and if you think about it this way
#help-26
calm trellis
if different sign do i subtract or add
dusky sentinel
-x represents the -1
calm trellis
same sign add ang keep the. differents sign subtract?
take the greater number then use it?
calm trellis
i get confused by the signs
calm trellis
no its not
calm trellis
yes
dusky sentinel
then if its regular adding
and subtracting
add them reguarly
like
if its -3
and then u have 2
just do
-3+2
in regular math you would get -1
which is equal to -x
calm trellis
okay i get it
dusky sentinel
yeah
dusky sentinel
okay i get it
may i ask what grade?
neat shell
.close
calm trellis
help
hallow depot
you don t have to solve anything ...this is just an exemple
fallow heart
The steps are there, factorization (of both numerator and denominator) and then simplification
Then the zeroes of f(x) occur where numerator=0
topaz sinewBOT
@calm trellis Has your question been resolved?
midnight fractal
Can anyone tell me way to use the Cauchy or Bunhiacopxki inequality to solve this problem?
topaz sinewBOT
Can anyone tell me way to use the Cauchy or Bunhiacopxki inequality to solve thi...
compact zodiac
!occupied
topaz sinewBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
rigid cloak
compact zodiac
lol
midnight fractal
can anyone help me?
compact zodiac
try to make the first equation a+b+c=9 similar to the expressions inside the square root
idk but that seems like it will work
topaz sinewBOT
@midnight fractal Has your question been resolved?
midnight fractal
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
minor compass
topaz sinewBOT
agile harness
use the kinematic equations
minor compass
i am trying but im not sure if i got the right answer
agile harness
which did you use
minor compass
which did you use
then i did t = (vf - v0)/a
idk what that one even is but i saw it in my textboook idk if it's right or not
i wasnt sure if i should use average speed or not either
in a dif eqaution
west dune
It’s a really dumb question but I need to prove that when a*b=0 a or b needs to be 0 I just don’t know how to write it down correctly
agile harness
It’s a really dumb question but I need to prove that when a*b=0 a or b needs to ...
!occupied
topaz sinewBOT
It’s a really dumb question but I need to prove that when a*b=0 a or b needs to ...
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
minor compass
ty
agile harness
so you solved for a though eighth
and just used that value to find t in the other equation
agile harness
well it should be negative
agile harness
what did you put for v and vo
minor compass
well it says initial v is the higher one
agile harness
mhm 26.5
agile harness
,w ((13.9)^2 - (26.5)^2)/790
thorny flameBOT
agile harness
,w calc (13.9-26.5)/-0.64435
thorny flameBOT
minor compass
so with significant numbers i should leave it as 19.6
bc there are 3 significant numbers in the equation
ok cool
thanks i will prob have a couple more questions if you are up for it
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
astral nova
What is gamma , beta functions and how walli's theorem is derived
topaz sinewBOT
What is gamma , beta functions and how walli's theorem is derived
@astral nova Has your question been resolved?
narrow wyvern
this is a question on computability theory
topaz sinewBOT
this is a question on computability theory
narrow wyvern
<@&286206848099549185>
topaz sinewBOT
@narrow wyvern Has your question been resolved?
topaz sinewBOT
@narrow wyvern Has your question been resolved?
topaz sinewBOT
@narrow wyvern Has your question been resolved?
topaz sinewBOT
@narrow wyvern Has your question been resolved?
topaz sinewBOT
@narrow wyvern Has your question been resolved?
topaz sinewBOT
topaz sinewBOT
Available help channel!
steep cliff
im being asked to show that 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 ..... = 1/3, but when i do it i keep getting 1 as my asnwer? what am i doing wrong
topaz sinewBOT
im being asked to show that 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 ..... = 1/3, bu...
cursive patrol
that is in fact 1
loud oasis
because it is 1
cursive patrol
im being asked to show that 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 ..... = 1/3, bu...
if you want to show something is 1/3, try 1/4 + 1/16 + 1/64 + ...
topaz sinewBOT
cursive patrol
🎉
topaz sinewBOT
Available help channel!
full bough
Hi, I'd appreciate a second pair of eyes on this calc hw (part b). I'm very tired so I could easily be missing something obvious, but this is something I get stuck on often, solving for zero when I can't isolate the variable easily.
Sample problem attached too--it's not helping me much since it doesn't elaborate on how that figure was reached.
topaz sinewBOT
Hi, I'd appreciate a second pair of eyes on this calc hw (part b). I'm very tire...
vernal matrix
Hi, I'd appreciate a second pair of eyes on this calc hw (part b). I'm very tire...
Do you know how to solve quadratic equations?
You have effectively the quadratic $t^2 - t - 2 = 0$ (from your working out)
full bough
I guess I'm not sure how to plug this into quadratic. Can we walk through it?
This class has me very stressed so I might be blanking on really obvious things.
vernal matrix
This class has me very stressed so I might be blanking on really obvious things.
It might be 
but sure we can walk through it 
full bough
Thank you so much.
vernal matrix
Do you e.g. know the quadratic formula? Did you like trying to factor to solve quadratic equations, if you've solved them that way before?
Oh wait-
thorny flameBOT
@vernal matrix
full bough
(t-2)(t+1) ?
vernal matrix
Fixed 
vernal matrix
(t-2)(t+1) ?
And yep 
there you go 
full bough
I'm not sure what to do with this now though to find the velocity. Which figure do i punch into v(t)?
vernal matrix
(t-2)(t+1) ?
Well, of course, you're happy that the solutions [to this = 0] become t = 2 and t = -1, right
full bough
yes--I get that part now I think
vernal matrix
Cool 
now, remember that you don't want negative time
full bough
Thank you for making it make sense lol
With my first calc exam coming up Thursday I WILL be in this server a lot this week
balmy cairn
i feel stupid ash sometimes bro cause i don’t really understand a lot of sh in school
vernal matrix
Wait a moment 
full bough
hm?
vernal matrix
Oh no I'm being slow 
never mind 
whew
vernal matrix
it accepted -48 as the answer on the hw site--does it look wrong somehow?
Noooo you were fine 
I just had a moment there 
full bough
If I want a sanity check on another question do I need to close this one out?
vernal matrix
If I want a sanity check on another question do I need to close this one out?
You can reuse this one if you'd like to 
full bough
Thank you 😄
This one...grr...by my logic the one I have selected is the only one that makes any sense. But the HW site is saying "one of your answers is incorrect" no matter which one I select. 
I can only assume it's getting confused by a written answer field on a math hw...
balmy cairn
Yo rabbit i got a question
full bough
Whats up? 🙂
full bough
College fresh, but it's my second bachelors
full bough
Thanks!
vernal matrix
This one...grr...by my logic the one I have selected is the only one that makes ...
Does it check the written parts? Which were the other questions?
full bough
The entire section is what you see-it says the written part "will be scored later"
I wonder if it's defaulting to assuming it's wrong until the prof goes in. -_-
vernal matrix
Hmmm, it might be something like that, yea 
It should be f'(x) + 3 after all 
vernal matrix
No problem
strong sable
#odes-and-pdes message I think I dont quite understand this hint, why did we do this substitution?
topaz sinewBOT
https://discord.com/channels/268882317391429632/908110794569449553/1285500961317...
@strong sable Has your question been resolved?
strong sable
Why nobody😭
rancid mauve
Instead of solving with the given y1 and y2, they’ve chosen a different y1 and y2 that share the same span as the original two solutions
This simply makes ur calculations easier
By all rights you don’t need to do this, but it will make ur calculations of the derivatives significantly easier
topaz sinewBOT
@strong sable Has your question been resolved?
topaz sinewBOT
topaz sinewBOT
Available help channel!
versed remnant
Is there a Pi but it like sigma?
topaz sinewBOT
Is there a Pi but it like sigma?
versed remnant
Like sigma is addition formula
cursive patrol
Is there a Pi but it like sigma?
ionic oar
[ \sum \prod ]
thorny flameBOT
ananas
versed remnant
My teacher told me that this cannot be added, big pi is doing multiplication.
fair thorn
what
thorny flameBOT
ren
versed remnant
While talking to my teacher about sigma, she told me about pi and it is the same formula as pi sigma, but the only difference is that instead of addition, multiplication is done.
Actually is it?
Because I still can't understand the issue.
odd pagoda
$$\sum_{i=0}^n a_i = a_0+a_1+a_2+\ldots+a_n$$
thorny flameBOT
Denascite
odd pagoda
compared to the picture above
so yes
its the same thing except addition vs multiplication
halcyon willow
how do i find mathematically sec^-1x >=1
topaz sinewBOT
how do i find mathematically sec^-1x >=1
cursive patrol
how do i find mathematically sec^-1x >=1
with inverse function, x = sec(1)
halcyon willow
yeah but
do i take sec on both sides
but theres the inequality
and this fn isnt inc or dec all together
odd pagoda
if you care about an inequality its always easier to first solve the equality
and then look on each side of the solution
halcyon willow
fair enough
but what would u do if u couldnt?
is applying sec on both side valid?
molten crystal
hey, refreshing some linear alg concepts here
if i have a matrix, if i consider the rows vectors and i take all the linear combintions between those vectors, that would be the row space, correct?
odd pagoda
yes
molten crystal
but this linear combination is not something that is "expressed" somewhere in the Ax=b for example. right?
to express that linear combination i would have to write...
row1 * c1 + row2 * c2 right?
c1 and c2 are scalars
molten crystal
yes
odd pagoda
just like A*x does columns
molten crystal
ah ok let me think about that one sec
topaz sinewBOT
im in the second grae
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
molten crystal
ok, yes. c is row vector before A ok.
next field
C=59(F−32)
The equation above shows how temperature F, measured in degrees Fahrenheit, relates to a temperature C, measured in degrees Celsius. Based on the equation, which of the following must be true?
A temperature increase of 1 degree Fahrenheit is equivalent to a temperature increase of 59 degree Celsius.
A temperature increase of 1 degree Celsius is equivalent to a temperature increase of 1.8 degrees Fahrenheit.
A temperature increase of 59 degree Fahrenheit is equivalent to a temperature increase of 1 degree Celsius.
A) I only
B) II only
C) III only
D) I and II only
night imp
next field
can u help me with that?
molten crystal
ok so when i have polynomials i write them in rows, and to solve for some value means i need to think about the combinations of the columns vectors really.
correct?
no it's not. i'm confused
yes it is, i need to find the linear combination of the column space of that matrix
right?
and my confusion is : if i think of the polynomial as a vector, can i graph it and think about it geometrically or not?
i mean can i graph the components? i mean i guess so, i would have a line and parabolas of higher degrees.. but it wouldn't have the same geometrical meaning as if i were using normal vectors
i need clarification on this ☝️
topaz sinewBOT
@molten crystal Has your question been resolved?
molten crystal
<@&286206848099549185> help
loud oasis
ok so we want to solve for when a polynomial is a linear combination of other polynomials. then we would want to write them as column vectors of a matrix, and solve the system Ax = b, because multiplying matrix A by a column vector x is the same as taking a linear combination of the columns of A using the entries of x as coefficients
you can think of a quadratic as an arrow vector in 3D space, with a constant axis, an x axis, and an x^2 axis. i'm not sure this is a very helpful interpretation though
molten crystal
ok
but usually i see to solve a system of equations i write the polys in rows
which is not what you wrote right? you want to find another polynomial, while i want to.... find... a what, a vector?
@loud oasis
a no, it would be like... geometrically, the intersection of the shapes of the polynomials
loud oasis
but usually i see to solve a system of equations i write the polys in rows
but say for example i want to calculate the linear combination [ a(3x-2) + b(7x+3) = x+9 ] then equating components we get [ \systeme{3a+7b=1,-2a+3b=9} ] in matrix form is [ \begin{amatrix}{2} 3 & 7 & 1 \ -2 & 3 & 9 \end{amatrix} ] see how the polynomials end up as columns?
thorny flameBOT
cloud
loud oasis
a no, it would be like... geometrically, the intersection of the shapes of the p...
i don't think that's really useful, because when we think of polynomials as vectors we are trying to find linear combinations (where we stretch and add graphs) to make their graphs identical
molten crystal
and.. when i have a simple system of equations, i just write the equations in rows , right?
loud oasis
yes, if we are solving a linear system of equations we write the equations as rows, and we can imagine the solution being the intersection of the rows
but for polynomials in linear algebra we are usually trying to solve for the coefficients of the polynomial rather than the variable
loud oasis
yes, if we are solving a linear system of equations we write the equations as ro...
we can also consider the problem of finding the coefficients of a polynomial given the points of that polynomial, but that turns out to be another form of a system of linear equations
molten crystal
ok i think my brain was mixing too many concepts.
I tought x^2+y^2 = 1 was a polynomial
it is not, right?
it is an .. equation?
loud oasis
well it's a polynomial in 2 variables (x and y), but not in 1 variable (like x)
usually for linear algebra we are dealing with polynomials in one variable
molten crystal
so if i want to find the intersection between 2 circles i would have to write the 2 equations in 2 rows
loud oasis
so if i want to find the intersection between 2 circles i would have to write th...
we can't use linear algebra to solve for that because circles aren't linear equations
molten crystal
intersection of planes works instead?
loud oasis
yes, because planes are described with linear equations
loud oasis
i think the confusion is that there are 3 contexts where polynomials show up in linear algebra:
- if a polynomial is linear, then it's a linear equation and you can solve for their intersection using systems of linear equations techniques
- if you have some points on a polynomial, you can solve for the coefficients because it's linear if you count the coefficients as variables instead
- polynomials form a vector space and any problems involving vector spaces can involve that polynomial vector space
molten crystal
i have experience with 1
point 2 is like when i find coefficients for the fourier series right?
point 3 not sure i understand
loud oasis
for point (2), if you have for example the points $(1,3)$, $(-4, 5)$, $(3, 9)$ and you want to find a parabola they are on, then you can use the equation [ y = ax^2+bx+c ] and plug in the points 3 times: [ \begin{cases} 3 = a(1^2)+b(1)+c \ 5 = a(-4)^2 + b(-4) + c \ 9 = a(3^2) + b(3) + c \end{cases} ] then that's a system of linear equations in terms of $a,b,c$ and you can solve it like in case(1)
thorny flameBOT
cloud
loud oasis
for point 3, have you learned the vector space axioms yet?
molten crystal
not sure what you refer to, the null space and co?
loud oasis
these
molten crystal
ah no i've never did this.
loud oasis
it will make sense after you've covered it then. don't worry about it for now
molten crystal
it's like the rules to be considered a vector space?
ok
ok thanks, I think i'm too tired now. It's better if i keep refreshing what i studied before
or i'll keep going in circles
i had to stop doing math for a while, now i'm slowly restarting, and new questions comes up
thanks @loud oasis
.close
topaz sinewBOT
frail reef
Take everything to the left side and try and get everything over a common denominator
See if you can get it into that form
You have 8/y
So you’re basically trying to get everything over a common denominator
Which is y
It’s like if you have 1/3 + 1/5, you need to get a common denominator like 15
So don’t do that
It’s not expecting you to do that
It just wants you to put every term over y so that you can add them
Instead of multiplying by y
As I said
Do not multiply both sides by y
It doesn’t want you to do that
Eventually in the solution it will want that
Probably
olive swallow
ok i think my brain was mixing too many concepts.
I tought x^2+y^2 = 1 was a pol...
Not really, it's more of a parametric.
frail reef
But for your question of how they got between those 2 steps, they don’t multiply both sides by y
frail reef
I mean it’s not something different, it’s just expressed in a different way
Like saying if y = 1 then 1 = 1/y
Different way of expressing the same information
$\frac{4y}{y} + \frac{8}{y} = \frac{10y}{y} - \frac{y^2}{y}$
thorny flameBOT
eugene_krabs_has_cake
frail reef
Taking things to the other side and combining the fractions gets you what it shows
As for whether it’s more practical to do this instead of just multiply by y and do it your way, I’ll say it’s probably more inefficient
But I’m purely answering your question
topaz sinewBOT
topaz sinewBOT
Available help channel!
robust spear
can someone help me with this <@&286206848099549185>
topaz sinewBOT
can someone help me with this <@&286206848099549185>
rocky dock
what would m=0 look like
gleaming estuary
Hm
robust spear
what would m=0 look like
the line is horizontal
rocky dock
yes
topaz sinewBOT
can someone help me with this <@&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.
robust spear
Try to graph it
hollow drum
This is vertical, not horizontal
robust spear
this is what it says when i try to do it
hollow drum
This is vertical, not horizontal
robust spear
so what point do i put to make it horizontal
hollow drum
Any point that would be on that line
robust spear
with this would i make it horizontal or vertical
hollow drum
Do you know what undefined slope means?
robust spear
u mean rise over run?
hollow drum
If you have 0/# that means the slope is 0, but if it's #/0 that's undefined. # is used to denote that it can be any value
robust spear
ok thanks
topaz sinewBOT
@robust spear Has your question been resolved?
topaz sinewBOT
@robust spear Has your question been resolved?
wild whale
I found the reccurance relation but have no clue how to do the induction proof at all
with n and b
yall r scared of this huh
keep doing calc 1 problems its chill
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
neon iron
uh i got a simple question, i aint got a clue what i did wrong here
whole geode
@neon iron closing parentheses
neon iron
<@456226577798135808> closing parentheses
wdym?
whole geode
You're missing them
hollow drum
How did you input that matrix? Did you not go to the matrix menu?
neon iron
oh i just realized i put in a paranthesis on accident
neon iron
How did you input that matrix? Did you not go to the matrix menu?
through the matrix menu
hold on real quick lemme re insert it
neon iron
i have NEVER had this issue that is so random loll. thank you
hollow drum
through the matrix menu
But how did that matrix appear? If you picked the matrix, it should have had rref([A])
Not the entire matrix
neon iron
But how did that matrix appear? If you picked the matrix, it should have had rre...
i did like uh
2nd then pressed matrix and scrolled to rref
and then i pressed alpha and zoom
and thats how i was taught
ohhh i just realized i misread my equation. sorry! but thank you for the help, i just did it correctly. have a good night/day :)
topaz sinewBOT
ohhh i just realized i misread my equation. sorry! but thank you for the help, i...
If you are done with this channel, please mark your problem as solved by typing .close
neon iron
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
knotty rapids
y=(x+y)(x+1)(x-1)² standard form?
topaz sinewBOT
y=(x+y)(x+1)(x-1)² standard form?
@knotty rapids Has your question been resolved?
brazen ridge
Need help with this
In Problems 15–22 determine whether the given set of functions is linearly independent on the interval (−, ).
topaz sinewBOT
Need help with this
In Problems 15–22 determine whether the given set of functio...
brazen ridge
Do I just have to conduct 3 ratio tests? to see if they're constants or nonconstants
frozen drum
It's nonchalant
loud oasis
can you think of any trig identities relating these 3 functions?
brazen ridge
Well from what I'm getting from my notes I have to setup a function with C1cos2x + C2 + C3cos^(2)x = 0
But it just says lin dependent after that so idk how to confirm it
My professor didnt clarify, this is diff eq btw
Idk if I have to use trig identities but i know cos2x = cos^(2)x -sin^(2)x
loud oasis
My professor didnt clarify, this is diff eq btw
Idk if I have to use trig ident...
is there any relationship between sin^2(x), cos^2(x) and 1 you could use on this identity?
topaz sinewBOT
@brazen ridge Has your question been resolved?
topaz sinewBOT
@brazen ridge Has your question been resolved?
fringe egret
hi im doing calc bc hw and there is a integration by parts question
integral [ sin(2 + lnx) ]
if anyone could help thatd be awesome 🙂
glossy mist
hi im doing calc bc hw and there is a integration by parts question
integral [ ...
Consider $\sin\left(2+\ln x\right)$ as $1\cdot\sin\left(2+\ln x\right)$
thorny flameBOT
harshul
fringe egret
u = 1 dv = sin(2+lnx)
du = 0 v = integral [ sin(2+lnx)
that comes back to where we started no
vernal matrix
You don't want to start off with integrating by parts
Think of a way you can convert that integral, somehow...
fringe egret
u = 2 + lnx
glossy mist
u = 1 dv = sin(2+lnx)
du = 0 v = integral [ sin(2+lnx)
that comes...
You'll get $\cos\left(2+\ln x\right)$
thorny flameBOT
harshul
glossy mist
And then do it once again
You'll get -sin the second time
So you get a equation which is of the form $I = f(x) - I$
thorny flameBOT
harshul
glossy mist
Where $I = \int\sin\left(2+\ln x\right),dx$
thorny flameBOT
harshul
fringe egret
is that not the og problem
glossy mist
**harshul**
Yes but from this equation, you've found $I$ to be $\frac{f(x)}{2}$
thorny flameBOT
harshul
glossy mist
So you're basically done
Let me work this out though since chartbit was pointing out something
fringe egret
You'll get -sin the second time
why
fringe egret
@vernal matrix help a brotha out
sharp shard
I'm actually a bit confused about the substitution
vernal matrix
(well, actually, on doing it, it seems you could do it directly too-)
sharp shard
If we use u = 2 + ln x
then won't dx = xdu
glossy mist
(well, actually, on doing it, it seems you could do it directly too-)
Yes
Just proceed like I told
fringe egret
If we use u = 2 + ln x
then won't dx = xdu
ya
vernal matrix
u = 1 dv = sin(2+lnx)
du = 0 v = integral [ sin(2+lnx)
that comes...
but you want to choose "dv" as 1, and "u" as sin(2 + ln(x))
glossy mist
You took du = 1 and v = sin(2+ln x)
By IBP the integral becomes uv - integral [ udv ]
u = x, dv = cos(2 + ln x) (1/x) dx
Don't know what's so confusing about this
fringe egret
but you want to choose "dv" as 1, and "u" as sin(2 + ln(x))
i get stuck again
glossy mist
i get stuck again
Do it a second time
fringe egret
integral [ cos(2+lnx) ]
glossy mist
And then do it once again
.
glossy mist
integral [ cos(2+lnx) ]
Yeah apply IBP again just like you did
du = 1 and v = cos(2 + ln x)
vernal matrix
i get stuck again
Have you e.g. seen the integral of something like $\int e^{x}\sin(x) \dd x$ before?
thorny flameBOT
@vernal matrix
glossy mist
You want the same integral to reappear
glossy mist
**harshul**
So that it gives you an equation like this
glossy mist
fringe egret
its too majestic
glossy mist
I've forgotten the constant of integration but you get the point
fringe egret
we saw an example like this in class and ur goated ass j reminded me
fringe egret
I've forgotten the constant of integration but you get the point
thats not real
glossy mist
thats not real
You'll believe it's real after losing a mark for not writing it
radiant onyx
topaz sinewBOT
radiant onyx
I am not sure how to proceed with t=tan(x/2)
sudden temple
I am not sure how to proceed with t=tan(x/2)
just find the value of x sub in the sine
and then you gotta do simplification
sudden temple
just find the value of x sub in the sine
or better use the relation of sin(2t) and tan(t)
yeah that'll be better
radiant onyx
Okaayy lemme try
What about the integral limits??
pi and -pi
Do they become infinity when I subsitute dt
sudden temple
you have to change it with respect to substitution
radiant onyx
you have to change it with respect to substitution
Yea so +inf and -inf ryt??
Okayyy thnx a lot everyone
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
violet sundial
heelo can i ask a question its a integration in partial fraction. How did it end up with B/x-2 dx? knowing that C already has (x-2)^2?
topaz sinewBOT
heelo can i ask a question its a integration in partial fraction. How did it end...
topaz sinewBOT
@violet sundial Has your question been resolved?
violet sundial
<@&286206848099549185>
vestal sigil
thats how it works, the number of terms is the order of the pole
if the pole x=2 was repeated 3 times for example, i mean (x-2)^3 in the denominator
you'd have 4 terms
A/(x-1) + B/(x-2) + C/(x-2)² + D/(x-2)^3
thorny remnant
heelo can i ask a question its a integration in partial fraction. How did it end...
ok i see thats the problem..
violet sundial
so if (x-2)^4..... then B/(x-2) , C/(x-2)^3, D/(x-2)^4 ?
thorny remnant
ok consider an fraction in the form of $\frac{1}{(x+1)(x^2+2)}$ this we can write it as $\frac{A}{x+1}+\frac{Bx+c}{x^2+2}$
thorny flameBOT
convergence
violet sundial
what it is called?
thorny remnant
now lets apply this same logic on this fraction $\frac{1}{(x-1)(x)^2}$
thorny flameBOT
convergence
thorny remnant
so we can get that to be equal to $\frac{A}{x-1}+\frac{Bx+C}{x^2}$
thorny flameBOT
convergence
violet sundial
**convergence**
A/x-1 + Bx+c?x^2
thorny remnant
**convergence**
did you understand this?
vestal sigil
convergence has a point here, solid example
hes giving you a simple example that leads to A/x + B/x², like why we do it like that
violet sundial
there's a difference between linear and quadratic
thorny remnant
yep ik that
thorny remnant
this is called partial fractions
violet sundial
ohh okay
violet sundial
this is called partial fractions
thank you sir i fully understand it now..
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
candid dove
scalar triple product is defined as
[a b c] where a,b,c are vectors
And I can interpret it as
[(a) (b) (c)] just to separate the vectors
Now here’s a lil property that says
[a+ b c d]=[a c d]+[b c d]
Am having trouble whether it’s saying
[(a+b)(c)(d)]
or
[(a)+(b c d)]
candid dove
ik I could jus derive it but that’s gonna take way too long
wispy pier
ik I could jus derive it but that’s gonna take way too long
<(a+b) c d>
frosty iron
"A rabbit races with a turtle over a distance of 1000 meters, the turtle starts with a velocity of 5m/min without breaks, but the turtle's velocity decreases by 0.001 for every 1 meter. The rabbit starts of with a velocity of 200m/min, and sleeps when it reaches halfway.
If the turtle won the race exactly 1 minute before the rabbit reached the finish line, find how long the rabbit slept (ln2 = 0.693, ln5 = 1.609)"
topaz sinewBOT
"A rabbit races with a turtle over a distance of 1000 meters, the turtle starts ...
frosty iron
i think i should find the function for the position of the turtle
but i have no idea how to start
merry hill
but i have no idea how to start
turtle's velocity is decreasing by 0.001 every 1 meter
frosty iron
yeah
merry hill
do you recognize whats it
like if u increase decrease a constant repeatedly from a term
frosty iron
deceleration?
merry hill
arithmetic progression
sudden temple
I kinda figured out something, but it might not be useful
frosty iron
?
sudden temple
1/5 + 1/{5+r} + 1/{5+2r} + ... + 1/{5+nr}
is there any way to find the value of some of series like this?
In my knowledge I can't think of any
neon iron
arithmetic progression
i think its more like 5-5*0.999^x cause they habe ln values given?
frosty iron
i think its more like 5-5*0.999^x cause they habe ln values given?
ln would come from the setup of a differential equation
frosty iron
In my knowledge I can't think of any
i dont think so
sudden temple
i dont think so
$t_{required}=\left(\frac{1}{5}+\frac{1}{5-0.001}+\frac{1}{5-2(0.001)}+...+\frac{1}{5-1000(0.001)}\right)-6$
zero idea how something like this could be solved
there is obviously some other way
thorny flameBOT
sudden temple
wait am I tipping or what
frosty iron
we both are
sudden temple
,w sum from r=0 to 1000 1/{5-r0.001}
frosty iron
can i set it up like dx/dt = (constant) x?
sudden temple
wtf
thorny flameBOT
Requested by seventysevensquare
frosty iron
<@&286206848099549185>
sudden temple
☠️
frosty iron
☠️
wolfram going crazy with this
wait
i got uh
dx/dt = 5 - (0.001)x for x meters travelled
sudden temple
dx/dt = 5 - (0.001)x for x meters travelled
yeah that's definitely better
merry hill
i think its more like 5-5*0.999^x cause they habe ln values given?
i totally forgot what i was doing 
frosty iron
yeah that's definitely better
i got x = 5000 - Ce^(-t/1000)
merry hill
^
neon iron
i totally forgot what i was doing <:bleakcat:913340873771716630>
no idea what theyre doung here 😭
merry hill
integrate from x=0 to x=1000
frosty iron
oh
merry hill
you'll get total time ig
frosty iron
my teachers have only used indefinite
sudden temple
at t=0 isn't x=0 too?
frosty iron
yeah
sudden temple
maybe that'll work
merry hill
,w integrate 1/(5-0.001x) from 0 to 1000
thorny flameBOT
merry hill
oh yeah my bad
sudden temple
"A rabbit races with a turtle over a distance of 1000 meters, the turtle starts ...
according to this the speed was changing instantaneously
so it was 5 for first minute
and just at the beginning of 2nd meter it turned into 5-0.001
so using integration gives only approximate answer
sudden temple
I wonder if there is any continuation to this to get the exact result
frosty iron
I wonder if there is any continuation to this to get the exact result
i put that in wolfram and it used some digamma function
sudden temple
i put that in wolfram and it used some digamma function
can you share it?
with the exact syntax you entered in it
merry hill
$t_{required}=\left(\frac{1}{5}+\frac{1}{5-0.001}+\frac{1}{5-2(0.001)}+...+\frac...
what is the -6 for
frosty iron
can you share it?
that was from your other message mb
sudden temple
how'd you find it?
merry hill
python
sudden temple
oh
sudden temple
with that -6 or not?
merry hill
without the -6 part
sudden temple
but what is it for
that series is just the time taken by turtle
tortoise whateve
but we need the time for which the bnuuy slept
merry hill
that series is just the time taken by turtle
not the series
the -6 at the end
what is that for?
sudden temple
but we need the time for which the bnuuy slept
that -6 is for thiss
frosty iron
5 mins and the turtle finished before by 1
sudden temple
how did i not read that part
lol
sudden temple
5 mins and the turtle finished before by 1
are you done with this problem?
merry hill
how would you actually solve that series
frosty iron
are you done with this problem?
i think so
merry hill
sudden temple
<:hmmcat:831508801646755850>
for human applications, just using an integral
merry hill
ig so
frosty iron
why do all the other problems look so easy compared to this one
merry hill
this was easy too tho
sudden temple
this was easy too tho
fr
sudden temple
why do all the other problems look so easy compared to this one
your other problems are generally way too difficult than this
frosty iron
lol
topaz sinewBOT
If you are done with this channel, please mark your problem as solved by typing .close
frosty iron
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
eternal nymph
topaz sinewBOT
rancid mauve
Yh
eternal nymph
oh
unreal bronze
like how g(4) is definitely greater than g(3), even though you don't know the exact values
eternal nymph
like how g(4) is definitely greater than g(3), even though you don't know the ex...
so is this the right arrangement:
$g'(0), 0, g'(4), g'(2), g'(-2)$
thorny flameBOT
Devil Wears Prada
rancid mauve
I think so, hard to say between 2 and -2 tho
unreal bronze
looks right to me
topaz sinewBOT
topaz sinewBOT
Available help channel!
halcyon willow
stuck on this:
topaz sinewBOT
stuck on this:
topaz sinewBOT
@halcyon willow Has your question been resolved?
hearty turret
tried breaking at integer^1/n but didnt really simplify idk what to do
that is basically what you do
i mean that should get you an answer
you might wanna set i.e. k^1/n < a <= (k+1)^1/n to get something nice
halcyon willow
you might wanna set i.e. k^1/n < a <= (k+1)^1/n to get something nice
Idk why i didnt get the correct ans
hearty turret
huh
halcyon willow
if anyone wanna try helping ping me
halcyon willow
how did u directly write the first step? 
hearty turret
as in my final line?
halcyon willow
first sorry
hearty turret
split it up into ur separate integrals
hearty turret
oh so i took a = k^(1/n) for now cus it's easy once we've done that
halcyon willow
replace a for k^1/n?
hearty turret
split it up into ur separate integrals
then $\int_0^1 \floor{x^n} dx = \int_0^1 0 dx$
thorny flameBOT
LY
halcyon willow
can u write the integral for this i didnt get it
hearty turret
$\int_1^{2^{1/n}} \floor{x^n} dx = \int_1^{2^{1/n}} 0 dx$
thorny flameBOT
LY
hearty turret
can u write the integral for this i didnt get it
$\int_{(k-1)^{1/n}}^{k^{1/n}} \floor{x^n} dx = \int_{(k-1)^{1/n}}^{k^{1/n}} k-1 dx$
thorny flameBOT
LY
halcyon willow
ohhhh
hearty turret
it should be 1 no here?
yep
hearty turret
i've assumed k is an integer for now
cus when a isn't of the form k^1/n where k is an integer
the final integral is easy
hearty turret
you might wanna set i.e. k^1/n < a <= (k+1)^1/n to get something nice
i.e. sps this
then set a = k^1/n + t
then the final one is just
$\int_{k^{1/n}}^{k^{1/n}+t} \floor{x^n} dx = \int_{k^{1/n}}^{k^{1/n}+t} k dx$
thorny flameBOT
LY
halcyon willow
**LY**
i dont see the t
in the integral tho
i get the how u made the integerals
since we gotta break floor fn when it is integer
but cant we not involve k and directly use a?
hearty turret
but cant we not involve k and directly use a?
like you can
but it's often easier for questions like these to leave ur answers in terms of k
halcyon willow
well k would be floor(a^n)
huhh
hearty turret
and then think about how you can find k in terms of a in the end
halcyon willow
but it's often easier for questions like these to leave ur answers in terms of k
yeah the book used a series summation
but
its kinda different
topaz sinewBOT
@halcyon willow Has your question been resolved?
limber burrow
i was wondering how to start this problem, if i could get help it would be nice to know where to start
topaz sinewBOT
i was wondering how to start this problem, if i could get help it would be nice ...
sweet shard
What's D?
sweet shard
Call D1 the region above the x-axis and D2 the region below the x axis
can you describe those x and y values?
topaz sinewBOT
topaz sinewBOT
Available help channel!
raven kernel
Am I doing this right?
topaz sinewBOT
Am I doing this right?
vernal matrix
Don’t forget you want h to go to zero, of course, and keep going 
topaz sinewBOT
topaz sinewBOT
Available help channel!
graceful leaf
cansomeone give me a scenario or question something that helps me apply this
graceful leaf
i get the concept but just want to be sure
like the more digits u have the less uncertainity
burnt badger
Example
Let's say we measure something as
3985.7 grams
If i round it to
4000
That's 1 significant digit
graceful leaf
yep
burnt badger
Because you are less accurate to call it 4000 than 3990 for example
Let's say
The measurement was
4000.1
Now it's much more accurate to say 4000
Right?
graceful leaf
yes
burnt badger
So then how can i tell from just seeing the number 4000 how accurate that is or how much we rounded?
Well
That's why it's better to use scientific notation
Rounding 3900 to 4000
It's 4 x 10^3
Rounding 4000.1 to 4000
It's 4.000 x 10^3
burnt badger
For sig figs the scientific notation helps you to see that
graceful leaf
Ok
burnt badger
Without a decimal or other description you can't say
topaz sinewBOT
@graceful leaf Has your question been resolved?
topaz sinewBOT
topaz sinewBOT
Available help channel!
final dust
Q6)
Part d, e, f and g,
Can anyone please explain how to solve them?
topaz sinewBOT
Q6)
Part d, e, f and g,
Can anyone please explain how to solve them?
@final dust Has your question been resolved?
final dust
Q6)
Part d, e, f and g,
Can anyone please explain how to solve them?
<@&286206848099549185>
topaz sinewBOT
@final dust Has your question been resolved?
topaz sinewBOT
@final dust Has your question been resolved?
topaz sinewBOT
@final dust Has your question been resolved?
opal tide
<@&286206848099549185>
the not equal sign in the piece-wise means > and also <
ping me if yo uneed more help
dusky plover
Shouldn't this just be 3?
topaz sinewBOT
Shouldn't this just be 3?
knotty jewel
uh mb
dusky plover
all good
topaz sinewBOT
@dusky plover Has your question been resolved?
opal tide
why are there so many physics problems here?
also, i suggest you make a free-body diagram for this problem (i did not label it correctly, that's for you), as it 'll help you visualize the internal forces, which have no effect on the system, and external forces, which do .
the two masses are right though and the tensions connecting
F = MA
solve
topaz sinewBOT
topaz sinewBOT
Available help channel!
errant path
if f(x) = (ax^2 + bx + 10) / (x^2 + c), and f(x) has a removeable discontinuity at x=-2 and a vertical asymptote at x=2 and the limit of f(x) as x approaches -2 is 1/4, what is b, and c
topaz sinewBOT
if f(x) = (ax^2 + bx + 10) / (x^2 + c), and f(x) has a removeable discontinuity ...
errant path
c is -4 b/c (x-2)(x+2) on the bottom makes x^2-4
and (x+2) has to be on the top as well for removable discontinuity
thats where im stumped idk what to do next
vernal matrix
Do you know what a is? (wow I can't actually read 
)
vernal matrix
and (x+2) has to be on the top as well for removable discontinuity
Anyways, do you know what (x + 2) needing to be on the top (i.e. is a factor) of the numerator means for ax^2 + bx + 10?
errant path
Anyways, do you know what (x + 2) needing to be on the top (i.e. is a factor) of...
(x+2)(ax+5)?
vernal matrix
errant path
much love chartbit
vernal matrix
All by yourself as well
errant path
Anyways, do you know what (x + 2) needing to be on the top (i.e. is a factor) of...
this is lowk what i needed
i cant lie
vernal matrix
Sometimes it's the small bits
topaz sinewBOT
topaz sinewBOT
Available help channel!
sacred folio
how do i factor this
topaz sinewBOT
how do i factor this
outer portal
can you factor 3x^2 + 4x + 1
sacred folio
i dont know how😰
outer portal
do you know how to factor x^2 + 2x + 1
outer portal
ok lets try something else
can you expand this
or do you need help on what it means to "expand" that
sacred folio
i need help
outer portal
you need to know how to factor
and since you dont know how to factor,
you need to know how to expand
outer portal
can you expand this
yes or no, can you expand this
sacred folio
what do you mean by expanding
outer portal
are you familiar with distributive property
sacred folio
i dont know the names but
if you show me an example
then i can tell if i know or not
outer portal
go guess what "expanding" means when given something like this and told to do something related to math on it
what things can you do to (x + 2)(x - 1)?
topaz sinewBOT
topaz sinewBOT
Available help channel!
next rain
May someone please explain how homie turned the 2 into 8/4?
topaz sinewBOT
May someone please explain how homie turned the 2 into 8/4?
next rain
Like I understand 8/4 = 2 but
-
Why express it as a fraction?
-
How did we know that?
-
My initial thinking was to do 2/1
fallow igloo
May someone please explain how homie turned the 2 into 8/4?
If yoy have 8 pieces of pizza, how many pizzas can a person have when distriubted to 4 ppl
next rain
If yoy have 8 pieces of pizza, how many pizzas can a person have when distriubte...
I mean like this reasoning is cool and all but what if in the future we dealing w/ more numbers and bigger numbers at that
fallow igloo
calculate
next rain
Like I can't say "Oh yeah so this integer just gonna be expressed as a rational because I'm hard like that"
Was my inital thinking of doing 2/1 correct?
royal sky
Was my inital thinking of doing 2/1 correct?
well look its not wrong but its a bit like
next rain
Idk if my algebra is wrong but I think I'm getting the wrong answer
royal sky
if someone says ill swin to that place when they can take a boat
youre complicating it
next rain
if someone says ill swin to that place when they can take a boat
Yeah I guess
royal sky
look at what they did
they put 2 to
8/4
and added all the /4 together
to then get the 9/4
so its pretty easy to make it like that
next rain
But I'm just thinking ahead yfm, like these lil shortcuts are cool and all but they don't last long, like for GCD for example, we can keep spamming our calculator until we find one, or we can learn Eucledian algo. type shit
royal sky
well i assume
theres some tests which your teacher wont allow calculators
so this is prety handy
topaz sinewBOT
topaz sinewBOT
Available help channel!
royal sky
topaz sinewBOT
agile harness
no
the third row of I is 0 0 1
three times the third row is 0 0 3
adding that to the first row which is 1 0 0 would give 1 0 3
agile harness
if they add 3 times third row wouldnt it be 6
you’re making the mistake of looking at the end result and then applying what they did
worthy storm
the wording is a bit vague, they meant "add 3 times the third row of I3 to the first row of I3"
lusty goblet
See if we multiply third row by 3 then [0 0 3]
Then add this to first row
Simple
royal sky
the wording is a bit vague, they meant "add 3 times the third row of I3 to the f...
ah
okay yeah wroding
ty
.close
topaz sinewBOT
topaz sinewBOT
Available help channel!
keen silo
topaz sinewBOT
compact zodiac
!15m
topaz sinewBOT
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.
merry hill
keen silo
need all 5 awnswers please put in format as:
- A
- B
3.C - D
- A
Example^
<@&286206848099549185> its been 15
topaz sinewBOT
need all 5 awnswers please put in format as:
1. A
2. B
3.C
4. D
5. A
Example^
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.
@keen silo Has your question been resolved?
topaz sinewBOT
@keen silo Has your question been resolved?
worldly oxide
could someone verify these 3 drawings are correct?
topaz sinewBOT
could someone verify these 3 drawings are correct?
@worldly oxide Has your question been resolved?
topaz sinewBOT
@worldly oxide Has your question been resolved?
topaz sinewBOT
@worldly oxide Has your question been resolved?
uneven gull
whats 2991- 81x
vivid pivot
topaz sinewBOT
vivid pivot
Is the answer key wrong, shouldn’t the absolute value of r be greater than 1 in order to get the interval of convergence?
woeful drift
If that thing is greater than 1 then the sum doesn't converge at all