so (t+1, t) - (1,0)
#help-36
old silo
so (t+1, t) - (1,0)
I’m not sure that’s correct
muted prairie
(t+1,t+1) - (1,0)?
I don't think the other person graphed t,t
idk, something like that
old silo
How the heck is it that none of us know how to integrate something like this in polar xD
muted prairie
idk probably a hard problem
old silo
There must be a method tho. It’s just a spiral
What if we go in reverse? Try to find an equation for a spiral that can be differentiated into the same form..?
What’s the velocity equation for…i dunno, r= (2t+1)θ?
final saddleBOT
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tranquil pine
Given a graph with n vertices, prove that if the degree of each vertex is at least $\frac{n-1}{2} then the graph is connected???????
final saddleBOT
Given a graph with n vertices, prove that if the degree of each vertex is at lea...
tranquil pine
$\frac{n-1}{2}$
soft zealotBOT
Idunno
desert mantle
take two vertices u and v
how many neighbors do they have
taking into account that there are n vertices in the whole graph
final saddleBOT
light wren
.coose
final saddleBOT
Available help channel!
gleaming anvil
help 7x+5
bleak granite
small gazelle
posting joke questions i think
final saddleBOT
@gleaming anvil Has your question been resolved?
soft zealotBOT
Kai The Doge
vagrant vector
Also @gleaming anvil very unfunny trolling, especially in a math server. Just get a life dude
tranquil pine
an equivalent trigonometric expression for tan(x+pi/2)
final saddleBOT
an equivalent trigonometric expression for tan(x+pi/2)
vital crag
,tex .shift trig
soft zealotBOT
riemann
viral ocean
an equivalent trigonometric expression for tan(x+pi/2)
Do you any other way of writing the tangent of a angle?
tranquil pine
wdym
vital crag
,tex .sum diff trig
soft zealotBOT
riemann
vital crag
you can also use sum addition for tangent as well
final saddleBOT
@tranquil pine Has your question been resolved?
violet rune
f a T-periodic function
how can i show that g is constant
final saddleBOT
f a T-periodic function
how can i show that g is constant
violet rune
$g(x) = \int^{x+T}_x f(t)dt$
violet rune
f(x+T) = f(x)
but not F(x+T) = F(x) so i'm kinda blocked
sinful tide
f(x+T) = f(x)
but not F(x+T) = F(x) so i'm kinda blocked
Do you see a way to get f(x+T)-f(x) from that equation?
violet rune
you mean g?
sinful tide
From the definition of g, yeah
violet rune
ah ye derivate it
sinful tide
Yep 
violet rune
.close
final saddleBOT
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Available help channel!
rain star
Did I do this partial correct?
final saddleBOT
Did I do this partial correct?
rain star
On the right you can see how I differentiated
If there is a more efficient way I’m all for it
I just need some guidance in taking partials of rational functions
Would appreciate the hel-
broken mantle
just treat the other variables as constants
rain star
Okay but Seth like this confuses me
Like I would think the partial with respect to x would be the same but multiplied by the derivative of the exponent with respect to x which would be -2x
So -2x*the original function
What step am I missing?
Is there a product rule in the beginning?
final saddleBOT
@rain star Has your question been resolved?
misty umbra
Hi this isn’t really a question I just wanted to see if my answers are correct in these 4 questions
final saddleBOT
Hi this isn’t really a question I just wanted to see if my answers are correct i...
junior radish
The first one is wrong
misty umbra
could u show me where
junior radish
1-5x = 36
-5x = 35
junior radish
Yes
fathom walrus
it’s good
junior radish
Yes
misty umbra
thanks for checking!
fathom walrus
zzZzZzzZzZzZZzZzzzz...........xdXDDDDDXDXDUWUWUWUWUWUWU
tranquil pine
are you good Stephen
grim badger
<:thonk:406575732563902485> are you good Stephen
Can't you tell stephen is sleep texting?
fathom walrus
tranquil pine
Ah yes
fathom walrus
@silent lark #❓how-to-get-help
misty umbra
thats qiqi's description
Unique
silent lark
Hello, I need help with equation on this that is “The product and Quotient”
fathom walrus
junior radish
Big brain
tranquil pine
Hello, I need help with equation on this that is “The product and Quotient”
This channel is already occupied. So open your own one from the available category
magic sparrow
Hello, I need help with equation on this that is “The product and Quotient”
Read #❓how-to-get-help and #rules any channel in the occupied section is occupied, and you need to use one from the available section.
misty umbra
Just substitute in f(x+31) and equate both equations
g(x) stays x right?
magic sparrow
Sorry to interrupt Qiqi
misty umbra
It’s ok Austin no problem!
I think I made a ton of calculation mistakes tho
Cause at the end the result was -10x= 2272
😬
Actually re-did it and it’s -10x=2192
tranquil pine
This seems like a proportionality question rather
misty umbra
🤔
tranquil pine
So what I said above isn't helpful
tranquil pine
I’m gonna try to solve the other questions @ me when you answer oki
Not quite sure how to go about it rn sorry
Brain not really braining
Oh wait I think I figured it out @misty umbra
tranquil pine
Also
So first solve the system of equations as is
I.e. figure out what x is knowing that the y's are equal
final saddleBOT
@misty umbra Has your question been resolved?
vale reef
for this i differentiated twice and got x in terms of a and b but not sure what to do after that or if thats useful
final saddleBOT
for this i differentiated twice and got x in terms of a and b but not sure what ...
tranquil pine
If you differentiate that equation you get a quadratic
Now you also get a local maximum and local minimum when you set that quadratic equal to 0
Can you connect the dots from there?
vale reef
lol thanks that explanation made sense
i got the ans
it doesnt seem worth seven marks
tranquil pine
Yes I believe that's the idea of the question
vale reef
i thought similar so was a bit thrown off
but it works out
i made it way more complicated than it was lol
mayve bc i saw seven marks
in reality that would be 3 max
vale reef
It does make sense why they chose 3ac
why?
austere ingot
Can someone help me solve this please? My teacher wants us to solve it by only manipulating one side, I’ve been stuck on this for a while.
final saddleBOT
Can someone help me solve this please? My teacher wants us to solve it by only m...
void valley
I'd start from LHS
tranquil pine
!status
final saddleBOT
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
Typically I try to convert to sin and cosine and try to solve from there
But that didn’t quite workout well
tranquil pine
Yeah that's a good first step
austere ingot
I’ve been trying to see if I could find any other good number combos but I’ve come up blank
tranquil pine
So what is tan rewritten in sin and cos
austere ingot
Cos/sun
*sin
Wait hold up
Lemme double check
It’s sin/cos
Got confused with cot
tranquil pine
Yeah alright
So if you rewrite tan as to that in the fraction
What do you have now
austere ingot
sin/cos/sinxcosx
tranquil pine
Don't forget parentheses! But simplify the fraction what do you get
austere ingot
Think you can get (sinx^2)(cosx)/cos right?
tranquil pine
Nope. Rethink this again
You have $\f{\f{\map \sin x}{\map \cos x}}{\map \cos x \map \sin x}$
soft zealotBOT
austere ingot
Would you be able to cancel out the sin of you split the fractions?
tranquil pine
Yep
austere ingot
Would you be able to go sinx/cos times 1/(cosx)(sinx)?
tranquil pine
Yes that's how it's meant to br
austere ingot
Ohhh
tranquil pine
So what do you get now
tranquil pine
Nope
austere ingot
To secx
austere ingot
Sec^2x
tranquil pine
No worries 👌
austere ingot
.close
final saddleBOT
Available help channel!
zenith nebula
Anyone know a good source to learn material on "Measuring Geometric Solids" ? Such as surface area and volume
final saddleBOT
Anyone know a good source to learn material on "Measuring Geometric Solids" ? Su...
vital crag
<@&286206848099549185>
!15m
final saddleBOT
<@&286206848099549185>
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
@zenith nebula Has your question been resolved?
zenith nebula
<@&286206848099549185>
cinder linden
Anyone know a good source to learn material on "Measuring Geometric Solids" ? Su...
khan academy
tawdry kelp
final saddleBOT
tawdry kelp
tawdry kelp
they're only dependent if the vectors are a multiple of each other meaning they overlap
just because they both lie on a line through the origin doesn't necessarily mean it overlaps
final saddleBOT
@tawdry kelp Has your question been resolved?
final saddleBOT
@tawdry kelp Has your question been resolved?
random loom
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Available help channel!
haughty moth
hello, idk how to find the limit of cos(x)/(2^x)
final saddleBOT
hello, idk how to find the limit of cos(x)/(2^x)
modern wraith
$\text{prove that} \forall x>0,2e^x>2+2x+x^2$
final saddleBOT
$\text{prove that} \forall x>0,2e^x>2+2x+x^2$
soft zealotBOT
bigpufik
formal trail
you could use the maclaurin series for e^x
modern wraith
and take c=1?
desert mantle
dont put text inside \text for stuff like this, just start the math mode later
maclaurin series is at 0
soft zealotBOT
bigpufik
soft zealotBOT
bigpufik
modern wraith
actually with c im not sure, cause just realizd my text book said for some c
we don tknow what c
right?
formal trail
modern wraith
yeah but i havent had infinite sums yet
formal trail
i think the point is that there exists some value c where this is true, you don’t necessarily have to ‘find’ c
as long as you choose an appropriate value for n
modern wraith
yeahhhh makes sense
JESUS YEAH U ARE RIGHT
u choose such a n that f^(n) = 0
yeahhh so the functions is flat on the nth derivative
and c dopesnt mastter
ok thank uuuu
.close
dim radish
hey, i have no idea how i went from [n+2] to [n+1]
final saddleBOT
hey, i have no idea how i went from [n+2] to [n+1]
@dim radish Has your question been resolved?
dim radish
please
final saddleBOT
@dim radish Has your question been resolved?
sinful tide
.reopen
sinful tide
please
Here's how t9 do it if you don't know https://www.freetext.org/Introduction_to_Linear_Algebra/Basic_Matrix_Operations/Expansion_by_Minors/
final saddleBOT
Here's how t9 do it if you don't know https://www.freetext.org/Introduction_to_L...
final saddleBOT
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Available help channel!
fallow goblet
I have a python question envolving cubic splines if anybody can help me I would appreciate
final saddleBOT
I have a python question envolving cubic splines if anybody can help me I would ...
@fallow goblet Has your question been resolved?
quasi lotus
If i have an integral of a function with two variables, f(x, t)
and it is being integrated with respect to t, with a limit of ln(x) to infinity, how can I evaluate this? Like is there a special formula for this very situation? I only know the formula for two constants or two functions as its limits, but not 1 function and 1 constant as its limit; d/dx ∫ f(x, t) dt (lnx to +infinity)
final saddleBOT
If i have an integral of a function with two variables, f(x, t)
and it is being ...
quasi lotus
Show the original problem
quasi lotus
Show the original problem
quasi lotus
Show the original problem
its not letting me send it here wtf
d/dx ∫ e^tx dt (lnx to infinity)
hybrid heath
This?
quasi lotus
The integral diverges
no wonder, cause i made it my self LOL
i couldnt find any good questions to practice
so i made my own
quasi lotus
can u tell me where i can find practice problems to use the leibniz integral rule
hybrid heath
I don't know any such resources
quasi lotus
(fyi: yes i googled it, but all i see are images of the general formula)
hybrid heath
I just used a calc book
quasi lotus
Oh, I don't have a calc book rn, im planning on buying one
mind recommending me one
?
hybrid heath
This was the book I used and it's the only book I know
There could be better or equivalent valculus books, but this was what I used
Covers all of Calculus I through III
quasi lotus
This was the book I used and it's the only book I know
👍
final saddleBOT
Available help channel!
pliant drift
how to calculate the intersection point between a y = mx + b line and a vertical one x = b ?
final saddleBOT
how to calculate the intersection point between a `y = mx + b` line and a vertic...
pliant drift
so y = mb + c ?
spring haven
where'd the c come from
rare quarry
where did the c come from
pliant drift
I replaced mx with mb from the x = b and renamed the old b from mx + bto c
spring haven
the 2 b's are the same
rare quarry
is it a different b
pliant drift
so the intersection point is y = mb + b ?
spring haven
if the 2 constants in the equations are the same then yes
otherwise you need to indicate that they are different
in the original equations
pliant drift
I don't know if they are the same they are variables
rare quarry
ok then theyre the same
rare quarry
so the intersection point is `y = mb + b` ?
then this is right
rare quarry
I don't know if they are the same they are variables
if this was how the problem was given in the first place
then yeah thats right
pliant drift
so the intersection between y = x + 4 and x = 2 is (2,6) ?
spring haven
yes
pliant drift
ok thanks
forest torrent
final saddleBOT
forest torrent
i dont understand the step after Rsin(wt+a)
this is simple harmonic motion in further maths
vital crag
the amplitude is given
vital crag
https://www.mathsisfun.com/algebra/amplitude-period-frequency-phase-shift.html
it's just this
the general solution to this
is that
Now you use given information
and match parameters
to conclude R=a
vital crag
the general solution to this
general meaning you don't know R
but once you incorporate given information, then you conclude R=a
tranquil pine
I have an unit circle equation, and I want to graph this on a polar coordinate.
tranquil pine
I know already that the radius is 1.
But what about its angle?
it's between [0, 2π].
If I graph the unit circle on a polar coordinate, do I get still a unit circle on a polar coordinate?
How can I imagine it in my head?
frail flax
i don’t get the question
vital crag
How can I imagine it in my head?
plot r = 1 for small values partitions of [0, 2pi]
like theta = [0, 0.01, 0.02, ... , 6.27, 6.28]
tranquil pine
plot r = 1 for small values partitions of [0, 2pi]
I do still get a unit circle on a polar coordinate.
I mean no matter which angle I'll get the radius will be always 1.
vital crag
I mean no matter which angle I'll get the radius will be always 1.
why is that a problem?
tranquil pine
It's not a problem, I was just saying it.
That's why I'll get a unit circle on a polar coordinate system too, right?
vital crag
If I graph the unit circle on a polar coordinate, do I get still a unit circle o...
great so that answers this question
tranquil pine
But, another question would be:
Should I expect a change of shape if I transform the equation from other coordinate system to another?
It seems to me, I don't know, but just weird. We still represent the same point on the plane but just with another coordinate system.
That's why the shape must stay still the same.
final saddleBOT
@tranquil pine Has your question been resolved?
misty mulch
help!!😭 whats 5+4!
final saddleBOT
help!!😭 whats 5+4!
vital crag
help!!😭 whats 5+4!
<@&268886789983436800>
opaque ember
tranquil pine
final saddleBOT
tranquil pine
where does sqrt 2 come from
tulip coyote
Norm of (1, 1)
tulip coyote
Magnitude maybe, if you've heard it like that?
tulip coyote
Yea that one 
tranquil pine
my school in highschool was weird, like in my calc class we did dot product and cross product and angle things
im trying to releard some of
relearn
sorry *
thank you
.close
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daring hedge
hi
daring hedge
do i find the antiderivative of u(9+16u)^1/2
would it be the antiderivative of u times the antiderivative of (9+16u)^1/2?
desert mantle
no
daring hedge
how shall i proceed?
daring hedge
the original problem is t(9+16t)^1/2 dt so make u equal to 9+16t?
for u substitution
desert mantle
yes
daring hedge
ok thank u
timid rock
Yo i dont know where to put this problem but could you help me solving 34
idk how to send a proper image either sorry
final saddleBOT
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wise crescent
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wise crescent
Is my solution correct?
I'm getting 2 answers but I think the question is asking for one singular answer
worldly vale
there was no need for you to square anything, your second line tells you what x - y = -4xy
spring haven
you created two different solution sets from squaring
final saddleBOT
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Available help channel!
weak tinsel
what's wrong with my answer for this true and false?
final saddleBOT
what's wrong with my answer for this true and false?
rain crane
whats Zii
weak tinsel
mod 11, sorry its written like that in the textbook
tranquil pine
it's $\mathbb{Z}_{11}$ not Zii
soft zealotBOT
Ayanokoji
rain crane
okie ken will help u
weak tinsel
it's $\mathbb{Z}_{11}$ not Zii
right thats what i was trying to write, my bad
weak tinsel
it's $\mathbb{Z}_{11}$ not Zii
any chance you might know where i made an error?
tranquil pine
well first off, if i understand correctly, these aren't even integer solutions
so I guess you made a mistake when re-writing -19 as an element of Z_11
desert mantle
you cant just blindly apply the quadratic formula
is there an element in Z_11 which squares to 3?
and which you could therefore call sqrt(3)?
the real number sqrt(3) would make absolutely no sense
weak tinsel
and which you could therefore call sqrt(3)?
i guess i was presuming that if the sqrt(b^2-4ac) was positive then the solution could show that there was an answer
someone suggested i prove it with quadratic residue but not sure how i would go about that
desert mantle
"positive" makes no sense in Z_11
but yes quadratic residue is the correct keyword
weak tinsel
but yes quadratic residue is the correct keyword
the thing is we havent covered anything like that so im not even sure if i can use that theorem
weak tinsel
well first off, if i understand correctly, these aren't even integer solutions
do the solutions have to be integers?
desert mantle
they have to be elements in Z_11
weak tinsel
.close
proven forum
Would anyone happen to know how to do this question?
final saddleBOT
Would anyone happen to know how to do this question?
jaunty turret
Did you draw the free-body diagram?
final saddleBOT
@proven forum Has your question been resolved?
proven forum
Did you draw the free-body diagram?
Figured it out
final saddleBOT
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latent trellis
can someone explain how to solve d?
final saddleBOT
can someone explain how to solve d?
latent trellis
there are 4 ace, and 13 diamonds
so i added them, 17
so my answer was 17/52
the book's answer is 4/13
cloud zephyr
Hint : You have a diamond ace
rich tide
can someone explain how to solve d?
There are 13 diamonds out of which one is ace
There are 4 ace
But you already counted one ace from diamonds
latent trellis
oh so 16/52?
rich tide
Yes
fiery prism
can someone help me with these
fiery prism
and explain Proportions to me by answering the questions
final saddleBOT
@fiery prism Has your question been resolved?
long copper
2 or 3 or both?
final saddleBOT
@fiery prism Has your question been resolved?
solemn vault
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dim radish
.rotate
dim radish
.rotate
thorn meteor
,rccw
soft zealotBOT
dim radish
yay
solemn vault
Sorry about that
This is my working out
Did I go wrong anywhere
If not how do I come to a concludion
dim radish
im terrible at linear algebra
i see a base
and vectorial plan
i don't know sorry..
solemn vault
Okay anyone that does????
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@solemn vault Has your question been resolved?
solemn vault
<@&286206848099549185>
thorn meteor
Ill try and help but i havent done this for a while
How did u get 2x-3mx-3c
It might be right im just confused
@solemn vault
solemn vault
sub in y=mx+c
next pagoda
Sadly I'm still on this problem. My understanding so far is the sample size is 19,600 which comes from 50 choose 3 where 50 comes from the number of tickets and 3 comes from the number of prizes.
Calculating the probability of the event of winning all the prizes is where I'm stuck. My guess was 4, because there's 4 groups that can win. Is that not the correct way to think about this?
final saddleBOT
Sadly I'm still on this problem. My understanding so far is the sample size is 1...
next pagoda
If it is correct, how do I approach B here
From my book, the method I understand is to first find the sample space. Then, I need to find n_a which is the sample space for an event. And n_a / N would be the probability of that event.
marsh temple
well the probability isn't 4, but yes there are 4 outcomes in which the organizers win every prize
marsh temple
there's 1 prize left to be given
specifically it's given to one of the non-organizers
marsh temple
the organizers win 2 prizes, and someone else wins 1 prize
next pagoda
Right
I follow that
I'm trying to figure out how to solve for n_a
Using a combination theorem
Cause in my book, the solution for b has n_a = 276 I think
marsh temple
in how many ways can the 4 organizers win 2 of the prizes?
next pagoda
6
marsh temple
which leaves how many people eligible for the third prize?
next pagoda
50-4?
soft zealotBOT
Result:
276
That looks like the MN rule
So
Can you remind me what that number represents
276 is the number of sample events for that event?
marsh temple
yes, 276 is the number of outcomes satisfying "the organizers win exactly 2 prizes"
marsh temple
np
final saddleBOT
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Available help channel!
vale reef
for part a
final saddleBOT
for part a
vale reef
i dont get why they used 21 in the second line?
final saddleBOT
@vale reef Has your question been resolved?
modest birch
i dont get why they used 21 in the second line?
the bag has 40 bulbs
so if you want more blue bulbs than white bulbs, you need 21 or more
final saddleBOT
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nova ferry
final saddleBOT
nova ferry
How do I find y value
cerulean igloo
warm python
I think you have to find te values of p for both values of x(if possible)
gritty solar
Shouldn't $\floor{\log_2 (x^2 - 2x + 5)}$ be discontinuous at $x = 1$
soft zealotBOT
neonperseus
boreal spruce
Problem: Given a circle $PQRST$ with $PQ=7$, $QR=9$, $\angle PQR=90$ degree and $\angle TRS=30$ degree, find the length of $RS$.
Using Pythagoras's Theorem, we can find that $PR=\sqrt{130}$. However, it seems impossible to solve for the length of $RS$ as none of the side lengths of $\triangle TRS$ are fixed. Is there a way to solve this problem?
final saddleBOT
Problem: Given a circle $PQRST$ with $PQ=7$, $QR=9$, $\angle PQR=90$ degree and ...
soft zealotBOT
trenton_math
final saddleBOT
@boreal spruce Has your question been resolved?
final saddleBOT
@boreal spruce Has your question been resolved?
boreal spruce
Connect the points P and T <:hmmCat:831508801646755850>
Ummm yes angle PTR is 90 degrees but how can I proceed further?
final saddleBOT
@boreal spruce Has your question been resolved?
umbral silo
Ummm yes angle PTR is 90 degrees but how can I proceed further?
Maybe trigonometry
Use trigonometry
boreal spruce
Use trigonometry
Alright but there is no other angles in PTR besides 90 degrees in the angle PTR, so trigonometry does not apply here
whole swan
Alright but there is no other angles in PTR besides 90 degrees in the angle PTR,...
Note that angle PSR = 90 degrees
Also, we can deduce that PR is a diameter
boreal spruce
Note that angle PSR = 90 degrees
Yes, but I still cannot apply the trigonometry
Unless there are some ways to relate RS
whole swan
Can't figure it out
Doesn't seem like there is a trivial way to find out RS, may require some tools I don't know about
Yo
Lol
What a waste of my time, we can't find RS
Lol
boreal spruce
So I am trying to find some counter examples
whole swan
There are multiple configurations where TRS is 30 degrees and the conditions are not contradicted
I already found one, I can make infinite different configurations with different lengths of RS
Using Geogebra
You are initial thought process was correct, there is no way to find RS
boreal spruce
ok I will try Geogebra
whole swan
I can share you the file
boreal spruce
Thank you for your time
whole swan
Np
boreal spruce
I can share you the file
oh thanks!
whole swan
In the first one, RS = 8.52, second one RS = 6.58. Counter-example
There are infinite such configurations
boreal spruce
Thank you so much
whole swan
Welcome
celest osprey
I have an issue with maclaurin expansions of composite functions with the lagrange remainder. Im supposed to get the maclaurin expansion to order two of the function ln(1+e^x). I know i can take the derivatives of the function but i'd much rather do a variable substitiution. I'd get ln(2+u) where u+1 is the maclaurin expansion of e^x to the second degree. The problem i encounter is; do i write out the lagrange remainder for the expansion of e^x, and if so what do i plug in as my unknown theta in the maclaurin expansion of ln(2+u)? Do i need to substitute the remainder of the expansion of e^x back in in every u of the expansion of ln(2+u)? Thanks!
final saddleBOT
I have an issue with maclaurin expansions of composite functions with the lagran...
brisk charm
I have an issue with maclaurin expansions of composite functions with the lagran...
Are you looking to just get the first few terms of the expansion or a general formula?
celest osprey
I'd say im trying to get the first few terms
brisk charm
Alright so you could approach this by expanding out the series but it is a little messy
You can use the formulas
ln(1+u) = u - u^2 / 2 + u^3 / 3 - ...
e^x = 1 + x + x^2 / 2 + x^3 / 6 + ...
celest osprey
yes!
brisk charm
And then you get something obnoxious like
ln(1+e^x) = (1 + x + x^2 / 2 + x^3 / 6 + ...) - (1 + x + x^2 / 2 + x^3 / 6 + ...)^2 / 2 + (1 + x + x^2 / 2 + x^3 / 6 + ...)^3 / 3 - ...
celest osprey
Yes hahaha
its only to two terms though
because i will be using it to integrate ln(1+e^x)
so the worst power i'll have to deal with is ^3
brisk charm
Yeah so then you have to deal with expanding that out which is quite annoying
I think you're probably better off just calculating derivatives
Because expanding that out is a mess haha
celest osprey
Yep now that i think about it it's probably a wise suggestion
e^x is pretty nice anyway
brisk charm
But for example to get the constant term it would be 1 - 1/2 + 1/3 - 1/4 + ...
Which is ln 2
celest osprey
that's a super cool way to get it, i figured i'd take the constant out of u so u approaches zero so i dont have to do a taylor expansion
brisk charm
And then the coefficient of x is 1 - 1 + 1 - 1 + ... which doesn't even converge so I guess you can't even get the next coefficient this way
brisk charm
that's a super cool way to get it, i figured i'd take the constant out of u so u...
I think you end up getting the same thing either way
celest osprey
Okay fair enough 😂
celest osprey
I think you end up getting the same thing either way
yes!
okay well thank you very much for the help! Hope you have a nice day and everything c:
do i write .close now?
.close
final saddleBOT
brisk charm
No problem!
tired walrus
the 45th parallel (depicted here) is a circle. what's the radius of this circle?
hexed sedge
root 2
tired walrus
❌
hexed sedge
1?
scarlet sequoia
doesn't really matter what the radius is here, since you're looking for a ratio. But if you want a hint at what it is, the answer is in a single word on your question
static fractal
the two lines here are radii of the earth so they're the same length
try figure out the length of the top side of the triangle there
final saddleBOT
final saddleBOT
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storm loom
why is it P(Z<-1), according to the initial equation they derived, shouldn't it be P(Z>-1)?
final saddleBOT
why is it P(Z<-1), according to the initial equation they derived, shouldn't it ...
wintry kindle
uh yes there rather seem to be multiple issues
Maybe they didn't find ≥ > ≤ on the keyboard so they just used <
P(Z > -1) also doesn't become 1 - P(Z < 1) but instead 1 - P(Z ≤ -1)
unless they utilised symmetry, which would hold if they at least used ≤
storm loom
P(Z > -1) also doesn't become 1 - P(Z < 1) but instead 1 - P(Z ≤ -1)
wait I thought the difference between P(Z>z) and P(Z>=z) would be negligible?
uh oh is it not
storm loom
unless they utilised symmetry, which would hold if they at least used ≤
in that case is P(Z>-1)=P(Z<1)
wintry kindle
in that case is P(Z>-1)=P(Z<1)
≤ then yes
storm loom
oh right right
storm loom
sorry im a little confused
storm loom
why is it P(Z<-1), according to the initial equation they derived, shouldn't it ...
this >?
wintry kindle
nw, if you have a symmetry at the y-axis then P(Z<A) = P(Z>-A)
storm loom
in that case is P(Z>-1)=P(Z<1)
so is this correct then?
wintry kindle
yes
storm loom
so would the answer to the question just be P(Z≤1.2)-P(Z≤1)
storm loom
wait hold on
1.2 on the sd table
is completely different
to the ans they gave
in the working
P(Z≤1.2)=0.5832
not 0.8849
?????????
storm loom
why is it P(Z<-1), according to the initial equation they derived, shouldn't it ...
@wintry kindle if you don't mind, could you please send the working for this question
lmao < and > make me dyslexic
wintry kindle
P(Z≤1.2)=0.5832
Still < btw
not ≤
but if it's a different value that would be funny as well
final saddleBOT
Available help channel!
jovial crane
final saddleBOT
jovial crane
I'm just lost on where to begin
do I multiply the entire thing by 8+sqrt2/8+sqrt2 or something else
ornate solstice
When rationalizing the donominator you multiply by the radical on the bottom so here you would multiply by rad 2 to the numerator and denominator.
rad 2 is just the sqrt of 2
jovial crane
oh gotchaa
dry light
Multiply by the conjugate
dry light
The conjugate of (a+b) will be (a-b)
jovial crane
OKay so 8-sqrt2?
jovial crane
Nothing on the bottom cancels out when I do that right?
I just hard multiply both of them
rare shale
uhm, so there seems to be a continuation of the assingment i sent here a few minutes ago. so now, how do you solve this one?
final saddleBOT
uhm, so there seems to be a continuation of the assingment i sent here a few min...
rare shale
idk. that's the only that's there
the instructions was cut off, since i can't access the g-drive directly and the photo isn't mine
here's the should be instruction
i've already answered no. 1-6
idk maybe its just an error?
rare shale
yeah ig so
my teacher isn't responding
well i'll just solve this later
thank you
.close
final saddleBOT
final saddleBOT
Available help channel!
fierce escarp
final saddleBOT
magic sparrow
32 to the power of 5, is 32*32*32*32*32, that you would agree with right?
fierce escarp
ye
magic sparrow
See if you can write just 32=2^a
fierce escarp
ok
magic sparrow
Basically, is 32 a power of 2? And if so what is the power
fierce escarp
See if you can write just 32=2^a
i cant
magic sparrow
Why not?
fierce escarp
it onbly lets me put in a number
fierce escarp
i dont really understand
magic sparrow
Basically, is 32 a power of 2? And if so what is the power
^
fierce escarp
32 to the power of 5 is 33554432 no?
magic sparrow
Not asking you about that
magic sparrow
…
fierce escarp
i mean ^5 sry
fierce escarp
ye
magic sparrow
32 to the power of 5, is 32*32*32*32*32 as we said earlier. Now we’ve just said that 32=2^5. So replace all of these 32’s with 2^5 and then simplify.
fierce escarp
so 2^5x 2^5x 2^5x 2^5x 2^5?
magic sparrow
Yes, but then you must simplify
fierce escarp
oh like that
magic sparrow
Use the fact that $a^b\cdot a^c=a^{b+c}$
soft zealotBOT
Austin
fierce escarp
so i only add the powers to gether i dont multiply the 2s?
magic sparrow
Yes
magic sparrow
Awesome
fierce escarp
appreciate ur help
magic sparrow
Np
final saddleBOT
vital crag
Help channels are for math problems. You want #discussion
tired walrus
i'd expect that "get ready for N'th grade" is some kind of review of material from grades 1 to N-1
but it's probably best if you just look at them
it won't hurt
robust mulch
Id think the Nth grade ones are for the topics in that grade while the get ready courses have the info prior
Like ann said
final saddleBOT
@polar elk Has your question been resolved?
buoyant prawn
I need help with the very last par tof my volume problem
velvet silo
final saddleBOT
velvet silo
can someone
read the cursive for me
like it's not very clear
especially 2nd sentence
Each x (around?)
is it around?
worldly vale
should correspond
celest crane
For a given function f(x) to have an Inverse as a function, f(x) must be one-to-one. Each x should correspond to one y and each y-value should correspond to exactly one x-value.
velvet silo
i hate it when math teacher's handwriting is shit like
math is already hard concept to
learn
velvet silo
For a given function f(x) to have an Inverse as a function, f(x) must be one-to-...
thanks so much 🙂
gritty zodiac
Thats called a bijection btw, idk why but that info might be of use to u
static fractal
in some literature, bijections are called one-to-one-correspondences
while one-to-one is reserved for injections (and onto for surjections)
gritty zodiac
I see
static fractal
but this uses the phrase "one-to-one concept" to introduce the notion of a bijection, so 
gritty zodiac
Yeah wait what? Why is the inverse function used as a definition for one to one concept
Or rather used for
glad basalt
I have
glad basalt
-2(q+h)(q+h)
I thought it didn’t matter the order that you multiply
But for some reason it does?
magic sparrow
It doesn’t
glad basalt
-2(q+h) THEN multiply that with (q+h) is not the same as (q+h)(q+h) times -2
hearty zephyr
,w (-2(q+h))(q+h) == -2((q+h)(q+h))
soft zealotBOT
soft zealotBOT
Requested by geoxcaliber
glad basalt
,w (-2(q+h))(q+h)
soft zealotBOT
glad basalt
,w -2(q+h)^2
soft zealotBOT
hearty zephyr
that's hard to answer when you haven't shown any work....
glad basalt
(Sending)
glad basalt
that's hard to answer when you haven't shown any work....
You should wait
In what I got
It doesn’t cancel
Idk how it cancels that much
.close
final saddleBOT
final saddleBOT
Available help channel!
bold leaf
someone please help me with functions
final saddleBOT
someone please help me with functions
bold leaf
i feel like an idiot. ive tried getting help multiple times
and im still not getting it at all
please help me out
tranquil pine
someone please help me with functions
whats your question
bold leaf
i need to understand these
but i dont
and its bothering tf out of me really
i know some of them like y=x^2
i know thats quadratic
y=1/x is reciprical
its just everything thats not similar to the toolkit functions
i dont know how to graph them or even where to start on it
its hella overwhelming to me
<@&286206848099549185>
please someone help me understand this after trying to get help i thought i understood it but i mostly dont
final saddleBOT
@bold leaf Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
tender rampart
final saddleBOT
tender rampart
had a similar question in here a half hour ago and it;s the same deal
why are we going back to sine
worldly vale
you are integrating cos(2x)
tender rampart
to get sin back
why
why arent i plugging the limits into cos(2x)
- i move pi outside
-i move a squared 2/3 outside times pi
- i square sin and integrate giving me 1/2(1-cos(2x))
obtuse heath
- i square sin and integrate giving me 1/2(1-cos(2x))
You got 1/2(1-cos(2x)) after integration?
tender rampart
wolfram says sin^2 is equal to that yeah
obtuse heath
Ok so it's before integration
obtuse heath
What's an identity substitution?
tender rampart
like that trig identity is equal
and me putting 1/2(1-cos(2x) isn't integrating sin^2
they're just trig identities
is that what you're saying?
obtuse heath
Yeah 1/2(1-cos(2x))=sin^2 x is just the half angle identity
tender rampart
okay yeah so not integration, correct?
worldly vale
you know when integration has occured because the integral sign will disappear
tender rampart
I'm doing this by hand lol
obtuse heath
okay yeah so *not* integration, correct?
What is not integration?
I mean what are you refering to?
tender rampart
the exact thing you just said
obtuse heath
Ok
tender rampart
is that correct?