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#help-26
topaz sinewBOT
Available help channel!
toxic aspen
topaz sinewBOT
toxic aspen
Could someone explain what each variable represents and how to use the formula?
Isn’t this formula equivalent to eulers
V - E + F = 2
toxic aspen
Does it say
The sum from k to n times x^k ?
raven sparrow
It`s a geometric sum. If x=1/2, you get the sum $1+\frac{1}{2} + \frac{1}{4} + \frac{1}{8} + \dots + \frac{1}{2^n}$.
Turns out, as the formula indicates, that this would be just $\frac{(\frac{1}{2})^{n+1} - 1}{\frac{1}{2} - 1}$.
thorny flameBOT
Azyrashacorki
toxic aspen
But what dictates x and n?
thorny flameBOT
Azyrashacorki
toxic aspen
Ok but
Say i have this and i want to calculate using Eulers poly formula
How do i know what x and n is?
raven sparrow
It's not clear to me what exactly you want to compute (the Euler characteristic?), and what it has to do with the geometric series. Is that part of a bigger problem you could share to help me follow?
toxic aspen
(a) through|E|=#(sectors)×#(edge persector);
(b) by using the relationship between the degrees of the corners and the number of edges;
(c) by using Euler's polyhedron formula.```I'm on C where i should use Euler's polyhedron formula
raven sparrow
I don't think that's called the polyhedron formula though.
The polyhedron formula is V + F - E = 2
raven sparrow
The sum you showed is just a finite geometric sum, and I don't think it helps much in this case
toxic aspen
Gemotrical sum
raven sparrow
It's just a way to express the sum of subsequent powers of a certain base x up to degree n
toxic aspen
It's so weird. We have recieved a sheet of formulas but i haven't used or know all of them..
raven sparrow
Odd that you haven't seen it in class; I feel like it's a rather commonly used formula
Maybe it's for a later portion of the course
toxic aspen
The course is sadly finished
If it isn't too much of a hassle, would it be okay for me to ask about what all the formulas are applied for?
Or rather, the ones i don't really understand
raven sparrow
Yeah I'll do my best
toxic aspen
So if i understand this correctly.
All these formulas are used withing Arithmetic mod or modulos, right?
raven sparrow
Yeah they all seem number theory / modular arithmetic oriented
toxic aspen
Lovely, okay:
If i were given a problem such as this. I'd be able to rewrite it using the first of the listed formulas right?
where i write it as 11 = 13x + 18t
raven sparrow
You can do it like that, but in a way I think it's easier to understand is as : 13x is 11 + a multiple of 18, i.e. 13x = 11 + 18t
But that's equivalent to what you wrote, so it's fine.
toxic aspen
Sweet but my teacher solves it like such:
raven sparrow
where i write it as 11 = 13x + 18t
Although written like that you can probably solve it using some form of Euclidean division
toxic aspen
Yeah i'm familiar with euclidean division! 
but why does he write it as 1
and not as 11
raven sparrow
Seems like a typo. Either in the solution or the problem.
drowsy surge
its not a typo
toxic aspen
raven sparrow
Wait
toxic aspen
Haha sorry :P
toxic aspen
@vernal matrix Do we have cat emotes for running or fleeing?
drowsy surge
and whats with the linear diophantine equation after something is congruent to 1
raven sparrow
I think he's just finding its multiplicative inverse mod 18 through Euclidean division to then cancel it out in the last line to compute [x].
toxic aspen
I would be able to solve it if i were given 13x+18y = 1 however
how do i go from [13x] mod 18 = [11] mod 18 too 13x+18y = 1
He is clearly using the first formula
raven sparrow
The thing is you have [13x] = [11], but you can't just divide both sides by 13
toxic aspen
but changing 11 to 1 makes no sense
raven sparrow
Because you need the modular inverse
They're just using the division algorithm to compute the modular inverse of 13
So they can then multiply both sides to solve for x
toxic aspen
I barely understand
$[13x]{18} = [11]{18} \implies 13x+ 18y = 1$
I want to understand this specifically
raven sparrow
To me it looks like they're using two different x's
Because you can't have both [13x] = [11] and [13x] = [1]
thorny flameBOT
Merineth
raven sparrow
**Merineth**
They're first using this to find the inverse of 13, here x is the inverse of 13. (Actually not that equation)
And then in the last equation they use the inverse to find the unknown x.
Their first implication is : $[13x]{18} = [1]{18} \Leftrightarrow 13x + 18y = 1$, which is just saying x is the modular inverse of 13. This is NOT the same x as in the question.
thorny flameBOT
Azyrashacorki
raven sparrow
Then they run the extended Euclidean algorithm to compute this x, i.e. $13^{-1}$.
thorny flameBOT
Azyrashacorki
raven sparrow
Once they have that, they can safely compute the question x, call it $x_q$ such that $[13x_q] = [11]$
thorny flameBOT
Azyrashacorki
topaz sinewBOT
@toxic aspen Has your question been resolved?
toxic aspen
.close
trail lake
topaz sinewBOT
trail lake
I didn't understand this explanation
sweet shard
I didn't understand this explanation
Why do you need to
trail lake
Just for increasing knowledge how zeta works and helps us
Even i have solved the question with stirling approximation
sweet shard
Just for increasing knowledge how zeta works and helps us
Did you look up the definition of hurwitz zeta
trail lake
I tried but I did not understand
sweet shard
Well do that first
sweet shard
I tried but I did not understand
What about it didn't you understand
trail lake
I am sorry i was wrong
This question is not solved by riemann integration as i got denominator n^2
trail lake
I solved it by squeeze theorem
sweet shard
I solved it by squeeze theorem
What is it
sweet shard
What question
.
trail lake
Ahh it's just inequality
trail lake
This one
sweet shard
Well if you're done do .close
sweet shard
I solved it by squeeze theorem
You're not done?
trail lake
I have a little doubt
sweet shard
I have a little doubt
trail lake
.close
neon iron
can someone help me solve this lol
topaz sinewBOT
can someone help me solve this lol
neon iron
it says it needs to be the exact value, not a decimal and idk how to do that
woeful drift
you were just helped with a similar problem
what about this specifically is giving you issue?
neon iron
you were just helped with a similar problem
i didnt really get what he was saying and i didnt wanna be rude/annoying so i just closed it 😭
its still confusing lol
woeful drift
bruh
sharp dew
i didnt really get what he was saying and i didnt wanna be rude/annoying so i ju...
It’s fine
I will help u
neon iron
ok ty
neon iron
yes
sharp dew
oh both are sqrt(2)/2
Yes
I suppose you are capable of finding the value of sin(-45) and cos(-45)?
neon iron
so its just move 45 degrees in the clockwise direction
sharp dew
Yes exactly
neon iron
so 315 on the unit circle, cos(-45)=sqrt(2)/2 and sin(-45)=-sqrt(2)/2
neon iron
yes
sharp dew
Then you might have to convert it into degrees
neon iron
yes
sharp dew
Which results in obtaining theta = -45 or 315
neon iron
yes
sharp dew
Then you have to be aware that sin45 and cos45 both equal to sqrt2/2
Then we sort of manipulate it on the plane, to get the value of sin-45 and cos-45
Which you are capable of
sharp dew
No problem
neon iron
.close
trail lake
topaz sinewBOT
elfin sparrow
Looks mostly fine, but the upper bound is -1/2, not 1/2
and sin^-2 x is not good notation. Use (sin^-1 x)^2
The -1 in sin^-1 signifies the inverse, it is not an exponent
topaz sinewBOT
elfin sparrow
no problem 👍
topaz sinewBOT
Available help channel!
obsidian acorn
topaz sinewBOT
obsidian acorn
attempting to understand the markscheme mainly the part that goes from:
"hence every subset is open and hence R^2 \ Q^2 is open"
woven creek
whch branch of math is this?
woven creek
ic
obsidian acorn
ok i asked my friend im just forgot a definition
if anyone was wondering if every subset of R^2 is open so is R^2 \ Q^2 as its a subset of R^2
apologies for not using latex to write 3 symbols i cba
.close
topaz sinewBOT
ocean terrace
if anyone was wondering if every subset of R^2 is open so is R^2 \ Q^2 as its a ...
noooo
I'm curious. but also isn't Q2 a subset of R2. so shouldnt it be open as it's a subset of R
obsidian acorn
ig its also open but doesnt really give us any info on its closure
but its a true statement
@ocean terrace
forgot to reply
topaz sinewBOT
Available help channel!
topaz sinewBOT
forgot to reply
obsidian acorn
.close
violet girder
if 2 equations are equivalent then they necessarily have the same solutions?
neon iron
if 2 equations are equivalent then they necessarily have the same solutions?
Yes, if 2 equations are equivalent then they have the same solutions
thats why they are callled "equivalent"
but if its an equation with variables only then it got infinite solutions
for eg $$ \frac{1}{x} \cdot 2c = y$$
thorny flameBOT
Snow
topaz sinewBOT
@violet girder Has your question been resolved?
prisma mulch
How can I create a graph that starts at 0,100 and goes through a user-specified point (for example, 75,75) and then farther down to 100,0?
topaz sinewBOT
How can I create a graph that starts at 0,100 and goes through a user-specified ...
prisma mulch
thanks for help
keen matrix
here's an updated one where you can move the point and added a few domain restrictions :)
prisma mulch
thanks 
keen matrix
thanks <:heart002:851106933112438824>
prisma mulch
.close
cyan condor
topaz sinewBOT
heady goblet
how is this true
sacred skiff
does X_i have a definition?
heady goblet
does X_i have a definition?
Xi are identical, independent random variables
sacred skiff
but it has a relation to the i found in the sum, right?
pale barn
Given the following functions find the image of 0, and 2 in each case, and the antiimage of –3, 0.
topaz sinewBOT
Given the following functions find the image of 0, and 2 in each case, and the a...
pale barn
.close
little ferry
topaz sinewBOT
cursive thorn
neon iron
how to solve
topaz sinewBOT
how to solve
thorny flameBOT
Al-Mardhikwar
neon iron
phew there
keen venture
Means either x - 3 = 0
Or ln(x) = 0
willow widget
i think the terms are separate
keen venture
If you're looking to type
(x - 3)ln(x) = 0
willow widget
probably $x-3\ln(x)$
thorny flameBOT
Quixz
thorny flameBOT
Al-Mardhikwar
thorny flameBOT
Al-Mardhikwar
keen venture
Here's the neat part: you don't!
icy sky
This is some W function stuff
neon iron
This is some W function stuff
I really need to learn what this W function thingy is
icy sky
You cant really solve for x
icy sky
I really need to learn what this W function thingy is
Meh not really necessary
keen venture
There's probably a W-function solution. But you shouldn't necessarily care
neon iron
so graphic solution it is?
icy sky
Just approximate by graph yeah
topaz sinewBOT
icy sky
👍
topaz sinewBOT
Available help channel!
glass sun
I don't understand how Fn+2 = phi^2Fn
topaz sinewBOT
I don't understand how Fn+2 = phi^2Fn
willow widget
$F_{n+2} = \phi F_{n+1} = \phi^2 F_{n}$
thorny flameBOT
Quixz
ivory sorrel
how would I find the number of roots of $x^6+x^3-1$?
topaz sinewBOT
how would I find the number of roots of $x^6+x^3-1$?
thorny flameBOT
Why am. I here
ivory sorrel
I first found the limits at -infty
and infty
then found the value when x=0
which led me to conclude that there are atleast 2 roots
neon iron
maybe set x^3=t and solve t^2+t-1=0?
acoustic tangle
Well that's just (x^3)^2 + (x^3) - 1 and observe that t^2 + t - 1 has no real solutions
ivory sorrel
maybe set x^3=t and solve t^2+t-1=0?
oh yeah, thanks
ivory sorrel
yes, thanks
icy sky
Number of roots is 6 by fta
icy sky
Ah
ivory sorrel
alternatively I was thinking of finding the number of turning points of the graph now that I've concluded there are atleast 2 roots
would that approach be right?
vale furnace
What do you mean by there are at least 2 roots
ivory sorrel
finding the limit at = infty , we get infty
similarly at -infty
now when x=0 , the function takes a value of -1
so there are atleast two roots
vale furnace
Ah it’s -1 thought ut was +1
vale furnace
would that approach be right?
Then yeah this would help
vale furnace
neon iron
can someone help me solve #32? I sketched the graph and I set the two functions equal to each other, and i got that the x values for the intersection points were 0 and 4, but when i graphed the functions on a calculator, it didn't seem acurate
topaz sinewBOT
can someone help me solve #32? I sketched the graph and I set the two functions ...
sturdy oracle
can someone help me solve #32? I sketched the graph and I set the two functions ...
Yeah no there are 3 intersection points but you only wanna look at the minimum and maximum x values listed
sturdy oracle
I mean it says to use a graphing utility
So you can just use desmos to get the intersections and save yourself pain
sturdy oracle
i forgot to break up the x^2 -4
Well x^4 - 2x^2 = 2x^2
x^4 - 4x^2 = 0
x^2(x^2 - 4) = 0
fast coral
topaz sinewBOT
willow widget
!status
topaz sinewBOT
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
willow widget
Ok
This is a density graph
Which means that the height of each rectangle is proportional to the number of samples in the corresponding range of x-values
willow widget
The height of the 8g - 17g rectangle is 7 boxes
willow widget
Hmm
The question says there are 126 coins in that rectangle
From there you might work out the scale of the y-axis
fast coral
126/63 boxes
willow widget
frequency density
fast coral
= 2
willow widget
i need more sleep
willow widget
126/63 boxes
you are correct
willow widget
2 coins per box
fast coral
im not
willow widget
but hold on
fast coral
im wrong
willow widget
2 coins per box is correct
fast coral
i think its 532
cos i forgot to times total by 2
266 is total number of boxes
mbbbbbbbbbbbb
willow widget
that sounds right
fast coral
nope im still wrong
diff q
same q with diff number
diff number between 8 and 17
willow widget
sorry friend im literally falling asleep at the keyboard so i'm going ot go take a walk
topaz sinewBOT
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
willow widget
266 is total number of boxes
the same technique should work
but maybe count the boxes a bit more carefully
fast coral
ok
ok
wait
its 9*8
2*5
5*14
so 272
and 144/72
=2
so 272 * 2
= 544
but thats wrong
@willow widget
willow widget
ok so
when you calculated 9*8 + 2*5 + 5*14 i think you left out the tall rectangle on the left
and, i don't htink 9*8 + 2*5 + 5*14 is 272
willow widget
yep
topaz sinewBOT
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
i think writing things down would help you quite a lot
topaz sinewBOT
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
6
fast coral
i think writing things down would help you quite a lot
yh prob
outer delta
Use .close
topaz sinewBOT
@fast coral Has your question been resolved?
topaz reef
got this integral (1/x^7-x)
topaz sinewBOT
got this integral (1/x^7-x)
topaz reef
im trying different things and im not getting anywhere
ive taken a usub of the bottom
changed it over to x^7 = u + x
ive tried mutliplying by 1 by using 7x^6
i dont want an answer but am i scratching down the right path here?
ah nm i did it
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
dreamy bobcat
help
mild hearth
well, you could try a point out
if z = 6i
|6i - 2i| =< 4
so 6i is in the region that satisfies the conditions
so the shaded region is the part that satisfies the conditions
dreamy bobcat
ah thanks
how do i know which region to shade for the perpendicular bisector?
how should i read the condition
mild hearth
how do i know which region to shade for the perpendicular bisector?
?
oh
essentially these are distances
|z + 4 - i| = |z - (-4+i)|
|z + i| = |z - (-i)|
so you want |z - (-4+i)| =< |z - (-i)|
you want points that are closer to -4+i than -i
and then similarly |z - 2i| =< 4 so you want points that are closer than 4 to 2i
topaz sinewBOT
@dreamy bobcat Has your question been resolved?
lone flame
hey
topaz sinewBOT
@dreamy bobcat Has your question been resolved?
topaz sinewBOT
@dreamy bobcat Has your question been resolved?
topaz sinewBOT
@dreamy bobcat Has your question been resolved?
urban grove
The graph looks correct. For part iv, show that the argument of z1 + z2 is exactly 5pi/24, and you'll get what you want.
fresh cloud
I thought the answer for domain was x>8
topaz sinewBOT
I thought the answer for domain was x>8
icy sky
Whats the domain for a log function?
wooden osprey
$\int \frac{2x}{x^2+1}dx$
topaz sinewBOT
$\int \frac{2x}{x^2+1}dx$
thorny flameBOT
FungusDesu
wooden osprey
how would i integrate this? the dem is unfactorable, so i cant do the usual way
worthy storm
yea
topaz sinewBOT
topaz sinewBOT
Available help channel!
buoyant tapir
I need assistance with understanding the box principle.
I understand that you need to sort the objects in their respective catagories/states in such a way that it is eavenly distributed. But the problem is, I have no framework or understanding of how to solve slightly complex problems.
For example:
You have a box of 40 gloves, each with 4 different colours.
(Question 1): If you know that at least that the amount of red gloves in the box is 8. Prove that you can at least fit 14 gloves of the same colour in one of those catagories or more of those catagories.
etc etc
^ Those questions confuse me, because according to my book YOU have to remove the first catagory, remaining 3 catagories are left. My teacher never mentioned of removing catagories.
buoyant tapir
In essence, I do not understand the point of the box principle and all of the stupid little exceptions it wants me to understand. There is no stable framework. <--- I am only saying this because I am about to enter into my breaking point.
I also do not understand how to answer shit sometimes, making me very confused.
Ig
topaz sinewBOT
@buoyant tapir Has your question been resolved?
gray ridge
***I need assistance with understanding the box principle.***
I understand that...
First of all, I'm not sure if i can help.
Secondly, I think it's generally called "Pigeonhole Principle".
https://en.m.wikipedia.org/wiki/Pigeonhole_principle
see if you can find the version in your language in the above wiki.
From my experience, it's hard to understand what to answer at first, and as you have said, there is no standard procedure (stable framework) on these type of questions.
I think the best way to understand is to read through and try out some exercise.
topaz sinewBOT
@buoyant tapir Has your question been resolved?
buoyant tapir
First of all, I'm not sure if i can help.
Secondly, I think it's generally call...
Yeah it is called the pigeonhole principle.
Like, I understand that the general idea of boxes is just... Are just catagories. Right?
For example:
50% of the human population have 5 000 000 human hairs or lower.
How many humans have the same amount of hair?
I know how to solve this, but you need the following variables:
Objects = (Catagories)*(How many objects you can fit in, with respect to no rest.) + 1
Objects there are: 500 000
Catagories: 5 000 001
Answer: (How many objects you can fit in, with respect to no rest.) + 1
Not a full solution, but this is how far I've gotten.
topaz sinewBOT
alpine mist
hiding what formula?
only because you foiled it out earlier
for any fraction (A/B)^2 = A^2 / B^2 , so you already had (-2x / 1 - x^2)^2 = 4x^2 / (1 - x^2)^2
I won't say never, but i certainly avoid it whenever possible
drifting swift
for any fraction (A/B)^2 = A^2 / B^2 , so you already had (-2x / 1 - x^2)^2 = 4x...
alpine mist
<:PARENS:371658456215584789>
(((-2)(x)) / ((1) - ((x)^2)))^2 = ((4)((x)^2)) / (((1) - ((x)^2))^2), better?
more... readable? 😜
yeah, there's no one way to do anything. So it takes practice. Sometimes things work and you learn and then sometimes things don't work and you learn more!
elder glacier
Can someone go through these tasks with me
topaz sinewBOT
Can someone go through these tasks with me
topaz sinewBOT
@elder glacier Has your question been resolved?
elder glacier
<@525764911968681989> how would you start the first one?
simplifying
opaque crow
How would you go about doing that?
elder glacier
Not sure
opaque crow
The first thing you’d want to start with is finding multiples of 75 and 48 that have perfect squares in them
For 48 you can find the multiples 16 and 3
opaque crow
5x15 and 6x8
If we’re trying to simplify the first question we want to be able to find a perfect square
What do you think the multiples for 75 would be?
elder glacier
whats the perfect square
opaque crow
Do you know what a perfect square is?
elder glacier
no thats why i asked
opaque crow
Oh mb, I thought you were asking what the perfect square of 75 was
Do you know what a square root is?
elder glacier
yes
opaque crow
Alright, so a perfect square is when you take the square root of a number and the result is a whole number
elder glacier
ohh
opaque crow
For example, the perfect squares are 4, 9, 16, 25, 36, etc.
Because if you take the square root it becomes 2, 3, 4, 5, 6, etc.
elder glacier
yeah
opaque crow
$\sqrt{75}-\sqrt{48}$
thorny flameBOT
peteozzy2018
thorny flameBOT
peteozzy2018
thorny flameBOT
peteozzy2018
thorny flameBOT
peteozzy2018
opaque crow
What do you think the left side would be simplified to?
opaque crow
Close, if you go through the factors of 75 are any of them a perfect square?
elder glacier
3x25
elder glacier
5sqrt3
thorny flameBOT
peteozzy2018
dusk garden
@opaque crow are you any good at matrix
opaque crow
Sadly no, still in high school
dusk garden
bru i need help wit this shit
opaque crow
Haven’t even started calculus yet😭
elder glacier
Now we can just subtract them and we get root 3
because 5sqrt3 - 4sqrt3 = 1sqrt3?
elder glacier
yes
opaque crow
$\frac{(2a^2)^2*9b^-3}{6(a^-4b^3)^2}$
thorny flameBOT
peteozzy2018
opaque crow
Alright
elder glacier
Was this right
opaque crow
Just imagine that it says 9b^-3 at the top there
opaque crow
Was this right
Looks perfect
elder glacier
Just imagine that it says 9b^-3 at the top there
what do we do with the other part
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
elder glacier
a
elder glacier
Do you still need help?
yes
opaque crow
Can someone go through these tasks with me
.
elder glacier
Any idea what the first thing we’d want to do is?
simplify everything above
then factorise it
and then simplify
i simplified everything above
36a^4b^-3
opaque crow
Close, but when simplifying you should’ve divided the 36 by 6 and gotten (6a^4)(b^-3)
elder glacier
Close, but when simplifying you should’ve divided the 36 by 6 and gotten (6a^4)(...
so i cancel the 6 out with the one below?
opaque crow
Do you have your work written down that I could see?
elder glacier
This is what I’ve done
opaque crow
Yes, so you would cancel out the 6 by dividing 36 by 6
elder glacier
Yes, so you would cancel out the 6 by dividing 36 by 6
how would that look like on paper
opaque crow
You could either factor out the six and cross them both out or just go straight to the next step and hope whoever is looking at it understands what you did
An example would be something like this
$\frac{36a}{6(4b)}$
thorny flameBOT
peteozzy2018
opaque crow
$\frac{6(6a)}{6(4b)}$
thorny flameBOT
peteozzy2018
opaque crow
$\frac{6a}{4b}$
opaque crow
That would technically work yes
And it’s not really necessary to show that work but can help other people understand what you did
elder glacier
do i do it like 6*6(a^4+b^-3)
when i do this the calculator is giving me a different answer
@opaque crow
opaque crow
That’s because we still have to do the bottom
elder glacier
isnt it jus (a^-8 b^6)
opaque crow
This is what I’ve done
So far we have $\frac{6a^4b^-3}{a^-8b^6}$
(It should be b^-3 and a^-8)
opaque crow
isnt it jus (a^-8 b^6)
Yep
elder glacier
(It should be b^-3 and a^-8)
bottom
opaque crow
bottom
The negatives are just acting weird with the bot
I was just correcting the one on the top and the one on the bottom
opaque crow
They are one term, so no
thorny flameBOT
peteozzy2018
elder glacier
yes
opaque crow
So now we can just use exponent laws to subtract a^-8 from a^4
opaque crow
One sec
elder glacier
i asked chat gpt and it got the same as me
elder glacier
but it says that this is the answer:
the calculator said this
hello?
@opaque crow
opaque crow
Sorry, let me see
Okay I seem to have gotten mixed up
Forget all of the stuff about crossing out the 6, I should’ve done distributive property and then squared it all
opaque crow
So $\frac{36a^4b^-3}{36a^-8b^6}$
opaque crow
but we still got the right answer no?
Very close to it
thorny flameBOT
peteozzy2018
opaque crow
but we still got the right answer no?
We would’ve just taken the 36 out
elder glacier
We would’ve just taken the 36 out
the calculator says what i got
or what we got earlier
i think what you do is wrong
elder glacier
because youre expanding 6 below but not up
elder glacier
**peteozzy2018**
therefore i dont think that way is right
elder glacier
the calculator says what i got
because if we simplify this its 36 and 6
so if you add the extra 6 to get 36
you need to add it above too
or youll get a different value
if im not mistaken
opaque crow
the calculator says what i got
I finally got a hold of a piece of paper and I got the same thing
It was probably just something I was doing wrong in my head then 😭
elder glacier
It was probably just something I was doing wrong in my head then 😭
how do i do this?
opaque crow
This one will just be a quadratic it looks like
Multiply both sides by 2, subtract 3 from both sides
$8x^2 + 2x -3 = 0$
thorny flameBOT
peteozzy2018
opaque crow
Do you know how to do complex trinomials?
elder glacier
i dont know how to factor that correctly
opaque crow
Alright
There are two ways you could factor this, you can use the quadratic formula or factoring it as a complex trinomial
Which one do you wanna go over?
elder glacier
Which one do you wanna go over?
quadratic
thorny flameBOT
peteozzy2018
thorny flameBOT
peteozzy2018
opaque crow
And then just evaluate
opaque crow
$8x^2 + 2x -3 = 0$
thorny flameBOT
peteozzy2018
opaque crow
$ax^2 + bx + c = 0$
thorny flameBOT
peteozzy2018
opaque crow
shouldnt b be 1
Why would it be 1?
ancient vector
I need help
topaz sinewBOT
I need help
knotty ledge
you need to ask your question
topaz sinewBOT
@ancient vector Has your question been resolved?
crimson kestrel
I worked out a and b but idk what to do for c
topaz sinewBOT
I worked out a and b but idk what to do for c
crimson kestrel
a) 25/21
b)3200/7
topaz sinewBOT
@crimson kestrel Has your question been resolved?
topaz sinewBOT
@crimson kestrel Has your question been resolved?
rustic linden
i know the answer is -12 and 5, but idk why we reject 5 here
topaz sinewBOT
i know the answer is -12 and 5, but idk why we reject 5 here
rigid ivy
i know the answer is -12 and 5, but idk why we reject 5 here
Consider denominators that are x-5
rustic linden
so if the answer is equal to any of the denominators, then its rejected?
loud oasis
consider what happens when you try to divide by x - 5 when x = 5
dusk prairie
topaz sinewBOT
dusk prairie
how did they get x^1/2
valid crescent
It’s the same as root x
true wagon
i think its just easier to turn this into x + 21 = 10sqrtx
valid crescent
Cuz (x^1/2)^2 is the same as x
golden zodiac
theyre just showing how it works
because when u square a square root its the number inside the root right
dusk prairie
uh ig
thorny flameBOT
zoom
golden zodiac
$(sqrtx)^2$
thorny flameBOT
zoom
dusk prairie
thorny flameBOT
zoom
dusk prairie
this will be the answer?
dusk prairie
this is equal x
yep i got it
golden zodiac
yeah
pseudo bear
this will be the answer?
What are you asked to do? Just factor it?
dusk prairie
yes
golden zodiac
if ur just factoring that is right
pseudo bear
Sure.
dusk prairie
.close
topaz sinewBOT
pseudo bear
That's up to you when you're done.
topaz sinewBOT
Available help channel!
tardy vapor
topaz sinewBOT
tardy vapor
wait would u subract it
thorny flameBOT
frozen pagoda
pretty sure you are meant to subract the powers here
thorny flameBOT
CaptainNova22
thorny flameBOT
wilder
hollow drum
$\frac{y^5}{5}$
Yes that's right
frozen pagoda
yeah that's good
topaz sinewBOT
topaz sinewBOT
Available help channel!
muted crow
topaz sinewBOT
daring urchin
show work
muted crow
bro
daring urchin
ya
shut belfry
show attempy
he done nothin
daring urchin
i mean what do u know to start with
forest bloom
,, \qty( \frac 38 x^2 \cdot \frac 12 x) + \qty(\frac 18 x^3 \cdot \frac 12)
thorny flameBOT
kanna
daring urchin
x cube
daring urchin
yea I thought that
yea like tell these things first
forest bloom
**kanna**
use this so at least you aren't confused over the order of operations
do the two parenthesis first then add them up
forest bloom
you can also factor but whatever floats your boat
daring urchin
yea ryt
muted crow
I did it one way but I dont think its right
muted crow
I did the first parenthases to get 3x^3/16
daring urchin
@forest bloom i was speaking and typing mb
forest bloom
I did the first parenthases to get 3x^3/16
correct
muted crow
then I added it it by x^3/16
forest bloom
what did you get upon adding lol?
daring urchin
xcube by 4
forest bloom
yeah
muted crow
but im not sure if thats how i am supposed to do it?
muted crow
no I am just not sure if thats how i am supposed to solve it
because before that I tried to do gcf
daring urchin
but im not sure if thats how i am supposed to do it?
first start by solving simple questions and build up....revise basics of algebraic and number combined operations
muted crow
but it didn twork
daring urchin
first start by solving simple questions and build up....revise basics of algebra...
take any basic practice set with solutions
muted crow
im doing derivatives tho
forest bloom
!show
topaz sinewBOT
Show your work, and if possible, explain where you are stuck.
muted crow
and my algebra is kind abad
daring urchin
and my algebra is kind abad
yea make ur fundas strong
muted crow
idk im just gonna keep doign pratice problems of derivatives
and figure out the algebra
but for this one did I do it right that way
or am I supposed to do it differently?
@daring urchin
forest bloom
!show
topaz sinewBOT
Show your work, and if possible, explain where you are stuck.
forest bloom
:V
muted crow
which work
daring urchin
but for this one did I do it right that way
the correct answer is xcube/4
forest bloom
you said you did it differently
and it didn't work^
forest bloom
okay so if i had to guess
muted crow
I had put like 1/8x^2(3/8
and then I didnt know what else to do so I just did it how I said before with multiplying and adding
daring urchin
if you have started something...get till the end confidently...dont doubt yourself
daring urchin
I had put like 1/8x^2(3/8
what did u do here
show ur work on paper if possible
like from start to end
forest bloom
u can do that yeah
muted crow
thats what I put on my paper
from the first step
but then I just did it the way that worked
daring urchin
explain
forest bloom
,, \frac 18 x^2 \qty(3 + x)
muted crow
wat
daring urchin
whats that
thorny flameBOT
kanna
muted crow
how did you do that
forest bloom
you just told me that's what you did
that's correct
you can factor the first and third term
daring urchin
mabybe that was rinos mistake
forest bloom
and do the same for the second and fourth
daring urchin
missed an x
forest bloom
muted crow
yea
daring urchin
take x cube common
daring urchin
there r three xs
daring urchin
im confused where you got the x in the 3+x
start from beginning
muted crow
oh wait nvm
daring urchin
explain what u did
forest bloom
i'm looking at the first and third term exclusively
muted crow
ok but if I do that thjen what do I do about 1/2x and 1/2
daring urchin
there r only two terms
forest bloom
ok but if I do that thjen what do I do about 1/2x and 1/2
u can factor that too
btw this does not help lol
muted crow
what
forest bloom
i'm just following your procedure
muted crow
how does it not help
forest bloom
and showing you that it might work but then you reach a dead end
forest bloom
how does it not help
how does that help with simplifying everything
daring urchin
write it in nv+nv format
muted crow
so this is not how im supposed to do it
forest bloom
,, \frac 12 (x + 1)
thorny flameBOT
kanna
daring urchin
write it in nv+nv format
n is number. v is variable
muted crow
ok
forest bloom
,, \frac 18 x^2 (3+x) + \frac 12 (x+1)
thorny flameBOT
kanna
forest bloom
it doesn't help so it should be a cue to try something new
muted crow
ok
so what is the correct way to solve this
the way I did it were it worked or something eles
forest bloom
i mean the correct and yet the most naive way to do it is to literally do the arithmetic lol
muted crow
is that what I did?
forest bloom
i just put the parenthesis to remind you of the order of operations
pemdas or bodmas or whatever u call it
then u just simplify by combining like terms yeah
nothing fancy
topaz sinewBOT
topaz sinewBOT
Available help channel!
lament depot
.close
topaz sinewBOT
Available help channel!
mental basin
If an exercise has F(X)=arctan(x)
topaz sinewBOT
If an exercise has F(X)=arctan(x)
mental basin
and it tells me to do an iteration starting at
what does that mean? what's arctan(x) for x in R²?
is it the angle between the x-axis in an R² plane and the vector from th origin to point (10,20)? is that a sensible interpretation here?
mental basin
to do a newton iteration for finding where F(X)=0
keen venture
Starting iteration should just be a real number
mental basin
f: R->R x|->arctan(x) is a different function from g: R²->R² x|->arctan(x)
what do you mean ❌? by definition it is
keen venture
There's no such thing as R² -> R² arctan(x)