wait
#help-0
oak chasm
I hope I didn't make any mistakes. Every term is positive except the subtraction, and 4n is larger than that term for all positive n. So, your expression is greater than 1/n for all positive n.
fiery galleon
ah yes calc 2
cursive edge
i c
how to find the sum of
1/n^2 tho
as series goes to infinity
and also thanks
oak chasm
how to find the sum of
Back. It's pi^2/6, but I don't know how to find it.
Finding the exact value is probably beyond an integral calculus course, I think.
lone heartBOT
@cursive edge Has your question been resolved?
modern gazelle
does anyone know how to do this
lone heartBOT
does anyone know how to do this
modern gazelle
I know what the answer is but im not sure how to achieve it
x = 0 but i dont know how to approach it
modern gazelle
so just u or smth
modern gazelle
ok
elfin bough
my bad
modern gazelle
but u = 1 if you do that
ocean whale
I think the suggestion is u = 9^x
So that way you have an equation with u instead of 9^x
ocean whale
So you got u = 1
But don't forget that you did u = 9^x
So you need to put back in 9^x to find x
Meaning 9^x = 1
ocean whale
Yep
terse scroll
Could I plz get some help regarding question c
lone heartBOT
Could I plz get some help regarding question c
terse scroll
oak chasm
OK, so you can separate it into a right triangle on the far left, then a rectangle, then a right triangle in the lower right.
You do that by drawing a line from the upper left corner straight down until it hits the bottom. Then you draw a line from the corner where the bottom starts to drop down straight to the right until it hits the right side.
That'll give you three things to find the area of.
Does that make sense?
@terse scroll
inner trench
o
inner trench
Does anyone here knows how to solva the gahdam Product Sudoku? 😭
shrewd lava
Hello, I am just curious to see if I got the right answer to this question:
shrewd lava
Answer:
last ether
Well one of the identities for tan(2a) is tan(a)/[1-tan^2(a)]
In this case, a = arccos(1/x)
last ether
Well one of the identities for tan(2a) is tan(a)/[1-tan^2(a)]
This identity is nice because you only need to find tan(arccos(1/x))
last ether
Well do you know how to simplify tan(arccos(1/x))?
shrewd lava
tan(2arccos(1/x)) can be translated as tan(2theta)
and then
theta = arccos(1/x) or cos(theta) = 1/x
then I would use a triangle while plotting cos(theta) = 1/x on it to find tan(theta) then eventuall tan(2theta)
?
last ether
Well one of the identities for tan(2a) is tan(a)/[1-tan^2(a)]
Literally use this identity
I gave you the identity
shrewd lava
oky
last ether
I also told you a = arccos(1/x)
shrewd lava
okay lets see
harsh oasis
how would one go about finding the slope of these lines? i tried some practice problems and i see that ln plays a huge role. I'm a bit lost outside of that I got the b value as 1 though
blazing steeple
To clarify, do you want to find the derivative of f(x)?
harsh oasis
trying to find the equation of the line in y=mx+b
blazing steeple
Ok, so you should have found that b=1 using the point of intersection at x=0.
Now, you have to use the point of intersection at x=log 7
harsh oasis
correct yes b is =1 so i would want to use the change in y over the change in x?
blazing steeple
Yes
harsh oasis
(1-10^x)/(0-log7)
blazing steeple
Yes, but x is equal to log 7
blazing steeple
yes
harsh oasis
i think i understand this now
blazing steeple
great, any more questions
harsh oasis
nope thats everything lol I was being confused as all my practice questions kept giving me ln instead of log
blazing steeple
understandable
harsh oasis
Thank you though very much
blazing steeple
of course
elfin kernel
lone heartBOT
ocean sealBOT
rustic coral
Yeah that seems fine
lone heartBOT
lone heartBOT
Available help channel!
daring rapids
Please explain what this means
lone heartBOT
Please explain what this means
daring rapids
Thx
last ether
If you had some line makes some angle θ anticlockwise from the positive x axis, then that "some line" is the terminal arm
Like
daring rapids
Yeah
last ether
It's giving you properties of the angle it makes
daring rapids
But idk how to determine from what they gave me
last ether
Well are you familiar with polar coordinates?
daring rapids
No
last ether
Alright well, for now, you can think of the x axis as cos(θ) and the y axis as sin(θ)
daring rapids
Ah i c
last ether
So when it says that cos(θ) < 0 and sin(θ) > 0, the arm lies in a quadrant where x < 0 and y > 0
last ether
No. Q3 has negative y values
last ether
Memorize this.
oak chasm
Yes, that's right.
lone heartBOT
daring rapids
🙇🏻♀️🙇🏻♀️🙇🏻♀️
lone heartBOT
Available help channel!
strong trout
Critical points are when f'(x)=0 would that mean that only be C,F,H?
oak chasm
f'(c) = 0 or f'(c) doesn't exist.
sage cargo
Critical points are when f'(x)=0 would that mean that only be C,F,H?
The critical points of f are when the function f' equals 0, which is when this graph is zero
Assuming there isn't some information that says there's a discontinuity, which, could cause a critical point. It looks continuous to me with the information given
oak chasm
Oh, and f(c) has to exist.
So, f(c) exists and f'(c) = 0 => c is a critical point. f(c) exists and f'(c) doesn't exist => c is a critical point.
strong trout
The critical points of f are when the function f' equals 0, which is when this g...
I see, will it be safe to assume here that C,H, and F are critical points of F since it does exist and when f'x=0?
oak chasm
Assuming that f(x) for each point exists, yes.
sage cargo
^
strong trout
got it ok and to clarify critical points of f'x can be either max/min or inflections using f''x?
sage cargo
I do believe so
I'm pretty sure that sometimes the critical points can also just be nothing, but it's been awhile since I thought about that
muted relic
lone heartBOT
muted relic
the last line: from a) letting k+1=n shouldnt k+1 C 1 + k+1 C 2 = k+2 C 2 ?
lone heartBOT
@muted relic Has your question been resolved?
muted relic
<@&286206848099549185>
lone heartBOT
@muted relic Has your question been resolved?
wary marsh
the last line: from a) letting k+1=n shouldnt k+1 C 1 + k+1 C 2 = k+2 C 2 ?
As much as i can see
What they’re doing here is breaking (k+1)C1 = kC0 + kC1 and so on
lone heartBOT
@muted relic Has your question been resolved?
reef heath
e
fierce prairie
2.718281828459045…
barren portal
$e = 1 + \frac{1}{1!} + \frac{1}{2!} + \frac{1}{3!} + \frac{1}{4!} + \frac{1}{5!} + \ldots$
ocean sealBOT
.doc
lone heartBOT
@reef heath Has your question been resolved?
lone heartBOT
@reef heath Has your question been resolved?
ivory pivot
$\lim_{n\to \infty}(1+\frac{1}{n})^n$
ocean sealBOT
everg
lone heartBOT
@reef heath Has your question been resolved?
languid belfry
$1+\sum_{n=1}^{\infty}\frac{1}{n!}$
oops
bruh
@ivory pivot
trying to write infinity in the bot
idk how
ivory pivot
$\infty$
ocean sealBOT
everg
ivory pivot
gg
ocean sealBOT
Alpha
languid belfry
idk im not sure
ivory pivot
no i don t think so
languid belfry
bruh
ivory pivot
but its is an instructive exercise
languid belfry
ok
foggy pecan
it is very nice to prove :
$\mathop {\lim }\limits_{n \to \infty } {\left( {1 + \frac{1}{n}} \right)^n} = \mathop {\lim }\limits_{n \to \infty } \sum\limits_{k = 0}^n {\frac{1}{{k!}}}$
ocean sealBOT
Joanna Angel
distant frost
function(x) goes trough coordinates (1,2) and has a minimum/maximum of (2,3) give the formula of function (x)
distant frost
this is the parabola that corrosponds to it, i know how to solve the parabola equation if i am given 2 sets of coordinates that arn't the minimum/maximum coordinates, i have no clue how to solve this version
drifting seal
function(x) goes trough coordinates (1,2) and has a minimum/maximum of (2,3) giv...
First thing u know, is that f(1) = 2
and f(2) = 3
distant frost
and then?
gray isle
start with vertex form since you're given the vertex
lone heartBOT
@distant frost Has your question been resolved?
distant frost
.close
wind thicket
hi could i get some help with this? i dont really know what to do
lone heartBOT
hi could i get some help with this? i dont really know what to do
@wind thicket Has your question been resolved?
lone heartBOT
@wind thicket Has your question been resolved?
smoky arch
Not sure how i can describe it well.
For example:
A = 0.08 (start)
B = 0.8 (end)
C = 6 (amount of times)
A1*X=A2, A2*X=A3, A3*X=A4, A4*X=A5, A5*X=A6 = B
X=?
So im searching for a formula that calculates x for a given start A and given end B, it being multiplied a given amount of times C in this way. 
prime badge
ocean sealBOT
Result:
1.4677992676221
tough lintel
lone heartBOT
lone heartBOT
@tough lintel Has your question been resolved?
wintry mango
the calculus doesn't seem correct
$f_{per}=\frac{a_0}{2}+\sum\limits_{n=1}^{\infty}(a_n \cos nwt+b_n \sin nwt)$
$a_n = \frac{2}{T}\int_{-\frac{T}{2}}^{\frac{T}{2}}f(t)\cos nwt dt}$
$b_n =\frac{2}{T}\int_{-\frac{T}{2}}^{\frac{T}{2}}f(t)\sin nwt dt}$
ocean sealBOT
pck
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
tough lintel
this is an odd function so a0, and an are 0
wintry mango
yes!
tough lintel
so i cut the intevral in half and multiply by two
and L in this case is 1- -1 / 2 == 1
so its 2/l integral 0 to 1 of x^3sin(npix) i thought
wintry mango
yes,your calculus expression is correct
tough lintel
sweet, i got it right
i looked up a youtube example from -pi to pi
with this pi cancels out in the sin expression when plugged into L
lone heartBOT
@tough lintel Has your question been resolved?
tough lintel
.close
valid wagon
lone heartBOT
valid wagon
im struggling to check it
this is the full thing, do i just sub x=acosu y=asinu ?
oh wait i think i also need to multiply the integrand by r as well ill try thatg
still having issues I get cos^2-sin^2
valid wagon
im a bit confused as to why the dx and dy are seperate
because i missed this lecture
I am re doing it
I didn't substitute right
tall topaz
they represent an infinitesimally small change in x and y along the path C2 here and we can parametise
tall topaz
I didn't substitute right
yeah
valid wagon
yeah I got it now, I was multiplying by r because I remember doing something similar when transforming integral into polar cooards for triple integrals
.close
clever obsidian
How would i go about solving this?
lone heartBOT
How would i go about solving this?
long axle
Were any of those originally trig values ?
clever obsidian
nope
this is the equation for surface area for a quadratioc function i have
there were no trig stuff involved
long axle
Ok
sharp thorn
is that 2pi the upper limit or a part of integrand
sharp thorn
then take it oout
carmine reef
$\int (c_1x^2+c_2x+c_3)\sqrt{1+(c_4x-c_5)^2}~dx$
ocean sealBOT
thewizardofOU
carmine reef
maybe u = tan(0.2628x - 0.7318)
clever obsidian
How would i substitute that in?
lone heartBOT
@clever obsidian Has your question been resolved?
lone heartBOT
@clever obsidian Has your question been resolved?
carmine reef
How would i substitute that in?
Then isolate x to substitute
Actually probably u=0.2628x-0.7318
Then split the integral up
Then v=tan(u) on the parts that need it
lone heartBOT
@clever obsidian Has your question been resolved?
fervent crystal
hello
lone heartBOT
The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.
fervent crystal
for (i)
cinder egret
!show
lone heartBOT
Show your work, and if possible, explain where you are stuck.
cinder egret
use the given : f(1) = 5/2
fervent crystal
then?
cinder egret
maybe try f(0.5 + 0.5)
fervent crystal
how do i get f(a+b)
cinder egret
try to think
fervent crystal
maybe try f(0.5 + 0.5)
a and b are natural numbers so they have to be integers
fervent crystal
thats what im trying
lone heartBOT
@fervent crystal Has your question been resolved?
fervent crystal
almost
fervent crystal
can
can someone check is f(2) is 11/4 or 21/2
im getting 11/4 but its saying 21/2
can someone do (ii)
i tried wont match
@cinder egret can you help please
😭
cinder egret
?
fervent crystal
i gooot it at laaaaaaaast
cinder egret
ur welcome
fervent crystal
.close
neat cipher
ight ty
vale crag
what's up ? you have a question ?
lone heartBOT
@neat cipher Has your question been resolved?
vapid shuttle
.close
last aurora
lone heartBOT
last aurora
Can someone help me understand why 4 and 6 are R- minimal?
If I let R be a partial order on A (R⊆AxA). Let B⊆A. b∈B is R-minimal if ∀x∈B(xRb) -> x=b
^ thats the definition given to me in class
Apply the definition i learned to the example in the photo
B= B_1 U B_2
B = {4,6,8,12,16...}
aka all numbers that are a positive multiple of 4 and 6
i see that 4R4 is true , and that implies 4 =4 which is true
6R4 is not true, and x doesnt equal b, which is true cuz 6!= 4
but 8R4 is true, but x is not equal to b
doesnt this contradict b∈B is R-minimal if ∀x∈B(xRb) -> x=b?
lament forge
...i don't think 8R4 is true
lament forge
like just expanding the definitions
8R4 iff (8,4) is in R, right? or am i getting that the wrong way round
and then (8,4) is in R iff 8 divides 4, but it doesn't (4 divides 8, 8 doesn't divide 4)
last aurora
Waiiiit
sorry hold up my brain is kinda slow
i thought 8|4 is true cuz 8 = 4k where k = 2
lament forge
yeah you got the definition of | the wrong way around
8 | 4 would mean that 4 = 8k for some k
last aurora
oops.
I just went back in my notes u are right i messed up
thank you so much! i get it now
.close
rustic nimbus
hello
rustic nimbus
how i determinate the range of f(x)=(x-3)/e^x
cinder egret
!show
lone heartBOT
Show your work, and if possible, explain where you are stuck.
rustic nimbus
im stuck because i dont know how to do it
cinder egret
just analyze the behavior of the f(x) as x approaches positive and negative infinity. so take the lim
vapid shuttle
both
vapid shuttle
not the only way
rustic nimbus
what are the other way
cinder egret
you can take the derivitve
but its complex idk if u could understand it
if u want me to explain i can
rustic nimbus
ok i want
cinder egret
just take f'(x) = 0 then find the f''(x) to determine concavity and identify local minima or maxima
rustic nimbus
i dont need to do f''(x)=0 ?
topaz nacelle
you could
cinder egret
no
u can also analyze the interval there is alot of way to be honest
but i would go for the first way
cinder egret
yup
cinder egret
yh
rustic nimbus
but how i could know the right thing is negative for all x ?
in the left i know because there is the "-"
cinder egret
its like multiplying by -1
rustic nimbus
yeah this is in the left
but in the right ?
i need to distribute ?
@cinder egret hey are you still here sorry to ping
<@&286206848099549185>
rustic nimbus
<@328315001427197954>
can someone tell me why the green thing is negative ?
lone heartBOT
@rustic nimbus Has your question been resolved?
indigo fulcrum
not sure how to go about solving this one
strange meadow
what are properties of a pdf?
indigo fulcrum
the integral should equal 1 as it approaches any number
from a to b sorry
not approaches
strange meadow
across the whole domain you mean
indigo fulcrum
yes
strange meadow
Does that help? Can you solve it now
indigo fulcrum
i know it should be the integral of x^3/4 from 0 -> C
strange meadow
What is that equal to
indigo fulcrum
1
indigo fulcrum
thank u, ill try that and lyk
strange meadow
✅
indigo fulcrum
i got c = 2, do you know if thats correct? it worked out nicely so im going to assume it is
.close
copper forum
yoooooo i need help with the last 2 boxes of this problem
lone heartBOT
yoooooo i need help with the last 2 boxes of this problem
lone heartBOT
@copper forum Has your question been resolved?
pseudo ice
Did you draw the picture? If so, could you share it?
azure shuttle
Solved?
copper forum
yea
lone heartBOT
Available help channel!
wispy ether
d)
lone heartBOT
@wispy ether Has your question been resolved?
lone heartBOT
@wispy ether Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
distant nymph
What’s my mistake?
lone heartBOT
What’s my mistake?
distant nymph
Im following the rules but Idk what mistake I did for Exponential Functions.
distant nymph
What’s my mistake?
It’s “incorrect”
long axle
1/3 to the -2 u sure about that?
Same with -1
Sarrangh
Try writing 1/3 to have a base of 3
Then raise it to the -2
distant nymph
wdym
long axle
$(3^{-1})^{-2}$
ocean sealBOT
Stephen
cinder egret
9
distant nymph
just 9
cinder egret
1/1/9
runic aurora
,calc (-1)*(-2)
ocean sealBOT
Result:
2
so 9 is the answer for that one?
cinder egret
yh?
alpine sable
I never used latex in my life so i have no clue what i am doing here. I want to get a very simple task done and don't want to learn latex just for that. How do i make these matrix definitions appear under each other instead of next to each other
remote heron
you can try the align* environment
alpine sable
u = [1 1 2]
[2 0 3]
[2 1 -1]
v = [-4 1 3]
[ 2 1 -1]
[ 0 2 0]
u*v = [-2 6 2]
[-8 8 6]
[-6 1 5]
I would do it like this using raw text
alpine sable
you can try the ```align*``` environment
How, where do i add it
ocean sealBOT
jan Niku
\begin{align*} u &= \mqty( \imat{2} ) \\ v &= \mqty( \imat{3} ) \end{align*}
remote heron
im using mqty but you dont have to
the idea is that you begin/end environment just like it is up there
and then you put & before the symbol you want to align on
here, i have it aligning on the equals
then you use \\ to start a new line
remote heron
How, where do i add it
you should try #latex-help in general, too, if you have other headaches
alpine sable
you should try <#840667252793802752> in general, too, if you have other headache...
I looked for a channel like this but didn't find this one. It's not shown in the channel list?
alpine sable
then you use ```\\``` to start a new line
alpine sable
\documentclass{standalone}
\usepackage{amsmath}
\begin{document}
\begin{align*} u &= \mqty( \imat{2} ) \\ v &= \mqty( \imat{3} ) \end{align*}
\end{document}
ah crap what gives align
ocean sealBOT
duvio
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
remote heron
is it not ams
oh
its complaining about mqty and imat
change it to be your matrices
just wrap it in that environment
you can use imat and mqty
but you need to \usepackage{physics}
alpine sable
F it, i'll just use raw text, it's not worth the effort
remote heron
whats your original matrices
remote heron
I never used latex in my life so i have no clue what i am doing here. I want to ...
here
\begin{align*}
u &= \begin{bmatrix}
1 & 1 & 2 \
2 & 0 & 3 \
2 & 1 & -1
\end{bmatrix} \
v &= \begin{bmatrix}
-4 & 1 & 3 \
2 & 1 & -1 \
0 & 2 & 0
\end{bmatrix} \
u \times v &= \begin{bmatrix}
-2 & 6 & 2 \
-8 & 8 & 6 \
-6 & 1 & 5
\end{bmatrix}
\end{align*}
ocean sealBOT
jan Niku
\begin{align*}
u &= \begin{bmatrix}
1 & 1 & 2 \\
2 & 0 & 3 \\
2 & 1 & -1
\end{bmatrix} \\
v &= \begin{bmatrix}
-4 & 1 & 3 \\
2 & 1 & -1 \\
0 & 2 & 0
\end{bmatrix} \\
u \times v &= \begin{bmatrix}
-2 & 6 & 2 \\
-8 & 8 & 6 \\
-6 & 1 & 5
\end{bmatrix}
\end{align*}
remote heron
@alpine sable :p
alpine sable
ChatGPT has at least one use
alpine sable
**jan Niku**
```latex
\begin{align*}
u &= \begin{bmatrix}
1 & 1 & 2 ...
I'll take that. Thanks!!
remote heron
just use latex
slow lance
lone heartBOT
ocean whale
Are you saying that's wrong?
slow lance
It won't take it as a correct answer
sour dove
ocean sealBOT
MellowDramaLlama
left scarab
how can i solve this:
((c^2 - b^2) - 5) + ((a^2 - c^2) - 5) + ((b^2 - a^2) - 5)
left scarab
i started with this problem
north perch
how can i solve this:
`((c^2 - b^2) - 5) + ((a^2 - c^2) - 5) + ((b^2 - a^2) - 5...
Just open bracket
old heath
You did it correctly
left scarab
Just open bracket
removing the brackets won't change the equation?
north perch
No
left scarab
oh cool
so after removing brackets, everything starts to cancel
and im left with -15
north perch
Yep
alpine sable
did i do this right, i am not so confident
lone heartBOT
did i do this right, i am not so confident
rich silo
Yes, it seems right
lone heartBOT
lone heartBOT
Available help channel!
north perch
A man has salary of 15k in the first month of his job and the salary in nth month is nk greater than the salary in (n-1)th month. find his annual income in the first year of job if k=1000
storm ridge
A man has salary of 15k in the first month of his job and the salary in nth mont...
So the salary increases by nk every month
north perch
yep
cinder egret
k is constant right?
north perch
k is 1000
storm ridge
So for 1st month, it's 15K
2nd, it's 15k+k
3rd would be 15k+k+2k?
Coz it increases by nk, in itself is a variable
north perch
2nd would be 15k+2k and 3rd would be 15k+2k+3k
north perch
no
storm ridge
Idts
Coz the difference needs to be constant in that formula
Here the diff(salary increase) itself is in an A.P
cinder egret
lets have an example lets assume that n = 3
so n = 1:
15k
n = 2
17k
n = 3
20k
@north perch
storm ridge
So for 1st month, it's 15K
2nd, it's 15k+k
3rd would be 15k+k+2k?
This is wrong nvm
Difference between salaries of 2 months= nk
cinder egret
so a_n = a_n-1 + n * 1000
lone heartBOT
north perch
so a_n = a_n-1 + n * 1000
a_n not s_n
lone heartBOT
Available help channel!
static panther
how do i start?
lone heartBOT
how do i start?
static flume
So whenever there is a math problem
you should try to find a simpler problem to start
I see two that might be usefull
one is find sin(cos^-1(x))
and the other is finding sec(tan^-1(x))
do you have any idea how to start now?
static panther
let me try that
long axle
Generally I just draw a right triangle for these types of problems
static panther
how does the abs value affect this
static flume
how does the abs value affect this
don't worry about it
when drawing the right triangle
you don't need to consider negatie angles
static panther
i got sqrt(2-x^2) but i stil ldont see hopw i got there besides algebra does someone mind explaining
static flume
i got sqrt(2-x^2) but i stil ldont see hopw i got there besides algebra does som...
For which one
sin(cos^-1(x))
static panther
as final amswer
static panther
tan
static panther
like the x is cos and y is sin?
static flume
yes
static panther
ok yes
static panther
ok
static panther
ok
static panther
yes
static flume
so basically taking
sin(cos^-1(x))
coverts the x cord into the y cord
makes sense?
static panther
yea
static panther
ok let me read that
static flume
basically what's happening is this(written out more formally)
cos^2(x)+sin^2(x)=1 (unit circle)
x=cos^-1(x)
cos^2(cos^-1(x))+sin^2(cos^-1(x))=1
x^2+sin^2(cos^-1(x))=1
sin^2(cos^-1(x))=1-x^2
sin(cos^-1(x))=sqrt(1-x^2)
static panther
i see
static flume
ok
now for the second part
sec(tan^-1(x))
do you have any idea on how to do this
static panther
based off what u said i should be x^2 +1
static flume
I don't think so
write now I have just simplified the inner part of the problem
oh wait
my bad
static panther
oh yea forgot to sqrt
static flume
ok
so now
sqrt(x^2+1) you know that this = sec(tan^-1(x))
and you know sin(cos^-1(x))=sqrt(1-x^2)
static panther
plug in the first part
static flume
sorry
static flume
wait how do i simplify sqrt(x^4-2x^2+2)
ye
so
sqrt(x^2+1)
plug in the other thing
sqrt(sqrt(1-x^2)^2+1)
then the sqrt and ^2 cancel
sqrt((1-x^2)+1)
and finally add the 1
and get
sqrt(2-x^2)
static panther
wait what im sorta lost
static flume
i got sqrt(2-x^2) but i stil ldont see hopw i got there besides algebra does som...
so yeah you were right
static flume
wait what im sorta lost
where
static panther
the simplifying portion
static panther
x^4-2x^2+2
static flume
sqrt(sqrt(1-x^2)^2<-write here+1)
static flume
x^4-2x^2+2
no remeber that the ^2 is outside of the sqrt
your taking sqrt(1-x^2) Then squaring it
static panther
OH I SEE IT
static flume
yup
static panther
BUT WHERE DID THE SQRT COME FROM IN THE FIRST PART
I THOUGHT THE FIRST PART WAS JUST 1-X^2
static flume
sqrt(x^2+1) you know that this = sec(tan^-1(x)) you told me this
and you know sin(cos^-1(x))=sqrt(1-x^2)
remeber this
static panther
no i kept forgetting a^2 + b^2 = c^2 was a + b = c and not sqrting the final
.close
lone heartBOT
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Available help channel!
kindred jacinth
I am currently stuck on (b). Not sure how i should continue to solve the missing digit. Also is part(a) correct ?
kindred jacinth
kindred jacinth
What is ISBN?
its a 10 digit bar code
lone heartBOT
@kindred jacinth Has your question been resolved?
kindred jacinth
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shut dove
am solving the 1-D advection-diffusion equation, but I am stuck on how to implement the formula into my code. I understand how to the the next time step when the advection term and diffusion term are separate, but I am stuck now when they are both together. I am using Crank-Nicolson for the Advection term and RK4 for the diffusion term. I am Able to get this far but i realize that RK4 is a multi-step method with 4 steps. What I have solved by mistake is RK2. How do I advance further than this? What i am trying to find the the next timestep U^n+1. In this image D1 is a derivative matrix for the 1st derivative and D2 is one for the 2nd derivative.
shut dove
how do i continue this so i am correctly using rk4 for diffusion and crank nicolson for advection
lone heartBOT
@shut dove Has your question been resolved?
shut dove
<@&286206848099549185>
plucky sluice
You might have better luck in the numerical analysis channel
shut dove
😅 thanks
plucky sluice
But someone might come along, depending on which helpers are available
shut dove
its not super urgent i got like 7 days to finish this.
plucky sluice
I sorta know what you're doing, but I'm wouldn't be confident enough to give help.
shut dove
well if you get the inspiration to try and help my dms are always open 😄
gonna close this so i dont take up room
.close
ember fiber
can anyone expalin why f'(x) does not exist at 0?
lone heartBOT
can anyone expalin why f'(x) does not exist at 0?
ember fiber
how does x^(-1/3) make it not exist at that point
storm ridge
how does x^(-1/3) make it not exist at that point
x^-1/3 =
ember fiber
ohh its clear once u convert to radical form
storm ridge
Np
ember fiber
Np
even if the derivative doesnt exist at that point, we still use that point on the function itself when trying to get min/max right?
storm ridge
even if the derivative doesnt exist at that point, we still use that point on th...
The point exists on the function, and also depends... If it's a local maxima/minima then yes, global I'm not really sure
ember fiber
oh right, i just remembered you can only use first derivative tests on continuous functions
ember fiber
The point exists on the function, and also depends... If it's a local maxima/min...
gotchaa
storm ridge
oh right, i just remembered you can only use first derivative tests on continuou...
Right...
lone heartBOT
@ember fiber Has your question been resolved?
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Available help channel!
ornate wyvern
can this be done on casio classwiz or any scientific calcs
lone heartBOT
can this be done on casio classwiz or any scientific calcs
@ornate wyvern Has your question been resolved?
upbeat hornet
can this be done on casio classwiz or any scientific calcs
Which step?
lone heartBOT
@ornate wyvern Has your question been resolved?
tacit jungle
can this be done on casio classwiz or any scientific calcs
im using casio 580 and the method i use is shift+solve
languid bolt
If I had a question like....
A^T + B^T = some random 2x2 matrix, how would i solve it?
languid bolt
the question is find A + B
Wait random question, would it be equal to (A + B)^T?
wait yeah?
.close
faint monolith
hi
faint monolith
wait
help with Q9 number 8 pls
cant think of how to make 6000 with the given numbers
snow cobalt
what did you simplify log(6000/7) to
gray isle
express 6000 as a product of 2s,3s,10s
snow cobalt
and what can you factorize 6000 to
faint monolith
idk i cant think of how those 4 numbers can factorise into 6000
snow cobalt
why not?
6000 = 6*1000
factorize 6
factorize 1000 in terms of 10
and then use log(ab) = log a + log b
snow cobalt
and then use log(ab) = log a + log b
which can be reduced to a simpler form using this
snow cobalt
yes
faint monolith
thanks
snow cobalt
no worries
faint monolith
.close
lone heartBOT
neat cipher
<@&286206848099549185> yo
solemn juniper
!15m
lone heartBOT
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.
@neat cipher Has your question been resolved?
neat cipher
<@&286206848099549185> pls
tight estuary
@vital scaffold what is your question?
neat cipher
.
alpine sable
where is the question in this
neat cipher
where is the question in this
that's what my teacher sent us😭
no question
just an equation
alpine sable
how are we supposed to help then
neat cipher
maybe an answer to the equation?
alpine sable
there are infinite values of y,l,f,n,s,w that satisfy this equation, what do you want exactly?
drifting seal
Prove that there exists infinitely many positive integers n such that 4n^2 + 1 is divisible both by 5 and 13.
zealous lichen
first find an integer that satisfy the conditions
then show that n+65k is also a solution for positive integers k if n is a solution
@drifting seal
drifting seal
O
I found that n = 1, it can be divisible by 5
if n = 4, it can be divisible by 13
@zealous lichen
zealous lichen
then show that n+65k is also a solution for positive integers k if n is a soluti...
Do you know how to prove this?
lone heartBOT
@drifting seal Has your question been resolved?
drifting seal
Do you know how to prove this?
Ys, MI?
@zealous lichen
Or idk
I set 4n^2 + 1 = 65l<
k
65k
<@&286206848099549185>
lone heartBOT
@drifting seal Has your question been resolved?
fading briar
The funtions f and g are defined as follows, where a and be are constants.
f(x)= 1+ 2a/x-a for x > a
g(x) =bx-2 for the x ε R
given that f(7) = 5/2 and gf(5) = 4, find the values of a and b
the answer is a=3 and b= 3/2 i have no clue how to get it
fading briar
storm ridge
Let's see now...
exotic canopy
lone heartBOT
haha yeah sorry for the bad quality
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
3
gray isle
in future if typing it out, ensure you use appropriate parentheses
(in this case to clearly indicate the denominator)
show your work
storm ridge
Can you plug in x=7 for me in f(x)
fading briar
in future if typing it out, ensure you use appropriate parentheses
(in this case...
yeah my bad
Here's what i did on a
it's wrong
got 11/3
gray isle
you didn't copy downt he question correctly
ocean sealBOT
Lorentz
gray isle
the 1 isn't part of the numerator in the question
fading briar
you didn't copy downt he question correctly
ah that might be why
storm ridge
Yeah
storm ridge
Yeah
storm ridge
Once you get a it's pretty much over ig
fading briar
so 2a/7-a=(5/2)-1?
fading briar
Thanks i got a=3 now
can you give me a hint on how to calc b i'm getting it wrong
Probably becuase i am copying the question wrong again
@storm ridge
storm ridge
can you give me a hint on how to calc b i'm getting it wrong
Well what is b?
I mean according to the q
fading briar
B should be 3/2
storm ridge
No I mean
fading briar
but somehow i'm getting 12/7
fading briar
i'm sorry i suck at these kinda questions
storm ridge
g(x) =bx-2
Also g(f(5))=4
storm ridge
i'm sorry i suck at these kinda questions
No it's alr mb
storm ridge
g(x) =bx-2
Also g(f(5))=4
You found f(5) right?
fading briar
No it's alr mb
no at all thanks for the help
fading briar
You found f(5) right?
I think so
storm ridge
What's it?
fading briar
i got it to 7/2
ocean sealBOT
Lorentz
storm ridge
And we found out the value of a
fading briar
i did f(5) = 1+2x3/5-3
storm ridge
Ye
fading briar
And we found out the value of a
Yeah the value of a was 3
fading briar
And 2a/x-a at x=5 would give you 3
ah
fading briar
4
fading briar
Ye so that's f(5)
so f(5) is 4?
storm ridge
Yeah, we just found it out didn't we
fading briar
yeah
storm ridge
Right
storm ridge
So g(f(5))= g(4)
And this is 4 according to the q
fading briar
how do i use this to find b?
storm ridge
how do i use this to find b?
Well g(x)= bx-2
And it's given that g(4)=4
Ig you can proceed
fading briar
Well g(x)= bx-2
And it's given that g(4)=4
Thanks for the help ❤️
storm ridge
Nice
fading briar
I know i'm a little behind haha
storm ridge
Thanks for the help ❤️
No problem
storm ridge
I know i'm a little behind haha
Wdym
fading briar
Wdym
idk i just have a hard time understanding stuff
but you explained it well so tahnks
storm ridge
It's alr man