I mean my latex skill problem
#help-42
lucid oxide
XD
Anyways yea, what i mean is the range is [0,pi] then after sub it its undefined
Well idk anyways XD
A damn it
potent lotusBOT
Catto Saint
neon sage
we can use arctan(a) - arctan(b) ig but im not sure it'll lead to anything
lucid oxide
we can use arctan(a) - arctan(b) ig but im not sure it'll lead to anything
I mean there is a /L there
So we cant just
Remove it
neon sage
yeah we cant
lucid oxide
So yea Idk how to continue this
But i guess it has to deal with something about $\alpha$ and $\beta$ just that idk what to do ( Or if my intergration method has problems which I dont think so cus its fluent to do so
potent lotusBOT
Catto Saint
lucid oxide
yeah we cant
Any ideas?
neon sage
Any ideas?
give me a minute im trying things out. no confidence that it's gonna work tho 
neon sage
Yeah I'm out of ideas. Don't see how alpha and beta are ever going to disappear
there's nothing else to the question right?
lucid oxide
Yeah I'm out of ideas. Don't see how alpha and beta are ever going to disappear
Hmm nothing else
lucid oxide
there's nothing else to the question right?
I provided every possible thing
neon sage
**Catto Saint**
consider if we pick a= 0, so that we have L = 1
the expression still depends on alpha and beta
lucid oxide
consider if we pick a= 0, so that we have L = 1
I doubt we can pick a now, cus we gonna prove stuff related to the value of a at part c
neon sage
maybe some mathemagician and stroll by and explain this lol
neon sage
wait I think you forgot to integrate 1/2
not sure if it really makes a difference though
lucid oxide
wait I think you forgot to integrate 1/2
Cus thats not the trouble so I left that
XD
Hmmm
I wonder anyone help
<@&286206848099549185>
<@&286206848099549185>
Help
(b)
O sure
$$\dfrac{\beta}{2} - \dfrac{\alpha}{2} + tan^{-1}(\dfrac{tan{\frac{\beta}{2}}}{L}) -tan^{-1}(\dfrac{tan{\frac{\alpha}{2}}}{L})$$
potent lotusBOT
Catto Saint
potent lotusBOT
Blaze
$\frac{β}{2} - \frac{α}{2} + \arctan\left( \frac{\tan\left( \frac{β}{2} \right)}{L} \right) - \arctan\left( \frac{\tan\left( \frac{α}{2} \right)}{L} \right) = - \frac{α}{2} + \frac{β}{2} - \arctan{\left(\frac{\tan{\left(\frac{α}{2} \right)}}{L} \right)} + \arctan{\left(\frac{\tan{\left(\frac{β}{2} \right)}}{L} \right)}$
```Compilation error:```! LaTeX Error: Unicode character β (U+03B2)
not set up for use with LaTeX.
See the LaTeX manual or LaTeX Companion for explanation.
Type H <return> for immediate help.
...
l.49 $\frac{β}{2}
- \frac{α}{2} + \arctan\left( \frac{\tan\left( \frac{β}...
You may provide a definition with```
lucid oxide
Use \beta and \alpha lol, its not defined here
I mean anyways the integration of this is really easy
But the alpha and beta after it
potent lotusBOT
Blaze
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lucid oxide
For $\alpha \in (0,\dfrac{\pi}{2})$ and $\beta \in (\dfrac{\pi}{2},\pi)
potent lotusBOT
Catto Saint
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lucid oxide
It is easy to integrate it
I am not wishing for an integration of it
But how the hell do I get rid of that alpha and beta
Aaaaaaaaaa
Anyways yea XD, integration of it is not the problem
It can be integrated really easily
But after that
You do know alpha and beta is not suposed to be in the final answer right?
And how do I apply this
Thats the problem XD
While maintaining the same result as doing the whole integration
I tried multiple it by 2 and only integrate from 0 to pi/2
Well
You can integrate something without alpha and beta with it ofc
But the answer is sadly wrong cus it cant satisfy the required result on part c
Anyone
Please help
potent lotusBOT
Blaze
calm coralBOT
@lucid oxide Has your question been resolved?
calm coralBOT
@lucid oxide Has your question been resolved?
calm coralBOT
@lucid oxide Has your question been resolved?
calm coralBOT
@lucid oxide Has your question been resolved?
calm coralBOT
@lucid oxide Has your question been resolved?
verbal stag
Can someone see for me how to do this question? Like I did it up to there but idk how to continue it to find the other value of X
strange lichen
yes
calm coralBOT
calm coralBOT
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fringe scroll
I need help with this question I got -2.3 but it says its wrong
fringe scroll
I need help with this question I got -2.3 but it says its wrong
<@&286206848099549185>
calm coralBOT
@fringe scroll Has your question been resolved?
verbal stag
The correct answer is only (1,8) but I got another point other than 1,8. Why is that?
tidal grotto
the line crosses through the curve twice, but only at one of those points is the line normal to the curve @verbal stag
verbal stag
the line crosses through the curve twice, but only at one of those points is the...
but how would i know which line is normal to the curve when there is two points?
how do i tell without drawing a graph?
tidal grotto
the normal to the curve is perpendicular to the tangent
you use the expression for the derivative to find the slope/gradient of the tangent, yes? just do -1/() and you get the slope/gradient of the normal line
calm coralBOT
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split meadow
can someone help me with this
calm coralBOT
can someone help me with this
candid gorge
observe that the two triangles together are a larger right triangle
the bottom is the hypotenuse of a triangle with legs √8 and √24
pallid halo
you may want to spend a moment to understand why the vertical line has length sqrt(6)
split meadow
why
pallid halo
because the result depends on that, and for all you know the picture is a lie
i could draw the same triangle but write sqrt(7) instead of sqrt(6)
how would you know that such a triangle didn't exist?
calm coralBOT
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gilded bronze
burnt pecan
Hey Guys, I need help with nr. 7 but I also took the other two in here because they connected
burnt pecan
Answer to 3 is x^2+y^2+6x-6y+9=0
Answer to 5 is (x-13.32)^2+(y-12.42)^2=3^2
now I need help with nr. 7
The biscuit (circle) diameter is 6 cm
burnt pecan
<@&286206848099549185>
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burnt pecan
<@&286206848099549185>
burnt pecan
<@&286206848099549185>
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burnt pecan
.close
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flint condor
\text{Let } a, b, c \text{ be non-zero real numbers such that}
$(a b + b c + c a)^3 = abc(a + b + c)^3.$
\text{Prove that the numbers } a, b, c \text{ in some order form a geometric progression.}
potent lotusBOT
kitten
fringe reef
RHS is $a^{3} b^{3} + 3 , a^{3} b^{2} c + 3 , a^{2} b^{3} c + 3 , a^{3} b c^{2} + 6 , a^{2} b^{2} c^{2} + 3 , a b^{3} c^{2} + a^{3} c^{3} + 3 , a^{2} b c^{3} + 3 , a b^{2} c^{3} + b^{3} c^{3}$
potent lotusBOT
artemetra
fringe reef
LHS $a^{4} b c + 3 , a^{3} b^{2} c + 3 , a^{2} b^{3} c + a b^{4} c + 3 , a^{3} b c^{2} + 6 , a^{2} b^{2} c^{2} + 3 , a b^{3} c^{2} + 3 , a^{2} b c^{3} + 3 , a b^{2} c^{3} + a b c^{4}$
potent lotusBOT
artemetra
fringe reef
okay nvm
calm coralBOT
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flint condor
<@&286206848099549185>
calm coralBOT
@flint condor Has your question been resolved?
winged smelt
Why do I feel like this will be solved with vieta
Have you tried vieta?
@flint condor
flint condor
Yes, but idk what to do next 😦
winged smelt
I feel like vieta + A.M\geqG.M can solve this
winged smelt
Yes, but idk what to do next 😦
Can you show your work
calm coralBOT
@flint condor Has your question been resolved?
hot prairie
Draw this complex loci: | z | > 3 > | z - 3 |
calm coralBOT
Draw this complex loci: | z | > 3 > | z - 3 |
pseudo wedge
Assume $z=x+iy$
potent lotusBOT
kheerii
pseudo wedge
The question is asking you what the locus is of all points z which satisfy that inequality
Do you know what a locus is?
hot prairie
Do you know what a locus is?
but there is 2 greater than signs
so I'm confused what to do
pseudo wedge
Yeah, which means both inequalities must be satisfied
Split the inequality in two, then tje locus will be thr intersection of both locuses(locii?)
hot prairie
uh so like | x + iy | > 3 > | x + iy -3 |
pseudo wedge
Yeah
hot prairie
so what do I do after?
| (x + 3) + i(y) | > 0 > | x + iy - 3 |
is it like this?
and same thing for other side
wait no
| (x-3) + i(y) | > 0 > | (x-3) + i(y) |
pseudo wedge
No, that’s not how modulus works
hot prairie
ah
ok
so do u sqare the sides?
the parts
wait so do you have to do x^2 + y^2 > 3 > (x-3)^2 + y^2 ?
<@&286206848099549185>
pseudo wedge
wait so do you have to do x^2 + y^2 > 3 > (x-3)^2 + y^2 ?
Close
It should be x^2+y^2>9>(x-3)^2+y^2
rose plaza
$\int{\frac{dx}{2x^2+1}}$ How to solve this? It should be in the form of $arctgx+c$ in the end
potent lotusBOT
danilojonic
rose plaza
Assume I dont know this formula, I need to solve without it
solving it I get $\frac{1}{2}\int{\frac{dx}{x^2+\frac{1}{2}}}$ Here the point is to take a sub lets say $t=x$ and express above mentioned arc integral
potent lotusBOT
danilojonic
rose plaza
but what should I do with 1/2?????
I knew this before but I forgot the idea
<@&286206848099549185>
topaz raft
!15m
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topaz raft
**danilojonic**
you can do something much simpler
topaz raft
**danilojonic**
do you see anything you can u-sub here
to get it in the form of the denominator x^2 + 1
rose plaza
do you see anything you can u-sub here
$2x^2$?
potent lotusBOT
danilojonic
potent lotusBOT
danilojonic
topaz raft
mhm
topaz raft
👍
orchid elbow
does anyone know how to make a polynomial equivalent to a summation?
orchid elbow
for any n values
because wen i use an online calculator
it changes, the more points you put in
i need it for for r=1 to n 9r^3+7r
slate raven
does anyone know how to make a polynomial equivalent to a summation?
Can you elaborate more on that
slate raven
Sorry I might be a bit slow on that one
you mean express any summation as a polynomial?
orchid elbow
well r=1 to n 9r^3+7r this summation
in particular as a polynomial
for any n value
because online calculators i use require me to put points in but the more points i put in like the polynomial changes
dull wagon
sum of first n integers/cubes identities
orchid elbow
what does that mean.
dull wagon
you're interested in
$$\sum_{r=1}^n \br{9r^3 + 7r}$$
right?
potent lotusBOT
ℝαμΩℕωⅤ
slate raven
**ℝαμΩℕωⅤ**
damn this makes so much more sense now lmao
slate raven
split into two summations and take 9 and 7 coefficients out
dull wagon
you can split that summation into
$$9\blue{\sum_{r=1}^n r^3} + 7\red{\sum_{r=1}^n r}$$
potent lotusBOT
ℝαμΩℕωⅤ
slate raven
then its just the formula for first n integers and first n cubes
orchid elbow
ok let me try
dull wagon
and there are pre-established identities for those
median stirrup
[\Sigma r^3 = \left(\Sigma r\right)^2]
potent lotusBOT
bruhh
slate raven
real men calculate the identities by hand
orchid elbow
and there are pre-established identities for those
wait i forgot the formula again ?
because isnt tehre
slate raven
\[\Sigma r^3 = \left(\Sigma r\right)^2\]
thats what i was gonna say
median stirrup
yep its easy way to rem it
orchid elbow
how is it equal
slate raven
it might seem crazy what I'm boutta say
slate raven
how is it equal
proof by induction is left as an excercise to the reader
median stirrup
[\Sigma r = \frac{n(n+1)}{2}][\Sigma r^2 =\frac{n(n+1)(2n+1)}{6}]
potent lotusBOT
bruhh
median stirrup
if i m not wrong
orchid elbow
hmm
slate raven
hmm
Do you need actual proof for the formulas or can you just use them with no justification
orchid elbow
um
its a school assignment
and
they were expecting mne to use an online calculaotr
but it wanted me to prove it by induction afterwards
that the polynomial i came up with is equal to the summation
but its not using an online calculator...
slate raven
does wolframalpha not work?
orchid elbow
um idk it comes up w some error
wait
can u try subbing 5 into
wait
ur formula
coz ur supposed to get
orchid elbow
wait
yk the other method u said
wen i subbed in 5 i got a different value
could u double check ?
slate raven
ok lets go back to the beginning
median stirrup
u are asking for proof of r^2 ?
slate raven
$$\sum_{r=1}^n \br{9r^3 + 7r}$$
potent lotusBOT
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slate raven
you split them up into 2
take coefficients out
ur left with
hold on i hate latex
median stirrup
or try to do intitutivly if u feel its hard
potent lotusBOT
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slate raven
oops
orchid elbow
hold on i hate latex
do u guys have to memorise like the code stuff
slate raven
$$\sum_{r=1}^n \br{r^3}$$
potent lotusBOT
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slate raven
this times 9
orchid elbow
yep
slate raven
and
$$\sum_{r=1}^n \br{r}$$
times 7
potent lotusBOT
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finite maple
do u guys have to memorise like the code stuff
$not_really$
potent lotusBOT
Kai
finite maple
lol that looks funky
slate raven
do u guys have to memorise like the code stuff
i mean its simple enough
or I just look at a cheat sheet
either way
orchid elbow
yea
slate raven
for both those summation theres a simple formula
median stirrup
[9.1^3+9.2^3+\dots +9.A^3+7.1+7.2+\dots +7.A] [\implies 9(1^3+2^3+\dots+A^3)+7(1+2+\dots+A)][\implies 9(\sigma r^3)+7(\sigma n)]
slate raven
whats that formula i like kinda forgot
potent lotusBOT
bruhh
median stirrup
ignore small sigma
that is basically fundamental addition of summations
look through wiki for more info
everytime doing this is time waste
orchid elbow
wait ik what i did wrong before
i forgot to square
is this
a known thing...
btw
slate raven
yeah
median stirrup
cal 1 ig
slate raven
nah man just do induction
median stirrup
nah man just do induction
how will u prove this using induction ?
slate raven
how will u prove this using induction ?
shi lemme think
median stirrup
lol is that the lowest
uk factor of x^n -1 ?
orchid elbow
(x-1)(x^n-1+x^n-2...+1)
right
i mean i just started doing that like not that long ago
for me thats like
median stirrup
yeah its correct
median stirrup
u have to diff and multiple by x 3 times to prove r^3 summation imo
orchid elbow
i dont think i need to prove it
my assignment just wants me to use online calc
but the other one i was using was a bit dodge
but i udnerstand
how i can do it manually
median stirrup
yeah but there is satisfaction when u know how it came instead of mugging it up
calm coralBOT
slate raven
.reopen
hold on lemme get the proof
@median stirrup
and then just show that it holds for one value of n
(1^3+2^3) trivially = (1+2)^2
median stirrup
i mean like this ofc u can prove it i thought u gonna use base case as something else
since fomula is correct its easily provable this way
slate raven
i mean people in the middle ages based it on ovservation first
median stirrup
but yeah valid proof ig
slate raven
but youre right tho induction is not for deriving
calm coralBOT
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crimson cliff
Consider the permutation group Sn, if I wanted to find a subgroup of order p, how should I proceed with this?
crimson cliff
is it related to sylows theorem, i haven't taken related to sylows theorem
glass heart
the easiest subgroups are always the cyclic subgroups
and it helps that in fact all groups of order prime are cyclic
crimson cliff
yes
glass heart
so you should try finding an element of order p
crimson cliff
element of Sp with order p?
glass heart
yes
glass heart
yes
crimson cliff
how do i procced?
glass heart
generalize this
crimson cliff
i mean, here which is the cyclic subgroup?
powers of the element a=(0,1,2,3,4,5,6)?
crimson cliff
let's say, I started with the set of elements generated by a
how do i prove closure under composition in this set?
glass heart
well the composition of powers of a is again a power of a
but you dont actually "prove" closure. when you say "set generated by a", then by definition this means it is closed already
thats what the word "generated" is for
crimson cliff
Well, the context is bit different
I’m given the set {0, a,a^2,..,a^6}
i need to prove this form a group
glass heart
of course you didnt ask your original question from the start
why would you
I hope you dont mean 0
and instead mean a^0 or id
crimson cliff
Let me brief real quick
Consider the additive group Z_n, i tried to represent the powers of generators as permutations
instead of 0,a,a^2,…,a^k i did (0,a,a^2,…,a^k)
did this for all elements in Zn
when n is a prime, I’m getting closure and it forms a group
so trying to see why
@glass heart
crimson cliff
and instead mean a^0 or id
identity yes
glass heart
Consider the additive group Z_n, i tried to represent the powers of generators a...
but why
Z_n is so much easier to deal with than S_n
you have actual "numbers" in Z_n
crimson cliff
yes, but i’m just trying it
like only additive powers of generators
when n is a not a prime, additive powers of few generators doesn’t give me closure
but when prime, it turns out to be a group
glass heart
the "additive powers" (which really should be called multiples in an additive group) always form a group
I dont know what mistake you made to conclude that it didnt
a^i * a^j = a^(i+j) to stick with multiplicative notation
crimson cliff
Consider Z_8, the generators are 1,3,5,7
using this I construct the set S={e,(0,1,2,3,4,5,6,7),(7,6,5,4,3,2,1,0), (0,3,6,1,4,7,2,5),(5,2,7,4,1,6,3,0)}
i have inverses for elements, are the reverse order is the inverse
but here, a^2 is not in the set
Thus cannot be a group, but when n is a prime, this construction leads to a group
@glass heart
glass heart
ok
crimson cliff
using this I construct the set S={e,(0,1,2,3,4,5,6,7),(7,6,5,4,3,2,1,0), (0,3,6,...
Notice i can map each generator to this set
but no closure
glass heart
so basically what you did, for every element $a\in \bZ_n$ you created the function $f_a:\bZ_n\to\bZ_n$ given by $f_a(x)=x+a$. which is a bijection and therefore an element of $S_n$ and you can write it in that tuple form
potent lotusBOT
Denascite
crimson cliff
Kinda of i mapped the cyclic subgroup generated by those generators
like each elements corresponds to a cyclic subgroup right? so here i tied each generators to it’s cyclic subgroup in permutation notation
crimson cliff
using this I construct the set S={e,(0,1,2,3,4,5,6,7),(7,6,5,4,3,2,1,0), (0,3,6,...
Here the cyclic subgroup generated by <3>= {0,3,6,1,4,7,2,5}
so i have the permutation (0,3,6,..,2,5)
glass heart
yes I understand your construction
crimson cliff
right
glass heart
I am trying to find the proper formalization
crimson cliff
thank you
glass heart
ok yes my earlier thought was correct. $f_a(x)=x+a$. and then when you compose them you get $f_a\circ f_b(x)=(x+b)+a = x+(a+b)=f_{a+b}(x)$
potent lotusBOT
Denascite
glass heart
so the reason this is not closed under composition is that for example 3+3=6 but you dont have f_6 in your set
the reason this works for n prime is that every (nonzero) element is a generator
crimson cliff
i didn’t get the function you wrote
can you please explain?
some sort of an automorphism ?
crimson cliff
and x runs through the set
Z_n
so you fix a generator ‘a’ and get this function?
glass heart
yes
crimson cliff
so how do i prove closureness ?
glass heart
which exactly describes the tuple notation you have
well for n prime every element is a generator
so you have all of the possible functions of the form x+something
and those are closed by composition
as I showed above
(and you took the "zero function" x+0)
crimson cliff
makes sense
calm coralBOT
@crimson cliff Has your question been resolved?
tawny wasp
iv
tawny wasp
.close
calm coralBOT
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remote mural
tried all properties of def. integration
calm coralBOT
tried all properties of def. integration
quaint sphinx
tried all properties of def. integration
the trick to this integral is: ||multiply top and bottom by something||
remote mural
the trick to this integral is: ||multiply top and bottom by something||
idk i get very stupid ideas, like by multiplying and dividing be x^2
then x^3 = t
and dont give a f about x^2 in the denominator....
i dont get it
hmm wait lemme try
i gave up on denominator
somehow the derivative of above times 3x^2 is on the bottom, but doesnt work
quaint sphinx
idk i get very stupid ideas, like by multiplying and dividing be x^2
if the multiplication or division u tried does not work, that is a sign it may be worth to try something else
remote mural
are you replying to the image i sent ?
quaint sphinx
no
quaint sphinx
y? i am telling u method for proceed
the method u use in that imge looks not correct
remote mural
oh alr alr
oh wait
what did i just
omg
my mind was looking for the something in denominator
thats why lol
calm coralBOT
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prisma needle
I had this problem (simplified):
log(x-3)
Then we need to write it in interval notation. I asked my professor afterward because I’m confused on what it means for something to converge.
He wrote the interval notation as (3, positive inf). The rationale being that it can’t equal 3 because you can’t take the log of 0.
But we can get infinitely close to 3. We could, for example, take the log of 3.000000000000000000000000000001.
If we can get infinitely close to 3, doesn’t it equal 3?
prisma needle
He said it does converge to 3, but that doesn’t mean it equals 3. Which I guess I don’t understand.
neon sage
Are you familiar with limits
probably any introductory text/course/video/whatever on limits should clear this up
prisma needle
I’ve seen very little on limits from my own studying. My guess is that it’s because 3 is only being approached from 1 side?
Maybe it needs to be from both sides so it’s sort of getting squished to 3?
amber bolt
great question never noticed this
graceful dust
what are you asking about?
what equals 3?
are you talking about a domain of a function?
prisma needle
x = 3. Since we get infinitely close to 3. And yes
graceful dust
nothing to do with convergence
and your question is still ill-posed
If we can get infinitely close to 3, doesn’t it equal 3?
what is 'it'
prisma needle
x. For all intents and purposes, I mean x
graceful dust
the x's for which log(x-3) parses as an expression are the ones that are greater than 3
log(x-3) does not parse when x=3
prisma needle
Yes, but it does parse if x = 3.000000000000000000000…1
amber bolt
they are saying we distinguish between interval [3,∞) and interval (3,∞) yet we don't distinguish between 3 and 2.999...
prisma needle
Or, reverse, 2.99999 lol
graceful dust
Yes, but it does parse if x = 3.000000000000000000000…1
this only makes sense with a finite number of 0s
which means x>3
sooo
prisma needle
this only makes sense with a finite number of 0s
I can add as many 0s as I’d like. I can add an infinite number of 0s
graceful dust
now we're getting into crank territory
prisma needle
I am so confused. How is it crank territory? I’m literally just trying to understand the difference.
Why do you seem hostile?
amber bolt
bad day
graceful dust
k sorry guess i'm irritable rn
amber bolt
happens to everyone
neon sage
if you accept that 2.999.... repeating = 3 in the same way we do for 0.9999.. = 1, then log(x-3) is undefined for both
amber bolt
you noticed a cool thing, but there's not much to discuss, like ok
neon sage
oh wait you mean from above
prisma needle
Yeah, sorry, above. I’m literally in my first semester lol
So I’m screwing some terminology and stuff up I assume
neon sage
it feels like they are different cases 
neon sage
if you accept that 2.999.... repeating = 3 in the same way we do for 0.9999.. = ...
im pretty sure about this
graceful dust
I can add as many 0s as I’d like. I can add an infinite number of 0s
3.00000...1 with infinitely many 0s then a 1 doesn't describe a real number. also sorry you're right that i was hostile, i dunno why
amber bolt
i would say it describes 3, it's just not part of the notation
neon sage
I don't think 3.000.....1 describes 3
amber bolt
i'm not sure if it's on topic or not lol
neon sage
seems it should be
amber bolt
it defintiely describes 3
neon sage
what makes you think so
amber bolt
there's a one, that you never reach so it's identical to 3.000.....
it also equals 3.0000...45
it's silly so it's not accepted
but you can see what point it's talking about
neon sage
there's a one, that you never reach so it's identical to 3.000.....
this feels like it's veering into limits territory again. if they were actually equal we'd have elementary ways to prove their equality like 0.9999... = 1
amber bolt
i don't get what you mean
neon sage
there's a one, that you never reach so it's identical to 3.000.....
we can arbitrarily get close to 3 sure, but we are saying there's 0.00000 ... 1 somewhere. shouldn't that make it larger than 3 by default
remote mural
Hello.
neon sage
I'm not sure I'm qualified to talk about this tbh can we get ramonov here
amber bolt
i think this is all off topic
neon sage
well then getting back to the original equestion
amber bolt
when you talk about intervals you can tell if it includes the last point or not
when you're trying to describe a point, you can't describe a point that's inifinitely close to 3 without being 3
slate raven
this feels like it's veering into limits territory again. if they were actually ...
Just define 0.99999... as does not exist
amber bolt
that's cleatly not a point then
slate raven
Since it doesnt make sense by itself it has to be a limit
🗿 when in doubt make shi up
amber bolt
so there's no immediate contradiction, it seems like they are allowed to be different in this manner
neon sage
when you talk about intervals you can tell if it includes the last point or not
...
"inifinitely close" => "equals" im not sure about this part, but I don't really know where to start with this
amber bolt
it's surprising, i was surprised, but like whatever
amber bolt
"inifinitely close" => "equals" im not sure about this part, but I don't really ...
i'm using basic intuition, of pointing at something
you point, if it's not 3 then it's not inifinitely close to 3 either
slate raven
"inifinitely close" => "equals" im not sure about this part, but I don't really ...
infinitely close =/= infinitesimally close
neon sage
infinitely close =/= infinitesimally close
huh? not sure I understand what you mean by that, can you define both of these for me?
actually nvm i think the channel is really getting derailed now
slate raven
huh? not sure I understand what you mean by that, can you define both of these f...
you can't have something infinitely close, calculus is all about studying tendencies of functions
neon sage
don't think I have anything more to contribute to this discussion somebody ping me later if this is settled properly
slate raven
so it tends to be very close
but never is at that point
but then in physics we define it as whatever we wish at the moment so
calm coralBOT
@prisma needle Has your question been resolved?
prisma needle
3.00000...1 with infinitely many 0s then a 1 doesn't describe a real number. als...
No worries! We all have bad days. Don’t sweat it 🙂
graceful dust
if you try to give the expression 3.00000...1 a real number meaning, whatever it is should imply 3.00000...1 is just 3, if anything
like, it should have the property that it's smaller than anything of the form 3.00...0010000 where ... is finitely many 0s
but in the way real numbers defined you can prove that any number with that property is less than or equal to 3 (and it shouldn't be less, so, should be 3)
prisma needle
Okay, thank you. I feel like a lot of my confusion is just that I don’t know calculus lol. Maybe this gets cleared up a bit more with limits. I’m looking forward to analysis as well.
Thanks for the help folks 🙂
calm coralBOT
graceful dust
wow that timing
calm coralBOT
Available help channel!
olive wigeon
calm coralBOT
olive wigeon
am I looking for the lime that’s adajacnet to 50 degrees or 40 degrees
cuz idk why im not understanding the last sentence
slate raven
you wanna find the base
mellow crater
adj to 50 deg
slate raven
using trig
x/35 = cos(50deg)
plug it into a calculator
make sure to use degrees and not radians
olive wigeon
ohh ok ty
olive wigeon
can someone walk me thru the first question
calm coralBOT
can someone walk me thru the first question
olive wigeon
I’m actually so confused with this question
slate raven
can someone walk me thru the first question
nahh man not again 
olive wigeon
nahh man not again <:opencry:586078614865444865>
lmaoo sorry im just rlly confused on how this question works
slate raven
you wanna find all trig function values
olive wigeon
like even if I have the angle
olive wigeon
you wanna find all trig function values
yea I get that part
slate raven
so do you know how trig functions work
you find the 3rd side using pythagorean theorem
olive wigeon
yea
slate raven
and take side ratios for functions
then to find an angle you have to take an inverse trig function
in the 1st triangle tan(theta) = 2/3
theta = inverse tan(2/3)
in 2. sin(theta) = 8/7
so on
olive wigeon
so on
yea so I did sin 33.7 = 2 / 3.57
cuz I have every number
So what am I solving for?
calm coralBOT
@olive wigeon Has your question been resolved?
olive wigeon
<@&286206848099549185>
olive wigeon
.close
calm coralBOT
calm coralBOT
Available help channel!
polar monolith
what kind of formula would I use to solve this?
calm coralBOT
what kind of formula would I use to solve this?
granite axle
what kind of formula would I use to solve this?
Draw out a diagram and label the sides. If the length is 9 more inches than the width. Call the width x, and you find then that the length is x + 9
then use the formula for the area of rectangle to find what x is
and substitute back in
polar monolith
ok i got it thank you
granite axle
np
polar monolith
.close
granite axle
.close
olive wigeon
Did I put 60 degrees in the right spot
calm coralBOT
Did I put 60 degrees in the right spot
olive wigeon
And if I did, did I do the rest of the question right
sterile wharf
Did I put 60 degrees in the right spot
I'm pretty sure yes
sterile wharf
And if I did, did I do the rest of the question right
No 🗿
It should be
Tan(60) = x/34
x= 58.8
calm coralBOT
@olive wigeon Has your question been resolved?
mossy wigeon
calm coralBOT
wraith robin
Yes, but you could just pull the -5 out of the integral and use 1 as dv and arccos as u
blazing coyote
or x=cos(u)
mossy wigeon
calm coralBOT
mossy wigeon
i put this in my calculator and
it alwyas shows smt like -145
but apparently its like -3 where am i doing wrong
swift laurel
are you in degrees mode?
mossy wigeon
i am yes
swift laurel
radians are the standard in calculus
calm coralBOT
calm coralBOT
Available help channel!
olive wigeon
calm coralBOT
olive wigeon
how do I solve this question
olive wigeon
these are both right angle triangles!!
but what do I do with that information
humble oyster
but what do I do with that information
remember, all the angles of a triangle are equal to 180
humble oyster
but what do I do with that information
we can tell that there is a 90 degree triangle on each of those two
olive wigeon
tan 14 = 30/x
how do u know it’s 30 tho?
olive wigeon
okk
humble oyster
draw them in
^^
that leaves one angle on the top and the bottom, lets start with the top and call that angle y, so if we know $$18+90+y=180$$
just solve for y to find the third angle
potent lotusBOT
Bestower
olive wigeon
top one so 72 and bottom one is 76
calm coralBOT
@olive wigeon Has your question been resolved?
calm coralBOT
@olive wigeon Has your question been resolved?
neon current
How is it solve? I give up
calm coralBOT
How is it solve? I give up
mellow citrus
i can
calm coralBOT
@neon current Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
steel tide
calm coralBOT
quaint sphinx
i assume term inside secant here should be 4 / n^2
also. don't know why the limit approaches 0
i assume that is supposed to say it approaches infinity
quaint sphinx
can u confirm
steel tide
I don't know exactly i took screenshot of the original post
steel tide
i assume that is supposed to say it approaches infinity
Okay can you help me with your method
quaint sphinx
r u familiar with riemann sum
for problem such as this it helps to frame the limit in terms of a riemann sum...
calm coralBOT
calm coralBOT
Available help channel!
rustic shell
help
rustic shell
make sense but choice e is wrong the answer is a and idk how
civic garnet
yeah i was just about to suggest that
rustic shell
mm
what do you do in this sitution do you go by the question or by what the teacher meant it
civic garnet
both
brittle crow
calm coralBOT
potent lotusBOT
pixel
harsh siren
pythagorean theorem
brittle crow
$C^2=A^2+b^2$
potent lotusBOT
pixel
calm coralBOT
calm coralBOT
Available help channel!
brittle crow
calm coralBOT
brittle crow
what was the point of using sine rule here
hardy maple
what did the question want
brittle crow
cause look
they got angle of BOA
just to not use it
👏 👏
unless im missing something here
dull wagon
to get the final angle
potent lotusBOT
pixel
full niche
uppercase is angle?
right
empty tartan
calm coralBOT
neon sage
!status
calm coralBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
i tried to do it but not sure
full niche
i tried to do it but not sure
what exactly did u do
empty tartan
i tried subbing in z=x+iy into the thing it satisfies
full niche
and whatd u get?
empty tartan
which gives me a c circle with radius one centred at 1,0
empty tartan
which is obvious though by the thing
full niche
right?
empty tartan
yeah
potent lotusBOT
❄ѕησωƒℓαкє❄
empty tartan
real component of z
empty tartan
RHS asks for 2x
full niche
do u see the rhs is correctly placed
empty tartan
yeah
empty tartan
x^2+y^2
empty tartan
ah so i rearrange the thing it satisfies and i get the result
potent lotusBOT
❄ѕησωƒℓαкє❄
empty tartan
yep
full niche
Np
empty tartan
to show arg(z) = theta/2, what would suffice?
actually not too sure how to show argz = theta/2
@full niche sorry for thing ping but could you explain how we know how to find argz
calm coralBOT
@empty tartan Has your question been resolved?
lime spear
What am I doing wrong
calm coralBOT
What am I doing wrong
lime spear
Left one is me and right one is nspire
blazing coyote
ln(e)=1
calm coralBOT
calm coralBOT
Available help channel!
woeful basin
Number 1.610
calm coralBOT
Number 1.610
woeful basin
I did the work but the question key said that I was wrong
mint verge
okay so let's say first road length = x
tribal marlin
Average Speed = the total road length/time
displacement/total time
mint verge
and elapsed time t
woeful basin
and elapsed time t
ok
mint verge
displacement/total time
its not velocity bro
am i wrong?
in the second rode it will be
x-3 and t+5
right?
woeful basin
hm
mint verge
so x/t = 45miles/hour
and (x-3)/(t+5) = 36miles/hour
so x = 45m/h × t
for the first equation
we can write this in second equation
mint verge
we will find what is t
let's say t = k×hour
it will be more easy
there will be those who simplify
but we still dont know what is k
i just added k so it's still valid for every time period
45m/h × t = 45m/h ×k×h
h's simplify
x = 45mk
mint verge
and (x-3)/(t+5) = 36miles/hour
considering that the thing called x is 45mk, let's write it here
then x-3 will be 45mk-3
and t+5 = kh+5
woeful basin
hmmmm
aren't we just adding more variables if do that? Or is it "trust the process"
wait nah i just realised something
bruh
wait
mint verge
no it's good i think
and actually
+5 is 5mins
which is h/12
and -3 is -3m actually
you know
miles
i mean
woeful basin
nope i'm wrong 😭
woeful basin
Well can i continue writing?
pls do so
woeful basin
the K is a constant
mint verge
yes
π or e or
whatever it is
1/28497294
51847284
2
If k = 1/60 what we actually have is 1 minute
mint verge
becaue h/60 = 1min
woeful basin
but turns out there's a page on how to get the answer on the back of the page 🙏
my bad i just found it