Any triangle will have the bottom as a side, so the only differentiating factor is what are the other two sides. How many ways are there to select two of those "vertical" sides?
#help-0
abstract fractal
alpine sable
Any triangle will have the bottom as a side, so the only differentiating factor ...
Ig 6
abstract fractal
How'd you get 6?
alpine sable
But this not the answer
abstract fractal
There's 5 "vertical" sides, and im pretty sure there's more than 6 ways to pick 2 out of 5 objects, even if order doesn't matted
alpine sable
There's 5 "vertical" sides, and im pretty sure there's more than 6 ways to pick ...
Oh right
10??
abstract fractal
Yes
alpine sable
There's 5 "vertical" sides, and im pretty sure there's more than 6 ways to pick ...
Oh
Thank you so much
.close
native cloud
lone heartBOT
native cloud
Can anyone help me with this question?
harsh scaffold
yea nvm you are a couple units above me
native cloud
y+5/x+2=-9
How did you get this answer?
gray isle
do you understand the notation in the question?
native cloud
What is f prime denoting?
gray isle
derivative / slope function
nocturne dove
The slope of the graph at x=-2
gray isle
(also h, not f)
h(-2) = 5 indicates that (-2,-5) will be a point on the graph
and h'(-2)=-9tells you that the slope will be -9 at that location
in simpler coordinate geometry non-calculus terms
the questions is pretty much asking for the equation of the line with a slope of -9 passing through (-2,-5)
lone heartBOT
@native cloud Has your question been resolved?
native cloud
in simpler coordinate geometry non-calculus terms
the questions is pretty much a...
Why are the answers not in "y = mx + b" form?
Or is it altered to make it confusing?
gray isle
actually they're not in y=mx+b form to make it less confusing
as if you're given a point and a slope
you'd usually start with the point slope form of the equation
next ridge
lone heartBOT
median dirge
Umm...? Which part do you need help with?
next ridge
A , i
median dirge
Cross multiply and rearrange
nocturne dove
Cross multiply?
median dirge
$6(x-2) = (x+4)(8-5x)$
ocean sealBOT
Muhammad Hussaini
ocean sealBOT
Rapiid
little drum
$-5x^2-18x+44=0$
Since it's an equation anyway, you can simply divide the whole thing with '-5' ?
... so your leading coefficient matches :D
rocky pulsar
,tex { \left( { x }^{ 2 } + \dfrac{ 3 }{ x } \right) }^{ 5 }
ocean sealBOT
Frieda_VI
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
rocky pulsar
How can I find the coefficient of x^4, without expanding it fully?
thick yoke
The binomial theorem
rocky pulsar
The binomial theorem
yes but how exactly
thick yoke
This is the formula
rocky pulsar
🥲 that's too advanced lemme show my workings
@thick yoke using this expression
How can I solve it?
thick yoke
in our case, n = 5
think for which values of r, you will get that: $a^{5-r} \cdot b^{r} = c \cdot x^{4}$
rocky pulsar
well now is the time that I show my calculations?
ocean sealBOT
Ariel1300
thick yoke
well now is the time that I show my calculations?
yes
there shouldn't be a lot of calculations tho
thick yoke
I don't really get this line, but it doesn't look like its the right way
rocky pulsar
ooh
thick yoke
**Ariel1300**
.
thick yoke
Oh, I get what you were trying to do, but note that the first line here doesn't equal to zero
it equals to the power of x (in our case 4)
rocky pulsar
it equals to the power of x (in our case 4)
oooh
thick yoke
and then you get: 4 = 10 - 3r
rocky pulsar
so 10-3r = 4?
thick yoke
and r = 2
alpine sable
Any help on this probability question?
lone heartBOT
Any help on this probability question?
alpine sable
I assume so, but no further information is given
I'm following, except how do I apply this to what you are explaining?
Just out of curiosity, would you know if this is possible to reproduce in Excel?
placid zinc
There's an excel formula for it already
alpine sable
No, I understood you very well, thank you
alpine sable
There's an excel formula for it already
Which formula would that be?
lone heartBOT
@alpine sable Has your question been resolved?
azure oyster
Is 21/8 correct?
lone heartBOT
Is 21/8 correct?
gray isle
show work
lone heartBOT
@azure oyster Has your question been resolved?
next ridge
lone heartBOT
gray isle
what have you tried?
next ridge
I have done i, ii and iii
gray isle
what ahve you tried for part iv)
next ridge
Nothing at the moment, it just isn't reading right for me
gray isle
first focus on the first line of part iv
next ridge
Edges of the cuboid are 180cm
gray isle
sum of the edges
and note that you have an expression for the sum of the edges in terms of x from part i)
and it still looks like some info is lacking in the question
just post the whole thing
instead of snippets
next ridge
.close
twin condor
Are ln|(x-1)| and ln|(1-x)| the same?
gray isle
yes
languid portal
gray isle
properties of absolute values
twin condor
.close
lone heartBOT
Available help channel!
cedar field
what do brackets mean in functions?
lone heartBOT
what do brackets mean in functions?
hard patio
can you elaborate on what you are trying to ask?
cedar field
can you elaborate on what you are trying to ask?
sure you know in functions there are sometimes brackets?
karmic rapids
@cedar field do you have an example
cedar field
ok
cedar field
<@953140475693514804> do you have an example
like with this one f(x)=3x^2-1
karmic rapids
like with this one f(x)=3x^2-1
you read it as "f of x"
so: the function output of a specific x value is equal to ...
f(3) = 2
the function output of 3 is equal to 2
cedar field
the function output **of** 3 is equal to 2
where did the 3x^2-1 go?
cedar field
just an example
oh and would you do this for all functions with brackets?
karmic rapids
functions as equations can always be written "with parenthesis"
cedar field
functions as equations can always be written "with parenthesis"
and does it mean a separate equations?
karmic rapids
wdym
gray isle
cedar field
<https://www.khanacademy.org/test-prep/sat/x0a8c2e5f:untitled-652/x0a8c2e5f:pass...
thanks
faint shard
lone heartBOT
wide raven
multiply the denominator of lhs on both sides
and then basically put values in the equation to solve
and then basically put values in the equation to solve
you will need to put 3 values as we have 3 variables
preferentially you can put the roots of the denominators
but actually any would do, the only difference would be that putting roots will make your work easier
faint shard
Nope, you lost me
wide raven
ohkay
what did u try?
i am supposed to ask that before i tell you but i'm in a hurry to go sleep
so anyways, please be quick
faint shard
I have a big mess
faint shard
I haven't gotten anything for this question yet
faint shard
multiply the denominator of lhs on both sides
This lost me
faint shard
Starting the equation
wide raven
just multiply the denominator of lhs aka (x-1)(x^2+2x+1) on both sides of the equation
so that there are no demoninators on both sides of the equation which will make things easier
did you follow?
wide raven
feel free to dm me if you come across any problems
you can also close the channel if you like
dawn oracle
Looking for someone to help with a math problem privately
lone heartBOT
Looking for someone to help with a math problem privately
worn fox
Looking for someone to help with a math problem privately
You should say what the problem is so people know whether they can help you
dawn oracle
.close
lone heartBOT
Available help channel!
lethal dock
lone heartBOT
lethal dock
I dont understand what this question is trying to say
slender gull
Since she earns $72000.
The question says, for the first $6000 she gets all of that money. As for the remaining $66000, there's 25% tax levied on $20000. Then after that there's 30% tax. So yeah you have to figure out the amount she pays in taxes.
lone heartBOT
@lethal dock Has your question been resolved?
ruby lion
Very quick :
How do you prove that if
k divides a
k divides b
then k divides a ^ b ( greater common divider )
ruby lion
I tried but I could only do it via prime decomposition
I'm 100% sure there is a more trivial way using Euclid's lemma but I just can't find it
OK forget it I'm so god damn stoopid
a ^ b = xa + yb = x a' k + y b' k = (xa' + yb' ) k
so k divides a ^ b
sorry
.close
lone heartBOT
mortal trellis
the gcd is also commonly defined as exactly fulfilling this property. that all dividers of a and b divide it
ruby lion
I mean yeah by definition it sounds trivial but I wanted a "real proof"
serene dune
Ik this is really stupid of me but can someone help me with this 2 questions and explan it?
lone heartBOT
Available help channel!
karmic rapids
in the lecture they said "the derivation of this is trivial and can be done by simple transformation of the equation", and now I have to do it as a homework exercise and have no idea how to do it lmao;
I have to show that the coefficients for the conjugate gradient method can also be represented as:
$$\alpha_k = \frac{r^T_kr_k}{s^T_kAs_k}$$
$$\beta_{k - 1} = - \frac{r^T_kr_k}{r^T_{k-1}r_{k-1}}$$
ocean sealBOT
illuminator3
karmic rapids
here's our lecture script (it's in german unfortunately though; can translate if requested)
lone heartBOT
@karmic rapids Has your question been resolved?
karmic rapids
<@&286206848099549185>
karmic rapids
first of all, why am I this stupid
I literally had that page open already
but just didn't read it
okay and
they have beta_i = + something
at the end
but it wants me to show beta_i = - something
@tacit arch
here:
this is what is written on wikipedia
tacit arch
where is the + something
karmic rapids
this is what they want me to show
tacit arch
but just didn't read it
read the wiki again
karmic rapids
read the wiki again
that's what they want me to show in my homework, but wikipedia is missing a minus sign or something
tacit arch
but it wants me to show beta_i = - something
yea i don't think you're being clear enough.
just read it again and compare more carefully
karmic rapids
just read it again and compare more carefully
I literally don't see it ._.
tacit arch
maybe write it down then
karmic rapids
specifically what?
ocean sealBOT
illuminator3
ocean sealBOT
illuminator3
tacit arch
the proof is based on the starting assumptions in the beginning of the wiki. you have to adapt to yours based off of your professor's notes
tacit arch
math isn't memorizing equations line for line, it's about understanding and applying
solid mural
So, I've tried to do it with formula 'an = Sn - S(n-1)' and ended up with "3^n - 3^(n-1) + 2". But the accepted answer is "2.3^(n-1) + 2". Is there a way to simplify my result or maybe there's another formula that results the accepted answer?
lime bobcat
I'm afraid the accepted answer is not right.
solid mural
It's results same sequence pattern if you tested both
solid mural
Yes, I meant •
lime bobcat
$3^{n-1}+3^{n-1}+2$
ocean sealBOT
jnkena
ocean sealBOT
jnkena
lime bobcat
$2\cdot 3^{n-1} =3^n-3^{n-1}$
ocean sealBOT
jnkena
lime bobcat
$3\cdot 3^{n-1}=3^n$
ocean sealBOT
jnkena
ocean sealBOT
jnkena
lime bobcat
Do you know now how to simplify your result? @solid mural?
solid mural
What's the rule that makes it equal?
ocean sealBOT
jnkena
solid mural
Ah, I see. So basically the power equation become 1+n-1?
lime bobcat
The exponent yes, 1+(n-1) = n
solid mural
Then, how it turned into the accepted answer from changing 3^n to 3•3^n-1?
ocean sealBOT
jnkena
lime bobcat
Do you understand the steps?
solid mural
What makes step 2 and 3?
lime bobcat
$3\cdot \text{something} - \text{something} + 2\$
$2\cdot \text{something}+2$
ocean sealBOT
jnkena
lime bobcat
something = 3^{n-1}
solid mural
So, it's like 3something - 1something right?
solid mural
something = 3^{n-1}
I see. I never see 3^(n-1) as a whole so I confused. Thanks
lime bobcat
You're welcome
solid mural
.close
dull needle
In this expression,
$\frac{d}{dx}(y) - (2xy^2+2x^2y\frac{dy}{dx})$
Does it make sense to do rewrite d/dx(y) as dy/dx in a next line?
ocean sealBOT
Jamestiago
dull needle
When factoring, in this case.
lone heartBOT
@dull needle Has your question been resolved?
alpine sable
I'm not totally sure what you're asking, but if I'm right, then yes
d(y)/dx is the same as dy/dx
alpine sable
lone heartBOT
alpine sable
Hey all, I'm stuck on this question
I know a 0 of it is 2
And ik I have to use tht 2 for synthetic division
And I get this by the end of it
Idk how to factor from here tho
That fraction is throwing me off
Also
I tried regular long division for it
I still get a remainder
Even though when I plug 2 into the original equation, I get a 0
I've checked my steps like 6 times 😭
lime bobcat
-28·2=-56
lime bobcat
No problem, that happens to everyone
Self-written notes are sometimes more difficult to assess for that kind of mistakes haha
alpine sable
For the constant
At the end of the original equation
The -30
I have to write it down aswell right?
It's 2 am, and I'm crunching for the final that's at 8 am
So forgive me if this is like a dumb question
safe mountain
hi
last ether
just post your question
safe mountain
how do i find the roots of this equation :
last ether
im assuming thats in radians
safe mountain
yes
once you make it = to 0 you can find 1 root
but how do you find the root thats next to it
last ether
well lets see
safe mountain
oh
once you rearrange and get -3/2sqrroot5
do you take the positive value
as well
3/2sqroot5
nvm
im so flipping confused
last ether
$$3+2\sqrt{5}\cos\left(0.5x+0.464\right)=0$$
$$\cos\left(0.5x+0.464\right)=\frac{-3}{2\sqrt{5}}$$
$$x=2\left(\left\pm(\arccos\left(\frac{-3}{2\sqrt{5}}\right)+2\pi n-0.464\right)\right)$$
safe mountain
there must be a line of symmetry somewhere
ocean sealBOT
Umbraleviathan
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
safe mountain
whats the n meant to be ?
last ether
any interger
safe mountain
any interger
do you mind explaining the equation to me
last ether
the 2pi(n) just means "for every revolution", which you know that if have an angle and you rotate it a full revolution it just ends up where it was
the + and - of an arrcos share the same "adjacent", thus the plus--minus
safe mountain
**Umbraleviathan**
Compile Error! Click the <:errors:504266556054962196> reactio...
im still not understanding exactly whats happening with the 2pi n
if i make n = 0
thats going to give me the fist root of the cycle
but then if i make it 1
i dont get the next root of the cycle
safe mountain
last ether
hm
last ether
maybe make n = 1 with the -arccos
last ether
WHY THOOOO
-arccos shares the same "adjacent"
and i guess with n=1 it just gets to the second one
why it's n=1, not sure
it just happens
probably because it's shifted 0.464 units to the left
usually for these, it's just trying a couple values of n
at least thats what i do lol
safe mountain
ohhhhhhhhhhhhhhh
safe mountain
-arccos shares the same "adjacent"
that makes sense
finding the negative value and adding 2pi
at least graphically it makes sense
last ether
yeah lol
safe mountain
usually for these, it's just trying a couple values of n
thanks for the trick
last ether
thanks for the trick
np
shy mortar
quick check: Does this look right to y'all? Thank you. :)
lone heartBOT
quick check: Does this look right to y'all? Thank you. :)
weary wyvern
yes
harsh girder
when x = -1, y=2/3<1
static raft
help
rapid nova
static raft
@heavy otter
lime bobcat
Which language?
rapid nova
how do you expect to get help without speaking english or even asking the question?
lone heartBOT
@static raft Has your question been resolved?
vital swift
$\text{For a certain aithmetic series, we know that } \ t_3+2t_5=10 \text{ and that }t_6-2t_2=22 \text{. Calculate } S_{15}$
ocean sealBOT
Nayvy
lone heartBOT
@vital swift Has your question been resolved?
harsh girder
$\text{For a certain aithmetic series, we know that } \\ t_3+2t_5=10 \text{ and ...
$t_n = t_1+(n-1)d$, then you can solve $t_1$ and $d$
ocean sealBOT
秋水
lone heartBOT
lone heartBOT
Available help channel!
random storm
shouldnt this be equal to 0 instead of $-\frac{\sqrt{2}}{4}$?
ocean sealBOT
Carpetoid
alpine sable
Why 0?
random storm
because if b = 0 then the denominator will equal 0 since b * (..)
and the numerator will also be 0
since 2-2
abstract fractal
0/0 isn't 0
After cancelling the 2 and -2, you can also cancel out a b from the numerator and denominator
random storm
i still dont understand sorry
can you elaborate?
Okay I get it now
thank you so much for the help
appreciated
.close
cosmic oar
how exactly does one use the change of base formula to get from the top to the bottom
cosmic oar
the explanation simply skips the steps and calculations in between
so how would that work? (step-by-step)
abstract fractal
Take the first term. Consider that 1/log_2(100!) = log_2(2)/log_2(100!)
Do you see how to progress from there?
abstract fractal
Do you remember the change of base formula?
cosmic oar
this ^, right?
cosmic oar
a is 2, b is 100!
ahhh, I see now
thank you!
so it was just rewriting 1 as log base 2 of 2
that was they key step, right?
abstract fractal
Yes
Same process for the other terms with writing 1 as log_3(3), as log_4(4), as log_5(5), etc
dusk tendon
lone heartBOT
rapid nova
nice question
static raft
<@842592261279449139> Has your question been resolved?
No
abstract fractal
You never asked a question
They did... 2 hours ago
rapid nova
They did... 2 hours ago
where?
dusk tendon
Sorry, that just popped up and I clicked it. 🥲 I'm trying to understand Bessel's correction a bit better and why it's considered "unbiased". I've crunched a bunch of numbers and noticed that for a smaller data set, it can actually lead to a number much larger to the population mean than the sample mean is smaller.
rapid nova
Look at the message they were replying to
there's no question
abstract fractal
Oh lol
abstract fractal
there's no question
I see now
dusk tendon
So what exactly does unbiased mean here if bessel's correction seems to introduce bias and if that's a dumb question, besides knowing the full population or the population mean, when should I not use it? Is there a cut off for sample size?
lone heartBOT
@dusk tendon Has your question been resolved?
dusk tendon
<@&286206848099549185> All I've been able to find is proofs for why the sample variance is smaller than the population variance and that bessel's correction inflates that, but it seems it definitely can overinflate it and I don't understand why it's considered to outright remove "bias" and if there's a sample size cut off when the correction would probably be better left out. Thank you in advance!
lone heartBOT
@dusk tendon Has your question been resolved?
tacit arch
Sorry, that just popped up and I clicked it. 🥲 I'm trying to understand Bessel'...
show your work
dusk tendon
show your work
tacit arch
that's really just numbers and not really a proof of anything
dusk tendon
the left side is the population, the right side is the sample. I used google sheets and stddevp which is the stddev formula using /n to produce the values listed below /n and stddev which is the stddev formula using /n-1 for the value listed bellow /n-1
then i inserted the delta for the standard deviations below each respective sample calculation
.close
lone heartBOT
lone heartBOT
Available help channel!
tough orbit
Could any1 give me a clue on what to start with?
lone heartBOT
Could any1 give me a clue on what to start with?
tough orbit
And could you please not tell me the answer
Only just like how do I start
Question 21
weary crag
radius of big circle minus the diameter of small circle
weary crag
radius of big circle minus the diameter of small circle
alright , i found a better approach
connect the centre of the smaller circles together so that they form a square
and let the radius of one small circle be r such that 2r = length of one side of the square
@tough orbit with me so far?
tough orbit
Yo I’m back sorry I was helping someone else witha problem
One sec lemme sketch that put
Out
weary crag
ok
woven wraith
I suggest to divide bigger circle in 4 quarters then calculate radius of circle inscribed in that quarter
weary crag
<@786519677228548117>
yep that's right
tough orbit
I suggest to divide bigger circle in 4 quarters then calculate radius of circle ...
That’s what I tried to do but idk how to get the radius of the smaller circle
That’s why you see those lines
tough orbit
Wiat a second @weary crag is the side of the circle 10 cm?
Or is the diagonal 10 cm?
woven wraith
Radius is 10 cm
weary crag
yep that's right
now draw a diagonal in the square. so diagonal becomes root 2 x 2r
weary crag
Radius is 10 cm
yep
tough orbit
Radius is 10 cm
Could you tell me how you derived that if it’s not a problem?
weary crag
Could you tell me how you derived that if it’s not a problem?
its given in the question lol
tough orbit
Radius of the small circle is 10cm?
weary crag
Radius of the small circle is 10cm?
no
tough orbit
its given in the question lol
Wiat I thought he said radius of the small circle is 10cm and I git confused lol my bad sorry
woven wraith
tough orbit
@weary crag is the side of the square 10 cm?
woven wraith
Calculate OB using pythagorean theorem
weary crag
<@786519677228548117> is the side of the square 10 cm?
bruh. the radius of the bigger circle is 10cm
woven wraith
It will be √2 OF
weary crag
this diagram is not very right ... wait, ill send a diagram
@tough orbit
do you want me to explain further?
woven wraith
How can you calculate 'r'
weary crag
How can you calculate 'r'
r is basically the radius of smaller circle. for now we treat it as a variable
weary crag
urban hearth
Yo can someone help me with conversion?
Just a simple quesiton tho.
I have
30 mL = 4.5 L and I want it to reduce to x mL = 1 L
woven wraith
Divide right side by 4.5 then you will have 1 L there
urban hearth
I didn't quite get that
woven wraith
I didn't quite get that
Uhh
urban hearth
Like this?
woven wraith
You need 1L in RHS yea?
urban hearth
Yeah
woven wraith
Now lets divide both sides with 4.5
urban hearth
AH
woven wraith
$\frac{30}{4.5}$ml$=1$L
ocean sealBOT
GG・Goof
urban hearth
Does that always work
what if like I say
30 mL = 4.5 L then I want it to be x mL = 2 L
woven wraith
Now divide by 4.5 and multiply it by 2
woven wraith
¯\_(ツ)_/¯
urban hearth
wait let me try show you what I recall
woven wraith
Hm k
urban hearth
This is awfully wrong right
woven wraith
Hm you can do that also
urban hearth
Oh yeah
urban hearth
Thank you
so our research paper
was wrong
I mean it's wrong
''4 liters per 30 mL of extract, the researchers used 1 L as a reference when formulating the amount of dose, the dosing will be reduced to match the water sample size, from 30 mL of extract it will be 7.5mL per 1L.''
oh
Thanks anyways
I'm gonna fix this one
.close
tawny fable
Hi there
tawny fable
I am a question here
idk if someone can help
It's (d)
Uploading my process
idk how to continue from here in order to find A and B
It's just algebra I guess but idk
harsh girder
you can solve f(x) from (c)
harsh girder
$$f(x) = 1+xf(x)+x^2 f(x)$$
$$(x^2+x-1)f(x)=-1$$
$$f(x) = \frac{-1}{x^2+x-1}$$
ocean sealBOT
秋水
harsh girder
$A(x-b)+B(x-a) = (A+B)x+-bA-Ba = -1$
ocean sealBOT
秋水
harsh girder
then
$$A+B=0$$
$$-bA-Ba=-1$$
ocean sealBOT
秋水
north adder
you get this?
looks like partial fractions
harsh girder
$$f(x) = \frac{A}{x-a}+\frac{B}{x-b} = \frac{A(x-b)+B(x-a) }{(x-a)(x-b)}$$
ocean sealBOT
秋水
tawny fable
yeah that is already done
then applying the equation
to replace the denominator
then using (c) to get the -1 on the other side
the thing is that I don't understand how from (A+B)x -Ab -Ba = -1 you get that A + B =0 and -Ab -Ba = -1
harsh girder
the thing is that I don't understand how from (A+B)x -Ab -Ba = -1 you get that A...
No matter what x is, it is -1, so the coefficient of x is 0
alpine sable
hello
tawny fable
what a shitty excercise
alpine sable
what does ffs mean?
tawny fable
No matter what x is, it is -1, so the coefficient of x is 0
thanks mate
you know some calculus as well? for the next items?
harsh girder
you know some calculus as well? for the next items?
for the next, you expand it to the power series
it's like
$$\frac{1}{1-x} = \sum_{k=0}^{\infty}x^k$$
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tawny fable
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Wdym
like the geometric one
but I need to use something to find R right?
I don't really understand what does it mean to show that it is in the neighbourhood of zero
like, to find the radius?
harsh girder
did you learn this https://en.wikipedia.org/wiki/Power_series
tawny fable
yeah
power series
ofc
I have this
So I need to find the radius in order to show that don't I?
harsh girder
$$\frac{A}{x-a} = \frac{-\frac{A}{a}}{1-\frac{x}{a}}=-\frac{A}{a} \sum_{n=0}^{\infty} \left( \frac{x}{a} \right)^n$
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tawny fable
**秋水**
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Where did you get this from?
I mean
don't I need to show it for the given series?
harsh girder
the question lets you conclude this
it's like
$$\frac{1}{1-x} = \sum_{k=0}^{\infty}x^k$$
ocean sealBOT
秋水
harsh girder
in (d). you get $f(x) = \frac{A}{x-a}+\frac{B}{x-b}$, now you need to expand this to power series
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lone heartBOT
@tawny fable Has your question been resolved?
harsh girder
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like this @tawny fable
tawny fable
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So you do this on A/x-a
and the for B/x-b
right?
tawny fable
then you get e
is that e?
harsh girder
yes, it's the same as in your question
harsh girder
compare with the 1/(1-x)
harsh girder
it's a common trick
tawny fable
lol
I see
anyways
in order to combine the both sums
I need to say that they both converge
harsh girder
converge when |x/a|<1 and |x/b|<1
harsh girder
https://web.ma.utexas.edu/users/m408s/m408d/CurrentWeb/LM11-9-2.php
you can read this, it's helpful
harsh girder
$\frac{1-\sqrt{5}}{2}<0$
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秋水
tawny fable
yeah
harsh girder
tawny fable
But I need to take the minimum between them?
harsh girder
so this is wrong
tawny fable
But that is my b
harsh girder
I mean $-\frac{1-\sqrt{5}}{2}>\frac{1-\sqrt{5}}{2}$
ocean sealBOT
秋水
tawny fable
hmmm
mb
so it's the opposite side
yeah
So now when I have these
I combine them
and find the minimum of convergece?
harsh girder
yes, the converge domain of the sum of the two parts is their intersection
harsh girder
yes
tawny fable
for f
tawny fable
yes
I have:
from Item (e)
and
from Item (b)
So I can say that:
?
or by induciton?
harsh girder
compare the coefficients of x^n
tawny fable
yeah
tawny fable
So I can say that:
That's this
harsh girder
yes
harsh girder
you can simplify
harsh girder
$$\frac{1+\sqrt{5}}{2} = \frac{2}{\sqrt{5}-1}$$
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秋水
harsh girder
1/(a/b)=b/a
harsh girder
why you don't have A,B
tawny fable
A is -1 and B is 1
harsh girder
ok
harsh girder
isn't that a plus?
you can check by calculate $(\sqrt{5}+1)(\sqrt{5}-1)$
ocean sealBOT
秋水
harsh girder
$\frac{1+\sqrt{5}}{2} = \frac{1+\sqrt{5}}{2} \times \frac{\sqrt{5}-1}{\sqrt{5}-1}$
ocean sealBOT
秋水
harsh girder
$x^2+x-1=0 \Rightarrow x = \frac{-1 \pm \sqrt{5}}{2}$
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harsh girder
@tawny fable your a,b are not correct
tawny fable
so it is (x+(1+sqrt(5))/2)(x-(-1+sqrt(5)/2)?
a = - ( 1+sqrt(5))/2
b = (-1+sqrt(5))/2?
harsh girder
yes
tawny fable
So A = 1 and B = -1
harsh girder
the thing is that I don't understand how from (A+B)x -Ab -Ba = -1 you get that A...
here
harsh girder
tawny fable
Ughhhhhh
ffs
sorry...
So I have this eventually
Can you explain the move the reverse the term?
like to change the denominator with the numerator?
harsh girder
because $\frac{1}{\frac{x}{y}} = \frac{y}{x}$
ocean sealBOT
秋水
tawny fable
hmmm
Yes
Ok thanks
So I have this now
and idk how to simplify it to get the resault
harsh girder
then rationalize
tawny fable
wdym
harsh girder
like this
$$\frac{2}{\sqrt{5}-1} = \frac{2}{\sqrt{5}-1} \times \frac{\sqrt{5}+1}{\sqrt{5}+1}$$
ocean sealBOT
秋水
harsh girder
$$\frac{2}{\sqrt{5}-1} = \frac{2}{\sqrt{5}-1} \times \frac{\sqrt{5}+1}{\sqrt{5}+1} = \frac{\sqrt{5}+1}{2}$$
ocean sealBOT
秋水
tawny fable
jesus
@harsh girder How come you don't have any badge that says EPIC ALGEBRA or smthing?
like
these tricks
Ugh
someone needs to save me from this test
exam
harsh girder
<@795717786709000193> How come you don't have any badge that says EPIC ALGEBRA o...
what's that?
tawny fable
lol
when you press on someone's Icon
you see the badges that they have
like Role
roles yeah
sorry
harsh girder
oh, I didn't add roles in this server
tawny fable
You can though
harsh girder
it's ok. I think you get the result.
tawny fable
hmmm
harsh girder
harsh girder
it's a famous example of generating function
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fading mauve
Desperately need help with this, it's a construction assignement so it has to be solved with a compass
I don't understand it at all
lone heartBOT
Desperately need help with this, it's a construction assignement so it has to be...
@fading mauve Has your question been resolved?
fading mauve
<@&286206848099549185>
vale wigeon
@fading mauve before you go into any of these constructions, do you understand that they are all essentially the same thing?
well, (3) involves a doubling at the end, but otherwise it is identical to (2), and (2) is identical to (1) up to a change in names
fading mauve
Id figure theyre similar to each other since r and s seems like the exact same length to a and b
wait theyre the exact same?
I dont think I understand how 1 and 2 are identical
vale wigeon
i can go into more detail why (1) and (2) are the same
fading mauve
id really appreciate that
vale wigeon
let's solve for x in a/x = x/b
multiply both sides of this equation by b and by x (or, if you want to do the same in one step, multiply both sides by bx), and you will end up with ab = x^2
and thus x = sqrt(ab)
does that make sense to you?
vale wigeon
probably to rack your brain a bit with it
i mean your teacher put the same (ish) thing thrice, because once you know how to do (2) you instantly know how to do (3) - doubling a line segment is quite an elementary affair after all
anyway there's this somewhat nontrivial construction for finding the geometric mean which involves taking your two given line segments a and b, constructing from them a segment with length a+b, and making that the diameter of a circle
i am not stating all the details here but it may be enough for you to recall it
fading mauve
I dont think my teacher mentioned anything like that unfortunately
fading mauve
nope all i have for this assignment is the print-out sadly, my school is pretty lazy
anyway about that diagram, isnt x suppose to be an arc? why is it an angle in the diagram
vale wigeon
it is not an angle
nor an arc
it is in fact a length
sorry, let me put in the other right-angle mark which i missed
fading mauve
ohhh I think I get it
vale wigeon
just so we're clear: when you see an angle marked with a little square shape, it always means a right angle.
fading mauve
so for that then the circle and the triangle are just construction right? and not part of the problem? (sorry if it seems dumb i just wanted to make sure ^^)
vale wigeon
right angles are special enough to warrant their own diagrammatic symbol
the triangle isn't really necessary for the construction
the only things you would be constructing are the a+b line segment and the circle (defined by having diameter a+b), and then the perpendicular erected from the meeting point of the a and b lengths and extended up to its intersection with the circle
which sounds clunky as hell when you say it like that lol
fading mauve
wording like that makes it sound pretty simple actually
just to make sure im understanding this right though:
first i make a line segment of a+b
then find the middle of segment a+b to get the radius, then i make the circle, and at the point where a and b intersect to the point it intersects with the circle is going to be x?
vale wigeon
the point where a and b meet. i wouldn't call it an intersection.
fading mauve
right, my bad
fading mauve
and then for #3 its just doubling line segment r+s? but then same process
vale wigeon
no, you would double at the end.
it's the x that you would need to double
but in fact if you draw the entire circle then doubling is easy - just extend it both up and down from the meeting point.
fading mauve
ohh that makes a lot of sense!! im going to quickly try and do the construction
i cannot stress enough how seriously grateful i am to you
ive asked for help from so many people but basically nobody has understood what my assignment was about
Sorry for poor camera quality
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muted berry
Can someone tell what is the derivative of e to the power minus x
muted berry
surreal sun
-exp(-x)
it's like when you derivate exp(2x), d(exp(2x))/dx = 2exp(2x)
except here instead of 2 it's -1
lone heartBOT
@muted berry Has your question been resolved?
high rapids
If the power were to be -2
e^-2 is a constant so its derivative is 0, just like derivative of 2390844
stable panther
guys, im kind of confused on getting remainders on base numbers
stable panther
say 18 base 10 converted to base 7
so, the first step is to divide 18 by 7 right?
wary stream
Yes
stable panther
right, so the answer is 2.5
from what ive heard, is that i have to multiply .5 by 7??
wary stream
Yes
stable panther
wait, do i round up?
the answer is 3.5 remainder
wait im not quite getting this
i found this on an online converter
i divide 18/7 and i get 3.5 and the remainder is 4??
wary stream
Wait, how did you get 3.5?
wary stream
No
stable panther
wait what
wary stream
That's rounded too much
The more exact answer is 2 r 4
7 goes into 18, 2 times with 4 left over
In other words $\frac{18}{7} = 2 \frac{4}{7}$
ocean sealBOT
dldh06
stable panther
wait.. i havent done math in a while
let me move on to another base number
29 base 10 converted to base 9
alright so, 29/9 is 3 R 2
wary stream
Yes
wary stream
Don't simplify
Take the quotient and keep dividing by the base, until you get a quotient of 0
When the quotient is 0, then you read the remainders from bottom to top, and that's the value in that base
So 3/9 is 0 R 3
So $(29){10} = (32){9}$
ocean sealBOT
dldh06
stable panther
alright, i think i get it now. finally lol
not sure what i was confused about
i think i just forgot what remainders were since im used to a calculator
wary stream
Now the multiply by part you were referring to applies to decimal numbers
So numbers like $(0.1234)_{10}$
ocean sealBOT
dldh06
stable panther
ah, is it better to just use the normal way??
wary stream
What do you mean by normal way?
stable panther
alright, so 0.1234 times the base right?
wary stream
Yes, for decimals, you multiply by the base
stable panther
ah, i think i get it now
wary stream
There are plenty of YouTube videos if you're still confused
stable panther
yea, i definitely have to watch some
timid yew
Can somebody tell how to solve question 16 1 St part
lone heartBOT
Can somebody tell how to solve question 16 1 St part
timid yew
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@timid yew Has your question been resolved?
elfin snow
my first idea would be to combine the fractions into one
low forum
<@&286206848099549185> Im confused on this like I have no idea where to start but this is trig honors
kind sierra
alpine sable
What exactly does theta ' refer to in this case?
low forum
OH DOES IT RELATE TO THE UPPER ONE 💀
but there was no theta up there
okay let me show the problem above
I was confused on that one too but it only asked for a side
so idk
alpine sable
No, it doesn't seem like they're related
low forum
Yeah thats why i was confused
alpine sable
So the questions wants us to find all angles theta between -720 and +720 degrees with the condition that theta prime is 35 degrees
only thing is I don't know what theta prime means in this context
alpine sable
did you ever use that notation in your class before?
low forum
