chilly idol
thank you for helping me
#help-0
rotund crater
what happen if x is x<0?
lone heartBOT
what happen if x is x<0?
tardy stag
negative things to non-integer exponents very quickly get out of hand
or you could say they go sideways
rotund crater
Where
rigid prawn
what happen if x is x<0?
for example if x=-1 we get (-1)^cos2 which is not defined for real numbers
if you are asking anything else make it clearer
rotund crater
I'm not that advanced but can derivatives exist in the complex world?
rigid prawn
well yeah
surreal topaz
Hello, I am having an issue with solving for a variable in the exponent of a fundamental theorem of calculus problem.
surreal topaz
rigid prawn
what s p(t)
surreal topaz
it should be 225/(t+1)^r
young finch
Hello, I am having an issue with solving for a variable in the exponent of a fun...
what are you having an issue with exactly
rigid prawn
225(t+1)^-r+1/r+1?
225(t+1)^(-r+1)/(-r+1)
everything you ve done seems correct what s the problem
surreal topaz
I need to find what r is on the interval 0<x<13
rigid prawn
for question d right?
surreal topaz
yes
rigid prawn
what s the equation you ll use?
to find r
oh you ve written something
this isnt correct
you need to evaluate this at 13 and 0
surreal topaz
ok, I will give that a try
So then I have (2925^-r+1)/-r+1, would I then use logarithms to evaluate the rest of it?
I am still having some issues with this
<@&286206848099549185>
alpine sable
Question?
surreal topaz
I don't know how to finish this problem, I am trying to solve for r and I don't know how
rigid prawn
from here we have 225(t+1)^(-r+1)/(-r+1) evaluated at 13 and 0 is 225*14^(-r+1)/(-r+1) - 225/(-r+1)
correct?
surreal topaz
yeah, it should be (2925^-r+1)/-r+1
rigid prawn
you just multiplied 225 with 14?
surreal topaz
and then subtracted it by 225
rigid prawn
no u did 225*(14^...-1)
surreal topaz
oh I see
rigid prawn
when you have a*b^x it is not (ab)^x
225(14^(-r+1)-1)/(-r+1) is not 225(13^(-r+1)/(-r+1)
which is also NOT (225*13)^(-r+1)/(-r+1)
surreal topaz
So, when I get to this point how do I solve for r?
surreal topaz
Thank you, I have been having a lot of trouble with this. I appreciate your patience.
.close
lone heartBOT
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Available help channel!
dawn crest
i feel like there has to be a smart way to do this . but idk how
dawn crest
i tried using taylors expansion but it didnt really help
vale wigeon
well you can simply not worry about the cos(1-x^2) factor
since it approaches 1
focus just on the $\frac{\sin( (x-1)(x+1) )}{(x-1)^2}$
dawn crest
well you can simply not worry about the cos(1-x^2) factor
yea the issue is sin(x^2-1)/(x-1)^2
ocean sealBOT
Ann
dawn crest
i thought about using sinx/x but i cant ;-;
vale wigeon
you can
you'll just end up with...
$\frac{\sin(x^2-1)}{x^2-1} \cdot \frac{x+1}{x-1}$
ocean sealBOT
Ann
vale wigeon
and (x+1)/(x-1) explodes so
dawn crest
why would i end up with that?
surreal meadow
factor the left term of the denominator
surreal meadow
**Ann**
here
you should see things cancelling out to give you the original denominator
twin nimbus
\begin{align*}
\frac1{(x-1)^2} &= \frac1{(x-1)^2} \frac{x+1}{x+1} \
&= \frac1{(x-1)(x+1)} \frac{x+1}{x-1} \
&= \frac1{x^2 - 1} \frac{x+1}{x-1} \
\end{align*}
vale wigeon
$\frac{1}{(x-1)(x-1)} = \frac{x+1}{(x+1)(x-1)(x-1)} = \frac{1}{x^2-1} \cot \frac{x+1}{x-1}$
ocean sealBOT
Ann
vale wigeon
also parentheses
surreal meadow
\cot 
ocean sealBOT
omnipotententity
dawn crest
**omnipotententity**
why does x-1 become negative in the second step?
twin nimbus
There are two copies of (x-1) and one of (x+1) in the denominator, I just used commutativity to swap their order
dawn crest
Why isn’t it like this?
twin nimbus
It looks like you're mixing up (x-1)^2 and x^2 - 1
(x-1)^2 = (x-1)(x-1)
x^2 - 1 = (x-1)(x+1)
dawn crest
omg thats true
sorry
nooo i really have to go rn but can i reopen the channel later asking about the same limit? bc im still a bit confused
twin nimbus
You can open a different one, and link back to this
dawn crest
that works too, thank you :)
lone heartBOT
@dawn crest Has your question been resolved?
fickle oyster
lone heartBOT
kindred anchor
!status
lone heartBOT
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'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
3
what i tried is i made a sample space
A B C
2 0 0
0 2 0
0 0 2
1 1 0
1 0 1
0 1 1
if number of jobs of B is 0
then those cases would be
2 0 0
0 0 2
1 0 1
and from these probability of getting 2 jobs for A is the first case
so
1/3
but this is wrong
fickle oyster
P(X=2 ∩ Y=0)/P(Y = 0)
fickle oyster
there's only two contracts right
yup
kindred anchor
1 0 1 can occur in two ways
vale wigeon
so i think it's better to consider the sample space as {AA, AB, AC, BA, BB, BC, CA, CB, CC}
that way we can be certain the outcomes are equiprobable too
kindred anchor
1 0 1 can occur in two ways
This is what he missed I guess.
vale wigeon
and P(X=2 | Y=0) now means "whats the probability both contracts were given to A, given that B didn't get any?"
fickle oyster
1 0 1 can occur in two ways
A B C
2 0 0
0 2 0
0 0 2
1 1 0
1 0 1
0 1 1
1 0 1
???
fickle oyster
and P(X=2 | Y=0) now means "whats the probability _both contracts were given to ...
1/4??
vale wigeon
yes
kindred anchor
A getting the first contract and C getting the second contract is not the same as A getting the second contract and C getting first contract
fickle oyster
A getting the first contract and C getting the second contract is **not** the sa...
but are we not taking about the number of contracts and not who gets what contract?
1/4 seems correct
thx for the help
.close
lone heartBOT
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Available help channel!
mossy wedge
lone heartBOT
lone heartBOT
@mossy wedge Has your question been resolved?
upbeat hornet
find the probability that x is 2 given x less than or equal to 2
mossy wedge
TY
lone heartBOT
Available help channel!
lapis fjord
Guys, how do I find the equation of a line for two points with the same x-co-ordinate?
tall shuttle
y = y-coordinate
lapis fjord
x-co-ord, my bad.
tall shuttle
x = x-coordinate
lapis fjord
I don’t quite understand, I think. I’m trying to find an equation for a line segment AB where A(2,-2) and B(2,6).
tall shuttle
The equation is x = 2. y can be any real number and this equation will be true, including -2 and 6
lapis fjord
Right, wow, that solved the whole sum for me. Thanks a lot, man.
tall shuttle
upbeat hornet
the derivative remains the same expression
this is a true statement
the derivative of x^2 is always 2x
the slope of the tangent is the derivative
the derivative changes
at each x
the derivative is a function of x
No, the derivative of x^2 is 2x, and 2x evaluated at 2 is 4
That is false if x is a variable and true if x means “times”
The first or the second?
Yes
4x is an expression, not an equation, and y = 4x does not go through (2,4)
It’s ok
y = 4x does not go through (2,4), but y = 4x - 4 does, and that’s the tangent to y = x^2 at that point
Because then it isn’t a tangent
The derivative tells you the slope, and the point together with it determines the line
What do you mean
what is epsilon
there are no infinitesimals in the reals, maybe you were thinking of h?
you know the slope, and you know the point, so you can get the equation
try shifting right by 2 and see what you get
this is right
it should, did you try?
oh wait, you only have to shift right by 1
look again
the point was that shifting this line right by 1 and shifting down by 4 are exactly the same
Yes!
Should be the same
find the derivative at a point, which is the slope of the tangent, then use the fact that it goes through the point
You can think of it that way
brittle portal
I still do not understand what was this algebraic manipulation
lone heartBOT
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Available help channel!
brittle portal
what is the answer?
I just wrote it down and realised that by the definition of function composition this was the same as
T(S(T(v)))
so you can write the composing symbol (the little ball) in both places
brittle portal
.close
lone heartBOT
upbeat hornet
checks another item off mathcord bingo
brittle portal
*checks another item off mathcord bingo*
what
oh I found in on the internet, lmao
long axle
Don’t expose state secrets…
peak bough
lone heartBOT
Available help channel!
smoky tangle
could someone explain these markings? I'm new to constructions in geometry and would help a lot if someone could introduce me to them:
next patrol
hi
smoky tangle
I know the first image shows corresponding and congruent angles, but what is the smaller arc on like HF?
ping @smoky tangle when responding
smoky tangle
okay
next patrol
need explanation on II?
smoky tangle
yeah
next patrol
which means splitting it into two equal smaller angles
smoky tangle
yeas
next patrol
how they did it is
one second
they measured a certain length up BE
and put their compass on that point
and used the compass to draw a curve
which is this one
then they got the same length they went up BE
and went up BF
and put the compass on that point
and drew the other cure
smoky tangle
oh okay
smoky tangle
does it mark anything?
next patrol
and then they draw a line from the angle through it
where they cross
which bisects it
equally
smoky tangle
thats the image
the question says "which of the following are a construction of an angle bisector?
you can choose more than 1
the answers were 2 and 3
next patrol
yeah
basc
the guidlines is the same thing as II
theyve gone up the length of the traingle
draw the cruves at the bottom
and bisected it
smoky tangle
lenfth of a side?
gone up that for slant 1, marked a cuve, then sllant 2, and marck another
and marked where they intersecty
and drawn a line through that to the angle
which also bisected the base on the way in
it has to be an equilateral triangle
am i right?
@next patrol
next patrol
yes you are right
sorry for the late reply
@smoky tangle
it would be helpful to try it urself on a piece of paper
vast sonnet
lone heartBOT
vast sonnet
is it correct to apply l'hopital like this?
individually to each fraction?
since i rewrote them so that they both equal infin/infin
neat sierra
Looks right.
Youre not doing any calculus up to that point.
Just basic fraction manipulation
vast sonnet
yep
neat sierra
yeah
vast sonnet
so its fine to apply it like that?
neat sierra
yep.
tall talon
What are the necessary steps in doing induction? E. g. If i wanted to prove that the sum of n smallest odd positive integers = n^2 , what would I need to do?
vale wigeon
do you know the "induction as stairway to heaven" metaphor
tall talon
yes, i am only confused with steps involving k
vale wigeon
you have your base case and you have your inductive step
pallid scarab
So induction has 2 steps, the rest is simply logic. Think of it as dominoes.
1st step : initialisation. You tip the first domino, as the sum of 1 smallest odd positive integers is = 1².
2nd step : "Induction". You make sure that for each domino tipped, the next one will tip as well. So, knowing that the sum of n smallest positive integers is n², we need to prove the sum of n+1 smallest positive integers is (n+1)²
vale wigeon
those are the only two "steps" that the method of induction itself is concerned with
how you prove either one is a different matter entirely
but it does help to have your statement written down formally
in your case $\sum_{i=1}^n (2n-1) = n^2$
ocean sealBOT
Ann
pallid scarab
So induction has 2 steps, the rest is simply logic. Think of it as dominoes.
1st...
Induction only has 2 steps
Once you know that the first domino is tipped, and that for each domino tipped, the next one is tipped, for sure, all the dominoes will be tipped in the end
So in your case :
We easily can see that for $n=1$, $\sum_{k=1}^12k-1 = 1$
ocean sealBOT
rafilou2003
wind cloak
in your case $\sum_{i=1}^n (2n-1) = n^2$
*(2i - 1)
pallid scarab
And 1² = 1
Now for the induction step
Let n be any positive integer
Let's suppose we know that $\sum_{k=1}^n(2k-1) = n²$
ocean sealBOT
rafilou2003
pallid scarab
We need to prove the following : $\sum_{k=1}^{n+1}(2k-1) = (n+1)²$
ocean sealBOT
rafilou2003
pallid scarab
And now we do some calculations :
$\sum_{k=1}^{n+1}(2k-1) = \sum_{k=1}^n(2k-1) + 2(n+1)-1$
ocean sealBOT
rafilou2003
ocean sealBOT
rafilou2003
pallid scarab
So $\sum_{k=1}^{n+1}(2k-1) = n² + 2n + 1 = (n+1)²$
ocean sealBOT
rafilou2003
pallid scarab
Which is the proof that we needed for "if a domino is tipped, the next domino is tipped as well"
pallid scarab
What are the necessary steps in doing induction? E. g. If i wanted to prove that...
Which concludes the proof of this statement
tall talon
Which is the proof that we needed for "if a domino is tipped, the next domino is...
because n+1 can become the new n ?
pallid scarab
Yes in a certain way
flat roost
just started learning non-homogeneous odes, not really sure how to get the complementary and particular solution thanks
tacit arch
Well did you do the substitution
flat roost
Well did you do the substitution
is t a constant ?
tacit arch
No
silk patio
is t a constant ?
nope.
flat roost
whaat
ive only learnt constants (for example a times d^2y/dx^2 + b times dy/dx + c times y) are c1 e^rx + c2 e^rx
sorry for bad notation
not sure how to do this type of question since its x^2 times the second derivative, not a constant
lime rose
I need help 😭
ebon sparrow
I need help 😭
!help
lone heartBOT
I need help 😭
Please read #❓how-to-get-help
ebon sparrow
this channel is occupied
lime rose
I'm seriously lost
ebon sparrow
bruh get your own channel
lone heartBOT
@flat roost Has your question been resolved?
flat roost
just started learning non-homogeneous odes, not really sure how to get the compl...
is this an euler cauchy equation
twin nimbus
@flat roost start with the substitution, after you perform the substitution (remember the chain rule for the differentials) share what you have and we can go from there. You'll generally use an ansatz to get the particular solution, but there are other more systemic methods as well, such as variation of parameters. To get the general solution you just add the homogeneous solution to the particular solution.
flat roost
<@343931343031500803> start with the substitution, after you perform the substit...
whats an ansatz
twin nimbus
A fancy word for guess
flat roost
i dont get how chain rule can be used here though?
twin nimbus
You need to convert dy/dx into dy/dt
twin nimbus
That would be how I approach it.
twin nimbus
Exactly
flat roost
ohh i see
thanks, ill try that
wait but
dy/dt x dt/dx
which one do i do?
i mean i dont even know what dy/dt is
but i do know dt/dx which would return something with x
twin nimbus
To be fair you don't know what dy/dx is either
flat roost
thats why im chain ruling
twin nimbus
Yup
flat roost
which would give dy/dt times dt/dx
twin nimbus
Yup
twin nimbus
So dt/dx = 1/x = e^(-t)
twin nimbus
I will need to double check it, but that looks about correct other than you dropped the t somehow on the rhs of the equation
@flat roost
flat roost
This is for the complimentary part(?)
twin nimbus
Ok
flat roost
like the c1e^rx + c2e^rx
flat roost
I will need to double check it, but that looks about correct other than you drop...
Thanks
twin nimbus
Unfortunately, it seems like I'll need to be afk for a while.
flat roost
thats alright
you got this
flat roost
wolfram says otherwise 😭
flat roost
can someone please help me double check, tysm
lone heartBOT
@flat roost Has your question been resolved?
nimble fern
can someone please help me double check, tysm
should be =t instead of =0
lone heartBOT
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Available help channel!
alpine sable
does this sum mean something like, assuming n is "4":
1/4 + 1/4 + 1/4 + 1/4
or
1/1 + 1/2 + 1/3 + 1/4
sinful nebula
bruv
this is sign of sigma
it means multiply
so it means
1/1
+1/2
+1/3
+1/4
hope it helped :)
alpine sable
hope it helped :)
but usually the variable used is the index
alpine sable
nah its not
sinful nebula
wtf
alpine sable
sinful nebula
i wait wait
alpine sable
this is the whole image
alpine sable
it's approaching infinity
alpine sable
idk if it's still considered constant
sinful nebula
yes
alpine sable
positive integers
sinful nebula
from k to n
alpine sable
I got it, thanks
vast sonnet
lone heartBOT
vast sonnet
Yes
minor needle
what's the answer in the book
minor needle
I'd say -2 is right
alpine sable
lone heartBOT
alpine sable
hi i'm trying to apply the rule to rationalize the expression and getting tripped up. how can i arrange the denominator properly to start
i'm getting really close but mixing up on algebra somewhere
nimble fern
or you can just use (a+b)(a-b)=a²-b²
nimble fern
$\frac{x+3}{4-\sqrt{2x+22}}\cdot\frac{4+\sqrt{2x+22}}{4+\sqrt{2x+22}}$
ocean sealBOT
biscuityxd
alpine sable
i keep getting a sign wrong somewhere
need to factor in such a way that i wind up w (x+3) in the denom
nimble fern
$\frac{(x+3)(4+\sqrt{2x+22})}{4²-(\sqrt{2x+22})²}$
ocean sealBOT
biscuityxd
alpine sable
yeah so here is where i'm getting mixed up. let's say the squared and the square root cancel each other out? then do i have to multiply a negative one through that expression? the implied negative one out front of it???
alpine sable
see i don't know how i would know that or how to memorize that
seems counterintuitive or arbitrary
nimble fern
or you can just use (a+b)(a-b)=a²-b²
just memorize this
alpine sable
my issue is w the algebra
nimble fern
well, you can just rough work to just write the denominator out step by step
like
4²-(2x+22)
16-(2x+22)
16-2x-22
alpine sable
if it were instead addition, one could simply remove the parenthesis at the second step? no changing of signs?
nimble fern
if it's addtion
like 4+(3+2)
we don't have to change sign inside brackets
alpine sable
oh i see it now. minus the quantity 2x and 22
nimble fern
just remember
-(2x+22)
is
negative of ( postive 2x + positive 22)
alpine sable
the 22 being positive would make no sense
you'd be ignoring the fact that you're subtracting it
alright thanks. you'd shudder if you knew what grade and program i'm in 😉
i might be stuck on the next if you're still around
nimble fern
i *might* be stuck on the next if you're still around
open a new channel for new question for better performance 😆
nimble fern
remember to close this one first ;P
alpine sable
.close
lone heartBOT
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Available help channel!
unreal badger
I need help finding angle EDC the topic is about cyclic quadriliaterals
unreal badger
weary wyvern
Deduce whatever angles you can
slow wraith
Since EF is parallel to CH, angle HCF = angle CFE = 46 °
unreal badger
oh
slow wraith
angle FBD = 90° - angle FBG = 90° - 58° = 32°
unreal badger
i see it now, thanks so much
slow wraith
You're welcome 🙂
unreal badger
.close
scenic wing
how do you do the power of -2
lone heartBOT
how do you do the power of -2
tardy stag
,tex .exp rules
ocean sealBOT
Hayley
scenic wing
,tex \.exp rules
so
scenic wing
,tex \.exp rules
$\frac{1}{x^2}$
ocean sealBOT
putridplanet
scenic wing
.close
lone heartBOT
tardy stag
i'm sorry?
@scenic wing why did you send me a message just containing the word "booba"?
scenic wing
coral thorn
fleet siren
Do similar triangles have to have all the same angle measures?
alpine sable
Yes
mental flame
Yeah, else they wouldn't be similar
alpine sable
Thats basically the definition of similar triangles
And if the have the same sides length they are called congruent
fleet siren
And if the have the same sides length they are called congruent
but at the same time if all three sides have the same ratio does it also determine they also have the same angle measures?
alpine sable
Yes
If all angles are the same the triangles are similar. If the ratio of the sides are the same they are also similar. Or if the ratio of two sides are the same and the corner in between those sides is the same then they are also similar
fleet siren
If all angles are the same the triangles are similar. If the ratio of the sides ...
okay thanks my friend
.close
vast sonnet
lone heartBOT
safe cape
how do I differenciate 1^2-x^2 into (1-x)(1+x)
lone heartBOT
how do I differenciate 1^2-x^2 into (1-x)(1+x)
safe cape
is there a method or is it just memorising
minor needle
a^2 - b^2 = (a-b)(a+b)
minor needle
it's called
minor needle
difference of squares
safe cape
so it's basically memorise
minor needle
it isn't that hard, let's be honest
minor needle
ah ye
minor needle
you can search for short multiplication formulas
minor needle
there should be a list or something like that
safe cape
what do you guys use to do maths when on paper
minor needle
with many examples
last tendon
The factorization is "obvious". Consider f(x) = 1-x^2. This is a quadratic polynomial with 2 roots. So either see what they are directly, x = +-1 or use the quadratic formula. In either case, take your pick of a factorization theorem to get (1-x)(1+x).
safe cape
there should be a list or something like that
yeah I'll try to remember them
last tendon
Difference of squares is the shortcut here. Anyone that would know it without it would probably have memorized difference of squares long ago
minor needle
necessarily do examples, not just learn them by heart
sour dove
Also if you need need a visualization, here's why the diff of squares works:
$\\ (a + b)(a - b)$
$\= a^2 -ab + ab - b^2$
$\= a^2 - b^2\\$
So now when you run across two squares (including an implicit $1^2$) being subtracted, then you can use the difference of squares trick.
ocean sealBOT
mellowdramallama
safe cape
I want some opinions
lone heartBOT
I want some opinions
alpine sable
Yes
safe cape
like can I get away with writing y' entirely in the exam
and not be risk of mark deduction
alpine sable
Yes
plain flame
well usually
safe cape
"usually"
safe cape
more like
alpine sable
Right
alpine sable
No provided y is a function of x
safe cape
to just write y' instead of the full thing
alpine sable
y’ is fine notation
safe cape
if I have time I'll write the full thing ig
but if I'm running out of time I'll do y'
tq
.close
lone heartBOT
safe cape
.reopen
lone heartBOT
✅
safe cape
yes
sour dove
do you guys think there is a risk
it depends on your professor. Most don't seem to care but I would just clear it with them. Symbollically they both mean the same thing (as long as y' is with respect to x)
safe cape
true
but I'm in a situation where I might not know who is marking the paper
but yeah I'll ask him if I can
.close
lone heartBOT
proven leaf
but I'm in a situation where I might not know who is marking the paper
or also write "Let y be a function of x"
that may help avoid confusion but kinda ruins the whole time saving point 
lone heartBOT
Available help channel!
vapid shuttle
lone heartBOT
vapid shuttle
I am done with this, I just have it on paper. One second while I type my question
Okay so my solution is $$y=\frac{1}{2}-\frac{e^{-2x}}{2}$$ for $0\leq x \leq 3$ and $$y=ce^{-2x}$$ for $x>3$
ocean sealBOT
austinu
vapid shuttle
I am wondering about part (c)
is the reason that this is not a "solution" because it isn't necessarily continous
depending on the choice of (c) this function may not be continous over the interval of our solution
so we can't really say it is a "solution" by the strict definition
that requires both y(x) and y'(x).... to be continous over the interval of solution
does that sound about right?
mortal trellis
sounds about right
surreal meadow
if that’s how “solution” was defined then i agree
but it depends on how they defined a sokution
vapid shuttle
well, a solution has to satisfy the equation over the interval of said solution, and also the solution and its nth derivatives (for an nth order equation) have to be continous over the interval of said solution
so this piece-wise function of mine satisfies the equation, but the continous part depends on my choice of c
mortal trellis
I think it should be impossible that both the function and the derivative are cont. feels like it
vapid shuttle
well I can easily verify tht
mortal trellis
they require different choice of c
vapid shuttle
there should only be 1 c that makes it continous
then I can plug that in and check if the derivative is continous
it probably wont be
got it
ty guys
.close
normal heath
i need help
lone heartBOT
i need help
normal heath
look im not smart like everyone else i struggle with math
tacit arch
mental flame
Send what you need help with and we'll be able to help
unborn stag
whats confusing about it to you
normal heath
i dont understadn how to solve it
look i dont learn by reading text i learn by someone being there
and telling me how to do it
lone heartBOT
@normal heath Has your question been resolved?
mental flame
first thing we need to do is determine how many solutions these systems have
do you know how to do that?
tacit arch
!help
lone heartBOT
Please read #❓how-to-get-help
tacit arch
that image says AVAILABLE help channel
mental flame
this isnt your channel
tacit arch
you're in an occupied one
tacit arch
we are in help 0
lone heartBOT
@normal heath Has your question been resolved?
ornate ore
I'm having trouble figuring out how to apply this formula
lone heartBOT
I'm having trouble figuring out how to apply this formula
ornate ore
To this equation
For further context I am talking numerically so
I have the values for Psi(Z) along a horizontal line in the complex plane described by x + is where x goes from -inf to inf and s is a fixed constant
I know there are poles at Z = Pe^(i*theta)
Which mess up my attempt at creating a contour integral around r (r is real here)
lone heartBOT
@ornate ore Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
ashen shore
How can I tell which has rotational symmetry? They both don't look like equilaterals
ashen shore
full image: i removed c and d because i knew they had rotational symmetry unless the star doesn't?
ionic jewel
full image: i removed c and d because i knew they had rotational symmetry unless...
the star does if it's regular
if you have to choose a single answer, B must be equilateral
so then it's gonna be A
ashen shore
oh
ionic jewel
but this is a bad question with bad art
tardy stag
the star looks kinda stretched too
scenic wing
why do they convert it to ln
lone heartBOT
why do they convert it to ln
scenic wing
so whenever you use the change of base the num and denom become natural logs
gray isle
you can change to any valid base you want
scenic wing
ok so why did they make it ln here
gray isle
part of the question was to get a rounded value
which requires you to use common log or ln in your calc, they've chosen ln
scenic wing
part of the question was to get a rounded value
which requires you to use common...
when i put this in my calculator i dont get the same answer
gray isle
what are you getting
scenic wing
0.092
young finch
,w calculate ln(9/7)/(6*ln9)
ocean sealBOT
gray isle
can you show exactly what you're putting into your calc
scenic wing
$ln(9/7)/6*ln(9)$
ocean sealBOT
putridplanet
gray isle
order of operations
young finch
paranthesis are your best friend
gray isle
you want to divide by "6ln(9)"
entering that, you're only dividing by 6 and then multiplying by ln(9)
scenic wing
paranthesis are your best friend
i used a bunch and it worked
young finch
cool
lone heartBOT
@scenic wing Has your question been resolved?
flat roost
should be =t instead of =0
no, this is for the complimentary solution
i wanna know if the quadratic is correct tho
lone heartBOT
lone heartBOT
Available help channel!
harsh crow
i brute forced it and got the answer
lone heartBOT
i brute forced it and got the answer
harsh crow
but surely theres another way to do it
tacit arch
(a^2 - b^2) =(a+b)(a-b)
harsh crow
ik that but how do i apply it to the question
tacit arch
(a^2 - b^2) =(a+b)(a-b)
Do this for every term
harsh crow
ohh wait
tacit arch
1-(1/2)^2 =?
harsh crow
i see
but then i have to go multiply 3/4 by 8/9 and so on and so forth
is there any way to make that part easier
tacit arch
3/9=?
harsh crow
1/3
tacit arch
Do similar cancellations for all the terms
upbeat hornet
but then i have to go multiply 3/4 by 8/9 and so on and so forth
you can factor the numerators
tacit arch
Welp that's not what brute force means but ok
harsh crow
oh ok mb
gray isle
but then i have to go multiply 3/4 by 8/9 and so on and so forth
keep stuff in factored form
leave (1-1/2)(1+1/2) as (1/2)(3/2)
etc
harsh crow
brute force would be doing 3/4\*8/9\*15/16 etc
that is what i did
harsh crow
leave (1-1/2)(1+1/2) as (1/2)(3/2)
oh ok
young finch
that is what i did
then you didnt do the method provided by riemann
harsh crow
ohh no i multiplied them
but cancelled it out
nvm
im just dumb dont mind me
how do i close the channel
tacit arch
Type .close
lone heartBOT
@harsh crow Has your question been resolved?
tacit arch
.close
short blaze
help
thorn monolith
There are typos
upbeat hornet
one is open and one is closed
short blaze
what does that mean
upbeat hornet
There are typos
just different notation
thorn monolith
Oh i havent seen that one
upbeat hornet
what does that mean
the fourth option does not include 2
short blaze
is the fourth one saying everything but -2 and 2
and 2nd one is saying only -2 and 2
?
😭
@upbeat hornet
i actually hate math so much
young finch
i believe its the same as (-2,2)
gleaming ridge
2nd: All numbers from -2 to 2 (-2 and 2 included)
4th: All numbers from -2 to 2 (-2 and 2 excluded)
short blaze
2nd: All numbers from -2 to 2 (-2 and 2 included)
4th: All numbers from -2 to 2 ...
and what about the 1st and 3rd options, what does it mean when [U] vs ] U [
upbeat hornet
and what about the 1st and 3rd options, what does it mean when [U] vs ] U [
[] includes endpoints
short blaze
oh so its the same
young finch
]U[ would mean the end points are included
short blaze
ok thanks
young finch
i dont like that notation
upbeat hornet
]U[ would mean the end points are included
isn’t it the opposite?
young finch
i wouldnt think so?
cause like [0,2[U[4,6] 2 isnt included right but 4 is
cause the [] is faced away
gray isle
omitting too much making it hard to read
young finch
() is superior notation for exlusive ranges
gray isle
no
short blaze
young finch
i thought it was infinite domain
short blaze
im dumb asf
young finch
desmos checks that out too but theres no option for ]-inf,inf[
lone heartBOT
lone heartBOT
Available help channel!
proven leaf
How would I solve something like $\frac{\dd y}{\dd x}=e^{y}$
proven leaf
ocean sealBOT
XxMrFancyu2xX
proven leaf
Kinda new to diff. eq so would really appreciate a kindergartner explanation
vale wigeon
ain't this separable tho
sour dove
that's solvable by separation. Divide both sides by e^y and "multiply" both sides by dx
then take the integral of both sides
it becomes $\int e^{-y} dy = \int dx$
ocean sealBOT
mellowdramallama
proven leaf
ohhh ok that makes sense, I only did the dx to both sides shenanigans 🫠
thanks Mellow 
sour dove
anything for you
proven leaf
.close
dapper bison
Bob goes to run. From his starting point, he runs due east at 10 ft per sec for 250 ft. He then turns and runs north at 12 ft per sec for 400 ft. He then turns and runs west at 9 ft per sec for 90 ft.
Express the (straight-line) distance from Bob to his starting point as a function of t, the number of seconds since he started.
That's the question and solution from here - https://www.freemathhelp.com/forum/threads/word-problem-find-distance-as-a-function-of-time.72575/
lone heartBOT
@dapper bison Has your question been resolved?
lone heartBOT
@dapper bison Has your question been resolved?
lofty fractal
merry herald
isnt the last step wrong?
lone heartBOT
isnt the last step wrong?
echo socket
Yeah it should say -k
merry herald
Yeah it should say -k
wait but how is it rearranged liked that
echo socket
P_0/P = e^kh
P/P_0 = e^-kh
P = P_0 e^-kh
lone heartBOT
tawdry nest
State The Value Of Digit 3 in number 121134₅ in base ten
a)15
b)25
c)50
d)123
lone heartBOT
Available help channel!
pine surge
can anyone show me how to find range of this function:
f(x)= x|x|
whole otter
The range?
pine surge
Yes
pine surge
Idk
echo socket
The domain is R, right?
whole otter
It’s most likely just all ranges
pine surge
The domain is R, right?
Yes
wind cloak
Write the function piecewise, it should make it easier to see
whole otter
All y values are in the range
wind cloak
I just told you
wind cloak
invert it and find the domain of the inverse
pine surge
I dont know inverse of function
wind cloak
I don't really see where the confusion is
whole otter
pine surge
I got range = R-{-3}
cosmic lark
whatt
wind cloak
,w range of 3x/(28 - x)
cosmic lark
where did that come from
ocean sealBOT
wind cloak
Correct
pine surge
Does this method work on all types of function to find the range
wind cloak
invertible functions
any linear/linear should work
for quadratic/quadratic or any quadratic you'd need to use the discriminant
pine surge
Does this work on under root func.
wind cloak
if you can write x in terms of y it works
wind cloak
well the modulus doesn't really have an inverse does it
there is no antimodulus
For modulus functions you need to just use the piecewise definition
echo socket
Yeah |x| has no inverse although the function that you had earlier involving the modulus did
pine surge
So every modulus function have domain =R and range =R??
echo socket
But you will want to use the piecewise definition to find its inverse as well
wind cloak
does |x| have range R
pine surge
Yes
wind cloak
uh
echo socket
Can |x| be equal to -1?
pine surge
Yes
cosmic lark
what, no it cannot
vale wigeon
give us a real number whose absolute value is -1
wind cloak
for what value of x
pine surge
does |x| have range R
Sorry positive R
vale wigeon
also let this be on record
echo socket
Nonnegative would be more precise
wind cloak
indeed
pine surge
Nonnegative would be more precise
Why??
pine surge
also let this be on record
Why
wind cloak
What's |0|
echo socket
Because it includes 0 whereas positive R does not
pine surge
0
wind cloak
Is 0 positive
echo socket
And we want 0 to be in the image because |0| = 0
pine surge
Nonnegative would be more precise
Nonnegative what ?? Real no.
echo socket
Nonnegative R
pine surge
Is 0 positive
No
I think?
wind cloak
it isn't
Saying the domain is positive R would not include 0
but the modulus function does have 0 in the range and domain
pine surge
Saying the domain is positive R would not include 0
👍
wind cloak
Which is why Lonely Bean insisted on non-negative R
pine surge
So, the question was can i use the method u said of writing x in terms of y work on modulus function
??
ocean sealBOT
neonperseus
echo socket
(You could write x in terms of y but the relation that you get would not be a function)
wind cloak
pine surge
Is there way to solve these question to find domain of mod. ( Without graph)
wind cloak
Piecewise definition I told you
pine surge
Piecewise definition I told you
Then can you give one example question?
To find range and domain
cosmic lark
Is there way to solve these question to find domain of mod. ( Without graph)
unless there is a restriction (a fraction, a root, log, or sth else), the domain of a mod is R
wind cloak
Find the range of $f(x) = x + |x - 1| + |x - 3|$
ocean sealBOT
neonperseus
wind cloak
domain is R but I asked for the range
wind cloak
you have to what
wind cloak
write the piecewise definition
wind cloak
Write the function seperately for when x < 1, 1 < x < 3, and x > 3