can you show your work?
#help-17
outer warren
Last warning.
heavy grail
I’m sad guys… I failed my exam and now I’m getting kicked out of Harvard
primal hedge
ive tried like million different ways to calculate it and every one is wrong
heavy grail
Last warning.
I’m sorry😢
outer warren
show the million different ways you've tried
vast shale
ive tried like million different ways to calculate it and every one is wrong
how did you get 1.097
outer warren
(or just the last one)
outer warren
try it again and show your attempt
primal hedge
i tried by finding the average rate of change
am i supposed to find it for each point?
outer warren
can you show what you mean
primal hedge
i tried by doing 3-0/475-357
low cradle
i think you might have to factor in the individual data points
primal hedge
like one by one?
low cradle
not too sure, what it wants either, but try 392/357, 431/392, 475/431, then the average of these factors will be closer to approximately 1.09987
outer warren
1.09987...
rounded to 3 dp will be 1.1
low cradle
an asymptote is a straight line that approaches a curve but does not meet it
low cradle
if u look at 4/(6x+5) it is a hyperbola
on desmos u can see that is is asymtote to two lines
specifically this two lines here (pardon the shitty drawing)
it is asking you for the equations of this two lines
primal hedge
like separately?
low cradle
yes, the trivial one here will be the horizontal asymptote which u can tell is at y=0
so the graph approaches the line y=0, but they will never actually intersect
primal hedge
whats the vertical one?
low cradle
the vertical asymptote occurs where the denominator is 0
so set the denominator to 0 and solve for x
there is easier tricks to finding the asymptotes that u can search online, but an easier way is to imagine "what are values of y/x that will never be reached" by the graph
and then develop an intuitive way to find them
primal hedge
is the restricion the same a range?
low cradle
i think it is asking u for what values x cannot be
so values of x where f(x) is undefined
low cradle
u got the wrong answers, equation definitely does not equal to 0 when x=0
try to solve for x again
primal hedge
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
vocal sleetBOT
paper depot
,rccw
twin meteorBOT
hard radish
Basically I got the solution which is (2024C2 - 3C1 x 1012 + 2) / 3! (Cus of my teach)
Ik why it's 2024C2
But idk why it's the rest
<@&286206848099549185>
vocal sleetBOT
@hard radish Has your question been resolved?
eternal relic
is this method of differentiation valid?
vocal sleetBOT
is this method of differentiation valid?
eternal relic
this lowkey produced the right answer for f''(2)
chilly condor
It seems like you… used the chain rule without using the chain rule?
You have dy/dx = dy/du times du/dx, so by product rule
$\frac{d^2 y}{dx^2} = \frac{d^2 y}{du^2} \frac{du}{dx} + \frac{dy}{du} \frac{d^2 u}{dx^2}$
The second term is zero because du/dx = 3.
twin meteorBOT
Bete Puttigieg 🐢
eternal relic
oh that makes sense thank you
chilly condor
You seem to have erroneously squared your du = 3dx expression, which is wrong, because $\frac{d^2 u}{dx^2} \neq \left( \frac{du}{dx} \right)^2$
eternal relic
oh
twin meteorBOT
Bete Puttigieg 🐢
eternal relic
damn it i thought i was onto something
chilly condor
Well, you were. You certainly can do what you were doing.
You were kind of exploiting the chain rule.
It’s just that du = 3 dx doesn’t really mean anything. What would be meaningful is writing du/dx = 3.
eternal relic
idk i was just in an integration by u sub mindset during this problem for whatever reason but i dont have a strong enough understanding of what du, dx etc actually mean and what you can do with them
chilly condor
Well you have defined u as a function of x. So I’m sure you know that $\frac{dy}{dx} = \frac{dy}{du} \cdot \frac{du}{dx}$
twin meteorBOT
Bete Puttigieg 🐢
eternal relic
yep
chilly condor
You sort of erred in the second differentiation, firstly by ignoring the second term from the product rule (which was luckily 0) and secondly by squaring both sides of your thingy
eternal relic
so if you have dy/du are you not allowed to sub in du = 3dx
chilly condor
Umm… hm
If you have dy/du, and you want to have dy/dx, by carefully saying dy/du = dy/dx * dx/du, you can do it that way
chilly condor
so if you have dy/du are you not allowed to sub in du = 3dx
And you would have dx/du = 1/3 in that case.
eternal relic
ohhhh that makes sense thank you
chilly condor
🕺
eternal relic
thank you so much for this insightful conversation i hope you have agood day
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
bleak glade
for part a, i tried to use the formula 1/2absinC to find angle SPQ but it gave me a non-real error??
vocal sleetBOT
for part a, i tried to use the formula 1/2absinC to find angle SPQ but it gave m...
bleak glade
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
twilit needle
vocal sleetBOT
paper depot
well the function is injective so f(x)=1 has at most one solution
you also need to show why it has at least one solution
edgy kayak
IVT perhaps
twilit needle
Aaah okay
twilit needle
Aaah okay
so I didnt think of it since IVT is only a closed interval right?
[a,b]
or do I pick an closed interval?
oak magnet
so I didnt think of it since IVT is only a closed interval right?
Works with limits
oak magnet
Hmmm I have never done that before
Never late to do it
oak magnet
could you maybe help me with that?
Sure
twilit needle
Never late to do it
exactly 🙂
twilit needle
But dont I say that already at f: R-> R?
oak magnet
Oh indeed
In that case just say its bijective cuz strict increasing 👍
And you have the exact sol
oak magnet
You stated a weaker result thats what they said
twilit needle
true
I missed the surjective part
which actually makes it that the solution exists
oak magnet
Exactly
oak magnet
Tbh just use continious + strict increasing => bijective
mild trench
vocal sleetBOT
edgy kayak
how did you get a^4 = 64
outer warren
how are you getting a^3 = 64
mild trench
how are you getting a^3 = 64
a--a^2
outer warren
show what's happening as a whole
mild trench
it's fine tho i got it in the end
outer warren
a/a^-2 will be a^3, where will that end up in the equation
vocal sleetBOT
@mild trench Has your question been resolved?
elder summit
vocal sleetBOT
elder summit
,rotate
twin meteorBOT
elder summit
Can someone spot what i did wrong?
gentle nimbus
Can someone spot what i did wrong?
first and foremost, you didn't differentiate the numerator
elder summit
first and foremost, you didn't differentiate the numerator
But would it matter ? Because i though i put the limit and i just get 2e^-2/ π
gentle nimbus
yes
that's how L'Hôpital's rule works
you have to differentiate both the numerator AND the denominstor
nvm im kinda of blind
elder summit
Wait i did differentiate the numerator though?
gentle nimbus
yes im just terrible at sight
elder summit
ya np my handwriting isnt the best
elder summit
so LH doesn't apply
Wait huh
I though it applies for everything aslong the result was 0/0 or inf/inf
elder summit
So wait what am i supposed to do
gentle sleet
oh -2 mb
I graphed it and saw it was different, but I was looking at x=2
sorry
elder summit
Np
gentle sleet
lemme graph your derivatives and see if they're correct
gentle nimbus
at the second appilcation of the rule
you have two sine ans cosine terns
the sine terms cancel out at x=-2
and the cosine reduces to 1
so @elder summit what is your issue?
elder summit
and the cosine reduces to 1
but the denominator will be equal to PI
elder summit
Why? We take derivative again or?
gentle nimbus
no we don't
since we got a finite value, we're done
over
then substitute for the numerator and you get the answer
elder summit
?
gentle nimbus
the answer is incorrect
elder summit
cant we get 2e^-2 - 4 somehow?
elder summit
can we check with wolfram alpha
gentle nimbus
can we check with wolfram alpha
sure but idk how i never use it
gentle sleet
the answer's right
gentle sleet
then substitute for the numerator and you get the answer
priv, can you show the process of you doing that?
elder summit
ok ill show
elder summit
gentle nimbus
elder summit
,rotate
twin meteorBOT
gentle nimbus
substitute for the first differentiation
since that doesn't lead to an indeterminate form
elder summit
substitute for the first differentiation
True ill check
gentle nimbus
always check after each differentiation 
elder summit
Oh
Ur correct
Pi is canceled
And i get 2e^-2 -4
Thank you guys for the help
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
vestal flume
Hi ! i'm new one the serve and i'm french, I need help for a own math problem where i'm stuck. So maybe there is no respond.
Here we go : I want to resolve this (Image 1)
here are some information :
- 0 < x < 1
- n belong to N* (natural number)
- This come from Binomial distribution
I want to find x(n) (x as a function of n)
vocal sleetBOT
Hi ! i'm new one the serve and i'm french, I need help for a own math problem wh...
@vestal flume Has your question been resolved?
vocal sleetBOT
@vestal flume Has your question been resolved?
vestal flume
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
candid socket
I need help understanding partition functions
vocal sleetBOT
I need help understanding partition functions
candid socket
Sorry generating functions
I really just want to understand how to translate from (word problem) to (factorization) and vis-Versa
Here is what I think for this problem:
(1 + x^1 + x^3 + x^5 + ….) accounts for the fact that I can either have 0 ones, 1 ones, 3 ones, 5 ones…
- (1 + x^3 + x^ x^9 + x^15 + …) accounts for the fact that I can either have 0 threes, 1 three, 3 threes or 5 threes
Is this general pattern correct?
I just realized I misread the problem. I thought it read that there can only be an odd number of any given integer part.”
vocal sleetBOT
@candid socket Has your question been resolved?
ruby atlas
vocal sleetBOT
ruby atlas
Hi, I have a quick question regarding angles. When we have all sides and we are supposed to find the angle how do I know which angle belongs to which?
SOH CAH TOA all give the same angle, but where do I put it? up or down?
does it even matter?
wary hull
Hi, I have a quick question regarding angles. When we have all sides and we are ...
This one we take sine of the angle on bottom
Or cosine of angle on top
cos=adj/hyp
vocal sleetBOT
ruby atlas
.reopen
vocal sleetBOT
✅
ruby atlas
@wary hull Sorry for the ping. Although it makes sense, when I calculate both top and bottom, I get the same angle: 10.39 (to 2 dec) shouldnt it be 180
like the total
or am I overthinking it and 180 - 90 - 10.39
wary hull
or am I overthinking it and 180 - 90 - 10.39
Yes
a+b=90 for non-right angles in right triangle
since 180-90=90
ruby atlas
Yeah
So basically top or bottom could be the 10 and the other side is the 180 - 90 - 10
twin meteorBOT
ruby atlas
Yeah I get that result
but the issue is that when I apply CAH or SOH I still get the 10.39
wary hull
but the issue is that when I apply CAH or SOH I still get the 10.39
Hmm
,w arccos(60/61)*180/pi
twin meteorBOT
ruby atlas
Ah
I wasnt using my brain
now it makes sense
I kept on assuming 11 was the opposite for some reason
I get it now, thank you again
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
velvet flame
does anyone know anything to do with stirling numbers? i have a code that's semi finished but i need some more help on it
vocal sleetBOT
does anyone know anything to do with stirling numbers? i have a code that's semi...
velvet flame
def S(p,n):
if n == p:
return 1
if n == 1:
return 1
ans = (nS(p-1,n) + S(p-1,n-1)) + (n(n-1)S(p-1,n) + (n-1)S(p-1,n-1)) + (nS(p-1,n) + S(p-1,n)) + (n(n-1)*S(p-1,n) + (n-1)*S(p-1,n))
return ans
velvet flame
use triple backticks
wdym
mild flower
i mean i can't read this
velvet flame
oh okay
'''ans = (nS(p-1,n) + S(p-1,n-1)) + (n(n-1)S(p-1,n) + (n-1)S(p-1,n-1)) + (nS(p-1,n) + S(p-1,n)) + (n(n-1)*S(p-1,n) + (n-1)*S(p-1,n))'''
how tf do i show it
it s a long line
but im only certain of half of it
mild flower
backtick is the key next to your 1 key
velvet flame
backtick is the key next to your 1 key
ohh i just never use it thanks
ans = (n*S(p-1,n) + S(p-1,n-1)) + (n*(n-1)*S(p-1,n) + (n-1)*S(p-1,n-1)) + (n*S(p-1,n) + S(p-1,n)) + (n*(n-1)*S(p-1,n) + (n-1)*S(p-1,n))
velvet flame
wait scrap that
keep it to this first
ans = (n*S(p-1,n) + S(p-1,n-1)) + (n*(n-1)*S(p-1,n) + (n-1)*S(p-1,n-1))
so first big bracket bewteen n*s(p-1,n) to S(p-1,n-1) is when there's only 1 person going to 1 group and hes fixed in that group and nobody else can be in his group
next bracket is when 1 person can be in 2 groups but in one of the groups hes in he'll be alone and nobody else will there with him
mild flower
i'd recommend making a table of small values to verify your equations
p on the top and n on the side
velvet flame
but i havent considered 2 more cases so my code wont fully work
i had another code in which i brute forced this question but now that i have this one which is a lot more elegant, i think ill use this one
velvet flame
but i havent considered 2 more cases so my code wont fully work
those 2 cases being 1 person in 1 group only but the rest can join him
and the last case being 1 person in 1 group and people can join him as well as him being able to join other groups
but then i feel like that defeats the purpose of the different criterias
vocal sleetBOT
@velvet flame Has your question been resolved?
vocal sleetBOT
@velvet flame Has your question been resolved?
velvet flame
<@&286206848099549185>
vocal sleetBOT
@velvet flame Has your question been resolved?
velvet flame
<@&286206848099549185>
grand raven
Nvm realised it was about stirling numbers im just dumb
vocal sleetBOT
@velvet flame Has your question been resolved?
spice knoll
does anyone understand affine matrix transformations?
vocal sleetBOT
does anyone understand affine matrix transformations?
reef agate
does anyone understand affine matrix transformations?
!da2a (i dont though)
vocal sleetBOT
does anyone understand affine matrix transformations?
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
spice knoll
the answer should be shifts of 2/3 for a few of them, but idk why its not 1/3
<@&286206848099549185>
vocal sleetBOT
@spice knoll Has your question been resolved?
vocal sleetBOT
@spice knoll Has your question been resolved?
wet halo
vocal sleetBOT
wet halo
Would a sufficient answer be:
Since the only solution to the homogeneous system is the trivial solution when reduced to RREF, Rank(A) = n
?
for both of them
is this a reasonable and true argument minus rigor?
bitter pilot
yes and you can also say that row rank = column rank
vocal sleetBOT
vocal sleetBOT
Available help channel!
wooden shell
how can i simplify this
vocal sleetBOT
how can i simplify this
paper depot
well the first order of business is to maybe physically lower the =t bit so it aligns with the longest fraction bar
but as far as simplifying $\frac{\frac{s}{p} - 1}{r}$ is concerned: multiply the outer numerator and denominator by $p$ so make it into $\frac{\paren{\frac{s}{p}-1}\cdot p}{r \cdot p}$...
twin meteorBOT
Ann
wooden shell
well the first order of business is to maybe physically lower the `=t` bit so it...
okay right that tracks
wooden shell
but as far as simplifying $\frac{\frac{s}{p} - 1}{r}$ is concerned: multiply the...
so s-1P/Pr=t?
paper depot
where did uppercase P come from?
also missing brackets around the fraction numerator
also $\paren{\frac{s}{p} - 1} \cdot p \neq s - 1p$ anyway
twin meteorBOT
Ann
wooden shell
also missing brackets around the fraction numerator
i went to add those but i second guessed 🫠
paper depot
err
wait no hold on
it does equal s - 1p
or just s - p
(s - p)/(pr) = t is correct
wooden shell
where did uppercase P come from?
it was an uppercase the whole time
and so is the s
paper depot
your handwriting didn't make that clear i admit
wooden shell
your handwriting didn't make that clear i admit
in my defence 1 how am i supposed to differentiate them 2 the positions on the lined paper means if anything its theyre both uppercase
paper depot
ok i guess p vs. P in this context is difficult
like actually i only saw your handwritten equation and not the printed version you copied from
mm idk whatever
wooden shell
like actually i only saw your handwritten equation and not the printed version y...
valid
doesnt matter though bc theyre still consistent between eachother
anyway
thank you for your help :)
.close
vocal sleetBOT
twin meteorBOT
w
hybrid flicker
!status
vocal sleetBOT
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
flat whale
no that's backwards
and also wrong
f(x) = 1/x is divergent, but so are 2/x and 1/(2x)
when the assumptions of the comparison test are satisfied
are you calling this the "basic comparison test"?
so yea you can use that whenever the assumptions hold true
f(x) = 2/x >= 1/x = g(x) on [1, inf) and int from 1 to inf g(x) dx diverges so does int 1 to inf 2/x dx
vocal sleetBOT
vocal sleetBOT
Available help channel!
inland flower
vocal sleetBOT
olive stag
I googled how to do it and apperently its this
where n is the size of the square matrix
idk what the proof of it would be thi
tho
inland flower
Yeah ion understand that
olive stag
$det(cA)$ literally is just "the determinant of the matrix cA"
twin meteorBOT
IronVoltage
olive stag
cA is just a constant c times the matrix A
and the equation is saying that
this is equal to $c^n \times det(A)$
twin meteorBOT
IronVoltage
olive stag
where n is the size of the matrix
vocal sleetBOT
@inland flower Has your question been resolved?
vocal sleetBOT
Available help channel!
grave cliff
Not sure how to do these types of problems. Anyone know? 
vocal sleetBOT
Not sure how to do these types of problems. Anyone know? <:sadcat:54712402458548...
@grave cliff Has your question been resolved?
wise drift
hi which question do you need help with first
vocal sleetBOT
vocal sleetBOT
Available help channel!
vast shale
vocal sleetBOT
vast shale
Im confused would it not be -8 as opposed to -6
im just asking for i
Yes it seems they forgot about the -2
cunning plaza
You're right, mistake in the book
vocal sleetBOT
@vast shale Has your question been resolved?
vale frigate
can anyone explain to me how did they get the bounds of integration on this
vocal sleetBOT
can anyone explain to me how did they get the bounds of integration on this
@vale frigate Has your question been resolved?
heavy yoke
which region in particular?
vale frigate
which region in particular?
all the 3 regions
paper depot
aren't most boundary points' coordinates given explicitly here
vale frigate
ok for example on d1 how did they come up with x = (-2, 0) y = (0, (x+2)^2)
i kinda dont get the process
civic otter
Look at the red arrow
vale frigate
Look at the red arrow
then
civic otter
I hope it could help you understand
civic otter
can anyone explain to me how did they get the bounds of integration on this
You go from bottom to top, so yellow to green
Therefore you fix the x value, and "brush" all the y values from the lower curve (y=0) to the upper curve (y=(x+2)²)
Afterwards, you can integrate over the x, from -2 to 0
vale frigate
Therefore you fix the x value, and "brush" all the y values from the lower curve...
how about d3
civic otter
It's similar, but horizontally
vale frigate
left to right?
civic otter
left to right?
Yep, because that's how the x-axis is oriented
twin meteorBOT
civic otter
This is better
vocal sleetBOT
@vale frigate Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
lost cipher
Yo
lost cipher
Can someone lmk if my answers are correct
<@&286206848099549185>
The answer for the first question should be 4056
Mb
I'm just confused about my second answer
vocal sleetBOT
@lost cipher Has your question been resolved?
lost cipher
.close
solemn crow
Can someone help me i figured out what on of the "a" equal but I can not figure it out and I know it does not equal -4
vocal sleetBOT
Can someone help me i figured out what on of the "a" equal but I can not figure ...
solemn crow
I am using the Rational Zero Theorem
edgy kayak
why did you go from product of two polynomials to difference of two polynomials
which one is it?
drifting jackal
why did you go from product of two polynomials to difference of two polynomials
That's factoring by grouping
edgy kayak
oh
sweet birch
That's factoring by grouping
it's missing a bracket around the whole thing, but the next line it's treated as a -8
$2a^2(a+4)(-8(a+4))$ is not $2a^2(a+4) - 8(a+4)$
twin meteorBOT
PrettyPrincessKitty FS
drifting jackal
$2a^2(a+4)(-8(a+4))$ is not $2a^2(a+4) - 8(a+4)$
My guess is he forgot the plus sign so it's supposed to be $2a^2(a+4)+(-8(a+4))$
twin meteorBOT
CaptainNova22
drifting jackal
Can someone help me i figured out what on of the "a" equal but I can not figure ...
Why did you break down 2a^2 - 8 to be that?
It's not a difference of squares
You can just do 2a^2 - 8 = 0 and solve for a
solemn crow
I was told by teacher to break it down because we have to find 2 different a's
drifting jackal
It's not a difference of squares with rational numbers like I stated
drifting jackal
You can just do 2a^2 - 8 = 0 and solve for a
You can do this to find the two different values of a
sweet birch
Can someone help me i figured out what on of the "a" equal but I can not figure ...
if $ab = 0$ then either $a = 0$ and/or $b = 0$, so $-8a - 32 = 0$ and/or $2a^3 + 8a^2 = 0$
twin meteorBOT
PrettyPrincessKitty FS
drifting jackal
if $ab = 0$ then either $a = 0$ and/or $b = 0$, so $-8a - 32 = 0$ and/or $2a^3 +...
You realize that they are factoring by grouping, correct?
sweet birch
You realize that they are factoring by grouping, correct?
and as far as I can see they have not factored correctly, so no
drifting jackal
I'm guessing the original problem is 2a^3 + 8a^2 - 8a - 32 so you group the first two terms and the last two and find the GCF of the two groups
drifting jackal
My guess is he forgot the plus sign so it's supposed to be $2a^2(a+4)+(-8(a+4))$
.
sweet birch
oh, it's not a quartic.
drifting jackal
,w expand (a+4)(2a^2 - 8)
sweet birch
it's just a cubic with some slightly confusing use of parentheses.
twin meteorBOT
drifting jackal
You can just do 2a^2 - 8 = 0 and solve for a
@solemn crow
solemn crow
Alright thank you
vocal sleetBOT
@solemn crow Has your question been resolved?
echo pawn
im a high schooler and i was trying to prove that the limit of x+2 when x approaches 3 is 5 after seeing a video about epsilon delta and i was wondering if this is a correct proof
vocal sleetBOT
im a high schooler and i was trying to prove that the limit of x+2 when x approa...
vocal sleetBOT
vocal sleetBOT
Available help channel!
timid rapids
how do i solve this part of the equation?
vocal sleetBOT
how do i solve this part of the equation?
timid rapids
do i have to make 1/x = s?
when i first tiredd this problem
i left it as 1/x
and evaluted limit as is
but it was undeifned
how do i solve this part
here is the full problem for context
flat whale
do i have to make 1/x = s?
no you don't have to
i left it as 1/x
if you got the right answer and justified your steps then your approach is correct
river tiger
vocal sleetBOT
river tiger
no l'hopital
river tiger
Multiply the insides first (if you want)
inf - inf case
river tiger
Or, better yet, take the log of both sides
p sure it's also inf - inf
quiet echo
p sure it's also inf - inf
You can do more.
grim lotus
[(e^u - 1)/u] * [u e^(1/u)]
left is derivative of e at 0
right is e^x/x as x --> infty which is infty
vocal sleetBOT
vocal sleetBOT
Available help channel!
ruby forum
in the following equation, why do we not leave it as it is just like the denominator?
vocal sleetBOT
in the following equation, why do we not leave it as it is just like the denomin...
lean iris
in the following equation, why do we not leave it as it is just like the denomin...
Depends on question
ruby forum
Depends on question
it simply just solving the equation
the answer of this equation should be 2x^2 - x + 6 / (x+4)(x-2) where x isn't 2, -4
lean iris
$\frac{2x^2 - x + 6}{(x + 4)(x - 2)}$
twin meteorBOT
SELVATOR
median knoll
Yo I’m so sorry someone pls just join my channel it will take 2 seconds my helper left me please bro please you don’t understand
I’m 1 second away from solving it
lean iris
**SELVATOR**
R u looking for Df?
ruby forum
what exactly is Df? just so we are on the same page
lean iris
$\mathbb{R} \setminus {-4, 2}$
twin meteorBOT
SELVATOR
ruby forum
oh, no I am just learning rational expressions
lean iris
in the following equation, why do we not leave it as it is just like the denomin...
Both are valid
One is simplified
Other is not
ruby forum
**SELVATOR**
so if I simplify it, I will get this as my answer but if I went with the other way, I would've gotten (x-3) + x
how exactly would that work?
lean iris
You can submit the full question for more information.
ruby forum
well it this
there no question
I'm trying to understand the reasoning behind why my teacher went with this method
lean iris
U are searching for denominator equal 0, right?
ruby forum
yes
lean iris
It doesnt matter for nomerator, being x¹⁰ or 3 or x(x² - 3)
Ur job is to find denominator, that's it
ruby forum
oh, so in this course all I gotta keep in mind is the denominator and that will give me the answer?
lean iris
Forget about nomerator's expression, and focus on denominator, (x+4)(x-2) = 0
Means x+4 = 0 or x - 2 = 0
Which is x = -4 or x = 2
ruby forum
oh okay that a nice way to understand it
just to be sure that I get this right
2x - 5 / x - 3, the answer should simply be x isn't equal to 3?
because if it was, the deno would = to 0
lean iris
If you are looking for the domain of function only, and you have x in the denominator and numerator, just look for numerator = 0.
lean iris
x² - 1 = 0
(x-1)(x+1)=0
x - 1 = 0 or x + 1 = 0
x = 1 or x = -1
lean iris
Is it ur teacher's work?
ruby forum
Is it ur teacher's work?
yes
ruby forum
what do u mean?
twin meteorBOT
SELVATOR
lean iris
$x = -2$ or $x = 4$
twin meteorBOT
SELVATOR
lean iris
I meant for (x+2)(x-4) to equal 0
After proving it, u should write ( no equal)
In Domain
ruby forum
so the answer is x isn’t equal to -2 and 4 only?
lean iris
Exactly!
ruby forum
I got another similar one but the answer isn't the same as what I got
I got x isn't equal to -7 but
does he add 5 and -2 because they were part of the denominator at some point?
lean iris
Maybe you learn it this way.
But in real, only the last result is considered
Because other steps are previous, so they arent considered in answer
Since he answers this way, the best advice is to follow his methods
ruby forum
hes setting me up for failure
alright, thank you for the help, I appreciate it
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
humble patrol
vocal sleetBOT
humble patrol
,rotate
twin meteorBOT
humble patrol
Am I setting this problem up right?
simple mason
Almost correct
But there is a little mistake in the implementation of the law
humble patrol
How
simple mason
Here you assigned a as the value of the length and you have been given the width and the height of the prism
In the second line you only put the height of the prism
You should put the width also in the equation
Also a should be squared there
In the last line you removed the square root without squaring both sides
simple mason
This 9 not a LOL
I was looking at it for 2 minutes till I saw it
simple mason
Yes it is right
vocal sleetBOT
@humble patrol Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
soft wharf
how do you differentiate 14^-x ?
vocal sleetBOT
how do you differentiate 14^-x ?
reef agate
how do you differentiate 14^-x ?
Do you know the product rule
Wait are you differentiating just 14^(-x) or the entire function
soft wharf
the end goal is the entire function so im thinking to differentiate each part, then apply the product rule
im doing the let u = 14^-x and v = sin(x) method lol
silk osprey
derivative of a^x is a^x ln(a)
reef agate
Anyways, $\dv{x} \qty(a^x) = a^x \ln(a)$
twin meteorBOT
King Leo
reef agate
You need to use the chain rule because the exponent is -x rather than x
reef agate
derivative of a^x is a^x ln(a)
As the derivative of a^x, i can confirm
-# /s
soft wharf
dang ok so its not really abt finding an actual value for it
soft wharf
**King Leo**
this is really helpful thanks!
soft wharf
derivative of a^x is a^x ln(a)
also idk if u remember but the other day u told me to watch this one khan academy video and it was super super helpful i really appreciated it!
silk osprey
also idk if u remember but the other day u told me to watch this one khan academ...
which one?
soft wharf
it was one abt product rule
once it was clear to me how to do it everything made sense
soft wharf
hahaha fr thank u
silk osprey
you’re welcome
soft wharf
okay so is the differentiated form 14^-x ln 14
i used an ai math thing to help me and its saying that i should also multiply by -1.. is that correct or is there something im missing
soft wharf
**King Leo**
oh so its not just this then
does that formula in the texit only refer to if the exponent is only an x
vocal sleetBOT
vocal sleetBOT
Available help channel!
pallid flax
Could someone help me by making some images of the problems? I’m genuinely so confused, my math teacher made us do like 3 and expects us to know it all
vocal sleetBOT
Could someone help me by making some images of the problems? I’m genuinely so co...
pallid flax
Anyone?
Worked on the second one, just asking if it’s correct for anyone to check
<@&286206848099549185>
Please anyone please I genuinely need this help so bad
I just need a small explanation please is there any helpers
vocal sleetBOT
@pallid flax Has your question been resolved?
pallid flax
No bro
vocal sleetBOT
@pallid flax Has your question been resolved?
pallid flax
Love how none of you helped me
vale frigate
im trying to get the derivative of this
vocal sleetBOT
im trying to get the derivative of this
ebon rapids
im trying to get the derivative of this
Have you heard of chain rule?
vale frigate
however the answer i got is
which doesn't seem right
the steps i did was chain rule -> logarithmic differentiation then product rule then solve for u
ebon rapids
Show your work
paper depot
discounting simplification BS, this does in fact look vaguely right
ebon rapids
the steps i did was chain rule -> logarithmic differentiation then product rule ...
But on first glance this process looks absolutely fine
twin meteorBOT
ebon rapids
I have a problem with this answer
Note that the power 4x-2 only applies to x, not to 9x
ebon rapids
so recheck your log diff
vale frigate
so recheck your log diff
wait so ln(9x^(4x-2)) != (4x-2)(ln(9x)?
ebon rapids
Yes because $ab^c\neq (ab)^c$
twin meteorBOT
CST (reply ping for help)
ebon rapids
recall order of operations, exponentiation first before multiplication
paper depot
ah so there was simplification BS
vale frigate
ok wait im stuck
vale frigate
so recheck your log diff
what would be the right way to do it
lets say from ln u = ln(9x^(4x-2)) what would be the next step
oh wait i think i got it sec
vast shale
How do i math
vocal sleetBOT
How do i math
thin vale
question #2850
paper depot
do you know exponent laws?
vocal sleetBOT
@vast shale Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
fathom trellis
vocal sleetBOT
vocal sleetBOT
Available help channel!
burnt nacelle
Find all values of m so that this equation has 4 unique solutions
I want to know what I should do to approach this question (I don’t know where to begin)
vocal sleetBOT
Find all values of m so that this equation has 4 unique solutions
I want to know...
paper depot
let z := 3^(x^2-2x+1)
note that:
a) z >= 3 always
b) any value of z strictly above 3 will yield two solutions for x
c) your equation is quadratic in z
solid sage
Why is z>=3 always
solid sage
Yep happens
mighty night
!help
vocal sleetBOT
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
vocal sleetBOT
!help
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
paper depot
@solid sage aside from that numerical mishap, what i said stands
solid sage
Yep
paper depot
z^2 - 2mz + 3m-2 = 0
you want this equation to have two distinct roots both of which are greater than 1
mild dome
Hello, can anyone check my work
vocal sleetBOT
Hello, can anyone check my work
mild dome
I have to find the volume with cross sections
The equation is x=y^2 and its bounded by x=9
valid path
what is the quesiton
mild dome
Its to find the volume
So the cross sections are squares
and they’re perpendicular to the x axis
The first equation is x=y^2, second is x=9
So I ended up with 162 but im second guessing myself
wraith python
Looks correct to me.
mild dome
Looks correct to me.
Thanks and if i can ask
why couldnt i do smth like
Shouldn’t this give me the same volume?
Because i think the curve of x=y^2 is symmetrical along the x axis
So i could just find the cross sections squares with only the top half
wraith python
You aren't calculating the area of the square correctly.
mild dome
wait what
So if this is correct, the graph
then shouldn’t the square be
Sqrtx by sqrtx?
So then i’d just find the area of the top half and the double it right?
wraith python
If you were calculating a side length from the x-axis to sqrt(x).
wraith python
Otherwise, if you are using a side length from one side of the parabola to the other, that would be 2sqrt(x).
wraith python
Yes.
mild dome
Hmm, i was referencing some older work and it was fine lemme see
wraith python
You could arguably multiply the integral by 4 rather than 2.
wraith python
Yes.
mild dome
alright is it ok if i show another problem and u can see if the set up is right?
wraith python
Sure.
mild dome
I also did the doubling thing here
i think? This is a more complicated example and i don’t even know how i did it tbh
Oh wait… that equation is a semi circle
wraith python
That's incorrect. You are assuming the side lengths of the square is sqrt(4 - x^2) which they aren't.
The side lengths of the square are 2*sqrt(4-x^2).
wraith python
Once again, you could multiply the integral by 4 rather than 2 because that's how the math works out.
mild dome
Wait so how did u get that side length?
wraith python
Let me make a graph that will illustrate the problem.
mild dome
So i graphed it and it looks like this
Wait i think i get it
Because sqrt(4-2x) is only half of the graph
And there’s two y distances
wraith python
The red area is what you are attemping to "simplify". It is only 1/4 the area of the actual square you need to integrate.
mild dome
Yeah i see, there’s two y distances so it makes everything change
So is rhis rhe actual integral?
wraith python
You do not need to multiply that by 2 as you are correctly calculating the area of the square correctly inside of the integral.
wraith python
Oh wait, you are integrating from 0 to 2, so that is correct.
mild dome
Oh wait
wraith python
It is symmetric about the y-axis so you can simplify it that way.
mild dome
So its been a while since i did integration but you can’t go from -2 to 2?
wraith python
You can.
mild dome
is it basically the same? I find the integral and plug in?
wraith python
Should be able to anyways, I think. You got me doubting now. 😄
mild dome
oh lol i dont know but in the end if 0-2 works thats all that matters
okay i get it now, thanks for helping me out! 💙
mild dome
Hmmmm, but i don’t remember doing it with negatives, i think we were taught not to do that
Probably involves more complicated math
mild dome
Oh, thanks
i have no idea how to set that up but its a nice reference for future problems
okay once again thanks
wraith python
yw
mild dome
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
brave raptor
from where did the root under 2 by 2 came
vocal sleetBOT
from where did the root under 2 by 2 came
bronze osprey
from where did the root under 2 by 2 came
you need to apply the chain rule, so sqrt(2x) gets differentiated as well
that explains the sqrt(2) on top
civic otter
from where did the root under 2 by 2 came
The numerator should have been a 2 actually, yeah
bronze osprey
wait should be just $\frac{\sqrt{2} \frac{1}{2 \sqrt{x}}}{4 + \sqrt{2x}}$, exactly
twin meteorBOT
south
brave raptor
here shouldnt the root 2 be in denomintor
bronze osprey
and then yeah should simplify
the chain rule on ln(f(x)) gives f'(x) * 1/f(x)
also write sqrt(2x) = sqrt(2) sqrt(x)
there you go
bronze osprey
here shouldnt the root 2 be in denomintor
no
brave raptor
(1/4+ root under (2x) ) . d/dx of (4 + root under (2x))
that equals
(1/4+ root under (2x) ) x (0 + 1/ 2 . root under(2x) . d/dx of 2x)
that equals
(1/4+ root under (2x) ) x (0 + 1/ 2 . root under(2x) . 2 that equals (1/4+ root under (2x) ) x (1/ root under(2x)
bronze osprey
(1/4+ root under (2x) ) . d/dx of (4 + root under (2x))
that equals
(1/4+ roo...
okay that is super confusing to read
brave raptor
ikkkk
brave raptor
okay that is super confusing to read
\frac{1}{4 + \sqrt{2x}} \cdot \frac{d}{dx} (4 + \sqrt{2x})
= \frac{1}{4 + \sqrt{2x}} \times \left( 0 + \frac{1}{2 \sqrt{2x}} \cdot \frac{d}{dx} (2x) \right)
= \frac{1}{4 + \sqrt{2x}} \times \left( 0 + \frac{1}{2 \sqrt{2x}} \cdot 2 \right)
= \frac{1}{4 + \sqrt{2x}} \times \frac{1}{\sqrt{2x}}
bronze osprey
wow thanks for the LaTeX
$$\frac{1}{4 + \sqrt{2x}} \cdot \frac{d}{dx} (4 + \sqrt{2x})$$
$$= \frac{1}{4 + \sqrt{2x}} \times \left( 0 + \frac{1}{2 \sqrt{2x}} \cdot \frac{d}{dx} (2x) \right)$$
$$= \frac{1}{4 + \sqrt{2x}} \times \left( 0 + \frac{1}{2 \sqrt{2x}} \cdot 2 \right)$$
$$= \frac{1}{4 + \sqrt{2x}} \times \frac{1}{\sqrt{2x}}$$
twin meteorBOT
south
brave raptor
?
bronze osprey
one sec, still checking
bronze osprey
**south**
I also get $\frac{\sqrt2}{(4 + \sqrt{2x}) (2 \sqrt{x})}$
excuse me, should have more explicitly said their answer was wrong
twin meteorBOT
south
bronze osprey
**south**
and then you can just divide top and bottom by $\sqrt{2}$
then $\frac{2}{\sqrt2} \sqrt{x} = \sqrt{2} \sqrt{x} = \sqrt{2x}$
twin meteorBOT
south
bronze osprey
also write sqrt(2x) = sqrt(2) sqrt(x)
this
so $\frac{d}{dx} (\sqrt{2} \sqrt{x}) = \sqrt{2} \cdot \frac{1}{2 \sqrt{x}}$
twin meteorBOT
south
brave raptor
ok ok got it thank you
bronze osprey
no worries!
brave raptor
.close
trail seal
I don’t understand the last part of the question
vocal sleetBOT
I don’t understand the last part of the question
trail seal
This is all I have about it being maximised in my notes
vocal sleetBOT
@trail seal Has your question been resolved?
bronze osprey
This is all I have about it being maximised in my notes
you want u parallel to the gradient of f, that's the key thing
call u = (p, q)
you need to do 1/sqrt(p^2 + q^2) * (p, q) so that u is a unit vector
so that u has magnitude (length) = 1
just take the gradient and normalise it to have unit length, in other words
trail seal
just take the gradient and normalise it to have unit length, in other words
R u saying just do this
vocal sleetBOT
trail seal
.reopen
vocal sleetBOT
✅
bronze osprey
,w d/dx (x^2 y + e^(xy) cos(y)) when (x, y) = (1, pi/2)
twin meteorBOT
bronze osprey
,w d/dy (x^2 y + e^(xy) cos(y)) when (x, y) = (1, pi/2)
twin meteorBOT
bronze osprey
R u saying just do this
yep!
vocal sleetBOT
bronze osprey
Ok tysm
one last word, it's cause a dot b = |a| |b| cos(theta)
so you just set cos(theta) = 1 to maximise the dot product of the directional derivative
trail seal
so you just set cos(theta) = 1 to maximise the dot product of the directional de...
Oh ok ye ty
vocal sleetBOT
Available help channel!
vast shale
vocal sleetBOT
vast shale
How do i math
paper depot
@vast shale i asked you this earlier but you disappeared: do you know exponent laws?
topaz eagle
!showwork
vocal sleetBOT
Show your work, and if possible, explain where you are stuck.
@vast shale Has your question been resolved?
atomic jasper
twin meteorBOT
Bonk
vast shale
Math is not for me
vocal sleetBOT
@warm eagle Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
prime moon
vocal sleetBOT
prime moon
Why do i have to pull out the 1/3 infront of (1+u), instead of multiplying like that??
pale perch
like what?
prime moon
the picture I sent
pale perch
you can do it like that if you want, theres no difference
pulling out constants is just for convenience, not necessity
prime moon
Hmmm then there is something else that is wrong with my calculation
the answer has to be
civic otter
Uhh that's quite subtle yeah
pale perch
keep note that the concept youre using is that the numerator is the derivative of the denominator, by making it 3+3u, your numerator is 1, when you would want it to be 3
if its 1+u then its 1 and all is well
civic otter
Uhh that's quite subtle yeah
You can see it this way:
$$\frac{1}{3}\ln{(3 + 3e^{3x})} + C= \frac{1}{3}\ln{(3\cdot(1 + e^{3x}))} + C= \frac{1}{3}\ln 3 + \frac{1}{3}\ln{(1 + e^{3x})} + C = \frac{1}{3}\ln{(1 + e^{3x})} + C_2$$
twin meteorBOT
Alberto Z.
civic otter
**Alberto Z.**
Where $C_2 = C + \frac{1}{3}\ln{3}$
twin meteorBOT
Alberto Z.
prime moon
what's C2??
civic otter
In other words, you can include whatever numbers (hence, constants) to your + C
civic otter
**Alberto Z.**
C2 is here
prime moon
isn't that just C, not C2?? sorry I don't understand😭
civic otter
C and C2 are just random names for a generic constant
So you can call it whatever you like
What I'm saying is that the C in your answer and the C in the teacher's answer don't have to necessarily have the same value, in this case indeed they're different
civic otter
What I'm saying is that the C in your answer and the C in the teacher's answer d...
This is from the theory actually, do you remember that the derivative of a constant is 0?
prime moon
yesyes
civic otter
So whether you call that C or C2 or Mickey or whatever name you like, when you differentiate the result the + C part disappears
Therefore you don't care what that constant is, you just have to know that there is
You'll probably see later how to find the value of that constant given some more information, when you'll do differential equations
vocal sleetBOT
@prime moon Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
royal tide
How do I solve this?
So I take the y’ and sq
vocal sleetBOT
How do I solve this?
So I take the y’ and sq
royal tide
No. 10
twin meteorBOT
King Leo
royal tide
So for respect to y and x axis is the same?
reef agate
Wait one sec
reef agate
So for respect to y and x axis is the same?
Wdym by x-axis
royal tide
Just respect to x
So for arc length it’s always respect to x
But the 8 and 9 what’s the formula
reef agate
So for arc length it’s always respect to x
Or rather, its always with respect to the independant variable
$$\text{Surface Area}$$
About the $x$-axis:
$$\int_a^b y \sqrt{1 + \qty(\dv{y}{x})^2} \dd{x}$$
About the $y$-axis:
$$\int_a^b x \sqrt{1 + \qty(\dv{y}{x})^2} \dd{x}$$
royal tide
**King Leo**
So remember this if I have to look for arc length
twin meteorBOT
King Leo
royal tide
Thank you, I’ll send my solution in a litttle if you can check if it’s wrong
Im confused now
I did the derivative wrong
This is how my friend did it but idk how it got to that
reef agate
I did the derivative wrong
Can you show how you did the derivative