resolved?
keen fulcrum
<@&286206848099549185>
hazy pumice
ok, and it's understood that the angle is clockwise under this standard?
that part at least feels familiar
your 280 degree T measure would be wrong then, since the angle is measured from "true north", wouldn't it?
keen fulcrum
your 280 degree T measure would be wrong then, since the angle is measured from ...
i don't think my diagram is wrong
because you start from north so 0 degrees then make a 280 degree rotation
hazy pumice
nothing is quite to-scale, obviously
you can get the missing distance using LoC
$c = \sqrt{900^2 + 1600^2 - 2\cdot 900 \cdot 1600 \cdot \cos{40}}$
thorny flameBOT
Disorganized
keen fulcrum
oh wait i realised what i did wrong
how do you know that the agnle is 50
in there
hazy pumice
I measured each angle off "true north"
and used opposite interior angles to get 50 off west
hazy pumice
now, if you do 360 - 280, you have 80 leftover...which is 10 degrees off west
so 50 - 10 = 40
keen fulcrum
**Disorganized**
wouldn't it be cos 40
keen fulcrum
ah ok
hazy pumice
got it?
hazy pumice
@keen fulcrum do you have the second part ok?
keen fulcrum
can you help me with that too
hazy pumice
ok. so you filled in the missing side, right?
hazy pumice
ok, so what ideas do you have on how to find the bearing from the airport at that last position?
what do we need
keen fulcrum
the angle between 900 and 1079
hazy pumice
yes
keen fulcrum
so cosine rule again
hazy pumice
Law of Sines
hazy pumice
if we call the top angle alpha
keen fulcrum
and then you can use the 50
hazy pumice
$\frac{\sin{\alpha}}{1600} = \frac{\sin{40}}{1078.791919}$
thorny flameBOT
Disorganized
hazy pumice
no, the angle is 40, remember
hazy pumice
multiply both sides by 1600 and arcsine it
then add that to the original bearing
$\alpha = \arcsin{\frac{1600\cdot\sin{40}}{1078.791919}}$
thorny flameBOT
Disorganized
keen fulcrum
72.39
keen fulcrum
then add that to 140?
hazy pumice
wat
keen fulcrum
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neon iron
topaz sinewBOT
neon iron
can someone solve this
<@&286206848099549185>
<@&286206848099549185>
<@&286206848099549185>
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topaz sinewBOT
topaz sinewBOT
Available help channel!
obsidian mountain
Hey, easy question but i got some logic trouble. What is diffrent between domain of main function and domain of her alternative from?
Easy example ((x(x^2-25)/(x+5))):
https://www.wolframalpha.com/input/?i=(x(x^2-25)%2F(x%2B5))
https://www.wolframalpha.com/input/?i=x(x-5)
topaz sinewBOT
Hey, easy question but i got some logic trouble. What is diffrent between domain...
@obsidian mountain Has your question been resolved?
topaz sinewBOT
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neon iron
topaz sinewBOT
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stone chasm
I am confusion
topaz sinewBOT
I am confusion
stone chasm
I don't get where the 7 in -6x^7 came from.
main mauve
@stone chasm they basically did exponent laws on all the x exponents except for the 2 in the denominator
so that would just leave us with (-3x^2)/(x^-2) * 2x^3 = -3x^4 * 2x^3 = -6x^7
also this is nowhere near fully simplified lol
stone chasm
Wait ill send the full simplified thing.
But I still don't get what you mean though 
main mauve
they did it a weird way
topaz sinewBOT
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stone chasm
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inland portal
What would the answer be for this question? I need help verifying. Thank You.
topaz sinewBOT
What would the answer be for this question? I need help verifying. Thank You.
@inland portal Has your question been resolved?
inland portal
<@&286206848099549185>
topaz sinewBOT
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spring storm
spring storm
Its a notation
wheat laurel
oh ok
spring storm
nCr
wheat laurel
yeah ik
i just thought c is a constant
@spring storm also
the fourth visible term
is it supposed to be 21C15?
@spring storm you here?
spring storm
Yeah
spring storm
is it supposed to be 21C15?
Not sure :(
thorny flameBOT
Adavocowana
south rose
Can someone go over this with me? I don't want the answer, I wanna know where I'm making a mistake
topaz sinewBOT
Can someone go over this with me? I don't want the answer, I wanna know where I'...
south rose
I know it's a tedious problem, but if anyone can help I will really appreciate it
topaz sinewBOT
@south rose Has your question been resolved?
south rose
<@&286206848099549185>
I will send my notes every step of the way, I will be easy to work with I promise
topaz sinewBOT
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coral knoll
Bit confused on part a)
topaz sinewBOT
Bit confused on part a)
coral knoll
$\abs{z-(2+i)} = \abs{(x-2) + (y-1)i} = 4$
thorny flameBOT
feather
coral knoll
$\Rightarrow {(x-2)}^2 + {(y-1)}^2 = 16$
thorny flameBOT
feather
coral knoll
That's a circle centered at (2, 1)? Which I guess on the complex plane is 2+i
But like
Is that it
coral knoll
That's a circle centered at (2, 1)? Which I guess on the complex plane is 2+i
This feels so handwavy to me
Oh wait
It's a circle centered at (2, 1) which is the complex number 2 + 1i
well that's not right
but I think I have the spirit
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topaz sinewBOT
topaz sinewBOT
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timber hill
Hi there, I am currently stuck trying to solve a task on my task sheet / preparation for my next university lesson (first semester of applied computer science (bachelor)):
My task is to find the rule/law or however it is called in English (I am german, so sorry if I sometimes use the wrong vocabulary) for the following sequence:
1; 1; 7/5; 15/7; 31/9; ...
By looking at this sequence I can easily see that after 7/5 every following number has a denominator which is +2 compared to the previous number's denominator and a numerator which is *2 + 1 of the previous number's numerator, but I have no idea how I could "access" just the nominator or the denominator of the previous number so I don't know what to do.
Here is an example solution for a different sequence:
Sequence: 0.2; 0.04; 0.08; ...
Solution: 1/(5^n)
I think that I need to use a recursive rule/law/whatever to solve this task because I do not see how this can be solved without using the previous number in the sequence to calculate the next one, but I could be wrong about this
topaz sinewBOT
Hi there, I am currently stuck trying to solve a task on my task sheet / prepara...
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timber hill
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