so the normal line is $-0.739x + 2.739$
#help-38
hot ore
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Devil Wears Prada
hasty temple
Can explain which one it is, I thought it was the first blue one
sacred sapphire
Can explain which one it is, I thought it was the first blue one
the first one has 2 negative roots and 1 positive root
sacred sapphire
does the graph look like a quadratic?
sacred sapphire
then its not
hasty temple
Its third one I meant
sacred sapphire
yes
hasty temple
Thanks
I need help with another let me find the question
It'll be a while until I find it, I'll close channel for now
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hasty temple
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wispy basin
I just don't know what this means, how am I meant to input this???
limpid dawn
<:AnnoyedPepe:766301120560627753> I just don't know what this means, how am I me...
If $x_1$ and $x_2$ are roots of a quadratic equation then
[ ax^2+bx+c = a(x-x_1)(x-x_2) ]
solid kilnBOT
bacc
limpid dawn
I guess they want it in linear factors
giving it a try now
wispy basin
oh
wispy basin
exotic tundra
if that doesn't work, maybe try
x=-6 or x=4
exotic tundra
heck yea
proud maple
x = -6, 4?
wispy basin
god I really despise this
exotic tundra
2 for 2
wispy basin
x = -6, 4?
alrdy what I tried the first time before coming here
u.u)
well at least im getting the math right
proud maple
What in the world is this website?
wispy basin
wispy basin
What in the world is this website?
something called Moodle webwork
either way I'm starting to really dislike it
fine for simple, 1 line numbers
but this is miserable
proud maple
Damn only 1 point? π π π
wispy basin
Damn only 1 point? π π π
I need a stupendously good grade so I have to do these as much as they're worth only like 5% of the final grade
π
wispy basin
what
daz what im saying lol...
well anyway ill go ahead and close this since it's resolved
limpid dawn
you are struggling more with the programm
wispy basin
u.u) I pray I do not need to return....
limpid dawn
than with the math
blergh
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exotic tundra
u.u) I pray I do not need to return....
if you do ping me
since apparently I'm pretty good at these lol
limpid dawn
if you do ping me
since apparently I'm pretty good at these lol
maybe you programmed them
exotic tundra
I wish
they're pretty decently programmed imo
exotic tundra
I mean, they could've put the answer structure there
but it's pretty hard to program something like that
by that I mean I couldn't figure it out
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wraith hinge
Don't know how to proceed further. Applied all the formulas I know.
high heron
you have a sign error
wraith hinge
ima try to help
excuse my handwriting, i chipped away my writers callus and i have to write with my ring finger
prisma elk
tht was quick
high heron
$\sin^2\theta=1-\cos^2\theta$
wraith hinge
you have a sign error
where?
solid kilnBOT
Edward II
high heron
not the other way around
prisma elk
excuse my handwriting, i chipped away my writers callus and i have to write with...
oh no worries i have bad handwriting as well
i think edward helped you
wraith hinge
not the other way around
im still stumped
in fact i dont even think i even needed to substitute sin^2 into the equation
high heron
do you know the double angle formulae?
high heron
ah
Ok I've found a way to do it directly
Now to figure out how to not just give you the answer
One important thing to note is that $1-2\sin^2x=\cos^2x-\sin^2x$
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Edward II
wraith hinge
One important thing to note is that $1-2\sin^2x=\cos^2x-\sin^2x$
uhhh
im a little confused
high heron
$1-2\sin^2x=\cos^2x+\sin^2x-2\sin^2x$
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Edward II
high heron
**Edward II**
alternatively just add $\sin^2x$ to both sides
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Edward II
wraith hinge
$1-2\sin^2x=\cos^2x+\sin^2x-2\sin^2x$
is this just a formula? we've never been taught this lol
all we can work with is cos^2 + sin^2 as of now
high heron
well if $1=\cos^2x+\sin^2x$, then you can add things like $-2\sin^2x$ to both sides and still have equality
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Edward II
wraith hinge
well if $1=\cos^2x+\sin^2x$, then you can add things like $-2\sin^2x$ to both s...
oh yeah
high heron
Also $1-2\cos^2x=\sin^2x-\cos^2x$ in the same way
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Edward II
high heron
Now there's a trick you have to use that I have no idea how you would spot without practice
but the numerator (correcting for the sign error) from your last line can be rewritten
using $1-4\cos^2x\sin^2x=\cos^2x-2\cos^2x\sin^2x+\sin^2x-2\cos^2x\sin^2x$
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Edward II
wraith hinge
(I leave it to you to figure out why)
yeah at first glance i have 0 idea
high heron
yeah same thing but I just realised I accidentally switched
high heron
yeah at first glance i have 0 idea
it's expanding the 1 out again
wraith hinge
it's expanding the 1 out again
my goodness this is a massive problem
bear with me if im being a bit slow, im still in 10th grade and this is brand new information to me
high heron
that is very understandable
it's essentially just practice to be able to do these sorts of problems
wraith hinge
it's essentially just practice to be able to do these sorts of problems
alright thank you for your help
it probably doesnt help that this question will come in my midterm test tomorrow and i have a sub-optimal math teacher lol
you gotta make do with what you get Β―_(γ)_/Β―
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fair forge
do they have a mistake here?
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do they have a mistake here?
fair forge
obviously according to the first line in the system, the bottom formula, right below the sigma notation, should end with:
"...<i_n<=n" and NOT "...<i_k<=n"
marble wharf
the sigma notation for the first line is $\sum_{1\leq i_1\leq n} \left(\prod_{j=1}^1 r_{i_j}\right) = (-1)^1 \frac{a_{n-1}}{a_n}$. aka $k=1$
or, after simplifying and renaming $i_1$ to $i$, $\sum_{i=1}^n r_i = -\frac{a_{n-1}}{a_n}$
fair forge
the sigma notation for the first line is $\sum_{1\leq i_1\leq n} \left(\prod_{j=...
youre wrong, there are only i_k indexes, so for k=1 like in the first line it would just be
$r_{i_j} = -a_{n-1} / a_n$
@marble wharf
marble wharf
the fact alone that j appears on the left but not on the right should tell you that its false
k tells you the number of indices
so for k=1 there is one index
fair forge
the fact alone that j appears on the left but not on the right should tell you t...
wdym? am i right?
fair forge
the fact alone that j appears on the left but not on the right should tell you t...
and also that how it should be if u looked at the system
marble wharf
you are wrong
you wrote r{i_j} = -a{n-1} / a_n. the j appears on the left but isnt summed or multiplied over
so it stays
but it doesnt appear on the right
fair forge
you wrote r{i_j} = -a{n-1} / a_n. the j appears on the left but isnt summed or m...
u already get that i just took k=1, i_k=1 (doesnt matter what i_p is)
for 1<=p<=n
just need to be distinct
marble wharf
wdym it doesnt matter what value it has lol
you are summing over all possible values it can have
fair forge
those are just indexes of roots, i can number and index my roots however i like
fair forge
you are summing over all possible values it can have
no we are not here, the formula is wrong
marble wharf
ok feel free to think so
fair forge
we are summing only i_k indexes for k=1, do you agree?
look at the bottom formula
u see it i know it
its very obvious
amber python
fair forge
<:k_what_wtf:971476939468582992>
look at this do u agree?
fair forge
we are summing only i_k indexes for k=1, do you agree?
this
fair forge
obviously according to the first line in the system, the bottom formula, right b...
im almost sure it should be this
fair forge
it has to be
fair forge
because otherwise the first row in the system is inconsistent
amber python
it is not inconsistent whatsoever
fair forge
you are not reading it correctly
they put in the sigma,
i_1, i_2, ..., i_k
so therefore only k indexes are being summed
for k=1, overall only k roots will be summed
amber python
you are contradicting yourself within that message
fair forge
yes
amber python
only k indexes are being summed
only k roots will be summed
contradiction
somber ginkgo
they put in the sigma,
i_1, i_2, ..., i_k
so therefore only k indexes are bein...
what?
somber ginkgo
ok so what do you think the expression wikipedia has means?
amber python
so you sum all n roots
fair forge
that 1 index runs over 1 to n
that one index is a scalar and is a number between 1 and n
amber python
yes so you get all the roots
denascite was even kind enough to write it out for you
fair forge
ok so what do you think the expression wikipedia has means?
"sum i_1,..., i_k times, the multiplication of r_i_k"
fair forge
denascite was even kind enough to write it out for you
it's only r_i_1
amber python
well [ \prod_{j=1}^1 r_{i_j} = r_{i_1} ]
solid kilnBOT
amber python
i agree with that
fair forge
so im right
amber python
so you get [ \sum_{1\le i_1\le n} r_{i_1} ]
somber ginkgo
total_sum = 0
for i_1 in range(1, n+1):
for i_2 in range(i_1+1, n+1):
...
for i_k in range(i_(k-1)+1, n+1):
prod = 1
for j in range(1, k):
prod *= r_i_j
total_sum += prod
amber python
so im right
no
you're wrong
,, \sum_{1\le i_1\le n} r_{i_1} = r_1 + r_2 + \dots + r_n
somber ginkgo
```python
total_sum = 0
for i_1 in range(1, n+1):
for i_2 in range(i_1+1, n+1)...
this is the loop written in a monstrous python/pseudocode mess but anyway that's loosely what the loop would translate to in code
fair forge
```python
total_sum = 0
for i_1 in range(1, n+1):
for i_2 in range(i_1+1, n+1)...
i_1 doesnt change its value
solid kilnBOT
somber ginkgo
^ so this is what our expression simplifies to for k=1
amber python
fair forge
there are too many variables in this sigma
amber python
what?
fair forge
now let's try k=2
alright
in the sigma
1<=i_1<i_2<=n
it's like 1<=i<j<=n type indexes now that i think about it
amber python
,, \sum_{1\le i_1<i_2\le n} \parens [\bigg] {,\prod_{j=1}^2 r_{i_j}}
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amber python
,, \prod_{j=1}^2 r_{i_j} = r_{i_1} r_{i_2}
solid kilnBOT
amber python
,, \sum_{1\le i_1<i_2\le n} r_{i_1} r_{i_2} = \begin{aligned}[t]
& r_1 r_2 + r_1 r_3 + \dots + r_1 r_n \
& + r_2 r_3 + r_2 r_4 + \dots + r_2 r_n \
& \vdotswithin+ \
& + r_{n-1} r_n
\end{aligned}
fair forge
,, \sum_{1\le i_1<i_2\le n} r_{i_1} r_{i_2} = \begin{aligned}[t]
& r_1 r_2 + r...
but then for k=2 would be have i_1=5, i_2=10 for example
which is inconsistent with row 2 of the system
solid kilnBOT
somber ginkgo
but then for k=2 would be have i_1=5, i_2=10 for example
wdym by this?
somber ginkgo
which is inconsistent with row 2 of the system
inconsistent with what exactly?
fair forge
exactly this!
amber python
that's precisely the second vietas formula
amber python
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tidal wren
Hey guys, can you help me solve this question?
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Hey guys, can you help me solve this question?
tidal wren
I don't understand. Could you explain it clearly?
unkempt fox
3x^2 + 6x + 14
b = 6 , a = 3
So p = 6/2*3 = 1
Plug -1 in 3x^2 + 6x + 14
We get 11
a stays the same
unreal stag
Hey guys, can you help me solve this question?
a(x+p)^2+q is the vertex form of the quadratic equation in where p is the x coordinate for the vertex and q is the y coordinate
unkempt fox
So its 3(x + 1)^2 + 11
unreal stag
(-p , q) is the local extreme
oh u explained it sorry didn't see
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echo jasper
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echo jasper
so the set up
9540000 acres times 43560ft/1acre times 1mile/5280ft?
,w 9540000 acres times 43560ft/1acre times 1mile/5280ft
solid kilnBOT
echo jasper
what in the
thats more than the total us land area
π€¦ββοΈ
is ft^2 making a difference
i think it is i will try
,w 9540000 acres times 43560ft^2/1acre times (1mile/5280ft)^2
solid kilnBOT
echo jasper
OH
14,906 miles
ya still more than total us land ok i give up
,5280 squared
,w 5280^2
solid kilnBOT
echo jasper
,w 9540000 times 43560 divided by 27878400
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echo jasper
,w 9540000 times 43560
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echo jasper
,w 415562400000 dvidd by 27878400
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Requested by ac9468
echo jasper
,w 415562400000 divdede by 27878400
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Requested by ac9468
echo jasper
,w 415562400000 divided by 27878400
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echo jasper
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echo jasper
is what i did to calculate v on my calculator valid
becuz its just a weird number but ya
still rose
correct
slender shard
,calc 4/3 * pi
solid kilnBOT
Result:
4.1887902047864
Yup.
still sierra
?
still sierra
Idk how its supposed to go
Does the possible outcomes become zero for no events?
i just typed zero and got it right but idk what it means
zinc ginkgo
to simplify, the question is asking what number between 0 and 1 probability(impossible) equals
yes probability(impossible) = 0
by definition, an impossible event means its probability of happening is zero
meager bloom
Does the possible outcomes become zero for no events?
If it is impossible, then number of ways event can occur becomes 0
tired shuttle
Let $p$ and $q$ be the minimum and maximum values ββof $a+b$ respectively with $a$ and $b$ natural numbers that satisfy $2a+ab+b = 838$. The value of $p+q$ is \ldots
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Let $p$ and $q$ be the minimum and maximum values ββof $a+b$ respectively with $...
tired shuttle
just to make it neat i guess
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raymondclie
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
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@tired shuttle Has your question been resolved?
somber ginkgo
**raymondclie**
Compile Error! Click the <:errors:504266556054962196> reaction f...
consider trying to factorise 2a+ab+b
you can't ofc, but can u add a constant term such that that factorises?
outer knot
can some one help me with this , i am unable to understand what the question asks . Thank you
zinc ginkgo
can some one help me with this , i am unable to understand what the question ask...
lines containing the origin are equations of the form y = mx for some real number m
there are only 3 categories of subspaces of R^2. show that if you have a subspace, then it's one of those 3: {0}, y=mx, R^2
carmine mauve
lines in R^2 are {y = mx or x = 0} for any real m.
zinc ginkgo
oh yes thanks for the correction i forgot vertical line
outer knot
lines containing the origin are equations of the form y = mx for some real numbe...
i thought of representing all lines as {av : a belongs to F and v belong to r^2 and v != 0} [I am using a general representation cos the next question after this is for r^3] , is it correct ?
outer knot
there are only 3 categories of subspaces of R^2. show that if you have a subspac...
i see so we are relating dimensions here 0 -> zero subspace , 1-> lines , 2 -> planes , 3-> space ?
solid kilnBOT
Shuba
outer knot
? i get the definition for subspace . am i missing smth ?
carmine mauve
? i get the definition for subspace . am i missing smth ?
add one to the dimensions.
every subspace contains the identity 0.
- 0d space has no elements, so is a subspace of itself by vacuous truth
- 1d space is the field, so any subfield is a subspace
- nd space (n > 1) has points, so the subspaces are lines (and the trivial identity)
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Shuba
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Shuba
outer knot
i get this but it is hard generalising for higher dimensions
carmine mauve
do this by taking any point in a subspace, multiplying it by a scalar, and showing that the result is also in the subspace
outer knot
do this by taking any point in a subspace, multiplying it by a scalar, and showi...
i thought all vectors start from the origin in maths( i saw 3b1b video for LA ) . so wouldn't all vectors excluding 0 be a part of the lines ?? this should obviously be not true as the above would imply the dim 2which is not true , where did i go wrong ?
carmine mauve
i thought all vectors start from the origin in maths( i saw 3b1b video for LA ) ...
well yes, but actually no
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outer knot
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β
carmine mauve
if you consider a vector to be an arrow, then yes it's tail is on the origin
(unless you're adding two vectors)
this is a good video on the subject
https://youtu.be/uPbBDToXjBw?list=PLJHszsWbB6hrkmmq57lX8BV-o-YIOFsiG
my point is, to solve your problem, you'll need to look at the definition of a vector space, and vector subspaces
you can think of "all the lines through the origin" as the set of all vectors, with their tails on the origin, if you want.
outer knot
i think i get it now (some sort )
carmine mauve
- if you add two parallel vectors, you end up with a third parallel vector (i.e. allong the line)
- if you multiply a vector with a scalar, it increases (or decreases) the length of the vector in the same direction (i.e. allong the line).
you'll need to prove this more rigerously
outer knot
actually scratch that if all lines are a subspace then (a,0) is a line also (b,0) is also a line , but (a,b) shouldn't belong to the subspace
carmine mauve
right, I understand your confsion.
it means, the line y = 3x is a subsapce, the line y = 4x is a subspace, etc... (they're all different subspaces).
outer knot
it means, the line `y = 3x` is a subsapce, the line `y = 4x` is a subspace, etc....
ok ok i guess i misunderstood the question
tysm for all help
carmine mauve
outer knot
this is a good video on the subject
https://youtu.be/uPbBDToXjBw?list=PLJHszsWbB...
will watch this playlist to better my understanding
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carmine mauve
it's worth a watch. 3blue1brown's series does a good job for "feel", this does a good job for definitions.
even if you don't understand much of it XD
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cerulean saddle
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cerulean saddle
Im currently working on the second one
whole coral
Your naturals include 0 by default? Eww 
cerulean saddle
but it's N*
cerulean saddle
Your naturals include 0 by default? Eww <:catangery:732013544186314834>
I know
whole coral
(I know, I'm teasing 
)
cerulean saddle
is it right to work with this method??
whole coral
It can be helpful, sure 
considering the "odd" and "even" subsequences
As long as you're careful though 
cerulean saddle
since they're positive and decreasing, i wrote 0 <= Un <= max(V1 , W0)
whole coral
I initiated Vn = U2n = 3/2n and Wn = U2n+1 = 1/(2n+1)
(oh, also, if you want to work with N*, the nonzero naturals, you may want to have U_{2n - 1}, so that n = 1 gets you U_1 and you don't miss the first "odd" term)
Or if your naturals usually include zero, then you can use what you have but start from n = 0 there 
whole coral
since they're positive and decreasing, i wrote 0 <= Un <= max(V1 , W0)
Oh, you've beat me to it, as I was typing it 
cerulean saddle
should i say also that n belongs N* or not
cause W exist with n=0
sorry for my vocab
I'm accustomed to french
whole coral
Hmmm, I mean, you'd probably have to be a bit careful to make clear that you have N* for V_n and N for W_n, but either case, it would end up being a more restrictive statement than anything, so not untrue at least
cerulean saddle
Im worrying about it since my instructors are very strict about everything
whole coral
If anything, just replace your odd one with 2n - 1 and you can say N* in that case 
cerulean saddle
@whole coral You're a genius
whole coral
Awwwww 
cerulean saddle
Thank you so much
whole coral
Awwww 
cerulean saddle
I cant help but be thankful to you and to the server
i'm currently living hell in my university
warped moss
cerulean saddle
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craggy jewel
help, is the inverse y = 1/x-1 or y=1/x + 1
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help, is the inverse y = 1/x-1 or y=1/x + 1
craggy jewel
whole coral
Are you saying here you factored xy - x into y(x - 1)?
(also be very careful about doing this here, you'll need to take care)
craggy jewel
Are you saying here you factored xy - x into y(x - 1)?
yup, just realized that's wrong, my bad sorry
craggy jewel
(also be *very* careful about doing this here, you'll need to take care)
can i know why?
whole coral
can i know why?
If I take the original function, $a(x) = \frac{x + 1}{x^2 - 1}$, it isn't defined at $x = -1$, but if you simplified that $\frac{x + 1}{x^2 - 1} = \frac1{x - 1}$, the $\frac1{x - 1}$ \emph{is} defined at $x = -1$ now
solid kilnBOT
@whole coral
whole coral
So e.g. you can either remove x = -1 from the original function's domain and the corresponding output it would give from the range, e.g. a(x) = 1/(x - 1) when x is not 1 or -1, and take -1/2 out of the range
The inverse function would be y = (1/x) + 1, but in addition to 0, you also don't want -1/2 in the domain (because -1/2 is not in the range of the original function, and the whole "swap domain and range" thing)
craggy jewel
im kind of confused, so my orig domain is, the x i got are -1 and 1.
whole coral
-1 and 1 are not allowed in the domain of your original function
whole coral
im kind of confused, so my orig domain is, the x i got are -1 and 1.
Are you happy with the whole "the domain of the inverse is the range of the original" thing?
whole coral
where did -1/2 come from tho
Your original function will have a hole at (-1, -1/2) (you can see this by the fact that when x is not -1, you can simplify (x + 1)/(x^2 - 1) = 1/(x - 1), and if you put x = -1 in the latter, that gives you -1/2 as an output)
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boreal burrow
can someone please help me with maths hw
its so late and i just want to go to sleep and i forgot everything about histograms and i left my book at school π
its due tmr since i fogor abt it
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gritty wind
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gritty wind
how did they go from that to that
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strange kelp
i need help proving this identity at the top
and i keep messing up the process along the way
this is what i got so far
starting from the left side
late laurel
combine the fractions on the numerator of the LHS
then solve the complex fraction and maybe you can see where to continue
strange kelp
combine the fractions on the numerator of the LHS
i did that on the right hand side
i multiplied the denominator and numerator by cosx and sinx for each fraction
late laurel
do you have to work on the RHS?
prisma stone
just multiply both sides by sinx * cosx
strange kelp
$\frac{\sin^2x-\cos^2x}{\sin^2xcos^2x}$
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strange kelp
$\frac{1}{\cos^2x} - \frac{1}{\sin^2x}$
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snooze
late laurel
and what is 1/cos^x
strange kelp
sec^2x
late laurel
and 1/sin^2x
strange kelp
csc^2x
late laurel
so did u prove it
strange kelp
but that was only the numerator what about the denominator
late laurel
oh?
strange kelp
that entire fraction was from the tanx-cotx
strange kelp
yeah you're right there but we broke this term out into the numerator
but thats also divided by sinxcosx
multiplied together
see
the original fraction from the numerator over the original denominator
this is what we simplifed it from, the original term
late laurel
but thats also divided by sinxcosx
why is this a problem?
its a complex fraction we'll solve after we combine
strange kelp
alright after i combined it all i got sec^2x-csc^2x
so it's (sec^2x-csc^2x)/(sinxcosx)?
late laurel
roll back
its not squared remember
also just combine these first
and tell me waht u get
strange kelp
**snooze**
i did up here already
strange kelp
to subtract the fractions the denominators need to be like terms
you need to multiply both sides by cosx and sinx
on each side
so wait
it's just cosxsinx at the bottom?
did i mislook that
late laurel
so what do u have
strange kelp
(sin^2x-cos^2x)/(sinxcosx)
strange kelp
yeah the whole term
strange kelp
yeah
late laurel
ok then do that
strange kelp
my bad that was a typo
strange kelp
im mixing up numbers bad today
late laurel
then separate the fraction into 2
.
strange kelp
late laurel
by keeping the same denom
.
strange kelp
now it is the original one we got earlier
from doing 1/cos^2x 1/sec^2x
i had just kept mixing up the multiplication
late laurel
lol yeah now its the whole thing
strange kelp
i see where i got off track thanks for helping me see that
i think ive been staring at this problem for too long
lol
i got it now
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untold phoenix
Yo
untold phoenix
Can u help me with this question
I tried to check if My = Nx
I dunno if I took the partials wrong but thatβs what I got and itβs wrong
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wraith hinge
can someone help me understand how to solve this
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can someone help me understand how to solve this
median torrent
can someone help me understand how to solve this
In a system of equations, both equations are true simultaneously
So the y they mention in the first equation, it's the same as the y they mention in the other
Whatever y = in the first
It's gotta be the same as what y = in the second
wraith hinge
not sure I understand
so do you mean I solve the first one and use it for the second
wraith hinge
ahhhh
median torrent
They must also be the same
wraith hinge
12x+15
median torrent
No not like that
It's an equation
5x + 7 = 7x + 8
You need to find x =
Solve for x
wraith hinge
oh ok
wraith hinge
I feel like I am doing something wrong I did -5x on each side and got 2x+15
or 2x=15
idk
but then I divded the 2 and ended up with 15/2
which doesn't sound right
x=15/2
gleaming compass
you get x=-1/2
wraith hinge
how ?
gleaming compass
subtract 5x from each side
wraith hinge
I did
wraith hinge
oh wait I see what i did
wraith hinge
you get 2x=-1
you can't leave the 2x like that can you ?
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weak spire
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maiden zinc
do you know derivatives
weak spire
do you know derivatives
I dont think so
maiden zinc
pretty sure u can use a calc
so i would just graph the function
and then use ur calc to find the max or min
weak spire
weak spire
and then use ur calc to find the max or min
Is there any way to find it without a calc
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indigo drift
what do i do after here ;-; i missed a few lectures and im lost
bright quarry
A(x+2) + B(x-2) = 1
faint schooner
The numerator is 1
indigo drift
o
bright quarry
because the LHS
faint schooner
From which it was bifurcated
indigo drift
LHS?
bright quarry
left hand side
zinc ginkgo
Look, Han Solo
faint schooner
Riemann
bright quarry
$\frac{1}{x^2 - 4} = \frac{A}{x-2} + \frac{B}{x+2}$
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knief
faint schooner
Something like that
bright quarry
yes by letting x = 2 and x = -2
bright quarry
no
indigo drift
uhh
bright quarry
uhh
zinc ginkgo
A(x+2) + B(x-2) = 1
@jova did you get this
indigo drift
yea
bright quarry
yes by letting x = 2 and x = -2
^
so that one term is zero
and you can solve for the other
indigo drift
yup yup
indigo drift
how do u know u have to set it to 2 and -2 btw
@bright quarry
bright quarry
because those are the two values that make the factors zero
indigo drift
i see
zinc ginkgo
Sometimes called the"cover up" method
bright quarry
$1 = A(x+2) + B(x-2)$
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knief
zinc ginkgo
Not a common name, but if you need to Google something
indigo drift
Not a common name, but if you need to Google something
ty
bright quarry
setting x = -2 would make the term with A be zero leaving us with just B
indigo drift
1/4 ln | x -2 | -1/4 ln |x + 2| ?
bright quarry
youβre welcome
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indigo drift
question
i was watching a video on the cover up method @bright quarry
and this guy is doing it a diff way,
bright quarry
BPRP
indigo drift
bright quarry
π
bright quarry
yea
indigo drift
would his way work in any case?
indigo drift
cuz it doesnt seem like he would get to this value if he did same problem i did
bright quarry
iβll apply it to this problem
bright quarry
$A = \frac{1}{2+2}$
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knief
indigo drift
ohh
bright quarry
and the denominator consists of the other factors when x=1
indigo drift
is there any cons to doing it this way
bright quarry
the factors that arenβt in the denominator of A when in split form
bright quarry
is there any cons to doing it this way
no
itβs the cover method
as riemann was saying
itβs the same thing
no difference
indigo drift
i c i c
bright quarry
just a shortcut in your head
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hardy mulch
@bright quarry πππsave the soul society
bright quarry
what have you tried
bright quarry
yea
indigo drift
cuz
bright quarry
because the degree is the same
bright quarry
whenever the degree of the numerator is greater than or equal to the degree of the denominator
you should
bright quarry
you donβt know long division?
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ember sleet
someone please help me do this assignment π i screwed up and i got so many other assignments to do i dont have time to do this one 
i will pay someone to do it PLEAASEEE
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someone please help me do this assignment π i screwed up and i got so many othe...
night patio
someone please help me do this assignment π i screwed up and i got so many othe...
i think u will find it difficult here to find someone doing it for money lol
ember sleet
i think u will find it difficult here to find someone doing it for money lol
its fine
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brazen gazelle
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vapid lynx
doesnt seem like it has enough info
night patio
unless u can leave it with variables
vapid lynx
well then just raise both sides to the power of 3
night patio
yeah it seems kinda pointless if the intent isj ust to rearrange
brazen gazelle
i think it is rearranging
night patio
well just raise both sides to the power of 3 as bunny suggested
brazen gazelle
how can i do that
vapid lynx
a=b -> 3^a = 3^b
brazen gazelle
ohh y^3=c-x^3?
sacred sapphire
move all logs to one side
vapid lynx
whats the word in english to say this
night patio
exponentiate
vapid lynx
to put both sides in the exponent
night patio
with base 3
vapid lynx
ok
sacred sapphire
use log properties, simplify
brazen gazelle
yes
night patio
3^1 = 3^1 as well
brazen gazelle
yes
night patio
10 = 10
3^10 = 3^10
so if a = b
then 3^a = 3^b
so similarly here
3^(left hand side) = 3^ (right hand side)
sacred sapphire
then 3^a = 3^b
if you ever solved index equations before you might have done this before
sacred sapphire
does that work
you're just moving that log on the right to the left
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graceful zenith
mellow tendon
The question involves some physics
It would certainly use the centripetal acceleration
@graceful zenith
Check this video
https://youtu.be/eGZWVwcaq0U?si=pb6E3NDfTIsyr5j5
It might help you solve the problem
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graceful zenith
<@991661711092355122>
Check this video
https://youtu.be/eGZWVwcaq0U?si=pb6E3NDfT...
ok thx
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leaden thicket
What am I missing here? Specifically at the part where I entered DNE for "does not exist" ?
bright quarry
infinity
leaden thicket
the limit as x approaches 1 from the right of 1/x-1 is undefined because it makes the denominator 0, correct?
ohhh
how do you get that?
bright quarry
id reserve DNE for limits whose left and right hand limits arenβt equal
leaden thicket
oh ok
bright quarry
how do you get that?
itβs just the limit
1/0
as the denominator gets closer to zero the quotient increases to infinity
leaden thicket
ok, I tried putting in 1/0, but it didn't like that answer. I'll try infinity
leaden thicket
as the denominator gets closer to zero the quotient increases to infinity
Oh I see
bright quarry
ok, I tried putting in 1/0, but it didn't like that answer. I'll try infinity
1/0 is undefined
but weβre taking the limit
dapper swift
also it's $x \to 1^+$, so from the right, and so $\frac{1}{x - 1} \to +\infty$
solid kilnBOT
higher's secret brother
bright quarry
youβre welcome
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fathom basin
How does the counter example they gave not satisfy the condition? I tried substituting and simplifying but I couldn't get the result
fathom basin
The condition being equation 15.100
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fathom basin
<@&286206848099549185>
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zinc ginkgo
plug in e^{t^2} for F(t) and find an M such that the inequality holds for all 0 <= t < inf
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valid karma
ok so i have an equation lemme plug it in rq
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ok so i have an equation lemme plug it in rq
valid karma
An athlete throws a ball into the air. The height of the ball can be modeled by the equation h(t) = -16t^2 + 23t + 6 where t is the time in seconds and h is the ball's height in feet. How high was the ball thrown?
now for how high the ball was thrown im trying to figure it out but im not sure if what all im doing is correct
i started by
doing -b/2a
to find x for vertex
and should i have gotten -23/-32
?
thats the first thing am confused on
fervent garden
yes
fervent garden
Itβs fine to have decimals
valid karma
ya ik its just that our teacher hasnt given any decimal problems till now
on the assignments
so i js wanted to check
would the answer be like
14.6
fervent garden
It is 913/64 or approximately 14.266
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echo jasper
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echo jasper
How does on get from mole to mg
Like
i did 2.25x10^26 magnesium atoms times 1mole/6.02x10^23 magnesium atoms so far
ionic pendant
you should look up the molar mass of magnesium (usually on a periodic table)
it's a quantity usually in g/mol
wary raft
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wary raft
Can someone guide me through some questions (four) I have on the last page of my hw
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wary raft
u don't say open
Oh I thought there was a bot command or smth
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knotty leaf
Can someone please help with understanding notation surrounding differentials?
I see a lot of statements like
dv = dx * dy * dz
in my physics textbook, which is apparently something called a differential form, but also not exactly since it's * and not a wedge product?
is
dy = (dy/dx) dx
or
dy = f(x) dx
also a differential form? or is it the same notation reused for communicating something different?
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Can someone please help with understanding notation surrounding differentials?
...
@knotty leaf Has your question been resolved?
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marsh forum
Trying to justify how the first answer is $R^{+}$
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Trying to justify how the first answer is $R^{+}$
solid kilnBOT
Veni, vidi, perii is not f(wai)
marsh forum
so I have to prove $\bigcup_{i\in\N} [0,i+1] \subseteq R^+$ and vice versa
solid kilnBOT
Veni, vidi, perii is not f(wai)
marsh forum
hmm, any interval, [0,a] , a \in \R is a subset of the positive reals
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wind python
For this I was thinking:
$\lim_{z \rightarrow 0} \frac{2(z \cos \theta)^2(z \sin \theta) \cos z}{z^2} = \lim_{z \rightarrow 0} 2z \cos^2 \theta \sin \theta \cos z = 0$
solid kilnBOT
Xide
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zinc ginkgo
,w plot 2x^2y cos(z) /(x^2+y^2)
dry copper
or can I not do it like this
the thinking is right, what you are doing is that you are changing into cylindrical coordinates
but to convert (x,y,z) to cylindrical coordinates (p, theta, z)
we use
$x=\rho , \cos(\theta) \ y = \rho , \sin(\theta) \ z=z$
solid kilnBOT
Emily
dry copper
you see, x is not z cos(theta)
but yeah, you still get 0 as limit
this is just the "right way" to do it
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wind python
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wind python
this is just the "right way" to do it
wait one more q
if I were to do this on a test or something
it would still recieve full marks right?
dry copper
no
wind python
oh because I was double checking on wolfram limit calculator and they did it this way too
symbolab*
dry copper
ow really
dry copper
in this context, you do know what a path is, right
wind python
right
dry copper
just like in 2D, you test (x,y) -> (0,0) with y=mxΒ² for example
it is still just one path
wind python
$x=\rho \, \cos(\theta) \\ y = \rho \, \sin(\theta) \\ z=z$
like Im still gonna change my solution so it matches this but just curious why symbolab did this way too
wind python
oh
dry copper
like Im still gonna change my solution so it matches this but just curious why s...
idk, it just happened to work out lol
cuz the limit actually exists
dry copper
so youre garanteed to get 0 whatsoever path you test
wind python
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wind python
mb aint see u typin
dry copper
alr ty Imma do it like u said
yeah, that is the actual way to do the conversion to cylindrical coordinates
conversion to cylindrical coordinates is bascially the 2D conversion to polar coordinates, but with 3rd dimension in play as well
thats all i wanted to say π