There's nothing special about this function or the problem
#help-13
dawn junco
raw hollow
dawn junco
You did the taylor expansion around x=0 didn't you ?
raw hollow
You did the taylor expansion around x=0 didn't you ?
How do I do it around pi/2
like this?
dawn junco
Yeah I wouldn't go that way personally for the x=pi/2 case but it's possible
First of all this is the taylor series of sin(x) around x=0, so you'd need to compute the one around x=pi/2
Then you take the taylor series of x around x=pi/2 which is pi/2 + (x-pi/2)
And then multiply these two guys
raw hollow
First of all this is the taylor series of sin(x) around x=0, so you'd need to co...
How do I compute the one around pi/2
dawn junco
How do you define taylor series in the first place ? You've surely seen a definition somewhere
My point is just to go straight back to the definition instead of being stuck trying to find a nice shortcut that might not exist
And then you could just apply the definition to x sin(x) itself instead of multiplying both taylor series
Which is what I would do here really
raw hollow
And then you could just apply the definition to x sin(x) itself instead of multi...
Is this the right solution?
dawn junco
I don't like the fact that you're using the same x inside the coefficients of the expansion, it's confusing
Call it a if you want, that's what's usually done, taylor expansion around x=a
So T(x) = (a sin a) + (sin a + a cos a) (x-a) is the taylor expansion of order 1 of x sin x around x=a
raw hollow
So I should use x only in the x-a part?
dawn junco
Then you can plug in a=pi/2 to get what you want
raw hollow
So I should use x only in the x-a part?
.
trim slate
find remainder when 8x^4 - 6x + 13 is divided by x^3 - 2x^2 + x using remainder theorem
dreamy void
find remainder when 8x^4 - 6x + 13 is divided by x^3 - 2x^2 + x using remainder ...
!status
cedar kilnBOT
find remainder when 8x^4 - 6x + 13 is divided by x^3 - 2x^2 + x using remainder ...
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
fallen heath
!show
cedar kilnBOT
Show your work, and if possible, explain where you are stuck.
trim slate
i am on pc
proud vigil
i am on pc
so u have no paper??
ok at least try to factorize x^3-2x^2+x first
also recall what the remiander theorem states
cedar kilnBOT
@trim slate Has your question been resolved?
brazen island
cedar kilnBOT
brazen island
in this question HP will use but idk how to solve it
cedar kilnBOT
@brazen island Has your question been resolved?
steel crest
look at the ratio of the band the flea covers in each move
cedar kilnBOT
@brazen island Has your question been resolved?
brazen island
look at the ratio of the band the flea covers in each move
hmm i reach few steps
is it correct ??
steel crest
yes
cedar kilnBOT
Available help channel!
compact parrot
I am having some trouble with understanding a concept in logic. I've just come across a Wikipedia webpage (https://en.wikipedia.org/wiki/Necessity_and_sufficiency) which explains the concept of necessity and sufficiency in logic.
Now, this line doesn't make sense to me: "For example, in the conditional statement: "If P then Q", Q is necessary for P, because the truth of Q is guaranteed by the truth of P." Shouldn't it be the other way around? When you say "If P then Q", you say that the truth of Q depends on the truth of P. Shouldn't it then be that P is necessary for Q?
limber merlin
is there somone who understand frensh
compact parrot
is there somone who understand frensh
Please stick to your own channel.
frigid dust
is there somone who understand frensh
!occupied
cedar kilnBOT
is there somone who understand frensh
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
dusky cape
Determinate the equation in the form of x^2 + bx + c = 0 knowing that -3 and -2 are the solutions to this equation
dusky cape
no idea how to do this or where to start
dusky cape
uh -5 and 6 but what does this has to do with my problem i am not following
earnest idol
now can you write those in terms of b and c?
fresh quarry
Other way:
You have two unknowns: b and c
And you know 2 roots, put them in the equation and you get 2 equations
2 equations and 2 unknown variables, solve
earnest idol
since you have the equation x^2+bx+ c=0
earnest idol
Other way:
You have two unknowns: b and c
And you know 2 roots, put them in the ...
we have a way shorter method available
fresh quarry
Okay..
solemn quail
we have a way shorter method available
True , but it's good to recognise this possibility because this technique will be useful in many other situations. And once OP has done this once, he'll find the shorter way.
earnest idol
what's the logic behind
wdym logic
dusky cape
wdym logic
like why is -b the sum and c the product. Why is it like this how can you prove that this works
is it a law or..
sharp pike
like why is -b the sum and c the product. Why is it like this how can you prove ...
This is the case if the quadratic is monic, i.e leading coefficient is 1
proper palm
like why is -b the sum and c the product. Why is it like this how can you prove ...
it’s a known formula
dusky cape
it’s a known formula
and that is
earnest idol
like why is -b the sum and c the product. Why is it like this how can you prove ...
for a quadratic equation ax^2+bx+c=0 the sum of the roots is -b/a and the product of the roots is c/a
if you dont know this, a better way would be to do how ash suggested
sharp pike
If your roots are r and s, then the monic quadratic factors into
(x-r)(x-s)
If you expand this, you see that r+s is -b and rs is c
proper palm
in your case you have a=1
stiff vigil
and that is
Vieta’s formula. In your case it is just with a quadratic
dusky cape
Vieta’s formula. In your case it is just with a quadratic
I am not advanced so idk what vieta thinky ur saying sorry:(
until now we learned how to solve ax^2 +bx +c = 0 but not doing it reversed
earnest idol
Other way:
You have two unknowns: b and c
And you know 2 roots, put them in the ...
you can do this
maybe you will learn it in the near future
solemn quail
All of these laws are unnecessarily complicated and unjustified at the moment. Just plug in, solve for two unknowns and see what happens.
stiff vigil
If your roots are r and s, then the monic quadratic factors into
(x-r)(x-s)
If y...
don’t worry, the above is a great explanation of how Vieta’s formula works. in reality it’s just writing it like this and equating coefficients
stiff vigil
All of these laws are unnecessarily complicated and unjustified at the moment. J...
yeah, this might be best suggested
wraith daggerBOT
Simon James B
dusky cape
5 is supposed to positive tho. I don't see why. you just said that b is the sum of the solutions
-3-2 is -5
ohh? Is it -(-5x)
we already had the - so by also puttin in a -5 it makes it positive?
noble flame
If your roots are r and s, then the monic quadratic factors into
(x-r)(x-s)
If y...
$(x-r)(x-s)=x^2-sx-rx+rs$ \
$x^2-(s+r)x+rs$, where $s+r=-b$, and $rs=c$ \
Notice how -b is equal to the sum of the roots, and c is the product of the 2 roots
wraith daggerBOT
AkitoLite
wraith daggerBOT
Simon James B
sharp pike
yes
dusky cape
gosh math is sure hard
sharp pike
I think it's important you understand more of the concepts behind where the vieta's stuff comes from
rather than forcefully memorizing r+s = -b and rs = c
noble flame
99% of the time it's the fault of the teacher I won't lie
sharp pike
If -3 and -2 are the solutions, then you have (x-(-3))(x-(-2)), or (x+3)(x+2), which expands to x^2 + 5x + 6
dusky cape
99% of the time it's the fault of the teacher I won't lie
our teacher showed us how to solve ax^2 +bx + c = 0 using quadratic and delta and stuff but now that i have for homework do this by inversed i am confused lol
dusky cape
can't
noble flame
I didn't see your original question mb
dusky cape
you have to do it from the answer to the original equation
cuz like why does she show us how to solve this equation but not to do it like in my problem
dusky cape
but we are supposed to do it for homework of course. Like i am a genius and i have to guess how to do it
noble flame
Just needs deduction, which I assume you haven't COMPLETELY understood exactly how the formula works
dusky cape
Just needs deduction, which I assume you haven't COMPLETELY understood exactly h...
for sure i have not i don't even understand the point of delta yet lol just i know its formula haha
ty
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
jade tundra
I have this question and I want to verify if it is true or false: If X is an infinite set, then it exists a surjection g:P(X) -> R.
jade tundra
My claim is that it is true. I have separated two cases: X is countable. Then Card(X) = Card(N) -> Card(P(X)) = Card(P(N)) = Card(R). Therefore, there is a bijection between P(X) and R
The problem is when X is not countable
cedar kilnBOT
@jade tundra Has your question been resolved?
jade tundra
<@&286206848099549185>
rocky harness
The problem is when X is not countable
Well if its not countable, and its infinite... will its cardinality be > or < N?
jade tundra
it will be > Card(N) since Card(N) is the smaller infinite cardinal
rocky harness
And do yk cantors theorem?
jade tundra
Yes, but how do I apply it here?
rocky harness
Then you can contain N in X,(via an injection), so P(N) is contained in P(X). Am i missing something?
|P(X)|>=|P(N)| =|R|, so you have a surjection to R
Actually you didnt even need cantors theorem
jade tundra
is f: N -> X inyective?
rocky harness
Well if |N| <= |X| that means there is an injection from N into X
jade tundra
I don't need to separates two cases, do I?
rocky harness
No,
jade tundra
Is there a proof of this implication: |X| > |N| then |P(X)| >= |P(N)||?
rocky harness
I mean, i can easily make one? Because $|X|>|N|\implies$ there is an injection $f$ from $N$ into $X$. Now my claim is the function $f':P(N)\rightarrow P(X)$ by $f'(S) = {f(s) | s \in S}$ is an injection. if $f'(S)=f'(T)$ then for every $s \in S$ there is $t \in T$ such that $f(s)=f(t)$. Since $f$ is injective, $s=t$. So $S \subseteq T$. Likewise for every $t \in T$, there is $s \in S$ such that $f(t)=f(s)$. Since $f$ is injective, $t=s$, so $T \subseteq S$. i.e $S=T$. Thus showing $f$' is an injection, thus $|P(N)|\leq |P(T)|$
jade tundra
Thank you!!
wraith daggerBOT
4573r01d|)d357r0y3r 45²
jade tundra
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
oblique flare
so I just want to check
is cos(3x)=4cos^3(x)-3cos(x) and
sin(3x)=-4sin^3(x)+3sin(x) ?
oblique flare
ok thx
oblique flare
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
crimson sedge
Hello
crimson sedge
Anyone willing to analyze a bunch of questions I did and my answers, I just want to see if im correct
you can do as many as your willing
buoyant latch
!da2a
cedar kilnBOT
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
crimson sedge
Tell me please if my answers are correct, its many questions but answer as many as your willing
crimson sedge
k
The answers
https://docs.google.com/document/d/1hcXObltWUq-bEMsAGkxiIixGCUatj9Ys/edit?usp=sharing&ouid=100790381489209099855&rtpof=true&sd=true
The questions
https://photos.app.goo.gl/jTeNJMRbnNZBbvtj9
frigid dust
The answers
https://docs.google.com/document/d/1hcXObltWUq-bEMsAGkxiIixGCUatj9Ys...
!ss
cedar kilnBOT
The answers
https://docs.google.com/document/d/1hcXObltWUq-bEMsAGkxiIixGCUatj9Ys...
Please post images (such as PNGs or JPGs) of the question rather than other filetypes such as PDFs which have to be downloaded. Non-image downloads can potentially contain viruses or other security risks.
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
@crimson sedge Has your question been resolved?
dire geode
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
limber merlin
Mine
dire geode
!da2a
cedar kilnBOT
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
dire geode
oh french uhhh there might be french speakers around
limber merlin
Dont u understand it??
dire geode
no comprende french
yo no comprende french
cedar kilnBOT
@limber merlin Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
rustic glacier
cedar kilnBOT
rustic glacier
how do i make my purple moon spin around and around
ive tried with my highlighted equation
butt
vague sparrow
can you send the desmos itself
rustic glacier
how
if you have access pls dont destroy i have faith in u
is on student desmos
u mean this: (x-(3+5\cos(\theta)))^{2}+(y-(3.5+5\sin\left((\theta)))^{2}<0.2\ \right)
cedar kilnBOT
@rustic glacier Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
spark trout
i need some intuition here
cedar kilnBOT
i need some intuition here
coral jewel
a linear map
hollow trail
depends on how you interpret the matrix itself:
- as a linear map (can visualize how it affects a sample object or vectors)
- as a system of linear equations (intersection of planes)
- as a bilinear form (only for symmetric matrices)
- as a tensor (e.g. the stress or strain tensors have their own visualizations)
cedar kilnBOT
cedar kilnBOT
Available help channel!
slim heath
can anyone help me with this question?
cedar kilnBOT
can anyone help me with this question?
kindred storm
OK, so Mike has as many brothers as sisters.
slim heath
yes
kindred storm
If Mike had 6 brothers, how many boys would be in the family?
slim heath
7
kindred storm
If Mike had 3 sisters, how many girls would be in the family?
slim heath
3
kindred storm
OK, so let's say b = boys, g = girls.
Mike has as many brothers as sisters.
Mike's number of brothers is b - 1.
Does it make sense why?
slim heath
yes
kindred storm
OK, so b - 1 = g.
Do you see how I got that equation from "Mike has as many brothers as sisters."?
kindred storm
Right.
slim heath
okay i see
kindred storm
How would "Kate has twice as many brothers as sisters." be written as an equation?
kindred storm
Right.
So, we have:
b - 1 = g
b = 2(g - 1)
So, we can use substitution to solve it.
In the first equation, b - 1 = g, so we can replace g in the second equation with (b - 1).
b = 2((b - 1) - 1)
slim heath
i see
kindred storm
Nope.
kindred storm
How did you get from b = 2b - 4 to 0 = 2b - 4? What happened to the b on the left side?
kindred storm
Right. What about the other sentence?
kindred storm
Right, so we checked our answer.
slim heath
can i ask you one more thing?
kindred storm
OK.
slim heath
the answer says that A does not work because it would mean that mike and kate are only children
and that 0 sisters means 0 brothers
what does that mean??
how does that make sense?
kindred storm
Well, if the number of girls was 2, then Kate would have a sister.
slim heath
yes
kindred storm
Plus Mike would be at least one brother.
slim heath
so theyre not only children
kindred storm
So, at least 3 people.
kindred storm
The people who wrote that were probably mistaken.
slim heath
but am i correct in saying 2 girls would mean mike would have 2 brothers
and then it doesnt work because kate has 1 sister but 3 brothers
kindred storm
Yes, from the "Mike has as many brothers as sisters."
slim heath
okay thanks chai t rex
kindred storm
You're welcome.
Oh, they probably thought the 2 in the answer meant total children.
kindred storm
Yes.
cedar kilnBOT
@slim heath Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
rancid cairn
I think I solved this incorrectly?
cedar kilnBOT
I think I solved this incorrectly?
rancid cairn
There shouldn't be x=0 (not sure...)
Oop nvm I incorrectly expanded ln
My bad
.close
cedar kilnBOT
peak minnow
couldve just done this @rancid cairn
rancid cairn
. reopen
peak minnow
.reopen
cedar kilnBOT
✅
rancid cairn
couldve just done this <@838305683015204874>
Oh yeah, I realised I used ln incorrectly 😭
peak minnow
that too but ln isnt useful right now here
rancid cairn
But tysm makes sense
cedar kilnBOT
cedar kilnBOT
Available help channel!
sweet phoenix
How to do 9i
cedar kilnBOT
How to do 9i
kindred elm
what have u tried?
idle flare
How to do 9i
Range for it to be valid will only depend on 9-2x^2 and 9-2x^2> or =0 for it to be valid
warm apex
√(5+2√6)
warm apex
how to proceed
opaque root
how to proceed
What have you tried?
warm apex
What have you tried?
nothing, i dont understand how to even proceed
opaque root
Well you have to know something, there is no way you know nothing or didnt do any similar exercises
Because then you are not ready for this exercise
You gotta give me something else than “nothing”
warm apex
I tried googling and it gave me
√2 + √3 because of "(a+b)²" but i dont understand how that could of be so i tried
√(5+2√6) = a²+2ab+b²
square both sides
5+2√6=a⁴+2(ab)²+b⁴ then i eventually realize that if the exponent were to go even higher then it would be harder to calculate
olive gust
$ \sqrt{5 + 2\sqrt{6}} $
warm apex
Well you have to know something, there is no way you know nothing or didnt do an...
i have done some square root exercises but not this one
olive gust
$\sqrt{5 + 2\sqrt{6}} $
warm apex
a square root inside of a square root is hard
olive gust
why isnt the bot working
queen ice
$\sqrt{5 + 2\sqrt{6}}$
wraith daggerBOT
FirstNameLastName
warm apex
$\sqrt{5 + 2\sqrt{6}}$
wraith daggerBOT
𝐵𝒶𝒷𝓎𝐹𝑜𝓍𝒢 💖
warm apex
why isnt the bot working
there was a space between "} $"
olive gust
there was a space between "} $"
ohh alr ty
olive gust
**𝐵𝒶𝒷𝓎𝐹𝑜𝓍𝒢 💖**
this is ur question?
warm apex
this is ur question?
yes
warm apex
You have to notice that 2sqrt6 is 2 * sqrt2 * sqrt3
yes i do know bout that but i dont understand how that could of help
opaque root
Is just a fact of practice
warm apex
And that 5 = 2+3
Oo
opaque root
Then use (a+b)^2
olive gust
alr let √(5 + 2√6) = √a + √b where a and b are rational numbs and square both sides
5 + 2√6 = (√a + √b)^2
and expand the rightside: 5+ 2√6 = a + b + 2√(ab)
warm apex
OH
olive gust
and the rational and irrational
a + b = 5
2√(ab) = 2√6
warm apex
that makes more sense
olive gust
Good!
and simplify the sec equation divide by 2 to get √(ab) = √6 and then squaring this gives ab = 6
warm apex
then make ab=6,a+b=5 the variables fit the condition in where
a=3
b=2?
warm apex
Because after finding the variables we could substitute now
√(5+2√6)=√2+√3
is this correct?
warm apex
ight tyvm
olive gust
yw!
warm apex
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
raw hollow
How do I tell if they're pairwise tangent? What do I need to check here?
frigid dust
they both have tangents at that point
but im not sure if they want those tangents to be equal
pastel vault
but im not sure if they want those tangents to be equal
yes I think this is what they mean
the curves are tangent to each other
frigid dust
then that aswell
raw hollow
So in other words they have to be differentiable at 1 and x^2 + ax + b = cx - x^2
is that right?
Are their derivatives also equal cause I couldn't solve it from just that
frigid dust
👍
weary ingot
,w y'' -2y' + y = 0
cedar kilnBOT
,w y'' -2y' + y = 0
wraith daggerBOT
weary ingot
not sure where xe^x comes from
i created the characteristic equation $r^2 - 2r + 1 = 0$
wraith daggerBOT
woomy
weary ingot
factoring: $(r-1)^2 = 0$
wraith daggerBOT
woomy
weary ingot
so wouldnt the solutions be y = Ce^x ?
crimson delta
multiple roots means you also put x^ke^lambda x
fallen heath
How do I tell if they're pairwise tangent? What do I need to check here?
||basically, 0.5y = x + 0.5a(x + 1) + b is equiv to 0.5y = 0.5c(x + 1) - x|| oop srry
weary ingot
multiple roots means you also put x^ke^lambda x
always?
fallen heath
btw not necessarily
weary ingot
also dont i only have one root
crimson delta
its a double root
fallen heath
Note that y = xe^x also satisfies y" - 2y' + y = 0
crimson delta
if you had (r-1)^3 you would take e^x, xe^x, x^2e^x
fallen heath
And so, the solutions must be a linear combination of e^x and xe^x
weary ingot
multiple roots means you also put x^ke^lambda x
wait so
if the roots of the characteristic equations are r1, r2, ..., rn
then the solutions are
crimson delta
I should have said repeated instead of multiple
weary ingot
ohhh okay so repeated right
also if roots are repeated then every root is the same right?
like if r1 = r2 then r1 = rn
n being the order or the polynomial
thus with characteristic equations i have 2 cases:
- distinct roots:
C1e^(r1 x) + ... + Cne^(rn x) - repeated roots:
C1e^(r x) + ... Cn x^n e^(r x)
crimson delta
you could have (r-1)^2(r-2)
1 is repeated, 2 isnt
e^x, xe^x, e^(2x) are the solutions (and their combinations)
(also note the degree of the x^k is at most 1 less than the relevant power in the polynomial)
cedar kilnBOT
@weary ingot Has your question been resolved?
polar root
Can someone help with this?
cedar kilnBOT
Can someone help with this?
polar root
I’m not sure how to calculate it
cedar kilnBOT
@polar root Has your question been resolved?
cedar kilnBOT
@polar root Has your question been resolved?
fathom nimbus
this questions seems too vague
cedar kilnBOT
this questions seems too vague
fathom nimbus
or is there something that im missing?
twilit bison
I think they want the average per year of the gray line
fathom nimbus
so days in 2010, 2012, 2014, 2016 and then divide by 4
or a better average would be to calculate 2011, 2013 and 2015 too and divide by 8?
worldly chasm
It looks like there are 4 data points
Rather than 7
So you would use the 4 data pt
The lines are a bit misleading, because they don't represent anything, they just connect the 4 data points visually
cedar kilnBOT
@fathom nimbus Has your question been resolved?
dull sky
give me some trigonometry proof questions to solve
cedar kilnBOT
give me some trigonometry proof questions to solve
frigid dust
!occupied
cedar kilnBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
blazing zephyr
prove that $\cos^2(10)+\cos^2(50)-\sin(40)\sin(80)=\frac{3}{4}$
wraith daggerBOT
skissue.in.a.teacup
blazing zephyr
i mean is this a proof question
cedar kilnBOT
@dull sky Has your question been resolved?
quartz coral
i mean is this a proof question
not really
it's more of
prove the trigonometric identity
type of question
you just use product to sum, sum to product, identity for $cos^2(x) = \frac{1+cos(2x)}{2}$
wraith daggerBOT
alex <3
quartz coral
and simplifying
blazing zephyr
how will you simplify it
near lantern
So im working on this question, i understand it untill they just take away the 1 randomly, can someone explain why you can just do that? i understand you can stripe off the x.
near lantern
the 1 with the circle is the one i mean
young portal
Cross multiplication, then divide the whole equation by tan(20°)
near lantern
OH I THINK I GET IT
young portal
ptan(20°) = tan(40°)
[ptan(20°)]/[tan(20°)] = [tan(40°)]/[tan(20°)]
p = tan(40°)/tan(20°)
near lantern
nvm i dont get it
near lantern
ptan(20°) = tan(40°)
[ptan(20°)]/[tan(20°)] = [tan(40°)]/[tan(20°)]
p = tan(40...
what happens on the second row
young portal
what happens on the second row
Divide both side by tan(20°) so that p will be left alone in the left side of the equation
cedar kilnBOT
@near lantern Has your question been resolved?
cloud thorn
hello
cloud thorn
if we had a square that's 1km by 1km then what is the surface area of this square?
frigid dust
if we had a square that's 1km by 1km then what is the surface area of this squar...
1km^2
pearl arrow
if we had a square that's 1km by 1km then what is the surface area of this squar...
1km bro
but a square
cloud thorn
1km^2
but if we said that 1km is 1000 meters and 1000 m x 1000 m = 1 000 000 meters square and 1 000 000 meters square is not 1km square right?
frigid dust
but if we said that 1km is 1000 meters and 1000 m x 1000 m = 1 000 000 meters sq...
yes, it is
cloud thorn
wut
frigid dust
1km^2=1.000.000 m^2
cloud thorn
how
frigid dust
,w 1km^2 to m^2
wraith daggerBOT
frigid dust
if its 1km:1000m
and the km is squared
then we take the conversion factor twice
1km^2:1000000m^2
1m:100cm
1m^2:10000cm^2
cloud thorn
1m:100cm
1m^2:10000cm^2
i'm still confused lol could you link some explain like i'm five article
calm wharf
hello
slate lintel
,rccw
wraith daggerBOT
calm wharf
in this pqrs is a cyclic quad
/u can see p+r=180 and q+s=180
how to find measure of angle p and q separately
plss
slate lintel
probably by measuring it
calm wharf
how tho
bro no diagram is given we have to draw on our own and write
...
broo T-T Where did u go
slate lintel
um, what else is on the page?
wraith daggerBOT
calm wharf
yup
slate lintel
making exact copies of those angles and cutting them out
calm wharf
the question is, u have a cyclic quad
and the sum ofopposite side is 180
find each angles ;--;
slate lintel
uhh no i think it's asking you to find the measure of angle P
like specifically the angle P that they gave you above
sly swan
what is tracing paper?
calm wharf
damn its to much foe me brane
calm wharf
what is tracing paper?
see through paper
calm wharf
let me do that
damn u may be right on this one
one sec
ahh shit i am dumb
thanksss guysss
very much
i write it down
thanks again
for helping my dumb ass
:))
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
rancid cairn
First part of the question pls
cedar kilnBOT
First part of the question pls
rancid cairn
I got 2 angles, how do I decide which one it is
cerulean sail
“The second one”
cerulean sail
First part of the question pls
rancid cairn
OH
Bro I swear I looked at the graph 4 times but didn't see the first intersection
😭
Tysm
cerulean sail
Sometimes it’s like that until it’s pointed out 
dire geode
try 5 times next time /s
rancid cairn
True 🥲
rancid cairn
try 5 times next time /s
😭😭 believe it or not I watched a video twice on this part and still didn't get it
rancid cairn
or maybe the hard way is failing the exam
Not the right time to say this 😞
cerulean sail
Best of luck for it 
hope it goes well 
dire geode
i have the utmost skill of saying things at the wrong time
cedar kilnBOT
cedar kilnBOT
Available help channel!
cinder belfry
Heyyy
cinder belfry
Limit[(40)Divide[(40)1-Sqrt[x-1](41),cos(40)Divide[π,x](41)](41),x->2]
Damn, I copied it from Wolfram, but this doesn't look quite right
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
cinder belfry
cedar kilnBOT
cinder belfry
heyall, I'm back cuz l' H doesn't help. Help. Im desperate. This is so embarassing. wtf. hwo did I get accepted here wtf wtf
dull oxide
heyall, I'm back cuz l' H doesn't help. Help. Im desperate. This is so embarassi...
!show
cedar kilnBOT
heyall, I'm back cuz l' H doesn't help. Help. Im desperate. This is so embarassi...
Show your work, and if possible, explain where you are stuck.
simple minnow
if l'H wont work then you have to use trig to get rid of function that cause the format of undefined
dusk finch
im pretty sure lhop should work
cinder belfry
!show
This message literally made me realize that I differentiated (is that what you call it in English?) as a whole, instead of just top and bottom separetely. Sorry yall, I'm cooked, but I'm sure you understand if you've been through the maths hellhole. I'll get back to yall soon.
dusk finch
!nohopital
why?
dull oxide
is that what you call it in English?
yes
clear ember
This message literally made me realize that I differentiated (is that what you c...
3rd time’s the charm
simple minnow
This message literally made me realize that I differentiated (is that what you c...
yo u can multiply the deno with sin(pi/x)
cinder belfry
real, that's my mindset going into these finals
dull oxide
This message literally made me realize that I differentiated (is that what you c...
This happens to people more than you would think
simple minnow
yo u can multiply the deno with sin(pi/x)
and divide it with sin(pi/x)
it will make cot(pi/x) and then put your limits
dusk finch
it will make cot(pi/x) and then put your limits
cot(pi/2) is 0, i dont see how it would help
fallen heath
$-L = \lim_{t \to 0} \frac{\sqrt{t + 1} - 1}{\sin \frac{\pi t}{t + 2}}$
wraith daggerBOT
Arya
fallen heath
is this so difficult to evaluate ;-;
simple minnow
cot(pi/2) is 0, i dont see how it would help
yeah ,,,, (i am drunk)
dusk finch
is this so difficult to evaluate ;-;
It's not, simple lhop makes it easy :]
fallen heath
$\lim_{t \to 0} \frac{\sqrt{t + 1} - 1}{\sin \frac{\pi t}{2(t + 2)}} = \frac{1/2}{\pi/4} = 2/\pi$
dire geode
did you already try multiplying by the conjugate
wraith daggerBOT
Arya
simple minnow
sine becomes zero
fallen heath
idts it's too difficult to evaluate this with just the basics
why'd you promote l'hop T-T
dusk finch
why'd you promote l'hop T-T
Differentiating simple functions isnt difficult either
fallen heath
but that's not how limits should be practiced ._> ruins their algebraic manipulation skills
that's how people get into DE classes and need assistance with rationalization
dusk finch
but that's not how limits should be practiced ._> ruins their algebraic manipula...
ig the advantage is that it improves differentiation skills
dusk finch
that's how people get into DE classes and need assistance with rationalization
this limit is hard enough to use lhop without any shame imo
dire geode
argue somewhere else. neither of you are helping sanity with the l'hopital conversation.
let them decide whether or not they want to/can use l'hopital and go from there
fallen heath
I hope you got this ^-^
-L = 2/pi
cinder belfry
This was the original for anyone interested. I am literally fried, so even though I got 1/pi instead of -1/2pi, imma take it as a win and take a nap
dire geode
yeah ,,,, (i am drunk)
or just leave since they're drunk
fallen heath
cedar kilnBOT
cinder belfry
.reopen
cedar kilnBOT
✅
cedar kilnBOT
fallen heath
btw ping if you're discussing 
tmrw
cedar kilnBOT
Available help channel!
formal patrol
cedar kilnBOT
formal patrol
dont know where to start
fair geyser
formal patrol
108
upper ruin
You have a trapezoid on the left and a triangle on the right
formal patrol
and 84 for the triangle
fair geyser
and there's a small triangle left
fallen heath
,calc 108 + 72 + 84
wraith daggerBOT
Result:
264
cedar kilnBOT
humble karma
The area of a circle is not 2*pi*r
formal patrol
oh
humble karma
That's the circumference
formal patrol
A = pi * r^2/2.
humble karma
Yep that's the area of the semi-circle
formal patrol
56.52
formal patrol
6x6 is 36, not 42
my bad i did another problem with 7
with this one it would be 11 x 3.14
then 5 x 11
i got 89.54
digital cliff
hm why?
lets condider the rectangular portion, what would the external perimeter of that section be?
you seem to have somewht combined perimeter and area in your calculations
digital cliff
ah, it happens, break it down
formal patrol
ah, it happens, break it down
am i right?
28.27?
@digital cliff
for the semi
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
novel bolt
What does the +2 do
cedar kilnBOT
What does the +2 do
dire geode
,tex .vert trans
wraith daggerBOT
riemann
cedar kilnBOT
cedar kilnBOT
Available help channel!
dire radish
Integrals By Parts
cedar kilnBOT
Integrals By Parts
dire radish
How do i properly select which one to be u and which to be dv?
is there a guideline i can follow
flint plinth
i think either way would work in this case, have you tried it?
flint plinth
you'll have to integrate by parts twice
dire radish
brauh
dire geode
tabular is just IBP
dreamy void
she's integrating by parts twice as we speak. don't interrupt.
i am sorry your excellence
dire geode
or do you mean you made a new method that does two IBP at the same time 
that'd be legit
flint plinth
isnt it easier
exp and sin are surely two of the easiest functions to integrate or differentiate, this isn't gonna be hard
dire geode
~~but it's so much more efficient to think of a completely new method that solves all double integration by parts problems first ~~
dire radish
or do you mean you made a new method that does two IBP at the same time <:pandat...
idk i talking about this https://www.youtube.com/watch?v=Yyic5aaXGaw&ab_channel=TheOrganicChemistryTutor
dire radish
ic
flint plinth
i was today years old when i first heard this called the "tabular method"
dire geode
a sign of a mature student. it's just a crutch
dreamy void
,texsp $\int e^x \sin(\pi x) : dx = \int \frac{1}{2}ie^{x-i \pi x}-\frac{1}{2}ie^{x+i\pi x} : dx$
wraith daggerBOT
anti-algebraist 𝔸dωn𝓲²s
dire geode
show off
cedar kilnBOT
Available help channel!
minor kelp
.reopen
marble notch
Hellooo! I have a probability question. So the other day I cycled somewhere and coincidentally parked my bike directly next to the person I was meeting. There were 5 different areas to put bikes, each with 15 racks. What is the probability that i put my bike right next to hers? I assume it's as simple as (1/5)*(1/15), so 1.33 percent chance. But my mate thinks the chance is 2.66, which is suspiciously double my answer, which I assume they doubled because there's 2 of us but I don't think that how probability works. It would be less if anything. I'm sticking to my 1.33 percent, does someone agree?
wraith daggerBOT
Result:
74
,calc 1/74
wraith daggerBOT
Result:
0.013513513513514
@marble notch Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
faint otter
so i know this is probably very simple but i want to relearn how to find what percentage of a number is a number, as in "what is 15 a percentage of 60", sorry if i havnt worded this properly
faint otter
(Example)
i need to find what percentage of 1920 is 1440
thorny drift
so i know this is probably very simple but i want to relearn how to find what pe...
(15/60)*100
so 15 is 25% of 60.
thorny drift
(Example)
i need to find what percentage of 1920 is 1440
same for this: (1440/1920)*100
So, 1440 is 75% of 1920.
does this help?
cedar kilnBOT
@faint otter Has your question been resolved?
grim thistle
cedar kilnBOT
grim thistle
i need help with part b and c
with part b on when the symbol is equal to 4
i got two equations
x1 + 3x2 = 0 and 2x1 + 6x2 = 0
slate lintel
sure
so that's really one equation
but yeah you can now make an eigenvector for that value
grim thistle
but yeah you can now make an eigenvector for that value
i tried but everytime i do it it's like a guessing game sort of
idk what i did but i got (-3 , 1) but the answer is (3, -1)
how can i get it 100% of the time
slate lintel
well i mean those are the same
in that they're both eigenvectors
idk what the standard is but those are in the same direction
sharp lotus
there's really an infinite number of eigenvectors for that eigenvalue, one of the two variables is kind of a free variable so you can give an expression for what all possible eigenvectors are for that eigenvalue in terms of that free variable
grim thistle
there's really an infinite number of eigenvectors for that eigenvalue, one of th...
how do i utilise the free variable
do i solve for x1 or x2 first?
and which equation do i start off with
slate lintel
you can't really solve for either one
you can choose x1 to be whatever you want, and x2 will follow
slate lintel
if v is an eigenvector (with value lambda) then 2v, 3v, 4v, -v, etc are all also eigenvectors
you can show this looking at the defn of eigenvector
grim thistle
but then i get x2= -1/3
slate lintel
yep
grim thistle
if v is an eigenvector (with value lambda) then 2v, 3v, 4v, -v, etc are all also...
so there is no right answer right?
sharp lotus
you can use either
so for example you have x1 + 3x2 = 0 gives you
x2 = -x1/3
so you can say any vector of the form
(x1, -x1/3) where x1 is any real number (assuming that's your field) is an eigenvector
slate lintel
(personally i'd say just writing down one example is fine since it's assumed that you can scale it by whatever)
grim thistle
i do have a question however
lets say i solve the first one using x1=1
for the second one when lamba is 11
do i have to use the same method?
and make x1=1?
slate lintel
"x1" is a concept that only exists in the hearts and minds of lambda=4
you will get the same set of answers regardless of what you choose as your free variable
grim thistle
ah i was going to say
slate lintel
and there will always be a free variable
grim thistle
i was so confused for a sec 😭
thank you so much again my friend 🫶
have a lovely day :)
slate lintel
you can show this looking at the defn of eigenvector
you too. prove this btw
grim thistle
you too. prove this btw
prove it!?
slate lintel
yes
grim thistle
i'm not that advanced yet 🥲
slate lintel
you can do it
sharp lotus
if v is an eigenvector (with value lambda) then 2v, 3v, 4v, -v, etc are all also...
btw spoiler: the set of eigenvectors always forms a vector space :p this thing hayley said relates to that
slate lintel
given matrix A, eigenvalue lambda, and eigenvector v, show that 2v is also an eigenvector with eigenvalue lambda
grim thistle
i had a vector calculus exam the other day and i didn't even know what a vector field was
grim thistle
given matrix A, eigenvalue lambda, and eigenvector v, show that 2v is also an ei...
it's just a scalar multiplier right??
slate lintel
it is a scalar multiple yes
remember, v is an eigenvector of A if there's a λ where Av = λv
sharp lotus
intuitively you can think: when i multiply this vector by the matrix, i get back the same vector, multiplied by some constant
grim thistle
intuitively you can think: when i multiply this vector by the matrix, i get back...
how do i prove it though
proof by contradiction?
slate lintel
no, it's a pretty direct proof
grim thistle
oh 😭
slate lintel
you just need to show that (2v) is also an eigenvector of A
sharp lotus
Consider A(2v)
grim thistle
so i need to show A(2v) = lambda (2v)?
sharp lotus
indeed
grim thistle
with A(v) = lambda*v
if we multiple both with 2?
A(2v) = lambda (2v)
i'm stuck here now 😭
sharp lotus
so i need to show A(2v) = lambda (2v)?
well think about how you can move the 2 around within these kinds of expressions
slate lintel
i mean basically yeah it's pretty simple, you just need to believe that 2(Av) is equal to A (2v) which you probably already knew
grim thistle
i see
the exam is in 12 hours
hopefully i can remember this
oh yeah part c sorry
sharp lotus
i see
if you replace 2 with c, some arbitrary constant, and apply the same idea you've now proven that the set of eigenvectors of this particular eigenvalue for this matrix is closed under scalar multiplication. you could also prove that its closed under vector addition and now you've proven that this set is a vector space
grim thistle
if you replace 2 with c, some arbitrary constant, and apply the same idea you've...
ah yes
sorry it's taking me so long to understand
it's 2am rn 😭
cedar kilnBOT
@grim thistle Has your question been resolved?
slow solstice
For this question the answer is sin45 x sin60 but I was wondering if this is a logical way of doing it and if so why or if its just coincidence that it multiples to become the answer
slate lintel
no yeah that makes sense
slow solstice
is it because sin theta is in between both of those angles ?
slate lintel
not really in between as much as like...... that triangle is like... the combination of those triangles?
45º is the wedge angle, and 60º is the side angle. theta is like the two of them combined
cedar kilnBOT
slow solstice
you can show it by using SOH a bunch of times to get the ratios right
yes that is what I did originally I solved for the sides but that took a while
cedar kilnBOT
Available help channel!
dire radish
sorry i asked this question before but, just to be clear
cedar kilnBOT
sorry i asked this question before but, just to be clear
dire radish
this is a recursive pattern right?
slate lintel
yea
slate lintel
one of those integrals where you turn it inside out like a shirt
dire radish
and i dont see any examples on how to do them (im probably blind but whatever)
slate lintel
how do i deal with them? i already did integration by parts twice
and you probably got back (a bunch of stuff) - (the original integral)
let $I = \int e^x \sin \pi x \dd{x}$
wraith daggerBOT
hayley, who shakes the world
dire radish
okay
slate lintel
do your IBP on the right, then you'll find that I shows up in there again
then solve for I
dire radish
do your IBP on the right, then you'll find that I shows up in there again
what does IBP stand for-?
is that tabular
slate lintel
oh integration by parts sorry
dire radish
no worries sorry i shouldve cleared it up
Here’s what I have so far, sorry for the messy handwriting just not sure where to go from here since it integrates repeatedly or something
wraith daggerBOT
hayley, who shakes the world
dire radish
yes
slate lintel
$I = e^x \sin\pi x - \pi\int e^x\cos\pi x$
wraith daggerBOT
hayley, who shakes the world
slate lintel
$I = e^x\sin\pi x - \pi\lp e^x\cos\pi x - \pi \int e^x \sin\pi x\rp$
wraith daggerBOT
hayley, who shakes the world
slate lintel
i think i did that right
$I = e^x\sin\pi x - \pi\lp e^x\cos\pi x - \pi \blue{\int e^x \sin\pi x}\rp$
wraith daggerBOT
hayley, who shakes the world
slate lintel
see how the original integral shows up in there?
dire radish
yeah... how does that work?
slate lintel
oh it's + on the inside, not - my mistake
slate lintel
i didn't bring it in there it just showed up on its own
dire radish
oh
slate lintel
just like it showed up for you
anyway now we can replace it with I
$I = e^x\sin\pi x - \pi\lp e^x\cos\pi x + \pi \blue{I}\rp$
wraith daggerBOT
hayley, who shakes the world
slate lintel
and you should be able to sort it out from here
dire radish
**hayley, who shakes the world**
isolate I on one side
and solve for I
then thats my answer
?
cedar kilnBOT
slate lintel
this is really lame (the problem)
it's kind of a trip, it's called circular integration by parts
dire radish
never heard of it
slate lintel
dire radish
cedar kilnBOT
Available help channel!
karmic cairn
how do i proceed from here? it's a non-linear system with trigonometric functions
cedar kilnBOT
@karmic cairn Has your question been resolved?
karmic cairn
<@&286206848099549185>
dire geode
Should show the original question and all work leading up to this point
karmic cairn
Should show the original question and all work leading up to this point
this is all i have lol
i just need to solve the system
is that even possible? to go from this step to theta 2 and 3 in terms of A, B and C
solution does not have to be unique
dire geode
this is all i have lol
Where did the equations come from then
karmic cairn
Where did the equations come from then
my friend sent it to me lol
dire geode
Then tell him to send you the original question
Or tell him to open his own help channel and do it himself
karmic cairn
ok
karmic cairn
is that even possible? to go from this step to theta 2 and 3 in terms of A, B an...
but out of curiosity, is it possible to go from this to here
also he's busy rn, so might have to resend later
hoary charm
For a Gaussian prime z, do we consider the trivial multiples (-z,iz,-iz) seperate gaussian primes?
cedar kilnBOT
For a Gaussian prime z, do we consider the trivial multiples (-z,iz,-iz) seperat...
@hoary charm Has your question been resolved?
worldly chasm
We consider 1, -1, i, -i to be a units. Factorization is unique up to units. So these are also prime.
hoary charm
We consider 1, -1, i, -i to be a units. Factorization is unique up to units. So ...
Ah in that case if I wanted to count all the gaussian primes in a radius of 10 from the origin
Ive figured out there are 12 prime gaussian norms up to 100 with 2 gaussian primes each, with the exception of (1 + i) with norm 2.
Aside from that there are 2 non prime norms 9 and 49 which are perfect squares of the integers 3 and 7 but we cant have norms of 3 and 7 so they are also Gaussian primes.
So 11 gaussian primes with 2 representations
And 3 with 1 representation.
Then accounting for all the trivial multiples of each representation we get
1124 + 3*4 = 100?
hasty pollen
hi idk where to start i dont have working out i just know that i hate dst questions and yeah! 😊😊😊
crimson sedge
The function is esetnailly a piecewise function
There are two different "ways" the man can travel
- at a speed of 2 kmph for 45 minutes
- at a speed of 4 kmph for 30 minutes
with this logic
--> a should give you the velocity of the man in teh 45 minutes time frame
--> c should be 45 minutes
similiarily try to figure out b, c, and e
figuring out d might be a challenge
but I can give you a hint for that