ok
#help-42
remote mural
$x\in(-\infty,-1]U[0,3]$
clear delta
what you wrote: $$x \in (-\infty, -1) \cup (0, 3)$$
potent lotusBOT
Haylsune Miku
clear delta
excludes the value of -1
remote mural
oh ri ght
clear delta
cmon, use \in at least
cool
lol no i mean
instead of e
which is a letter
use \in which is the set includes symbol
clear delta
\textbackslash{}in $\in$ \
\textbackslash{}infty $\infty$
steep nest
hey, can someone explain what the image and rank of f are, please?
steep nest
i get what a monomorphism and an epimorphism is
but how would i prove that f is either??
also, how can Imf = W when Imf is a subset of W
or subspace??
stoic oyster
also, how can Imf = W when Imf is a subset of W
subset also contains the "the two sets are equal" case usually
V is a subspace of V for example
it's useless to say but it's true
steep nest
huh
stoic oyster
i get what a monomorphism and an epimorphism is
did you solve the previous parts then ?
steep nest
yh, i've done (i), i've found the kerf, the null is the same as the kernel
steep nest
oh, i needa find the dimension?! 😩
the basis for the kerf is (0,0) which confirms it defo maps to the zeroth vector
stoic oyster
the zero vector can't be part of any basis
cause that screws up linear independence
steep nest
oh right
stoic oyster
you can take it as a definition if you want, dimension of the 0 space is 0
(there are technical reasons for that to work)
steep nest
i'm kinda struggling to visualise this whole vector space stuff. i learn better when i can imagine what i'm working with. like when we worked with mapping functions in the real space, that's pretty much minecraft but labelled correctly. aghghghghgh
steep nest
you can take it as a definition if you want, dimension of the 0 space is 0
oki
so null(f) = dimkerf = 0. is this always true coz kerf has to map to the zeroth vector??
stoic oyster
if x is a vector in ker f, that means f(x) = 0
what dim(ker f) = 0 means is that, if f(x)=0 then x has to be the zero vector
welcome to lin alg, precise language is important here
stoic oyster
it is a subspace of the input space of f yes
steep nest
oh ok
okay, i got that for the most part. what's an image? the notes say it's all the possible output vectors
steep nest
output vectors from V to W??
steep nest
oh-
steep nest
from the diagram, W has Imf and the zeroth vector, are those outputs??
stoic oyster
yes they are the outputs from f
the zero vector is inside Imf indeed
cause you always have f(0_V) = 0_W [the subscripts are just to say in what space these objects are], whatever the linear transformation f you have
stoic oyster
f is the transformation
f(0_V) is the result of when you give 0_V as an input to f
and that result is a vector in W
since the transformation f goes from V to W
steep nest
f(0_V) is the result of when you give 0_V as an input to f
ohhh
wait, the Imf which is the output is just what was spat out -> (a_1 + a_2, 0, 2a_1 - a_2) and its basis would be the coefficients i think (1, 0, 2)
no?
steep nest
(╯°□°)╯︵ ┻━┻
steep nest
Im f is also a vector space, a subspace of W
yh
stoic oyster
it consists of all the vectors f(x) for some x in V
steep nest
yh
steep nest
it consists of all the vectors f(x) for some x in V
i now understand that
stoic oyster
alright
steep nest
do you know of any yt vid that explains this thoroughly?
stoic oyster
https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab if you want something with intuition
https://ocw.mit.edu/courses/18-06-linear-algebra-spring-2010/ if your linalg classes suck and you want to see the clasees from a guy from MIT
steep nest
thank you 🫡
steep nest
finish, i can watch the vids at a later time
okay, i asked my course mate for some more help and looked at the notes again, at the rank-nullity thm formula
"dimkerf + dimImf = dimV"
stoic oyster
yep
steep nest
my friend subbed in the standard bases for R^2 -> (1,0) and (0,1) into the thingy on the right hand side
i've done that too
stoic oyster
to get a basis of the image yeah that's fine
stoic oyster
"(0,0,-1)" you mean (1,0,-1)
steep nest
no no
steep nest
hey, can someone explain what the image and rank of f are, please?
(a_1 + a_2, 0, 2a_1 - a_2). sub in (0,1), a_1 as --
yes i have 🤦♂️
yh (1,0,-1)
then its dimension would be the number of vectors in the basis
which is 2 here
so slay
stoic oyster
yeah be careful there's no linear dependencies in here
in this scenario R^2 -> R^3 there's no problem
if you go from the bigger space to the smaller space you'll have issues like that
stoic oyster
so dim ker f is 0, dim im f = 2 then
steep nest
okay, last one. monomorphic or epimorphic? or both? 🤨
steep nest
so dim ker f is 0, dim im f = 2 then
yep
monomorphism is an injective linear transformation
points in vector space V would map to at most one point in vector space W
from my understanding of it
and then epimorphism is just surjection
stoic oyster
and then epimorphism is just surjection
and yes
let's think about epi first cause it's easier
we have dim im f = 2, does that tell you anything about surjectivity of f ?
stoic oyster
what's the dimension of the output space R^3 ?
stoic oyster
so do you think im f = R^3 then ?
that's what it means for the transformation to be surjective
being able to access every output from one input by f
stoic oyster
yeah I guess I'll let you reread your notes then
steep nest
[resending so i don't have to scroll up]
stoic oyster
the question should be very easy to answer when you know nullity and rank of f
steep nest
okay, hold on
stoic oyster
I gtg quite soon though
stoic oyster
indeed
steep nest
so ours is monomorphic
steep nest
"a function is a monomorphism if its kernel is zero"
but why and how
stoic oyster
they didn't show you the proof or what
steep nest
i haven't read it, it's a paragraph. but i will do so now
thanks a lot
i don't wanna keep you longer :p
stoic oyster
g'night
steep nest
night ^^
vernal coral
isnt it supposed to be dv=6e^6xdx?
calm coralBOT
isnt it supposed to be dv=6e^6xdx?
half jolt
How are we supposed to know if you don't give us the original question?
remote mural
How are we supposed to know if you don't give us the original question?
wow
half jolt
Though I'm guessing it's
remote mural
good guess
half jolt
$\int x \cdot e^{6x} \dd x$
potent lotusBOT
RedstonePlayz09
vernal coral
yee
remote mural
<@456226577798135808> my honest reaction: 🗿
:moyai
half jolt
If so, then no.
.
vernal coral
ye why
half jolt
I mean, why yes?
There is no 6 in the integral.
You choose one part to be u, and the other to be dv
In this case we chose u = x and dv = e^(6x)dx
vernal coral
arent you supposed to apply exponential function rule?
half jolt
Sorry I don't understand what you mean
half jolt
Ok, but we aren't differentiating e^(6x)
tired wasp
can someone check my answer for the new equation, i usually mess up plugging it in and putting the wrong parantheses. and if you can show me the step by step process
calm coralBOT
can someone check my answer for the new equation, i usually mess up plugging it ...
@tired wasp Has your question been resolved?
tired wasp
<@&286206848099549185>
tired wasp
<@&286206848099549185>
calm coralBOT
@tired wasp Has your question been resolved?
tired wasp
tired wasp
.close
calm coralBOT
calm coralBOT
Available help channel!
azure willow
why are these different?
calm coralBOT
why are these different?
azure willow
i used laplace transform to obtain the expression
but wolfram alpha gives another solution that (seems) not the same
both also give sin2t
calm coralBOT
@azure willow Has your question been resolved?
azure willow
i don't think either one is right
huh
taking the second derivative of them + them = sin2t, no?
calm coralBOT
@azure willow Has your question been resolved?
azure willow
<@&286206848099549185>
calm coralBOT
@azure willow Has your question been resolved?
calm coralBOT
@azure willow Has your question been resolved?
dim glade
how many boolean functions of f(x,y,z) with 3 variables x,y,z where the following conditions apply: f(0,0,0) = 0, f(0,0,1) != f(0,1,0) and f(1,0,0) <= f(1,1,1) exists? with != i mean not equal
dim glade
I understand that you have to divide the problem in 2 cases, one where f(1,0,0) is equal to f(1,1,1) and other where f(1,0,0)<f(1,1,1) but I don't really know how to solve it from there.
<@&286206848099549185>
calm coralBOT
@dim glade Has your question been resolved?
amber bolt
there are three cases rather, they are equal because both 1, or they are equal because both 0
or f(1,0,0)<f(1,1,1)
then you have 2 cases for f(0,0,1) != f(0,1,0)
3 Fs remain free, so 2 cases three times, and that's the solution
calm coralBOT
@dim glade Has your question been resolved?
dim glade
So 2^5+2^4 where 2^5 is the amount when equal and 2^4 when f(1,0,0) = 0 & f(1,1,1) = 1?
weak rapids
how do i find orthocentre if i dont dont know the angles of the triangle
weak rapids
,,\triangle
potent lotusBOT
🚗
still marlin
Is there a specific problem ur working on
weak rapids
yes
the midpoint of the sides of a traingle are 5,0 5,12 and 0,12. find orthocentre
i have finded the vertexes of this triangle
but cant move further
still marlin
Oh well from this triangle it's not too bad, pythagorean theorem shows it's a right triangle
weak rapids
the answer should be 0,0 then
how do you know its a right angles triangle?, like you calculated it fast i suppose, was there a trick you used?
still marlin
well 5-12-13 is a pythagorean triple
weak rapids
you calculated thier distance first that means
still marlin
Well in this instance I didn't have to cus I just saw the 5's and the 12's and recognized it as a part of a common set of integer triples which satisfy a^2 + b^2 = c^2
Another rly common one is 3-4-5
weak rapids
ah yea got it, thanks 992qqoloy, i suppose thats your real name
still marlin
Yeah lol
crystal venture
calm coralBOT
crystal venture
Could someone teach me how to do this question?
potent lotusBOT
everg
torn gorge
now to satisfy b search a,b real number such that $af(x)+b$ satisfy b
clear ?
now to satisfy b search a,b real number such that $af(x)+b$ satisfy b
potent lotusBOT
everg
calm coralBOT
@crystal venture Has your question been resolved?
Available help channel!
Available help channel!
vale mantle
can someone help me with this question?
calm coralBOT
can someone help me with this question?
vale mantle
ok holup
vale mantle
Put values
sinAcosB + 48/65
vague needle
Sina is 3/5
vale mantle
what rule is that
vague needle
Pog
kindred estuary
what rule is that
Pythagorean theorem
calm coralBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
vague needle
👍👍
calm coralBOT
kindred estuary
R u like 15?
You can hint to them about pythagorean theorem, not do it for them
vague needle
Okay sir
calm coralBOT
Available help channel!
tribal idol
i am confused where the y prime comes from, I agree with everything else there from the product rule but where does a y prime come from
calm coralBOT
i am confused where the y prime comes from, I agree with everything else there f...
@tribal idol Has your question been resolved?
tribal idol
<@&286206848099549185>
tribal idol
so you are saying that the chain rule must also be applied within the product rule?
half jolt
The product rule requires you to differentiate e^y
Which gives e^y * y'
So yes
Also why is there a minus over there
Unless I'm not seeing the whole question where this somehow makes sense
tribal idol
ye it should be a plus
and like
if you have y^3
would you have to do the same thing then
tribal idol
if you have y^3
would you have to do the same thing then
like im thinking the derivative is jus 3y^2
half jolt
It isn't
If y is a function of x, and you're taking the derivative with respect to x
You also need to multiply by the derivative of y
For example if y was x^2
Would you say the derivative of (x^2)^3 is 3(x^2)^2?
(It isn't)
It's 3(x^2)^2 * 2x
(Of course you can just simplify it to x^6 and then take the derivative normally)
tribal idol
It's 3(x^2)^2 * 2x
well this would be the chain rule, how am I meant to apply the chain rule to one variable tho (y)
tribal idol
for example
tribal idol
if you have y^3
would you have to do the same thing then
in this case, there is only one term (y)
in your case, there were 2 terms (x^2)
half jolt
You know y is a function of x
You can think of it as if y is some expression involving x, but we don't know what
And you want to take the derivative of that expression, cubed.
What if you had:
(x^2 + 2x - 1 - x^100)^3
You can't just say the derivative is 3 * (x^2 + 2x - 1 - x^100)^2
You have to multiply by the derivative of the "inside" aswell
In your case, we're using y to denote a function of x.
tribal idol
okay i see that then but, if we do the chain rule doesn't it become multiplied by g prime of x. in other words multiplied by the inner fumctions derivative
half jolt
So although we don't know what y is, we know that by the chain rule we must multiply by its derivative.
half jolt
okay i see that then but, if we do the chain rule doesn't it become multiplied b...
Yes
That's what we're doing
For example
e^y
Let's define f(x) = e^x
We want the derivative of f
I mean
Of e^y
e^y is just f, after plugging in y (which is again, some function of x)
tribal idol
well isn't the inner function derivative of y^3 just the derivative of 3
which is 0
half jolt
So when taking the derivative, you take the derivative as if it was e^x (you get e^y) and then you multiply by y'
half jolt
well isn't the inner function derivative of y^3 just the derivative of 3
which ...
?
No
For the derivative of y^3
It's like x^3 by plugging in y
so you take the derivative of x^3, which is 3x^2
plug in y, you get 3y^2
and finally multiply by y'
tribal idol
okay let me try asking a different question
what is the inner and outter fucntion of
y^3 ?
half jolt
Outer function is x^3
inner function is y
Can you show me how you were introducted to the chain rule?
Like what's the phrasing of the theorem you are familiar with?
I'll try to explain it according to how you learned it
tribal idol
yeah so i waas told
tribal idol
Outer function is x^3
X ??
half jolt
So you are given that y is a function of x.
And you want the derivative of y^3
So let's say f(x) = x^3, and y(x) is some function of x we don't know
y^3 is just f(y(x))
Now, differentiating gives you f'(y(x)) * y'(x)
f'(x) = 3x^2 so f'(y(x)) = 3y^2
tribal idol
hummm
half jolt
I gtg right now, if you still have questions you'll have to wait for someone else.
tribal idol
alr thanks
tribal idol
interesting
so only when there is a Y in the part you are solving for is when you do this chain rule
if it were an X we dont do it
can someone verify?
calm coralBOT
@tribal idol Has your question been resolved?
blissful inlet
calm coralBOT
blissful inlet
someone please help me?
remote mural
people who havent finished 4 years / total of people that did college
blissful inlet
people who havent finished 4 years / total of people that did college
?
remote mural
its asking for the probability that someone hasn't finished 4 years of college
blissful inlet
i understand what you're saying
how can i find the number of ppl that didnt finish the college?
remote mural
it says in the table
vestal bison
How do I get help
remote mural
vestal bison
That didn't help
remote mural
well i dont know
it says years of college, right?
blissful inlet
rigght
remote mural
theres a section that says 4 years or less
coral osprey
That didn't help
theres a category called "math help (available)"
blissful inlet
ohh i thought that meant as in
vestal bison
@coral osprey where
blissful inlet
people who finished college less than 4 years
coral osprey
<@349354952961032192> where
literally in the section above this one
remote mural
haha word problems
blissful inlet
right here
blissful inlet
<@349354952961032192> where
no more question
ur distracting me
theres ur answer
remote mural
yes
hollow perch
do you still want help on it lmao
hollow perch
based on this, it looks like they want you to include people who haven't attended college at all
keep in mind that probability of not __ is the same as 1-the probability of __
hollow perch
uhh 47
blissful inlet
WHAT
blissful inlet
47 is the denominator?>
coral osprey
people who have completed 4 years
its asking who has not completed (wrong reply lol)
hollow perch
the probability that they have completed 4 years is 47/167
and then find the opposite, who haven't completed
blissful inlet
uh
oh
LOl
wait yeah but its asking for ppl who didnt complete
so why isnt it 39
coral osprey
people who didnt go to college in the first place cant complete, can they?
hollow perch
yeah so the people who haven't completed is everyone else, including people who didn't attend college at all, i.e. 1-the probability
remote mural
167-47 / 167
blissful inlet
interesting
ok
so
47/167
now what
oh wait
i got it
120/167
thank you!!
/close
.close
molten bear
What is the units digit of the following product? 8433165483x946621539x5514381138
ionic loom
The units digit is the rightmost digit of every number
molten bear
Isn't it the digit which only appears once?
ionic loom
No
Consider the number 324
That's the same as 3 * 100 + 2 * 10 + 4 * 1
So 3 is the hundreds digit, 2 is the tens digit, and 4 is the ones digit, or the units digit
ionic loom
Just ignore everything except the rightmost digit in each of the 3 numbers
ionic loom
Just multiply those together and the rightmost digit of that will be the answer
molten bear
If you added up all the factorials of the whole numbers from 0! to 100!, what would be the unis digit of the sum?
hollow perch
try writing out some factorials, up to like 12 lmao
remote mural
If you added up all the factorials of the whole numbers from 0! to 100!, what wo...
try to find some sort of pattern so do the sum of a few smaller ranges
dusky jolt
how do i find the nth term for this sequence?
calm coralBOT
how do i find the nth term for this sequence?
deep pike
Do u see the pattern
dusky jolt
the pattern is decreasing
first to second is +8/15
second to third is +8/35
so idk how
deep pike
It's better to look at the pattern of numerator and denominator seperately
It's easier then
dusky jolt
then what to do from there ?
deep pike
Do u see the pattern
deep pike
Ohk
An AP is a sequence where the difference between any 2 consecutive term is constant
calm coralBOT
@dusky jolt Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
flint wasp
calm coralBOT
flint wasp
is this how youre supposed to do ghost points with this boundry condition??
is this like obscure math or something?
calm coralBOT
@flint wasp Has your question been resolved?
calm coralBOT
@flint wasp Has your question been resolved?
calm coralBOT
@flint wasp Has your question been resolved?
calm coralBOT
@flint wasp Has your question been resolved?
mellow osprey
.reopen
junior fern
is this a glitch on desmos?
calm coralBOT
is this a glitch on desmos?
astral holly
no problem
leaden thunder
is this a glitch on desmos?
What is "this"
junior fern
What is "this"
like is the derrivative it gave wrong?
did i write it out wrong?
the green graph and the black one should match if i did it right
and i did it like 3 times
frosty leaf
use a derivative calculator
frosty leaf
is this a glitch on desmos?
actually it works for me
lol
disable the green function
the black function going under it
the vertical lines might be a bug, idk
junior fern
maybe it was simplifed somehow
i havent graphed trig functions in a while lol
by hand
frosty leaf
I mean use desmos
to check if the graphs are the same
because sometimes you can simplify trig functions and the answer might look different
storm vine
can someone help me
calm coralBOT
can someone help me
crimson sorrel
what's your problem
calm coralBOT
No need to ask “Can I ask…?” or “Does anyone know about…?”—it’s faster for everyone if you just ask your question! See https://dontasktoask.com/
@storm vine Has your question been resolved?
rustic wren
calm coralBOT
rustic wren
alright
i need help taking the derivative here
my first idea is to take out 331.3 as a constant and then work with (1+c/273.15)^1/2
then power rule and chain rule here
crimson sorrel
do you know the derivative of the square root of a function?
rustic wren
no id just rewrite it
crimson sorrel
then power rule and chain rule here
you're correct
rustic wren
okay
so its
1/2(1 + c/273.15)^-1/2 * d/dx (1 + c/273.15)
so working with the right side
dull wagon
d/dc, variable here is c , not x
rustic wren
d/dc, variable here is c , not x
we have d/dc(1) + d/dc(c/273.15)
yeah mb
now the derivative of the fractional is where i seem to be struggling in my calculations
i simply cant wrap my head around the rule
i havent used it enough
becase d/dc of 1 is 0
so were just left with d/dc (c/273.15) to solve
crimson sorrel
and like how you said in the other channel, d/dc(c/273.15)) is (1/273.15)*d/dc(c) =1/273.15
rustic wren
well yeah i tried that and i got the wrong awnser
dull wagon
c/273.15 is the product of
c and 1/273.15
rustic wren
i checked with my calc using d/dx function and got the wrong awnser, maybe i put it in wrong..
rustic wren
and like how you said in the other channel, d/dc(c/273.15)) is (1/273.15)*d/dc(c...
so i can choose my constant
?
oh wait
thats a dumb question
c is never constant
rustic wren
c is a variable
alright
so when i type it in
im getting 1.29
when the correct awsner should be
.54
this is where im confused
crimson sorrel
rustic wren
thats the issue this whole time
crimson sorrel
in case you'd want to compare
crimson sorrel
this is .54
crimson sorrel
with c = 60 yup
rustic wren
the plus one was the issue
i had it right in the very beginning before i even asked the question
i guess i just need to be careful
dont miss numbers
lawl
preciate ur time bro
means alot
.close
junior fern
how do i do this efficiently?
calm coralBOT
how do i do this efficiently?
junior fern
39 43 and 45
we dont need to go through the answer, but i feel like it would be guess and check to see what works after you get the derrivative
calm coralBOT
@junior fern Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
rigid root
calm coralBOT
rigid root
so far i took the derivative so it would be f'(t)=-2cos(t)-2cos(2t)
to evaluate, would i have to use a double angle formula on the second half?
civic dirge
Yes
rigid root
once i have 2cos^2(t)-1=cos(t), how would i solve for t?
grim musk
I just have a quick little question, when a matrix is in standard form, online i see it written as $ax + by + cz + d = 0$ and $ax + by + cz = d$. Which side is d actually positive on?
potent lotusBOT
Raforawesome
grim musk
I know its ridiculous to use a channel for this but i legit cant find the answer anywhere 😭
calm coralBOT
Available help channel!
raw yarrow
calm coralBOT
torn gorge
mh..
raw yarrow
?
raw yarrow
sorry can u explain that?
torn gorge
yes ...because they are coprime there exists some x,y integers s.t. xc+yn=1 right ?
raw yarrow
yes
torn gorge
so..
$(a-b)c\equiv0 \implies (a-b)xc\equiv x0 \stackrel{bezout}{\iff} (a-b)(1-yn)\equiv 0$
but now by using $1-yn\equiv 1$ you get the claim
is it clear to you ?
potent lotusBOT
everg
raw yarrow
so currently all I have is n is divisible by (a-b) and I factored out a c
potent lotusBOT
everg
torn gorge
a-b is divisble by n*
raw yarrow
yea
torn gorge
so you are done
raw yarrow
Like this right? n | c(a - b)
raw yarrow
but don't you start with ac = bc modn?
torn gorge
yes i start from that (and gcd n,c=1)
and i end up to "a-b is divisble by n"
or "a=b mod n"
raw yarrow
so start with this, then add the property at the end?
torn gorge
what's property ?
raw yarrow
bezout
raw yarrow
ok
so by bezouts idenity it would be cx + ny = 1?
cause all I have now is n divided (a-b) times c
idk what to do past that
calm coralBOT
@raw yarrow Has your question been resolved?
calm coralBOT
@raw yarrow Has your question been resolved?
fallen whale
is f(x) = x_1 x_2 convex? ive done some work on it and shown it is not convex but my proof is really bad idk if its right so i wanna know if it is convex or not
calm coralBOT
is f(x) = x_1 x_2 convex? ive done some work on it and shown it is not convex bu...
@fallen whale Has your question been resolved?
sharp knoll
i don't understand your function
sharp knoll
have you tried finding f''(x)?
fallen whale
no i used this, if this holds then it is convex
lethal gazelle
calm coralBOT
@fallen whale Has your question been resolved?
calm coralBOT
@fallen whale Has your question been resolved?
calm coralBOT
@fallen whale Has your question been resolved?
remote mural
Find Horizontal Asymptote for the following function
$\dfrac{5x-5}{x^2+4}$
indigo gust
Qstn?
potent lotusBOT
RecRio
remote mural
Usually what I'd do for this is take the coefficents but that gives me a weird answer
*wrong answer
so I take L.C of numerator and denominator and get my H.A at 5
by dividing the two
viral escarp
isnt it 0
viral escarp
beacuse bottom is x^2
and top is 5x
if u plug like a big number 100000000000000000000000000
viral escarp
the bottom one is gonna be come very big while the top is gonna be a lot smaller
basical it apphroaches 0
potent igloo
As x becomes huge, the -5 means very little
supple needle
You are always welcome to open your own help channel via #❓how-to-get-help
viral escarp
i did
supple needle
Many many people can help with calc
remote mural
so essentially just 5x/x^2
potent igloo
so basically 5x-5 is kinda just saying 5x
remote mural
ok yeah that makes sense
remote mural
but what I've done for limits so far is with a given limit, is this just the opposite?
potent igloo
So instead of x²+4, you can just approximate it as x²
So, putting it together, $\frac{5x-5}{x^2+4}$ is close to saying $\frac{5x}{x^2}$ for very big $x$
potent lotusBOT
SWR
potent igloo
But you can simplify that to $\frac{5}{x}$
potent lotusBOT
SWR
potent igloo
And for very large x, you should know that its asymtope is 0.
remote mural
oh okay
my teacher did it in a
weirder way
@potent igloo
this made no sense so
indigo gust
Rule is to divide all terms by highest degree term
remote mural
Rule is to divide all terms by highest degree term
so by x^2?
indigo gust
Yes
remote mural
5x/x^2 gives. you 5/x
ok that makes sense
but why is there
an x^2
on the outside
remote mural
oh righttt
ok
ok cool
rest of the steps make sense
in what cases would you do this though
instead of the normal L.C of largest degree/L.C of largest degree
coral dew
How to turn 3y+12=6x into slope intercept form?
calm coralBOT
How to turn 3y+12=6x into slope intercept form?
coral dew
I don’t know the first step. If I should -6x on both sides or divide by 3 or idkkk
sinful pond
Do you know what slope intercept form looks like?
coral dew
Y=mx+b
sinful pond
Yes, so the first step would be to isolate y
Do you know how you do that with this question?
coral dew
Divide by 3?
sinful pond
Yep now you need to get y by itself
So you have y + 4 = 2x now, how can you get y by itself from that
sinful pond
Nice yeah that's it
steep vine
calm coralBOT
remote mural
Do you know about AGP series?
It may have another name as the name AGP is commonly used in JEE
These are my notes
try this formula
calm coralBOT
@steep vine Has your question been resolved?
steep vine
It may have another name as the name AGP is commonly used in JEE
I don't know how to apply this one here
remote mural
Hmm
Wait a min
I'm gonna look for a study material
Hey
Do you understand Hindi?
If you do understand
this explains the Concept
calm coralBOT
calm coralBOT
Available help channel!
outer halo
outer halo
<@&286206848099549185>
outer halo
.close
tribal idol
I was wondering if I am meant to do chain rule for those square roots or product rule
calm coralBOT
I was wondering if I am meant to do chain rule for those square roots or product...
@tribal idol Has your question been resolved?
topaz raft
Is this implicit differentiation
tribal idol
yes
topaz raft
Convert the other square root to an index as well and then use the chain rule when you implicitly differentiate y
calm coralBOT
@tribal idol Has your question been resolved?
tribal idol
hummmm, what would i be solving for then? i dont think there is a y prime i can make
latent trout
im stuck at finding probabilities
austere surge
If I remember correctly, then if f is joint pmf of two rv X and Y, then f(x,y)=P(X=x, Y=y)
So you'll have to go case-by-case to find the joint pmf. N ranges from 1 to 3, and X1 ranges from 0 to 3
brittle crow
calm coralBOT
brittle crow
what does it mean by position vector
is it like
expressing it in terms of 'i' and 'j'
clear delta
yeah
clear delta
,calc (5*sqrt(2) + 5) * sqrt(2)
potent lotusBOT
Result:
17.071067811865
yep
brittle crow
ok now i need uh
help with checking answer
i got c for this, is this correct?
I got A for this, is this correct?
I got C for this, is this correct?
ping me when reply pls
calm coralBOT
@brittle crow Has your question been resolved?
calm coralBOT
@brittle crow Has your question been resolved?
harsh siren
i got c for this, is this correct?
yep
harsh siren
just draw a diagram
the river is flowing west
the boat is going north
whats the resultant vector
harsh siren
yeah
brittle crow
yeah
and for B
would answer be 72+270?
i found 72 by doing arc tan(12/-4)
(rounded up)
and then uh + 270 cause its in that last quadrant
and it asks for BEARING
so yeah
harsh siren
yeah
brittle crow
yeah
wait
for (c)
if we're travelling 500m
and we are going 12km an hour
that means
6km in 30 minutes
1km in 5 minutes
500m in 2.5 minutes
so answer is 2.5 minutes?
harsh siren
we have to account for the river flow tho
you need to know the magnitude of the resultant vector
harsh siren
yeah then you just divide by the distance
harsh siren
time
harsh siren
wait no i fucked up
its distance divided by velocity
not velocity divide by distance
harsh siren
oh so velocity is 12km/hr right
velocity is still the magnitude of the resultant vector
harsh siren
yep
brittle crow
oh alr
harsh siren
and that should be it for your problem
brittle crow
velocity is still the magnitude of the resultant vector
wait to clear things up for me, why did we find magnitude of resultant vector
harsh siren
because we want to know how fast the boat is going when its flowing through the river
and velocity of the river current is 4km/h
brittle crow
.close
brittle crow
calm coralBOT
hollow kestrel
yes
brittle crow
yes
wait doesn't ] mean that it ends there?
and ( means it doesnt?
or like
idk
what do they mean
i forgot
hollow kestrel
So (a, b) means all the numbers between a and b excluding a and b
And [a, b] includes a and b
brittle crow
why other way around
hollow kestrel
In order for f(x) to be -2, x has to be 7. But x is less than 7 so x cannot be 7
But 7 is in the range of f(x) since f(-2) = 7
and -2 is in the domain of f(x)
hollow kestrel
domain = all the values of x
range = all the values of f(x)
-2 is in the domain, but 7 is in the range
pastel heart
do make it equal to 0
calm coralBOT
do make it equal to 0
pastel heart
then I just solve for x
which I could find the roots which would be the interval.
if so, then i dont really know how to get x on its own.
velvet osprey
then I just solve for x
you can't solve for x just by algebraic means
calm coralBOT
@pastel heart Has your question been resolved?
hollow perch
and you're not really using ivt