It’s wtv guy is a troll
#help-38
raw magnet
young ice
dude
young ice
It’s wtv guy is a troll
dude i just need help
wraith hinge
question*
young ice
we need to evaluate the expression (1/1000)^1/3
now pls walk me thru the steps
i’m sorry for saying ur a bad jelper
i didn’t mean it
wraith hinge
we need to evaluate the expression (1/1000)^1/3
we already did this
bright quarry
i’m sorry for saying ur a bad jelper
he apologized
young ice
that wasnt even ur question
wait whoops
wraith hinge
u did this question in a different channel
young ice
i copy and pasted the wrong thing
wraith hinge
bruh
bright quarry
assuming it’s 125^(8/3)
young ice
what do we do to evaluate the expression
young ice
assuming it’s 125^(8/3)
i just said it is
raw magnet
assuming it’s 125^(8/3)
Yeah I’m confused
bright quarry
what do we do to evaluate the expression
they have a common base of 125
young ice
they have a common base of 125
kk
bright quarry
u can subtract the exponents
young ice
wait is (125^8)/3
leave this chanel
wraith hinge
no
young ice
channel
young ice
u can subtract the exponents
Ah
bright quarry
leave this chanel
🤨
wraith hinge
im tryina clarify sm
young ice
u can subtract the exponents
air gut so
wraith hinge
or 125^(8/3)
^
sick onyx
see
bright quarry
no
young ice
but we need positive exponents
bright quarry
3=9/3
sick onyx
thats why I couldnt help him-
bright quarry
9/3 - 8/3=…
bright quarry
wait wait what??
they need a common denominator
young ice
how did u get 9/3
sick onyx
its just modified into a fraction
young ice
they need a common denominator
OH
raw magnet
thats why I couldnt help him-
Can everyone leave but knief and Rick
young ice
so we multiples numerator by 3 and denominator by 3
bright quarry
yes
young ice
25
bright quarry
or what number multiplied by itself 3 times is 125
bright quarry
yes
young ice
so that’s it?
bright quarry
mhm
bright quarry
ur welcome
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restive basin
Would this be 5 because there are 4 turning points?
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Would this be 5 because there are 4 turning points?
tepid hamlet
how do you know they are all turning points? it isn't given that the values are given in order of increasing x or anything
restive basin
Or roots, or x intercepts
yes, they are zeros
short kiln
Guys it doesn’t matter the minimum is 7 by theorem
restive basin
Guys it doesn’t matter the minimum is 7 by theorem
wtf
tepid hamlet
it's telling you it has these "function values" i.e. values of y isn't it?
short kiln
Graph x^2
restive basin
wait no
restive basin
it's telling you it has these "function values" i.e. values of y isn't it?
yeah
restive basin
Or roots, or x intercepts
they aren't
restive basin
so the minimum degree is just 1 isn't it? what am i missing?
its not a line
like you can tell where it turns
tepid hamlet
its not a line
any line with non zero slope takes on y-values with these values for some x doesn't it?
tepid hamlet
like you can tell where it turns
it's just giving you a set of y values...it isn't saying that these y values are occurring in some particular order
restive basin
its in assending order
tepid hamlet
the line y = x has y values of 9, 7, -9, -2, -5, -3 and -10 for x values of 9, 7, -9, -2, -5, -3, and -10 respectively doesn't it?
tepid hamlet
its in assending order
where does it say that? it's just giving you a set of y values
short kiln
No it’s 7
restive basin
its ascending
short kiln
Well unless it’s just y = C
tepid hamlet
its ascending
where the heck does it say that in the problem statement? 🤔
restive basin
where the heck does it say that in the problem statement? 🤔
its ascending in all the problems that the teacher did
like for this question, the answer was 3.
tepid hamlet
its ascending in all the problems that the teacher did
then it's just a badly written problem, it should incorporate all information in the problem statement, not expect you to know that based on "other problems" you do in the class, that's not how math works
restive basin
then it's just a badly written problem, it should incorporate all information in...
its not that deep
tepid hamlet
you're missing the point, this is bad math
there is literally no information about expecting these to correspond to ascending values of x in the problem
left oriole
the only thing you can really say is that it's not degree 0
tepid hamlet
exactly
tepid hamlet
the only thing you can really say is that it's not degree 0
thanks for joining, finally i feel like i'm not talking to a wall
restive basin
the real problem is that I haven't gotten my answer checked
that seems kinda rude, mb
it just is in ascending order
why would anyone mix it up while making the question wording horrible
tepid hamlet
it just is in ascending order
the correct answer is call out your teacher on bad problem writing during class so they can do better
😄
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tight sage
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tight sage
I need help on question 11
crisp flame
I need help on question 11
!status
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I need help on question 11
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
1
tight sage
no I think that is my problem]=
crisp flame
wait have you been taught vectors?
tight sage
It was todays topic and the teacher didnt explain it because he wants to set us up for failure
crisp flame
It was todays topic and the teacher didnt explain it because he wants to set us ...
well then I suggest you atleast learn the basics first
you can watch this or khan academy both are good
tight sage
ya alright I know all that
but thats for right angle traingle thats easy
its when its not
it makes it confusing
I just need to see someone doing it and I should be fine from there
crisp flame
let me draw a diagram rq for the question
crisp flame
I just need to see someone doing it and I should be fine from there
is there anything you dont understand in this diagram
tight sage
Alright
crisp flame
or is that 200N
yes 200 sorry
tight sage
oh alright
crisp flame
We havent learned that yet
welp then you cant really solve this
you can either watch the video to understand how to take components
tight sage
Wow truly set up for failure from the teacher
crisp flame
lol thats sad
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grim summit
Let P be a convex polygon in the plane, and let P’ be an enlarged version of P, dilated by a scale factor of 2. Show that seven copies of P can completely cover P’.
grim summit
I apologize for posting this so many times
But I got it closed accidentally + wasn’t able to get an answer
tepid hamlet
Let P be a convex polygon in the plane, and let P’ be an enlarged version of P, ...
that doesn't seem true
!original
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Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
tepid hamlet
if you are stretching out a polygon by a factor of 2 in each direction then the area will increase 4-fold not 7-fold...think about it with a square for the simplest example (four small squares will fit inside a square with double the side) or with triangles:
grim summit
that doesn't seem true
It is still true
In the case of an equilateral triangle, yes u only need four copies but seven still technically work
To show that four doesn’t always work
Consider a regular hexagon
Or more obviously
A regular 1000-gon (basically a circle) so u will need seven copies
tepid hamlet
grim summit
what?
did I do something wrong?
@tepid hamlet
for a circle four copies won’t fit the bill
tepid hamlet
did I do something wrong?
yeah...just to give one example a hexagon's area can be computed based on its side length for a regualr hexagon:
A = (3√3 s^2)/2
if you double the length of s, again the area increases by a factor of 4 as I said before
so not sure why you are claiming you could cover that area with 7 copies of the smaller version, since that would imply the area increases by a factor of 7
tepid hamlet
i just don't know where you are coming up with 7
grim summit
i just don't know where you are coming up with 7
that’s the problem statement
just because the area is 4 times does not mean u can physically cover it
tepid hamlet
I don’t remember the original source exactly
i guess you must be just misremembering something if you aren't even sure this is the correct problem statement
grim summit
I am not misremembering
I don’t know what u don’t get
pls show me how this is possible with a circle
this is what it is for a circle
7 also
@tepid hamlet
tepid hamlet
oh i see i misinterpreted "cover"
grim summit
yeah
tepid hamlet
yeah i wasn't understanding the problem properly
grim summit
so then what can u do?
tepid hamlet
that's actually quite an interesting problem then but i am not sure how to approach it
grim summit
that's actually quite an interesting problem then but i am not sure how to appro...
yes
it’s hard
tepid hamlet
since they're convex polygons, is there some method for inscribing a circle into a arbitrary convex polygon? maybe those circles would be sufficient to cover? i dunno, just one random thought
grim summit
u can’t but I wish
wraith hinge
so seven copies can overlap , they dont have to be edge to edge ?
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grim summit
so seven copies can overlap , they dont have to be edge to edge ?
yes
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wraith hinge
and the degree of overlapping or the extent upto which it can overlap doesnt matter
?
wraith hinge
i see okay
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scarlet cosmos
hi can anyone help me understand how to get to the third line from the second ?
forest egret
it factored -2x(x^2+1)
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marsh forum
I know I asked this yesterday, but I'm still not sure I understand how to solve something like $\frac{dy}{dx}=\frac{\left(x+y+1\right)}{x-y+2}$
solid kilnBOT
Why am. I here
marsh forum
just a hint please
tepid rock
👀
ripe valley
hi
tepid rock
Is it fine I still continue telling you the same way I told you before?
ripe valley
wait u were doing this yesterday no?
tepid rock
well you want to find the intersection of the numerator line and denominator
Let's say that's (a,b)
marsh forum
why, what's the motivation behind that?
tepid rock
Well because you were going on about something to do with u = y/x
Or x/y
This is applicable if the DE is homogeneous.
Like the rhs
And once you let it be that, you get two new lines. It'll give you a homogeneous curve.
You can then let u = Y/X without any pain.
But only then.
marsh forum
,w x+y+1=0; x-y+2=0
solid kilnBOT
solid kilnBOT
Why am. I here
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tepid rock
I've already asked them about their username origin, it's not the same as me.
trail ingot
whenever i saw either of you separately
hallow crane
honestly you were one person in my head <a:joyspin:690630295548067981>
same thoughts tbh 😭
tepid rock
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last falcon
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last falcon
Can someone help me find the coordinates of M
Dont tell me the answer pls just show me a way
i’ve though of calculating AB and divide it by 2 but i dont think it works the same with vectors
violet sigil
Do you know how to find midpoint
last falcon
i saw that during school so yeah
but
im self studying this book
and this one doesnt show that so i suppose i should use another way?
So far it showed me this and until this section i havent seen that formula in the book
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last falcon
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safe shuttle
The answer is C. How do I solve this?
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The answer is C. How do I solve this?
lusty delta
The answer is C. How do I solve this?
consider how u normally solve a linear system of equation in 2 var
u can use elimination or substitution (hint: ||i recommend elimination here||)
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lusty delta
why do i need to use elimination here?
did you try it?
safe shuttle
Nope. The answer was that bacause the equations are proportional to each other, they represent the same line in the plane thus having infinitely many solutions
lusty delta
that's true
and immediately noticeable if u try to eliminate a variable
ax + by = c
dx + ey = f
multiply 2nd equation by a/d = b/e = c/f
becomes
ax + by = c
receive same line; therefore infinite solution
safe shuttle
ahh ok i understand it better now thanks!
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wraith hinge
ok so, for every rational no there is an integer and vice versa (bijection between them) so, we can say: In x^p, the p is the integer and x is the rational no and so, for every x, there is p and vice versa hence bijection proved. is this right
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``ok so, for every rational no there is an integer and vice versa (bijection bet...
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wraith hinge
<@&286206848099549185>
runic dew
Your phrasing seems it bit odd when you use "no". It is not clear what you are trying to say
charred trail
No means number I assume
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wraith hinge
Your phrasing seems it bit odd when you use "no". It is not clear what you are t...
number
wraith hinge
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silver gust
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silver gust
Is there a solution for this?
sharp heart
marsh forum
$9^x -25 \cross3^x=54$?
solid kilnBOT
Why am. I here
marsh forum
Probably, try subbing $3^x=u$
solid kilnBOT
Why am. I here
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orchid wagon
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rough goblet
jesus chr7st
orchid wagon
i dont know how to solve the funny quintic
rough goblet
what abomination have you cooked up
orchid wagon
i like doing functional equations
rough goblet
lmao
you introduced me to them i like them too
,w factorize(x^5 + 4x + 3)
hmmm
this is weird
orchid wagon
indeed it is
rough goblet
btw, what does upside down A w/ x mean
orchid wagon
for all x in R
frozen plover
sub x = t^5 + 4t + 3?
rough goblet
sub x = t^5 + 4t + 3?
where, exactly
orchid wagon
nope
frozen plover
in the integral
rough goblet
i was thinking of that
no idt that'd work
thinks
,w x^5 + 4x + 3 = t solve for x
orchid wagon
in the integral
even then we will have to deal with the fourth degree polynomial
frozen plover
$\int_{-37}^{\text{<whatever>}} f(x^5 + 4x + 3)(5x^4 + 4)dx$
rough goblet
hm
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frozen plover
do that and check your DMs
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orchid wagon
**NEON**
oh my god why didnt i think of that
but wouldnt that make the upper bound really large
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eager mortar
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eager mortar
How do you solve this
crisp flame
How do you solve this
do you know l hospital rule?
eager mortar
What is that
lapis star
do you know l hospital rule?
no need
eager mortar
Like expand the bracket?
eager mortar
5^2-x^2-4x-4
eager mortar
(5+x+2)(5-x+2)
lapis star
(5+x+2)(5-x+2)
u there?
eager mortar
(7+x) (7-x)
crisp flame
(5+x+2)(5-x+2)
you forgot the brackets here
eager mortar
Oh
crisp flame
its (5-(x+2))
lapis star
its (5-(x+2))
let em do it on their own
they will figure it out prolly
what to do next also
crisp flame
let em do it on their own
im just telling whats wrong i didnt expand it fully
lapis star
im just telling whats wrong i didnt expand it fully
np they could have found it out it kinda helps but ok
eager mortar
(-5x+10)(5x+10)
^
eager mortar
(-5x+10)(5x+10)
lapis star
no way u will get 5x
eager mortar
Ur left with -(7+x)?
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forest niche
$\frac{x^3 - 3x^2 + 3x - 1}{|x| (x^2 - 2x + 1)} \div \frac{|x - 1|}{2x},$ if $0 < x < 1$
solid kilnBOT
asm
forest niche
i solved the expression by itself, but i don't understand what does it mean by "if 0 < x < 1"
since the answer equals to negative 2 in the book for this expression
tepid rock
You can rewrite those absolute values if you know the interval for x.
forest niche
🤷♂️ it only asks me to simplify the rational expression
"if 0 < x < 1" is new to me
tepid rock
For simplifying this, you need to rid yourself of these absolute values.
forest niche
i've simplified it up to this point
$\frac{2x(x - 1)}{|x(x - 1)|}$
solid kilnBOT
asm
forest niche
how can i get rid of the absolute value here?
are there any resources that explains those?
forest niche
from my understanding, if you calculate an absolute value and get an negative, it's gonna turn into an positive
tepid rock
Correct. Do you also know\
$|x| = \begin{cases}
x, x > 0\
0, x = 0\
-x, x < 0\
\end{cases}$
solid kilnBOT
! What the hell am I doing here?
forest niche
don't know that but i did understand it except for the last one
-x,x < 0?
can an absolute value equal to that?
tepid rock
Yes.
forest niche
alright
forest niche
yea i understand
tepid rock
Then use this for x(x-1)
If 0< x < 1 then you should be able to tell if x(x-1) > 0 or < 0
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marsh forum
kind of stuck
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kind of stuck
vernal raptor
oooh okay
then you know what is an odd funtion?
what it is and what its function equivalancy like
take as an example
sinx and cosx
which is a odd one and which is even?
vernal raptor
its said rt its an odd one?
so you can for odd one's
as odd functions have f(-x)=-f(x)
vernal raptor
yeah
no its not
odd f(x) have a property
that
they are sym. with opposite quadrants ig
yes they are
like sine function
ripe valley
kind of stuck
it is sufficient to prove $\int_{a}^{T} f(x) dx = \int_{a}^{T} f(x+kT) dx$
solid kilnBOT
カナヴ
ripe valley
the question is how would I do that
probably, FTC and/or kings theorem ig
marsh forum
so using King's rule this would become f(T+a-x)
hallow cliff
it is sufficient to prove $\int_{a}^{T} f(x) dx = \int_{a}^{T} f(x+kT) dx$
No, the +kT should be in the upper limit
If I'm not wrong
ripe valley
No, the +kT should be in the upper limit
oh right
ripe valley
the integral is periodic
vernal raptor
kind of stuck
and change the limitsyoure right that the upper limit is T?
and not something like a+t
or
ripe valley
so if u let $\int_{a}^{x} f(x) dx = F(x)$, then we have to prove $F(x) = F(x+kT)$ for some k
hallow cliff
Use the fact that $\int_{a}^{x+kT}= \int_{a}^{x} + \int_{x}^{x+kT}$
solid kilnBOT
smidgin
ripe valley
**smidgin**
uhhh i still dont see +kT in the upper limit
vernal raptor
uhhh i still dont see +kT in the upper limit
it should be there right?
hallow cliff
F(x)= \int_{a}^{x} f(x)
ripe valley
F(x)= \int_{a}^{x} f(x)
ah
hallow cliff
Int_{a}^{T} would just be a constant
solid kilnBOT
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ripe valley
Int_{a}^{T} would just be a constant
yes, sorry for the inconvenience
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last mantle
Need help finding an idea to do a research paper about. More context: My professor has assigned us the task of writing a research paper about any topic in mathematics. I am in my first semester, and I'm not that creative so I just cannot think of any idea or way to find ideas, and I'd appreciate it if someone were to give me ideas or ways of finding ideas that I could do a research paper about.
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last mantle
<@983466587396923513> Has your question been resolved?
No
lime prairie
Need more background here. What are you interested in? What level of math are you looking for? What type of research paper is it supposed to be?
zinc ginkgo
Need help finding an idea to do a research paper about. More context: My profess...
this is more of a #discussion or even #「graduate-lounge」
grim summit
.reopen
last mantle
Need more background here. What are you interested in? What level of math are yo...
I guess I'm interested in calculus, 2-dimensional geometry, and algebra for now
last mantle
this is more of a <#268882317391429632> or even <#987466119692570694>
No access?
last mantle
Need more background here. What are you interested in? What level of math are yo...
Im looking for middle level, I'm still learning and I'm not that well educated on advanced topics, the research paper is supposed to be about taking a certain field, theorem, or any sort of mathematical concept and simplifying it in a unique way or trying to improve upon it
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atomic moat
I'm having slight trouble understanding these logarithmic properties, as there are no arguments in some of the logarithms.
atomic moat
thank you for informing me, but my issue is trying to identify the logarithms without an argument
$log_x$
solid kilnBOT
becoming
austere cedar
atomic moat
let me see..
zinc ginkgo
,calc 1/log(e, 10)
solid kilnBOT
Result:
2.302585092994
this should read $\frac{1}{\log_{10}(e)}$
solid kilnBOT
riemann
tepid hamlet
just wondering if someone could help me get a bit better intuitive understanding of Taylor polynomials. I guess I've heard to think of each term added as a successively better approximation of f near x = a, that much makes sense, but I was wondering if there's some way to understand intuitively where the whole scaling each term with increasing factorials comes from or why the power of the (x-a) increases on each term and if this can be understood better from some perspective
left oriole
try taking the n'th derivative and evaluating it at x=a
all the terms with powers less than n are gone when you take the n'th derivative
all the terms with powers greater than n are zero when you evaluate at x=a
that just leaves the n'th derivative of the n'th term
and it's not too hard to see that the n'th derivative of the n'th term is just the constant f^(n)(a)
trail ingot
it comes from assuming a function can be represented as a power series and how this uniquely determines the coefficients
say $f:\bR\to\bR$ is a function and for some sequence ${a_n}$, $$f(x) = \sum_{n=0}^\infty a_n x^n$$ for all $x$. then it's true when $x=0$, so $f(0) = a_0$. differentiating $f$ and evaluating $f'(0)$ uniquely determines $a_1$, and so on
tepid hamlet
ok i need to digest these for a min, I'm slow : )
solid kilnBOT
chmonkey #1 simp
trail ingot
the factorials are going to show up from repeatedly differentiating
tepid hamlet
try taking the n'th derivative and evaluating it at x=a
all the terms with power...
how come "all the terms with powers greater than n are zero when you evaluate at x=a" ?
tepid hamlet
the factorials are going to show up from repeatedly differentiating
OHHHH
left oriole
how come "all the terms with powers greater than n are zero when you evaluate at...
because they still involve (x-a) to some power
so when you plug in x = a, that becomes zero
tepid hamlet
OHHH
oh man yeah this is exactly what i was looking for
that makes so much more sense
that's actually really cool : )
thank you
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indigo crest
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twin mortar
how do i do this i need help?
trim joltBOT
how do i do this i need help?
zinc ginkgo
you need to stop opening and closing channels
twin mortar
you need to stop opening and closing channels
no one is helping
zinc ginkgo
no one is helping
doesn't matter
kind wasp
Why is this wrong? How is it below the LCL?
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Why is this wrong? How is it below the LCL?
hallow spruce
i suppose it's due to this point
kind wasp
It looks exactly on the LCL to me
But I guess thats just slightly below
🥲 thank you
.close
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Catgod
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chilly bobcat
1 min lemme try
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wraith hinge
1 min lemme try
This is now 1 hour
frail heron
LOL
chilly bobcat
This is now 1 hour
i have no idea
I suck at remainder problems
frail heron
This is what I have done so far
Still working on it
okay, I’ve stuck
Find another helper
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wraith hinge
so you can use CRT
Thank you
wraith hinge
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wraith hinge
I used a different method
onyx forge
oh lmao
cosmic meadow
Because he is splitting
onyx forge
the above one
cosmic meadow
in 2 fractions
wraith hinge
I've sent above
steep patio
you cannot pull the x out of the integrand in the step where you changed colours
cosmic meadow
integrate by parts after u split
wraith hinge
you cannot pull the x out of the integrand in the step where you changed colours
why ?
won't the x will be treated as a constant?
cosmic meadow
why ?
won't the x will be treated as a constant?
this should be confusing even you xd
wraith hinge
yeah
wraith hinge
do u study in allen or smtg/
nah
(I'm in 10th)
just doin' calc for fun
trim thicket
nah
(I'm in 10th)
just doin' calc for fun
ok my advice would be go touch some grass
wraith hinge
why did you throw a variable out of the integral?
I mistakenly assumed it as a constant
dry viper
and you're in 10th man chill
steep patio
nah
(I'm in 10th)
just doin' calc for fun
that's awesome, keep at it
lapis star
nah
(I'm in 10th)
just doin' calc for fun
which school
fair goblet
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fair goblet
with cii), i got the formuila and everything but when i put in the calculator it goes to wack
i got 1440cm/s (turned radians to degrees)
anyone have an idea what im doing wrong?
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@fair goblet Has your question been resolved?
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@fair goblet Has your question been resolved?
ornate glade
Can someone help me solve the 1st question
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Can someone help me solve the 1st question
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
@ornate glade Has your question been resolved?
ornate glade
No
solar pelican
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dry viper
yes
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regal brook
Could the a be -1 ? so that it's F(s-(-a)) = F(s+a) ?
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Could the a be -1 ? so that it's F(s-(-a)) = F(s+a) ?
@regal brook Has your question been resolved?
tribal fractal
how would i evaluate this integral, im not sure what to do
tribal fractal
$\int^{\pi/4}_0{\sqrt{1+\tan^2(x)}\mathrm{d}x$
solid kilnBOT
talk_less
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
tribal fractal
finding the antiderivative straight up is pretty messy
stiff fjord
What's integration of secx
tribal fractal
maybe i should do u substitution on tan(x)?
tribal fractal
What's integration of secx
integration or differentiation?
stiff fjord
Integration
tribal fractal
its pretty complicated right?
digital bolt
$1 + \tan^2(x) = 1 + \frac{\sin^2(x)}{\cos^2(x)} = \frac{\cos^2(x) + \sin^2(x)}{\cos^2(x)} = \frac{1}{\cos^2(x)} = \sec^2(x)$
solid kilnBOT
Kaisheng21
stiff fjord
We use direct formula of Integration of secx
tribal fractal
We use direct formula of Integration of secx
ln |sec x + tan x|?
but we have sec^2(x)
tribal fractal
wait wdym
tribal fractal
ln |sec x + tan x|?
is this right?
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@tribal fractal Has your question been resolved?
radiant scroll
Its not really a math question i need solved. but can someone explain points of discontinuity to me with examples? i really dont understand it.
radiant scroll
im a junior in highschool, algebra 2
red loom
discontinuity as in removeable and non-removeable? holes and asymptotes
,tex [
\begin{tabular}{|c|c|c|c|c|}
\hline
\text{Removeable?}&\text{Hole or Asymptote}&\text{Example}&\text{Hole}&\text{Asymptote}\
\hline
\text{Yes}&\text{Hole}&$\frac{\cancel{(x-1)}}{\cancel{(x-1)}}$&$x=1$&\text{None}\
\hline
\text{No}&\text{Asymptote}&$\frac{x-1}{x-4}$&\text{None}&$x=4$\
\hline
\end{tabular}
]
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PajamaMamaLlama
red loom
a hole occurs when the discontinuity is "removeable" i.e. you can cancel it like in the example
yes it simplifies to 1 and the function $\frac{x-1}{x-1}$ is indeed 1 everywhere except at x=1 where there is a hole
solid kilnBOT
PajamaMamaLlama
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@radiant scroll Has your question been resolved?
radiant scroll
so how would i solve something like x+3/x^2-6x+5
red loom
well first factor x^2-6x+5
radiant scroll
and then what, since its not removable
red loom
yep so then tells you what type of discontinuity it is
radiant scroll
non removable right
red loom
yep but more specifically they're asymptotes
$\frac{x+3}{x^2-6x+5}=\frac{x+3}{(x-1)(x-5)}$
solid kilnBOT
PajamaMamaLlama
radiant scroll
i cant send a photo rn. but youd put dotted lines at x=1 and x=5 right
like on a graph
honest trench
How many different code words of length 3 do you have a
arrangement using an alphabet consisting of only 5 symbols?
vernal wraith
Didn't get your question ? Can you please elaborate ?
honest trench
How many code words of length 3 (different) do you have a
arrangement using an alphabet consisting of only 5 symbols?
vernal wraith
$5C3 * 3!$
solid kilnBOT
Solomaniac
vernal wraith
Is this right ?
neon grotto
solid kilnBOT
alee
honest trench
x = 125
vernal wraith
That's what. Thequestion seems unclear
honest trench
is right?
vernal wraith
It says alphabets. Then symbols. Then combinations
honest trench
.close
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nimble wind
I have a relatively basic question that im stuck on
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I have a relatively basic question that im stuck on
gaunt wave
Speeding up refers to acceleration, which is the derivative/slope of velocity for (a) question 1, where does the graph have a positive slope
(b) where does the graph have a negative slope
gaunt wave
From my knowledge, the function is positive when t is positive
Not necessarily, 'the function' can be positive or negative. also, since t is in reference to time, t will never be negative
nimble wind
Speeding up refers to acceleration, which is the derivative/slope of velocity fo...
ohh okay i see
so the right answer would be from (0,1)
gaunt wave
Should be yes
nimble wind
at t = 3 the slope is about to be 0
nimble wind
Should be yes
with interval notation can their only be one point?
gaunt wave
with interval notation can their only be one point?
Wdym?
gaunt wave
at t = 3 the slope is about to be 0
No?
nimble wind
Nvm, looked at the wrong graph
All good
heres an example of interval notation from a previous problem i had
gaunt wave
heres an example of interval notation from a previous problem i had
What does the graph look like
nimble wind
Not sure if you can work with that
its when the a and v functiona are both the same sign
gaunt wave
Also this covers every possible point the gap between 3 and 4 is stated in the slowing down part
If acceleration and velocity are the same signs than yes they will be increasing in speed, only thing that really changes is direction I believe
So no, the function may not have just one point?
nimble wind
Im confused
nimble wind
I have a relatively basic question that im stuck on
The only interval in the first quesiton here i see is from 0 to 1
Because the line from those points is positive and nowhere else on that graph
gaunt wave
Uhh, what is your level of mathematics.
nimble wind
Calculus 1
gaunt wave
The only interval in the first quesiton here i see is from 0 to 1
Yes, this is true
nimble wind
https://math.stackexchange.com/questions/336419/when-is-the-particle-speeding-up-and-when-is-it-slowing-down Im reading this right now
gaunt wave
Wait, give me a sec. Sometimes I hate the terms of acceleration 2 to 3 I think is also a point since the acceleration is negative and so is velocity (slope of graph and the function)
nimble wind
Okay !
gaunt wave
So [0, 1)U(2, 3)
gaunt wave
Let me restate everything needed, same signs for acceleration and velocity equals speeding up so, if negative slope and negative outputs & positive slope and positive outputs equals speeding up.
Negative slope and positive outputs & positive sloped and negative outputs equals slowing down
From (1, 2) the slope is negative but the outputs are positive
nimble wind
From (1, 2) the slope is negative but the outputs are positive
I get this and I agree
gaunt wave
U also means excluding the points in between so [0, 1)U(2, 3) means excluding the points between 1 and 2
nimble wind
Yeah
gaunt wave
Do you have the second graph from here?
nimble wind
U also means excluding the points in between so [0, 1)U(2, 3) means excluding th...
I found the exact problem on youtube and this guy gives a pretty good explanation so i dont need anymore help
thanks though!
.close
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mortal dune
How could I do this problem?
trim joltBOT
How could I do this problem?
raw magnet
How could I do this problem?
well I can help you assuming you know how to interpret derivatives on a graph
and you can do the rest
mortal dune
I do not 😔
raw magnet
but the product rule states that (f(x)g(x))' = f'(x)g(x) + g'(x)f(x)
mortal dune
We haven't talked about any graphs ahahhaa
raw magnet
We haven't talked about any graphs ahahhaa
it's alr
raw magnet
but the product rule states that (f(x)g(x))' = f'(x)g(x) + g'(x)f(x)
@mortal dune
mortal dune
Right, yeah
mortal dune
Would I look at both graphs to find h'(2)?
raw magnet
Would I look at both graphs to find h'(2)?
well give me it in terms of f', g' and f,g first
raw magnet
but the product rule states that (f(x)g(x))' = f'(x)g(x) + g'(x)f(x)
^ use this
mortal dune
I'm still super confused on how to find f(x) on the graph, am I looking at both red and blue?
raw magnet
I'm still super confused on how to find f(x) on the graph, am I looking at both ...
let's first translate this problem
you are getting ahead of yourself
tell me about h'(2) in terms of f',g',f, and g
mortal dune
💀
raw magnet
guys how to divide fractions
I don't think Someone appreciates you interrupting their channel
mortal dune
Uhhm
main skiff
ok il get out of here
mortal dune
oh that's what you wanted
raw magnet
and we said (f(x)g(x))' = f'(x)g(x) + g'(x)f(x)
mortal dune
yeah lol
raw magnet
so what would h'(x) be
mortal dune
so i presume the red one is f(x)
mortal dune
damn
raw magnet
don't worry about the graphs for now
mortal dune
okay
mortal dune
right
raw magnet
right
now what I want from you is to find h'(x) (ignore the graphs) in terms of f, g, g', and f'
now my hint is
product rule gives us that (f(x)g(x))' = f'(x)g(x) + g'(x)f(x)
raw magnet
it would be f'(2)g(2) + g'(2)f(2)
okay great
so the information we need to find is f(2), g(2), and f'(2), g'(2)
mortal dune
right
raw magnet
amazing
okay so let's focus of f(2)
so @mortal dune given that (2,-19/5) is a point on our graph
what does that tell you f(2) is
mortal dune
f(2) = -19/5?
raw magnet
f(2) = -19/5?
great
mortal dune
then f'(2) is the tangent line, meaning it's the -19/5 - -7/5
raw magnet
raw magnet
then f'(2) is the tangent line, meaning it's the -19/5 - -7/5
very close
mortal dune
rip
mortal dune
yikes
raw magnet
remember slope is change in y/change in x
mortal dune
right, yeah
raw magnet
right, yeah
wanna calculate that for me
raw magnet
shouldn't it be divide 2-0
yeah
mortal dune
sickk, same thing to g now
raw magnet
sickk, same thing to g now
yep
raw magnet
f = -19/5
f' = -6/5
g = 2
g' = 5/2
(-6/5)(2) + (5/2)(-19/5)
yes
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@mortal dune Has your question been resolved?
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@mortal dune Has your question been resolved?
limpid dawn
then I just kinda do the same steps
Do you need help?
mortal dune
I might on one of the chain rule ones, but for now, I think I'm good
I'll open a new thing in a few hours if I can't figure out the chain one, but I'm sure I'll be fine
might just need a double check lol
limpid dawn
might just need a double check lol
ok sick
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@mortal dune Has your question been resolved?
mortal dune
next time it pings me I'll make it as resolved
limpid dawn
next time it pings me I'll make it as resolved
can't you type .solved or .close?
mortal dune
Yeah, but by the time it pings me again, I should pretty much be done
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@mortal dune Has your question been resolved?
tribal fractal
how would i evaluate this integral?
trim joltBOT
how would i evaluate this integral?
marsh forum
Try a u-sub
marsh forum
1+81x would be the correct sub, yes
marsh forum
That looks wrong to me
tribal fractal
wait i messed up the latex
solid kilnBOT
talk_less
raw magnet
with this i got $\int^{81}_{244}{\frac1{81}\sqrt(u)\mathrm{d}u}$
From here
Just rewrite u as a power
Then it’s trivial
tribal fractal
Just rewrite u as a power
wdym
oh for the antiderivative?
im kinda confused
so does that turn into $\frac{1}{81}\cdot\frac{2u^{3/2}}{3}$ and then FTC
solid kilnBOT
talk_less
tribal fractal
@raw magnet
with 811 and 244
if i do that i get a different answer
from
you there??
<@&286206848099549185>
bruh
can anyone help please
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@tribal fractal Has your question been resolved?
wraith hinge
yo
tribal fractal
still need help?
yes
tribal fractal
no worries