Got it ! What symbol should I use though?
#help-28
oblique kraken
Woops accidentally cropped out the numbers lmfao
It's #3 and then below is #4
I used the table this time!
Get the degree of freedom then add that to the significance value then find it on the table right?
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oblique kraken
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β
oblique kraken
I hope I got it rightπ’π’π’
Yeh I think I'm done for todayπ€ I ain't sure if my answer's correct but I learned smtg and that's all that matters ig WHHAHAHA
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calm flint
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calm flint
I've done limits before but idk what to do with that ugly looking numerator
factor? but idk how
onyx glen
I've done limits before but idk what to do with that ugly looking numerator
before thinking about this
can you say what the denominator goes to?
calm flint
0
toxic field
Have you learned about the differentiation method
calm flint
Have you learned about the differentiation method
no, can you tell me about it?
onyx glen
Have you learned about the differentiation method
do NOT suggest l'hΓ΄pital.
calm flint
sorry i got so used to seeing complicated limits being = 0/0
onyx glen
not least bc it's both inapplicable AND unnecessary here
calm flint
do NOT suggest l'hΓ΄pital.
oh yes ive heard of lhopital
toxic field
Awh
onyx glen
the denom approaches something that isn't 0
you can literally just plug -2 in
without a care in the world
tight quest
lol lhop
calm flint
is this 5/2
tight quest
is this 5/2
check your signs
calm flint
check your signs
ty. -23/6?
tight quest
ty. -23/6?
can you evaluate the numerator first
write out the process here
evaluate the numerator at x = -2
mighty dew
-32+12 + 4 +1
tight quest
yes
calm flint
thankiesss
onyx glen
I wanted to bring a tank
more like a nuke tbh
calm flint
is this 1/2
mighty dew
yep
if the denominator isn't going to zero when you input x the limit is the value of f(x)
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@calm flint Has your question been resolved?
calm flint
yep
if the denominator isn't going to zero when you input x the limit is the val...
so we only bother doing other things when the denominator is 0?
and 0/0
but 0/non-zero is just fine right
mighty dew
so we only bother doing other things when the denominator is 0?
there are a bunch of undefined forms that u need other methods to solve
mighty dew
but 0/non-zero is just fine right
yes
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@calm flint Has your question been resolved?
calm flint
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autumn sleet
yes
autumn sleet
the eqn in numerator
calm flint
how do i rotate ππ
calm flint
LOL
glossy valveBOT
calm flint
is this correct
calm flint
yes i believe so too
autumn sleet
see break x^2 - 1 in x-1 and x=1 and then take common
calm flint
is x(x-1)(x-2)-2(x-1) your numerator
calm flint
π
autumn sleet
calm flint
can u explain how did that happen π
autumn sleet
carazy
see when you reached the final equation right? try to open it and see if you get same thing as question
i was pointing out that you took the wrong thing as common
calm flint
so if i multiply this i get the same original limit?
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torn nebula
This is so annoying, i dont understand why im not getting the right answer
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haughty plover
hello I need some help with this to solve for x and y
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hello I need some help with this to solve for x and y
haughty plover
<@&286206848099549185>
limpid junco
What did you try
haughty plover
honestly.. I have nothing so far
mighty dew
hello I need some help with this to solve for x and y
it'll be very complicated if u try doing it algebraically
trial and error is easy
think of 3^x is closest to 25 and what u needa subtract
and see if ur guess fits the second eqn
torn jolt
I dont think its about the result but the way
thick hedge
change of base is the way to go
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haughty plover
is this right?
mighty dew
,rotate
glossy valveBOT
mighty dew
no... i'm pretty sure not
it needs to be in the form of log(a) = log (b), both with the same bases to be able to remove the log
what grade work is this
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haughty plover
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β
haughty plover
no... i'm pretty sure not
it needs to be in the form of log(a) = log (b), both w...
well it is
we have log(2) in every one of them
haughty plover
what grade work is this
10th grade olympiad
mighty dew
well it is
no it's not
the second term on the left side cannot be simplified as it is a multiplication of logs
it strictly has to be one logarithmic term with the same base on each side
haughty plover
does it require a proof
yes it does
haughty plover
what kind of exam format
I'm not sure..
mighty dew
yes it does
god bless you
haughty plover
π
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torn jolt
U still need help?
dim dragon
I have need to study all these topics for my exam tomorrow. Is there any book I could refer to for the theory? I have already done first half of unit 1.
dim dragon
I know its just fu**ed up π
slender onyx
whatever book your prof uses
clever flicker
forget the book... u need a sparknotes version lolol
dim dragon
The thing is they don't use any good book
dim dragon
yes thankyou
bleak aurora
The thing is they don't use any good book
Good?
clever flicker
im in this class too
gritty rose
yes thankyou
!done
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If you are done with this channel, please mark your problem as solved by typing .close
dim dragon
From an exam point of view
bleak aurora
Ohhh i sss
gritty rose
if you want to continue chatting go to #real-complex-analysis
clever flicker
weve covered up to cauchy riemann equations plus logarithm and line integrals
dim dragon
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unique wigeon
hiya, this isnt very complicated in comparison to what others are putting but oh well.. what in the world happens between step 3 and 4? how does 2x*5 become 2x again?..
raven river
This is a simplification, note the elimination of the denominator and the coefficient of 5. Only left.
bleak aurora
hiya, this isnt very complicated in comparison to what others are putting but oh...
Divison, 2x*5 have 5 in denominator.
You also shouldn't compare this level of mathematics to others, it's fine, it's also mathematics. 
It's equally welcomed.
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torn jolt
yes, please..
praying for you twin
bleak aurora
Yes
This question isn't mine, this is actually of @haughty plover's, Lol
Let me bump the original text
bleak aurora
hello I need some help with this to solve for x and y
Here
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late blade
why is y=x^2 assumed?
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why is y=x^2 assumed?
late blade
can y be any expression in terms of x as long as it stays 0 according to x=0?
glacial pasture
because then you get two x^4 in the denominator, which is convenient
since its in the numerator
theyre going down the path y=x^2, but yeah you could go down any path for y really (if tends to 0)
late blade
so y= any constant times a single x term raised to any power
glacial pasture
sure, could even do y=sin(x) if you wanted to be a weirdo
though it wouldnt help much
glacial pasture
so y= any constant times a single x term raised to any power
power would have to be positive
late blade
but if i made it polar the limit becomes 0
slender onyx
but if i made it polar the limit becomes 0
its not in the form where we can apply the polar theorem
it must be $F(r)G(\theta)$ with $G(\theta)$ bounded and $\lim_{r\to0}F(r)=0$
glossy valveBOT
π‘ππππ£π£πβΰ¨ΰ§ββ₯ β‘ <πΉβ€
late blade
im not familiar with notations like frgtheta
whats f(r) in x=rcostheta?
whats a bounded gtheta? isnt the point of making limit only in terms of r to allow theta to be anything?
slender onyx
i mean $f(r\cos\theta,r\sin\theta)=F(r)G(\theta)$
glossy valveBOT
π‘ππππ£π£πβΰ¨ΰ§ββ₯ β‘ <πΉβ€
late blade
do i have to know what gtheta is?
slender onyx
basically when converting to polar the f must become a function of r times a function of theta, with the constraints i mentioned
if all these are satisfied then the polar limit theorem says the limit at the origin is 0
if not then we have to use another method to evaluate the limit
slender onyx
nah
late blade
how to identify which f(x,y) can have its limit computed in terms of r?
slender onyx
exactly as i said above
basically when converting to polar the f must become a function of r times a function of theta, with the constraints i mentioned
late blade
so i first convert anyway, then if it looks complicated i undo it
slender onyx
if its not in this form
function of r times a function of theta, with the constraints i mentioned
then use another method
like computing limit on different paths
late blade
my slides didnt mention that, how would that work?
do i hold y constant while doing lim(x->0) ?
but then if the function is x+y the limit would be y and x vice versa, 0 doesnt show up
slender onyx
my slides didnt mention that, how would that work?
exactly like in the solution
the first path is y=x^2 so plug it in f then take x->0
late blade
that path is arbitrary tho
if it works it works?
would letting y be anything else ruin it?
slender onyx
any pair of paths that give you different limits is enough
so you must explore a bit
you can make smart choice of path based on f
in this case its good to turn the bottom into a single term
so y=x^2 is smart
late blade
huh alr
slender onyx
y=-x^2 is also smart bc y^2 removes the -
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slender onyx
np
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compact ermine
Our prof said to prove by contradiction but so far I just have a smallest irrational number named "x"
torn jolt
o
slender onyx
Our prof said to prove by contradiction but so far I just have a smallest irrati...
use x to make a smaller positive irrational
compact ermine
use x to make a smaller positive irrational
Isn't that what I just did though? or am i misreading
slender onyx
Isn't that what I just did though? or am i misreading
thats how u get the contradiction
assuming such number leads to even smaller number
drowsy ivy
What didnt I posz smth here
slender onyx
What didnt I posz smth here
the question is for him not u
slender onyx
chill yo
compact ermine
If you deleted it then I didn't see it dw
but I'm to look at my profs hint rq because it said to recall a past problem that is in the same assignment
slender onyx
the other problem strategy is probably just like this
assuming such number leads to even smaller number
drowsy ivy
Expression
dry arch
assuming a smallest positive irrational number exists is not the same as using that number to make a smaller positive irrational number
slender onyx
ie if u assume the smallest exists and call it x then u can still get smth smaller than x
compact ermine
ok yea yea I see it
slender onyx
thats the contradiction hence the smallest doesnt exist
compact ermine
Because we literally did this in another problem on the hw
dry arch
you can use that
slender onyx
now can u do this
use x to make a smaller positive irrational
dry arch
it's clear that (1/2)x is smaller than x, but it's important to show that (1/2)x is irrational
compact ermine
yeah I get it now ty
slender onyx
np
compact ermine
it's clear that (1/2)x is smaller than x, but it's important to show that (1/2)x...
I was just worried because I didn't know how I could say that it would be irrational without having to write a whole explanation
slender onyx
even if u forgot the other problem the proof is pretty short
dry arch
you can either repeat the answer to the other problem, or you can just say "this is true as shown in the other problem"
if you didn't do the other problem, then yeah you probably have to write an explanation
slender onyx
you do but itll be one line
slender onyx
dry arch
Because we literally did this in another problem on the hw
do you want help with this one?
compact ermine
do you want help with this one?
no i did it already I looked at it and realised what i could do
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hidden belfry
Hey guys can someone help me find the summation for an arithmetic series?
cursive condor
$S=\frac{n}{2}(2a+(n-1)d)$, where $d$ is the common difference, $n$ is the amount of terms, and $a$ is the starting term of the sequence.
glossy valveBOT
mathisfun
hidden belfry
$S=\frac{n}{2}(2a+(n-1)d)$, where $d$ is the common difference, $n$ is the amoun...
Itβs to infinity
cursive condor
Ah
hidden belfry
Yea
cursive condor
The series is $ 2/(2n+1)$
$\sum_{n=0}^{\infty}\frac{2}{2n+1}$?
glossy valveBOT
mathisfun
cursive condor
(It diverges)
cursive condor
(It diverges)
||Harmonic series||
onyx glen
Why it not printing lol
bc the first dollar is separated from the formula by a space
onyx glen
So thereβs no answer?
there is. the answer is that this series diverges
hidden belfry
Huh?
onyx glen
if you were to even assign a value to it, that would be +β
hidden belfry
But the fraction becomes smaller each time tho
onyx glen
"answer" != "numerical value"
cursive condor
Hey guys can someone help me find the summation for an arithmetic series?
In regard to this question, it would just be does not exist, I suppose.
onyx glen
But the fraction becomes smaller each time tho
true, that it does!
it is counterintuitive at first.
hidden belfry
So the fraction is still significant enough to make a difference?
onyx glen
but in fact, as you add on more and more terms, the running total will eventually surpass any upper bound you could put on it
cursive condor
Also you can use integral test, etc.
onyx glen
So the fraction is still significant enough to make a difference?
yes, in a sense this series diverges really slowly
hidden belfry
Ok so then I got the wrong solution for my actual question then π
cursive condor
I'm trying to remember an exercise my teacher gave me
It was some pariwise->triplet->... grouping of the fractions
onyx glen
but in fact, while $\sum_{n=1}^{\infty} \frac1n$ diverges, the deceptively similar series $\sum_{n=1}^{\infty} \frac{1}{n^2}$ is convergent!
glossy valveBOT
Ann
cursive condor
$1+\qty(\frac12+\frac13)+\qty(\frac14+\frac15+\frac16)...$
onyx glen
$\sum_{n=1}^{\infty} \frac{1}{n^{1.01}}$ also converges
glossy valveBOT
Ann
glossy valveBOT
mathisfun
cursive condor
In general $\sum_{n=1}^{\infty}\frac{1}{n^p}$ for $p>1$ converges
glossy valveBOT
mathisfun
onyx glen
Ok so then I got the wrong solution for my actual question then π
what was your actual one
hidden belfry
Yea I learned about geometric series but not a lot on arithmetic series
hidden belfry
what was your actual one
For $0 \leq x \leq 1,$ the function $f(x)$ satisfies the relations $f\left(\dfrac x{x+1}\right) = \dfrac{f(x)}2$ and $f(1-x) = 1 - f(x).$ What is the value of the expression
[f\left(\dfrac23\right) + f\left(\dfrac25\right) + f\left(\dfrac27\right) + \dots + f\left(\dfrac2{2n+1}\right) + \dotsb,?]Express your answer as a common fraction.
glossy valveBOT
Ryxo
cursive condor
Woah
hidden belfry
I thought f(x) was just x
onyx glen
guhhh
hidden belfry
Yep
cursive condor
That is quite different from what you proposed?
onyx glen
f(x) isn't just x that is for sure
onyx glen
That is quite different from what you proposed?
yeah we just got massively XY'd.
hidden belfry
I did some tests and it seemed f(x) =x
hidden belfry
That is quite different from what you proposed?
Yea π
onyx glen
cursive condor
$\frac{x}{x+1}\neq \frac{x}{2}$
glossy valveBOT
mathisfun
hidden belfry
But itβs (x/x+1) = f(x)/2
cursive condor
Oh wait
onyx glen
But itβs (x/x+1) = f(x)/2
x/(x+1) not (x/x+1)
onyx glen
<@183668144404037632> ||Is this function symmetric about x=1/2 or am I tripping?...
||symmetric how||
hidden belfry
x/(x+1) not (x/x+1)
Ye Iβm on phone so me no type very good :((
cursive condor
||symmetric how||
Ah wait I'm stupid
onyx glen
anyway i go sleep
hidden belfry
Oh aight well gn
cursive condor
Let me see
hidden belfry
Thx for helping tho
hidden belfry
Oh yea so how I got f(x)=x is bc when I substituted 0 and 1 it gives me f(x)=x
hidden belfry
There is something from my textbook very similar to this
Really?
hidden belfry
Hmm
cursive condor
Well subsituting $x=1$ we have $f(0)=1-f(1)$ and $f\qty(\frac12)=\frac{f(1)}{2}$
glossy valveBOT
mathisfun
hidden belfry
Yea I did a whole lot of substituting
So if f x / x+1 = f x) /2 x:0 then f x must be 0
Sorry for lame typing Iβm on phone
cursive condor
Imma try and solve it
hidden belfry
Ok thx
cursive condor
Or wait
Do we even need to solve the FE to answer this question?
Try to plug in x=2/3, 2/5... 2/(2n+1) into the function equations and see what happens
hidden belfry
Yea I did
It gives f(2/3) : f(2/5) and so on
So like f(2/ 2n+1) : f(2/3) + 1/2f(2/3) and so on
So we can just try to find f(2/3) then multiply by 2 since the summation of that geo series is 2
But idk how to find f(2/3)
cursive condor
But idk how to find f(2/3)
Plug it in. Give it your best shot.
cursive condor
But idk how to find f(2/3)
You can use the 2nd function equation to do so.
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@hidden belfry Has your question been resolved?
hidden belfry
You can use the 2nd function equation to do so.
I like tried but it gave like -1/3 and stuff and it just didnβt work
hidden belfry
I got the question wrong and the solution was 3/2 :/
Anyways thanks for your help @cursive condor
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daring parrot
Calculate the distance from the vertex of the right angle C to the center of the inscribed circle O.
cursive condor
i got that r = 3 but
How so?
daring parrot
wait
hidden belfry
Use inscribe circle stuff
cursive condor
Note that $[ABC]=rs$, where $r$ is the inradius of the triangle, and $s$ is the semiperimeter.
glossy valveBOT
mathisfun
daring parrot
could it be if i were to draw a line from C it would be like 2:1
daring parrot
Oh
cursive condor
could it be if i were to draw a line from C it would be like 2:1
Look at what I sent.
Notice anything?
daring parrot
wait that makes sense π
daring parrot
do i just do the pythagorean theorem?
austere siren
Is it possible to convert a sin to a cos ?
cursive condor
do i just do the pythagorean theorem?
Yep.
daring parrot
okayy thank you!
cursive condor
Is it possible to convert a sin to a cos ?
$\sin(\frac{\pi}{2}-x)=\cos(x)$
glossy valveBOT
mathisfun
austere siren
**mathisfun**
We werent doing that in class but I will do anything at this point thx
Chat gpt told me its 90-alfa
primal viper
Chat gpt told me its 90-alfa
It just used a different variable. There's no difference.
Also, sin(A)^(2)=1-cos(A)^2
Depends on the context which one you need.
gritty rose
Chat gpt told me its 90-alfa
!nogpt
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Chat gpt told me its 90-alfa
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
austere siren
!nogpt
So people here are okey with doing my homework for me without them getting antyhing rather than thanks?
gritty rose
no idea what you're saying
cursive condor
So people here are okey with doing my homework for me without them getting antyh...
Hm?
Where did your English go?
cursive condor
If given 3 arbitrary points on a quadratic we can use gaussian elimination to solve for coefficients, correct?
umbral dome
yes, it becomes a system of 3 equations (3 points) in 3 unknowns (3 coefficients)
same applies to n + 1 points on a degree n polynomial
cursive condor
same applies to n + 1 points on a degree n polynomial
That is what I was thinking
So we can just use some nxn matrix, correct?
Or
yeah nxn coefficient matrix with constants
umbral dome
well it will be an nxn matrix augmented with a nx1 column vector
cursive condor
So nx(n+1)
slender onyx
fun fact, this is the motivation of least squares curves
cursive condor
What is that?
slender onyx
remember line/curve of best fit?
umbral dome
least squares regression is finding the least squares solution to an overdetermined system with more points than n + 1 (i.e. more equations than unknowns)
slender onyx
you can find a best fit of any type of curve with any number of parameters
you first learn with polynomials
but sines are common too
cursive condor
Ahh
slender onyx
you pretend the points lie on your modeling curve
you get a linear system in terms of the parameters
and find a least squares solution
slender onyx
oh yeah welcome to AI
cursive condor
No
umbral dome
using the normal equation A^T A x = A^T b
cursive condor
Ahhh
slender onyx
umbral dome
interestingly while gauss did not invent gaussian elimination he did invent this type of least squares modeling
slender onyx
heres the simplest least squares
find the line of best fit $y=\beta_0+\beta_1x$ for the points $(1,0),(2,3),(6,3)$
glossy valveBOT
π‘ππππ£π£πβΰ¨ΰ§ββ₯ β‘ <πΉβ€
slender onyx
you can in theory solve this now by doing
you pretend the points lie on your modeling curve
you get a linear system in terms of the parameters
and find a least squares solution (using the normal equation A^T A x = A^T b) (if solving Ax=b)
followup: find the parabola of best fit $y=\beta_0+\beta_1x+\beta_2x^2$ for the points $(1,0),(3,6),(6,5),(10,2)$
glossy valveBOT
π‘ππππ£π£πβΰ¨ΰ§ββ₯ β‘ <πΉβ€
slender onyx
i just made these up so i dont have sols
but if you setup the right system you can just ask wolfram to do least squares
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slender onyx
very fun stuff
when i ta'd linalg this was at the end of the course which was a bummer
slender onyx
bc 95% of the students were cs majors
heavy chasm
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cursive condor
?
heavy chasm
wtf why is this channel not getting removed i was testing
cursive condor
Do you need help?
heavy chasm
no
cursive condor
wtf why is this channel not getting removed i was testing
It doesn't get automatically removed.
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cursive condor
It doesn't get automatically removed.
^
cursive condor
It's fine.
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hybrid plank
related rates question
im trying to find a way to relate the variables, ive gotten as far as i could to finding the values of the other sides, but im stuck on setting the equation up to take the derivative of to find the rate of cart B in the figure
hybrid plank
Sorry if scratchwork is messy/hard to read
royal holly
Let AQ be x and then solve for QB in terms of x you know dx/dt = 2 so you can find the vale of dQB/dt
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hybrid plank
Let AQ be x and then solve for QB in terms of x you know dx/dt = 2 so you can fi...
when im making an equation to take a derivative for by solving QB in terms of x, how can i get both AQ and QB in the same equation so that i can find the value of dQB/dt
royal holly
do what you did for AQ =5
use pythagoras then since the length of the string is constant you can find out the other hypotenuse
Hence find QB
It will be messy but since you just have to plug x=5 later itβs no big deal
hybrid plank
@royal holly like this?
royal holly
start from AQ not QB let AQ be x
grim forum
i think its C but AI keeps telling me B with insufficient reasoning
grim forum
i think its C cuz the 2F downward force is closer to the reference point so torque is bigger the counterclockwise way
<@&286206848099549185>
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cerulean cargo
the ai fails to see where teh axis is
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torn jolt
Need help understanding portion Iβve marked with blue
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onyx glen
@torn jolt from $k < \frac{2c-1}{2}$ multiply both sides by $2$ to get $2k < 2c-1$, then subtract $2c-1$ from both sides to get $2k-2c+1 < 0$.
glossy valveBOT
Ann
torn jolt
<@456226577798135808> from $k < \frac{2c-1}{2}$ multiply both sides by $2$ to ge...
How did they get to k < (2c-1)/2?
onyx glen
@torn jolt they solved the equation D'(k) = 0.
@torn jolt this is how (2c-1)/2 happened.
torn jolt
<@456226577798135808> they solved the equation D'(k) = 0.
Yes I follow up until that point
Wait
Okay I understand now that they are trying to see when the numerator of Dβ(k) is positive. To run first derivative test
onyx glen
@torn jolt this entire blue part is a justification of why k = (2c-1)/2 really is a minimum point for D(k).
torn jolt
But how they happen to conclude that it is minimum, Iβm really having trouble visualizing
onyx glen
@torn jolt D is decreasing before this point and increasing afterwards.
@torn jolt that's a minimum point.
torn jolt
No sorry Iβm unable to process it
The fact that it is also in y coordinates and I keep trying to lose track of what the variables mean each time I try to process it
onyx glen
@torn jolt
@torn jolt just because it has to do with the y-coordinate of something geometrically doesnt mean the basic principle of function behavior around extrema stop working
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torn jolt
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β
thick hedge
Given the domain [1,2] find the values of $a$, such that f(x) is increasing on [1,2]
glossy valveBOT
What a wonderful world !
onyx glen
@torn jolt f is increasing <=> f'(x) β₯ 0
so what you want is that f'(x) β₯ 0 should be true for all x β [1, 2]
@torn jolt you need to find the set of all values of a which make that happen
torn jolt
2x+a>=0.
But how do I reason further?
onyx glen
@torn jolt you want 2x+a β₯ 0 to be true for all x β [1,2].
@torn jolt you may notice that 2x+a β₯ 0 is equivalent to x β₯ -a/2, so the interval [1,2] must be contained in the interval [-a/2, +β)
torn jolt
a = -2 would correspond to point 1 in [1,2] then?
onyx glen
@torn jolt a=-2 would mean that the solution set of 2x+a β₯ 0 is [-1, +β), which works.
@torn jolt i do not feel like saying it "corresponds" to point 1 or anything like that.
onyx glen
@torn jolt no.
@torn jolt $[1,2] \subseteq [-a/2, +\infty)$ means $1 \geq -\frac{a}{2}$.
glossy valveBOT
Ann
torn jolt
Just to summarize the argument:
To be increasing, 2x+a>= 0
So x in [-a/2, inf)
But we want to focus on only x in [1,2]
So we say that [1,2] is a subset of [-a/2 , inf)
So that means 1 >= -a/2 (itβs the extreme point of the interval)
-2<= a.
The minimum value of a is -2.
There is no maximum value of a. So [-2, inf)
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golden shore
mixed number is unnecessary.
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mixed number is unnecessary.
golden shore
argue with me.
sacred yarrow
Whatβs that?
hazy lance
not the place for that, go to #discussion
golden shore
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hazy lance
thanks
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vale zealot
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onyx glen
where is your question/doubt
vale zealot
If the ans is correct or nah
onyx glen
you've found the value of k, and it looks like you've done that correctly (even if you took a very roundabout route)
but you haven't found what they asked for
vale zealot
I put the value of k and x in there?
onyx glen
you know what p(x) is
it's x^2 - 3x - 10
you also know for free that it has (x-5) as a factor
factorize it in full
find its other root
vale zealot
factorize it in full
onyx glen
p(x) not p(5). and x^2 - 3x - 10 not x^2 - kx - 10.
but your factorization is correct.
so what are the zeroes?
vale zealot
5 and -2
vale zealot
so what are the zeroes?
Thats it?
onyx glen
well
do you think that's it or do you think you have to do something else for this question?
vale zealot
do you think that's it or do you think you have to do something else for _this q...
Uhm..hopefully thats it..
vale zealot
And reaaranged to get zero of polynomial
onyx glen
the question asks you to find the zeroes of a polynomial.
have you found the zeroes of the polynomial? yes or no
vale zealot
No?
(5 and -2 arent?)
onyx glen
do you hear yourself right now?
"Have you found the zeroes?" "No. Here are the zeroes."
vale zealot
π
onyx glen
then what are 5 and -2 if they are not the zeroes?
vale zealot
They are..they are
onyx glen
so, have you found the zeroes of the polynomial? yes or no
vale zealot
have you found the zeroes of the polynomial? yes or no
Yes
onyx glen
does the question ask for anything ELSE besides this? yes or no
vale zealot
No
onyx glen
so, are you done?
wheat garden
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wheat garden
How to Evaluate
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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
triple integrals are evaluated inside out
wheat garden
do i do like $3\int_0^1\int_{-z}^ze^{-zΒ²}\dd{y}\dd{z}$
glossy valveBOT
Jash
minor crater
no, inside out
wheat garden
but e^-zΒ² is not integrable
minor crater
but e^-zΒ² is not integrable
how would you evaluate $\int_{-z}^z e^{-z^2}\dd{y}$
glossy valveBOT
artemetra
wheat garden
idk how to do that one
minor crater
hint: the integrand does not depend on y. e^(-z^2) is a constant
minor crater
yes, and plug in the bounds
glossy valveBOT
artemetra
wheat garden
so do i do u=-zΒ² now
wheat garden
$\int_0^3\int_0^{-1}-e^u\dd{u}\dd{x}$
glossy valveBOT
Jash
wheat garden
is it that
minor crater
yes
wheat garden
so -e^u from 0 to -1
-e^(-1)-(-1)
1-e^-1
isnβt that constant
so itβs just 3(1-e^-1)
wheat garden
alr ty
minor crater
wheat garden
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swift fulcrum
Hello
swift fulcrum
Are my answers correct?
granite torrent
a and d are correct
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swift fulcrum
a and d are correct
What did I miss for b and c?
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rough mesa
This might be a dumb question But How do i solve this? Looks easy
gritty flax
!nogpt
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Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
gritty flax
@vale zealot you can help but don't ask gpt for the sol and send it
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calm flint
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calm flint
is item (2.1) between -2 <= and <=2
cursive condor
is item (2.1) between -2 <= and <=2
What is m?
cursive condor
(This is not technically correct)
Try to find the max and min of $\sin(x)+\cos(x)$
glossy valveBOT
mathisfun
calm flint
whats wrong with this, given x is sufficiently positive
are u asking me to spot my mistake or π
cursive condor
whats wrong with this, given x is sufficiently positive
Try it yourself
cursive condor
Well they arrived at the max and min incorrectly
cursive condor
Right answer, wrong method
tulip marlin
u dont need the max and min
u just need some bounds
and those bounds are sufficiently good to use squeeze
cursive condor
I am trying to correct a mistake
tulip marlin
The first 2 inequalities are added to give the 3rd
divide through by a positive x for the 4th
cursive condor
Well they arrived at the max and min incorrectly
To fix this, OP may or may not know how to arrive at it correctly
tulip marlin
???????
cursive condor
It might be problem in the future
tulip marlin
I'm saying I see nothing wrong with their working (apart from x > 0 needed)
cursive condor
Bruh
tulip marlin
**mathisfun**
I dont understand why this is necessary at all
calm flint
@cursive condor can you show me how to arrive at it correctly?
cursive condor
<@1340453306207572073> can you show me how to arrive at it correctly?
$\sin(x)+\cos(x)=\sqrt{2}\sin(x+\frac{\pi}{4})$
glossy valveBOT
mathisfun
tulip marlin
but thats completely unnecessary for the purpose of this question
tulip marlin
this is valid (bar x > 0) and what id expect people to do
tulip marlin
Sure, but in analysis, you often need to bound stuff
and you should always go for the easiest bounds possible
in this case -2, 2 is sufficiently good without overthinking
cursive condor
Ah whatever
I guess it won't matter when OP ends up making a mistake with specific bounds
tulip marlin
**mathisfun**
if theyre asked to find the inf and sup of cos + sin then yes theyll need to do this
cursive condor
I like to cover my bases
^
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wary condor
(3 , 8 , 15 , 24..., 440)
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(3 , 8 , 15 , 24..., 440)
wary condor
(3 , 8 , 15 , 24..., 440)
it wants the "formula?" for this sequence
okay i figured it out π
.close
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remote zenith
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remote zenith
Iβm in Algebra 2 and I donβt know what to do once I find the common monomial because itβs 1,
Weβre supposed to solve this by factoring
modest maple
Iβm in Algebra 2 and I donβt know what to do once I find the common monomial bec...
This is a BiQuadratic Equation, i Guess
I am assuming that, you are familiar with equation like of xΒ² + ax + b
Is that right?
remote zenith
Yes
modest maple
I am assuming that, you are familiar with equation like of xΒ² + ax + b
You make it look like in this form
basically, you let pΒ² = t and substitue and proceed it
remote zenith
For the unit we havenβt used substitution when solving polynomials
modest maple
For the unit we havenβt used substitution when solving polynomials
Hmm, so we cannot go through that?
remote zenith
I have the lesson worksheet the question is from if that could help?
modest maple
Maybe it can help
remote zenith
modest maple
Hmmm
What about you treat the given problemxlike a normal qiadratic problem?
You kknow how we think of two numbers, which on product makes constant term (40 in here), and on addition make the coeffecient of x ( -14 in here)
remote zenith
Yes
modest maple
Yes
Then think of such two numbers for this problem
Hint: you always think of the constant term, you factorise it in possible ways and then check the sum. For example of 40,
1Γ40
2Γ20
4Γ10
5Γ8
8Γ5
10Γ4
20Γ2
40Γ1
and their all negatives, as negative into negative is positive
remote zenith
Yes, with p^4 included and finding the common monomial, itβs 1 and Iβm not sure if that makes any difference when solving the rest
modest maple
Yes, with p^4 included and finding the common monomial, itβs 1 and Iβm not sure ...
It would have make difference if there were pΒ³ or p
But since its just pβ΄ and pΒ² we could solve it like a qiadratic equation
remote zenith
I know for certain questions if we canβt use the trial and error method we use the quadratic formula, should I use that?
modest maple
I know for certain questions if we canβt use the trial and error method we use t...
But we are supposed to solve it by factorisation
You could get values by quadratic formula, but those values would be for pΒ² not for p itself
What i am trying to say is that, whenever you see an equatiom of format, xβ΄ + axΒ² + b, it can be treated as a quadratic eqiation to get values, or to factorise in terms of xΒ². This can be factorised into, (xΒ² - h)(xΒ² - k).
And that can be further factorised using (aΒ² - bΒ²) = (a - b)(a + b).
@remote zenith
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remote zenith
Iβm sorry Iβm having a hard time understanding
modest maple
Iβm sorry Iβm having a hard time understanding
It is fine hmmm let me think
cursive condor
Iβm sorry Iβm having a hard time understanding
You can still factor it.
modest maple
This
cursive condor
Just think, instead of in terms of p, p^2.
modest maple
I want you to tell me how do we facforise a qiadratic equation, @remote zenith
remote zenith
I donβt really remember how
modest maple
I donβt really remember how
oh okay
You earlier talked about qiadratic formula, do you know how to use it? @remote zenith
remote zenith
Yes
cursive condor
I want you to apply it
modest maple
Are you looking?
remote zenith
Yes
modest maple
see
This important
Let
F(x) = xΒ² + ax + b
Put pΒ² instead of x
F(pΒ²) = pβ΄ + apΒ² + b
Tadaa
Did it help?
Its just a quadratic equation in disguise
remote zenith
It should look like this? :
F(p^2) = p^4 + p^2 + 40
cursive condor
It should look like this? :
F(p^2) = p^4 + p^2 + 40
(you're missing the coefficient on the p^2)
remote zenith
I think, then I use the quadratic formula?
modest maple
I think, then I use the quadratic formula?
Yes, but answer me two things before soing that
Will you?
remote zenith
Yes
modest maple
Yes
F(x) = xΒ² + ax + b
If we apply qiadratic formula on it, it gives us value for x, True or False
remote zenith
Yes
modest maple
Yes
Now, if we apply qiadratic formula on F(pΒ²) = pβ΄ + apΒ² + b
It will give us value of?
(We just replaced x with pΒ², right?)
remote zenith
Calculator says undefined when I try to square root -365 and I think we have to use imaginary numbers right?
modest maple
In first step, it would be (14)Β² instead of -(14)Β², under the root
discriminant is (b)Β² - 4(ac),
b = -14
abstract zodiac
a
modest maple
bΒ² = (-14)Β²
remote zenith
So the values would be 10 and 4?
modest maple
So the values would be 10 and 4?
Yes! And they are values of???
remote zenith
P (or x)
modest maple
F(__***x***__) = xΒ² + ax + b
If we apply qiadratic formula on it, it gives us v...
From here
modest maple
I forgot it was squared
Lol, it is fine
remote zenith
These are also the solutions?
remote zenith
I think for the square root of 10 since itβs not a perfect square I have to enter the answer differently
slate violet
the original equation is p^4 - 14p^2 + 40 = 0, guys!!
slate violet
So the values would be 10 and 4?
yep
slate violet
I think for the square root of 10 since itβs not a perfect square I have to ente...
you should be able to type the square root then
remote zenith
We have this method that ends up with a number outside the radical and one under
slate violet
We have this method that ends up with a number outside the radical and one under
well that doesn't apply here
remote zenith
Iβm trying to find it in my packets to remember how
slate violet
you're thinking of something like $\sqrt{12} = \sqrt{4} \sqrt{3} = 2 \sqrt{3}$ right
glossy valveBOT
south
remote zenith
Yes
slate violet
yeah so we can only do that because 12 is a multiple of a perfect square (4)
if we look at 10 = 2 * 5, there are no perfect squares to begin with
(by has a perfect square, I'm including 2^3, 2^4, 2^5... cause those are all multiples of 2^2)
remote zenith
I think I was struggling so much because Iβm supposed to go based off a different example in this packet that my teacher never showed us
Which looks exactly like the original equation π
slate violet
I think I was struggling so much because Iβm supposed to go based off a differen...
yeah you don't seem confident in factoring quadratics
or maybe you're struggling cause the other example is not as neat
the key thing is that we subbed say x^2 = t
once we find t, so t = 4, 10 in your question
we need to undo the substitution (to find x) and so you have x^2 = 4, 10
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fleet harbor
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sharp lagoon
,rccw
glossy valveBOT
sharp lagoon
!status
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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
Hint: Try adding up second row in the first place
fleet harbor
what first place
slate violet
what first place
try adding up the second row, and do that first
fleet harbor
k
sharp lagoon
See how I added the boxes up, left to right?
sharp lagoon
Yes, combine like terms.
fleet harbor
okay so 2x-1x+1x = 2x
sharp lagoon
OK, what about the constants (the numbers without a variable attached)?
fleet harbor
2x-2
slate violet
-3 + 3 + 2 = .....
fleet harbor
-3+3+2
sharp lagoon
No, try the constants again.
sharp lagoon
OK, so you have 2x + 2.
fleet harbor
mb i flipped the sign
sharp lagoon
Now, what it says is that all the columns and rows add up to 2x + 2.
fleet harbor
okay
sharp lagoon
So, find a row or a column that has only one unfilled box.
sharp lagoon
OK, add together the boxes that are filled in.
sharp lagoon
You have to be careful with the signs.
Do you know about the distributive property?
sharp lagoon
OK, so separate out the like terms, like -2x + 4x + 3x.
sharp lagoon
Why do you think it's negative?
sharp lagoon
OK, so the thing is that the minus sign only applies to that number, not the answer at the end.
Like -2x is negative two times x.
But the negative isn't on any of the other x terms.
So, you have like -2 + 4 + 3 with xs on each one.
fleet harbor
so thats 5
sharp lagoon
OK, what does that sum to?
fleet harbor
-2
fleet harbor
okay
sharp lagoon
Now earlier, we figured out it has to add to 2x + 2.
So far, we have 5x - 2.
What do we need to add to 5x - 2 to change it into 2x + 2?
fleet harbor
so we add 3x+4?
sharp lagoon
Almost.
fleet harbor
wait subtract 3x
sharp lagoon
No, the box at the end of row 3.