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#help-28
random shoal
clever iris
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hexed hearth
please help
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hexed hearth
open zinc
please help
Have you heard of the vertical line test?
hexed hearth
Have you heard of the vertical line test?
Yes
hexed hearth
the main part
no thats the full question
hexed hearth
Have you heard of the vertical line test?
Oh so we have vto use that here
alright
so it should intersect only at one point
right?
warm siren
could someone help me figure out whats going on in this question?
warm siren
i undrstand whats happening until the k = 2 and k = 1/2 business
And then i have no clue what to do
i mean the whole multiplication zero equality doesnt work here because its an inequality yeah?
umbral dome
well the points where the equation stops being positive are the same points where it's equal to 0
so it can often be useful to solve an inequality by considering the associated equation
open zinc
k > 2 and k < 1/2 ? Are those the answers?
k=1?
warm siren
what?
open zinc
yeah there’d be two real roots
There should be one at x=-1/2
warm siren
Okay
open zinc
k > 2 and k < 1/2 ? Are those the answers?
All this to say 1/2 < k < 2
open zinc
Shouldn’t you have +18 instead of -18
warm siren
Oh right, thanks
open zinc
Other than that you’re right
open zinc
Unless you should say the divide by x portion goes to zero in the limit
warm siren
What?
open zinc
Yeah you’re supposed to ignore the last remainder
open zinc
What?
And the intuition for this is that the asymptote is what the curve approaches but will never reach, so you can plug in a large number like 1000 and see that the equation is (2,000,000 - 5000 - 12)/(1000+2) = 1991.00599 which is very close to 2x - 9 = 1991 but is off by just a little, specifically your 6/(x+2) = 6/(1002) = 0.00599 term
But since that 6/(x+2) will get closer and closer to zero as x gets larger, we drop it from the slant asymptote equation
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wary tendon
why does my fx-991es plus calculator gives me the wrong answer in indefinite integration, if i do it with my hand i get the answer 17 and with calculator its 17.88888 btw the value is 3 upper bound 2 lower bound, and 4x2-3x btw the 2 is squared
wary tendon
wdym
hot herald
from what you typed, it sounded you were trying to do
$$\int_2^3 4x^2-3x \dd{x}$$
glossy valveBOT
ℝαμΩℕωⅤ
wary tendon
yes this
hot herald
so you want to do that and not $\int_2^3 8x - 3\dd{x}$?
glossy valveBOT
ℝαμΩℕωⅤ
hot herald
because those aren't the same thing
hot herald
you're conflating integrands with antiderivatives
wary tendon
just what i have typed in the calcultor
hot herald
what are you typing into your calc
wary tendon
**ℝαμΩℕωⅤ**
.
hot herald
then, yeh, the calc will give you a different result than intended
since that's not what you want
if you shove this into your calc, it'll give 17
wary tendon
btw do you know where i can study plane geometry and trignometry (ratios, functions, equations, identities)?
hot herald
khan academy for the basics
wary tendon
i have a uni test in 2 days
im dead
its an addmisson test and im studying these things for the first time
hot herald
is that stuff you should've already learned before taking integral calculus
wary tendon
i was a ib student but took ai sl course not aa
wary tendon
btw do you know where i can study plane geometry and trignometry (ratios, functi...
so i never studied this
wary tendon
is that stuff you should've already learned before taking integral calculus
but integration is ok
hot herald
antiderivative of 8x-3 is 4x^2 - 3x, yes
lilac axle
Can someone help on this stats question?
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lilac axle
I do not understand the last part of the answer at all
For example, why is the first one P(X=2 and Y=1) when that would mean P(X=2) = 1/6 and P(Y=1) = 2/3 which means that Y>X
Not X>Y
Is it because its not about P(X) > P(Y)
But instead that the particular variable of X is > than Y
So X=1 isnt there because its bigger than none
then X = 2 > Y=1
But why is there no P(X=8 and Y=1) P(X=8 and Y=3) etc????
I don't understand that
Basically I am asking why is it only P(X=8)
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glass gulch
i was trying to derive the mean and variance of discrete uniform
what is this parameter C exactly
can we treat it as a constant?
wooden yarrow
what is this parameter C exactly
it says right at the top, C is a finite, nonempty set of numbers
e.g. C={1,2,3,4,5,6} if it was the roll of a die
glass gulch
then c = 6?
glass gulch
can we treat it as a constant in the summation?
ah nvm
thank you
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torpid perch
let $f(x) = \ln(1+x)$ qnd let $p(x)$ be the taylor polinomial of third order centered at $x_0 = 0$ show using the middle value theorem (cauchy theorem) that $\frac{f(x)-p(x)}{x^4} = \frac{f^{(4)}(c)}{4!}$ for some c between 0 and x
glossy valveBOT
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clever forge
What have you tried, @torpid perch?
torpid perch
nothing much
I read some things about ivt
we know its centered around 0
but cant seem to find a way to use ivt here
also the clue: "for some c between 0 and x" what does that mean
<@&286206848099549185>
clever forge
Do you know what the IVT states?
torpid perch
if a function is continuous over a closed interval [a, b], it encompasses every value between f(a) and f(b) within that range.
does close or open interval matter?
clever forge
I think the question isn't asking about the IVT
I think it's asking about the Mean Value Theorem
torpid perch
ahh mvt u mean
clever forge
(which talks about there being some c in the interval at which the slope is equal to the slope between (a,f(a)) and (b, f(b)))
torpid perch
if f is continuous over the closed interval [a,b] and differentiable over the open interval (a,b), then there exists a point c∈(a,b) such that the tangent line to the graph of f at c is parallel to the secant line connecting (a,f(a)) and (b,f(b)).
clever forge
that's the one
torpid perch
ok mvt is hard for me
clever forge
(I think they call it the Cauchy MVT as well)
have you tried to draw a picture
or Google the name to get a picture?
clever forge
yea
clever forge
ok mvt is hard for me
so why's it hard?
torpid perch
I was studying ivt instead of mvt I thought it referred to ivt, but makes sense that is mvt instead
mmh dunno if hard, but im new to the mvt
also, secant line?
clever forge
yea it's like the tangent line
but it's between two points
(instead of the tangent line which has only one)
clever forge
torpid perch
mmm
how does the derivative play a role here?
I am still confused as hell
I need more hints
clever forge
try and think about what a Taylor polynomial of third order (at 0) looks like
and what it represents
torpid perch
mmm
an approximation?
idk what it represents?
specially centered at 0
btw
f(0) = ln(1) = 0
but dunno how that helps
clever forge
try and think about what a Taylor polynomial of third order (at 0) looks like
can you write it out?
these are basic things that you're not doing tbh
show some effort
torpid perch
okay
,, P_3(0) = \frac{f(0)}{0!}(x-0)^0 + \frac{f'(0)}{1!}(x-0)^1 + \frac{f''(0)}{2!}(x-0)^2 + \frac{f'''(0)}{6} (x-0)^3
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938c2cc0dcc05f2b68c4287040cfcf71
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torpid perch
how to use mvt here? wtf
clever forge
have you seen Taylor's theorem with a remainder?
clever forge
what does f(x) - p(x) look like?
clever forge
what does f(x) - p(x) look like?
looks like R_n to me for some suitable n
clever forge
I am not spelling out every single thing for you bruh
just sit and think for a bit
or move on and let it work in the background of your mind
(it's good to struggle a bit)
(and try things out)
torpid perch
but if n = 4, shouldnt it be n = 3 since poly of 3rd degree?
clever forge
half of math is doing the wrong stuff and reorienting yourself 
torpid perch
this f^4(c) stuff means they are talking about R_3
problem is where is this (x-a)^n+1 stuff is going
we know a = 0
x^4 cancels from numerator and denominator
R_3 <= f(x) - p(x)
mayhaps.
torpid perch
maclaurin polynomials is the taylor polys centered at 0
ohh, there is a remainder section
$R_3(x) = \ln(1+x) - P_3(x)$
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938c2cc0dcc05f2b68c4287040cfcf71
torpid perch
wtff! I need more hints
clever forge
You will not get any.
Look at the proof on that page.
It literally spells out your problem step by step.
torpid perch
the one that uses rolles theorem? or which proof specifically 😭
clever forge
bye
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tame bobcat
Hi everyone!
I have a question regarding this excerpt from a book.
Specifically the part that I marked in orange. I provided the rest for context.
I know the concept of probabilistic method and ramsey etc. But I do not understand what the author is trying to tell me with this line (the orange one) How is this to be understood ?
Thanks in advance !
tame bobcat
nova basin
sounds like they're just making a general condition for which the theorem's hypothesis is verified
tame bobcat
sounds like they're just making a general condition for which the theorem's hypo...
I am sorry, but I dont understand this as well
could you explain what you mean ?
oh hang on
it is no longer n chose 2
nova basin
oh
tame bobcat
you mean they generalized the expression such that it would be true for k colours instead of 2 ?
nova basin
look at the proof, it was never meant to be since the proof (at the union bound part) uses nCk ... < 1 at the end of the line
so it could be that the theorem contains a typo
tame bobcat
wait I feel like the expression in the theorem is wrong
ah yes
what you said
ok so lets say it is a typo
I still dont get what the orange part is trying to tell me
somehow it doesnt make sense
nova basin
yeah I agree it's weird
maybe they mean doing this abstract calculation to find this criterion is simpler than checking whether 1000C20 x 2^(-20C2 + 1) < 1
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tame bobcat
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tame bobcat
@nova basin btw yes it is a typo
I used an older version on my pc
on my other device I saw it says n C k
just wanted to let you know
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raven vine
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raven vine
How to calculate variance
open zinc
How to calculate variance
What’s the formula for variance?
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ember shadow
what formulas do they give you
torpid perch
let $f(x) = \ln(1+x)$ qnd let $p(x)$ be the taylor polinomial of third order cen...
let $f(x) = \ln(1+x)$ qnd let $p(x)$ be the taylor polinomial of third order centered at $x_0 = 0$ show using the mean value theorem (cauchy theorem) that $\frac{f(x)-p(x)}{x^4} = \frac{f^{(4)}(c)}{4!}$ for some c between 0 and x
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studying_calc_real_analysis
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how is it wrong
grave elm
Well so first thing that's weird is they are asking about placement of point A, such that rectangle BCDE is formed
grave elm
i think its just wrong
the question
placement of point A has nothing to do with rectangle BCDE
grave elm
Assuming they meant rectangle ABCD, your answer should be correc
severe badge
i messed up these as well
grave elm
,rccw
glossy valveBOT
torpid perch
let $f(x) = \ln(1+x)$ qnd let $p(x)$ be the taylor polinomial of third order cen...
let $f(x) = \ln(1+x)$ qnd let $p(x)$ be the taylor polinomial of third order centered at $x_0 = 0$ show using the mean value theorem (cauchy theorem) that $\frac{f(x)-p(x)}{x^4} = \frac{f^{(4)}(c)}{4!}$ for some c between 0 and x
glossy valveBOT
studying_calc_real_analysis
static folio
Can you write it out? f(x)-p(x)/x^4
glossy valveBOT
studying_calc_real_analysis
static folio
what I mentioned
torpid perch
i did
static folio
p(x) I guess..
torpid perch
oh, its of third order
centered at 0
,, P_3(x) = f(0) + f'(0)(x-0)^1 + \frac{f''(0)}{2!}(x-0)^2 + \frac{f'''(0)}{3!}(x-0)^3
glossy valveBOT
studying_calc_real_analysis
torpid perch
,, \frac{\ln(1+x) - \left(f(0) + f'(0)(x-0)^1 + \frac{f''(0)}{2!}(x-0)^2 + \frac{f'''(0)}{3!}(x-0)^3\right)}{x^4}
glossy valveBOT
studying_calc_real_analysis
static folio
Yes, but you can do more
Try to play with it, seems like you didn't give it a try yet
static folio
I mean, you know what f is
torpid perch
oh
okay give me a second
,, f(x) = \ln(x+1) \ f(0) = 0 \ f'(x) = (x+1)^{-1} \ f'(0) = 1 \ f''(x) = -(x+1)^{-2} \ f''(0) = -1 \ f'''(x) = 2(x+1)^{-3} \ f'''(0) = 2
is this correct?
,, \frac{\ln(1+x) - \left(f(0) + f'(0)(x-0)^1 + \frac{f''(0)}{2!}(x-0)^2 + \frac{f'''(0)}{3!}(x-0)^3\right)}{x^4} \ = \frac{\ln(1+x) - \left(0 + 1\cdot(x-0)^1 + \frac{-1}{2!}(x-0)^2 + \frac{2}{3!}(x-0)^3\right)}{x^4} \ = \frac{\ln(1+x) - \left((x)^1 + \frac{-1}{2!}(x)^2 + \frac{2}{3!}(x)^3\right)}{x^4} \ = \frac{\ln(1+x) - \left(x - \frac{x^2}{2} + \frac{2x^3}{6}\right)}{x^4}
now what?
@static folio
static folio
@torpid perch
torpid perch
<@1187916384341078070>
I need more hints with the exercise
I already threw all out there that I know
how does even the mean value theorem relate to this polynomial in question?
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wheat spruce
if anyone could please take a look at this and tell me if i've solved ok so far i'd be extremely grateful
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if anyone could please take a look at this and tell me if i've solved ok so far ...
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torn jolt
no idea how to do matrices at all, this was given as sub work but my teacher never taught us this
hazy lance
no idea how to do matrices at all, this was given as sub work but my teacher nev...
so do you know how to multiply a matrix by a scalar
torn jolt
ive only done adding and substracing a matrix
umbral dome
multiplying a matrix by a scalar (a number like 2, 5, -8) just means multiplying each entry by that scalar
torn jolt
okay thank you!
jaunty narwhal
okay thank you!
Do you have any idea about order of matrices? Just asking
You'll apply it everywhere when you go to matrix multiplication 😅
torn jolt
Do you have any idea about order of matrices? Just asking
no i dont
static ore
how do i do this
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how do i do this
umbral dome
if $\vec a = (a_1, a_2, a_3)$ and $\vec b = (b_1, b_2, b_3)$ then [ \vec a \cdot \vec b = a_1 b_1 + a_2 b_2 + a_3 b_3 ]
glossy valveBOT
cloud
static ore
if $\vec a = (a_1, a_2, a_3)$ and $\vec b = (b_1, b_2, b_3)$ then \[ \vec a \cdo...
why does this work though
😢
umbral dome
take it as a definition
static ore
bet
open hemlock
can anyone tell me WHY -3^4 equals a negative number
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can anyone tell me WHY -3^4 equals a negative number
umbral dome
by convention we set the order of operations so that [ -3^4 = -(3^4) \ne (-3)^4 ]
rapid rain
it's - (3^4)
lofty lynx
because -3^4 = -(3^4)
glossy valveBOT
cloud
lofty lynx
IF it were (-3)^4 it would be positive
lofty lynx
because -3^4 = -(3^4)
You can also think of it being -1*3^4 = -3^4
Has your question been solved?
steel cove
think of it as -x^4 with x being 3 and it makes more sense
open hemlock
so if i have a geometric sequence with thr common ratio of -1 and 1st value of 2/3 what would be the nes 2 values
steel cove
so if i have a geometric sequence with thr common ratio of -1 and 1st value of 2...
-2/3, 2/3
open hemlock
So this is wrong
hot herald
and for that you'd need () around the -1
without them, you're getting the wrong signs
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midnight dew
whats the formula for the equation of a plane that passes through a specified point?
midnight dew
<@&286206848099549185>
lofty lynx
midnight dew
ok ty
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torn jolt
oi
daring bay
just find AB vector
torn jolt
yh
daring bay
then divide it by its magnitude, so you get a unit vector
torn jolt
the magnitude is 5 roor 5
torn jolt
daring bay
yes
daring bay
isnt unit vector 1/magnitude x normal vector
normal vector divided by its magnitude
what i said
yes
daring bay
antiparalle to AB
daring bay
1/magnitude x vector
yes
torn jolt
its the same thing?
daring bay
its the same thing?
yes
torn jolt
the x,y,z components of a vector
i havent done matrices
torn jolt
if it asked me
daring bay
the negative too
daring bay
so 0 difference
they are not the same
if thats what youre asking
but their direction is the same
torn jolt
the parallel of AB and the unit vector
torn jolt
okay look at this
yh
daring bay
torn jolt
yh
daring bay
notice how both these vectors are parallel
even tho one is i+j
and the other is 2i+2j
glad escarp
I got it
torn jolt
whats common is that the
2:1
daring bay
the i and j components are same
glad escarp
It's -4i +7j
daring bay
It's -4i +7j
?
glad escarp
torn jolt
we just need like a multiplier
daring bay
we just need like a multiplier
ye
daring bay
p is 3
torn jolt
daring bay
u messed up the factorisation bit
daring bay
this is the
glad escarp
I c
glad escarp
Mb mb
torn jolt
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formal monolith
please help, i do not know where beta - alpha/6 comes from
ive gotten (beta - alpha)/4, but it wasnt a strick inequality either
narrow ermine
I mean you can always find m such that 3^{-m} < (beta-alpha) / 4 strictly. I don't think you need the /6 for it to work.
formal monolith
yeah thats what i was thinking
but i just wasnt sure why he put the /6 in the first place
narrow ermine
Might be arbitrary. Like to make it definitely smaller than (b-a)/4
narrow ermine
Yeah
formal monolith
im having a bit of trouble parsing it, and i was wondering if u could help elaborate on it
okay thank u
one sec
"Intervals of the form (3k+1/3^m, 3k+2/3^m) are the "middle thirds". These
are the intervals that are being systematically taken out in the process of constructing
the Cantor set. Here k ranges from 0 to 3^(m-1)-1. So for m = 1 we have just k = 0
and we take out the middle third (1/3,2/3). For m = 2, k = 0,1,2, and there
are three middle thirds of length 1/9: (1/9,2/9), (4/9,5/9) and (7/9,8/9). In
general, there are 3^(m-1) middle thirds of length 1/3^m, which are taken out
at each step of the construction. In the notation of Rudin
( I have the third edition ):
E_1 = [0,1/3] U [2/3,1] = complement of (1/3,2/3) relative to [0,1]
E_2 = [0,1/9] U [2/9,1/3] U [2/3,7/9] U [8/9,1]
= complement of (1/9,2/9) U (4/9,5/9) U (7/9)
...
...
E_m = complement of U ( (3k+1)/3^m, (3k+2)/3^m ) relative to [0,1], where
the union is taken over k = 0,2,..., 3^(m-1)-1.
Since P = intersection of all E_m's, and each "middle-thirds" interval
does not intersect some E_m, it follows that P does not intersect any of the
"middle thirds" intervals.
Given an interval (alpha,beta), we ask whether we can fit into it a "middle thirds"
interval, that is, an interval of the form ((3k+1)/3^m, (3k+2)/3^m). Now Suppose
(alpha,beta) contains an interval of the form [j/3^(m-1),(j+1)/3^(m-1)]
for some j=0,1,...3^(m-1)-1. Then it will also contain the 'middle third' of
that interval, namely -- it will contain ( (3j+1)/3^m, (3j+2)/3^m ). So
how can we ensure that (alpha,beta) contains an interval of the form
[j/3^(m-1),(j+1)/3^(m-1)] ? A sure way is to require that half of our interval
will be longer than 1/3^(m-1) (=the length of [j/3^(m-1),(j+1)/3^(m-1)]). In that
case, if we slide in steps of 1/3^(m-1) starting from zero, then if the first time
we hit (alpha,beta) we are not already inside, then we will have covered less than
half of it (by our requirement) so that in the next step we will be inside.
So we require:
(beta - alpha)/2 > 1/3^(m-1), which amounts to
(beta - alpha)/6 > 1/3^m"
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grave elm
<@&268886789983436800>
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orchid lynx
can someone check my working? this is on boolean algebra
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atomic folio
torn jolt
What’s up
torn jolt
Can you guys explain how to get from left side to right side of the circled sections ?
That’s all I need
My algebra skills kind of rusty
Appreciate it
Thxs
marks ?
hot herald
cancel qq_3,
cross multiply
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fair iris
Could someone pls define commutative, associative, identity, inverse, zero product, distributive, reflexive, symmetric and transitive properties with examples ?
thick hedge
like in which branch of maths?
plucky helm
Could someone pls define commutative, associative, identity, inverse, zero produ...
these are context dependent, so you're gonna have to give us more than that
thick hedge
will this do?
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thick hedge
desert cypress
,rotate 270
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desert cypress
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desert cypress
question
for line 4
how did they factor out power of -11
when theres only -10
on the let side
fierce gyro
from there
desert cypress
yes il
ik
but there isnt -11 on the left side
so the highest u can take is -10
just like how we took ^9 and not ^10
bec left side only had nine
and not ten
im confused
fierce gyro
because ^9 is the lowest, and ^-11 is the lowest too
fierce gyro
so the highest u can take is -10
you need to take the Lowest exponent
-11 is lower than -10
desert cypress
how can u take -11 out of -10
fierce gyro
(1-x^2)^-11 • (1-x^2) = (1-x^2)^-10
fierce gyro
me neither it's a nasty exercise too
fierce gyro
🫡 seeya
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bright yoke
In a drawer Sandy has $5$ pairs of socks, each pair a different color. On Monday Sandy selects two individual socks at random from the $10$ socks in the drawer. On Tuesday Sandy selects $2$ of the remaining $8$ socks at random and on Wednesday two of the remaining $6$ socks at random. The probability that Wednesday is the first day Sandy selects matching socks is $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers, Find $m+n$.
whats wrong with my solution:
let all socks be unique: a1a2b1b2c1c2d1d2e1e2.
there are 10c2x8c2x6c2 ways to choose socks for each day; that is the denominator.
we do not want to choose a pair on the first day. there are 10x8 ways to do that. wlog let the chosen socks be a1b1.
now lets do casework on the second day:
case 1: 2 socks from pair in day 1
there is only one way to choose the socks on day 2: a2b2. there are 3 more ways to choose a pair: c1c2/d1d2/e1e2. 3x1=3
case 2: one sock from pair in day 1 + another one
there are 2 ways to choose a sock that was from day 1: a2 or b2. we choose another sock, not from day 1: c1c2d1d2e1e2 which is 6 days. there are 2 pairs left, and we choose a pair. 2x6x2=24.
case 3: all socks not from day 1
we choose 2 socks from c1c2d1d2e1e2 that are not a pair. 6 ways to choose the first, 4 ways to choose the second. there is only 1 pair left. 6x4x1=24.
we now have 10x8x(24+24+3)/(10c2x8c2x6c2) which simplifies to 68/315 = 383. this is wrong. the answer is 26/315
glossy valveBOT
Aurora
bright yoke
problem source: 2015 aime i p5
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torn jolt
hi i dont understand how they got this step
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hi i dont understand how they got this step
thorn pasture
erm what the sigma
keen vector
lol
torn jolt
shrewd hamlet
@torn jolt whats another way to write Y bar
torn jolt
<@456226577798135808> whats another way to write Y bar
sum of Y_i / n
keen vector
Var(aX) = a^2 Var(X)
shrewd hamlet
good:
torn jolt
shrewd hamlet
so now we have
torn jolt
Var(aX) = a^2 Var(X)
hows this useful
shrewd hamlet
Var$(\bar{Y}) = $ Var $(\frac {\sum_1^n Y_i}{n})$
shrewd hamlet
ok does that make sense
torn jolt
yeah
glossy valveBOT
torn jolt
thanks @shrewd hamlet
shrewd hamlet
np
torn jolt
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proud tendon
something to do with the disk & washer method
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something to do with the disk & washer method
proud tendon
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mellow bone
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mellow bone
I have solved this question and got 19.11 to two d.p after using the sine rule about 5 times and after finding the difference between the two congruent triangles and by finally adding 5 please check this answer @velvet sedge since you helped me to solve it. I would really appreciate that and if you can, tell me if there is a quicker way to solve this. thanks for your help.
limber forum
But I checked anyway
19.11 is right
You can avoid a little undue suffering with the sine rule though
Let the height = x, horizontal distance to the tower = y
That means tan25 = x/y, and tan19 = (x-5)/y
2 eqns 2 unknowns solve
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mellow bone
19.11 is right <:catthumbsup:614540188747563008>
Thanks for checking but since I'm only a GCSE student can you explain more on how you would do the two equations and two unknown solves and how that would work to get you the height, if you can simplify
limber forum
So I would probably divide equation 2 by equation 1, $$\frac{\tan{19}}{\tan{25}} = \frac{x-5}{y} \cdot \frac{y}{x}$$
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TayBee
limber forum
the y's cancel, so you can bring the x in the denominator up, put all the x's on one side, then factorise/divide through to make it the subject
But I feel like GCSE doesn't do much in the way of dividing equations
So
Alternatively
Using equation 1
y = x/tan25
You can substitute that into equation 2
$\tan 19 = \frac{(x-5)\tan 25}{x}$
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TayBee
limber forum
A little bit of rearranging again and you'll get x out of it
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mellow bone
thanks so much this question plagued me for the last 3 days, I finally understand it now thanks to your help, and that other guy I tagged earlier taught me how to do it but using the sine rule it takes a good 10 minutes. I don't know if you'll agree with me on this (since you're probably a math genius) but I don't think it's reasonable for 15 year olds having to go through this in the UK. Well ,at least I finally understand it now, Thank you so much again @limber forum 🙏
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copper vortex
i cant understand a question where i need to write an equivalent linear system where both equations have the same x and y coefficients
glacial pasture
would you mind showing it?
copper vortex
glacial pasture
in a for example you could multiply the second equation by 1/3 and the first by 3 for (i)
scalar multiplication seems like the easiest way here
actually no thats not what it meant
you can just do one of the two things i mentioned
then its fine
copper vortex
scalar multiplication seems like the easiest way here
Never heard of that tbh
glacial pasture
if you multiply an equation by a number, say 5, it will have the same solutions as before
you just need to do some multiplying that gets the needed coefficients to match
copper vortex
Ngl i looked at the answers and it still confuses me
The answers were i) 3x - 6y =-18 and 3x - y = 2, ii) x-2y=-6 and 6x - 2y = 4
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zealous wren
Assignment: just calculate this.
I quite literally tried everything. Separating in 2 integrals doesnt help, no u-sub works, dividing the function inside by cos x or sin x to get tan x or cot x doesnt help either, and kings rule leads to a phd
granite torrent
this is linear system of equations problem
ur goal is to rewrite the integrand in the form (constant1) + (constant2 * u'/u); after u do this u can directly integrate
u can internally justify this bcz the numerator contains a linear combination of the denominator and the derivative of the denominator
zealous wren
ur goal is to rewrite the integrand in the form (constant1) + (constant2 * u'/u)...
i've seen this and unfortunately this is for college adimssion exam and way higher than the normal highschool standard here
no other way to solve it?
never seen the u' thing.
granite torrent
i've seen this and unfortunately this is for college adimssion exam and way high...
it is high school level
zealous wren
not here i mean
granite torrent
ik this because it only uses methods u wrote
zealous wren
i am not from the US
granite torrent
"Separate in 2 integrals" and "u-sub"
there is nothing more advanced than that going on here
zealous wren
I know for example that u rewrite f(x)=1/(x+1)^2 as A/(x+1) + B/(x+1)^2
but the u', thats what trips me up
granite torrent
it's just how i wrote a u-substitution integral
in ur example it would be a constant * (2cosx - sinx) / (2sinx + cosx)
2sinx + cosx (denominator) is u
the derivative of the denominator is u', and this function above ^ is something you can directly integrate with a u-substitution
zealous wren
well where do i even start thinking about how to rewrite this?
i dont want just the pure result because it wont help me when encountering similar or new problems
so it would help me a lot if you give me a little hint and start trying on my own
granite torrent
u can internally justify this bcz the numerator contains a linear combination of...
these msgs
that message i replied to in particular should be a good hint for this problem though if needed i can explain more
zealous wren
ah i see
i understand now
and this way i can even verify my work
because whatever i come up with should still be equal to my f(x)
tardy ore
sd
rapid rain
yes
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torn jolt
how exactly do you get e, the coprime here of 1740, do you just bruteforce or is there an actual method
boreal marlin
Any coprime works
torn jolt
is there a way to find coprimes easily
boreal marlin
Any prime is also a coprime of that
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merry crescent
ok so I am looking at this question and attached answer scheme. For the last case where x and y are non zero, they immediately conclude that $x^2=y^2=\frac{1}{(2*\lambda)}$. What I did was treat $x^2=\frac{1}{(2\lambda)}$ and $y^2=\frac{1}{(2\lambda)}$ as separate cases and I plugged both in individually to equation 3 to find x and y. However, this approach while being correct took more time and I'd like to understand their thought process as well.
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odd laurel
How would I find area of this?
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How would I find area of this?
torn jolt
Do you know the coordinates of the vertex ?
odd laurel
yes
torn jolt
Hmm so do you have idea about the area in terms of coordinates using determinants?
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torn jolt
XD not overkill
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distant berry
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distant berry
So the indefinite integral should be arctan(x)
arctan(x) is divergent (I think)
but the answer is not DNE
so I must be doing something wrong
wide sundial
Try graphing it
viral jasper
arctan(x) is divergent (I think)
consider what arctan represents, and what its domain and range might be
rapid rain
it's not
distant berry
pi over 2 
distant berry
so it's arctan(2)+pi/2
viral jasper
arctan is the inverse of tan
Inverse, not reciprocal
worldly thunder
recipy??
viral jasper
sec cot is reciprocal of tan
worldly thunder
trolling rn
wide sundial
Huh???
worldly thunder
cot
wide sundial
Cot is the reciprocal of tan
viral jasper
trolling rn
!redir
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trolling rn
This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.
wide sundial
What is happening
distant berry
so it's arctan(2)+pi/2
Is this correct
distant berry
F(b)-F(a) right
wide sundial
All g
distant berry
My brain is a little fried it's like 2AM
viral jasper
same
rapid rain
so it's arctan(2)+pi/2
this is correct
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rapid rain
34, you need t <= 34 and t >= 1
pseudo cape
34, you need t <= 34 and t >= 1
Yep, because it says "there are", so we can be sure there is atleast 1, right?
rapid rain
<@&268886789983436800>
pseudo cape
34, you need t <= 34 and t >= 1
Do you see how my teacher would've thought it could be 35 or 36?
rapid rain
Do you see how my teacher would've thought it could be 35 or 36?
because they thought that they only needed to consider t !=0
pseudo cape
36 is when it can be 0
rapid rain
and forgot t!=35
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modest grotto
how do i find the vector of 2 points in 3d space
i need to find OA vector which O is (0;0;0) and A is (3;1;4)
modest grotto
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silver sinew
Pretty small question, but, in this question where I need to factorise
silver sinew
can i leave my answer as: (x+9/2 +/-sqrt45/4)^2
sweet ingot
can i leave my answer as: (x+9/2 +/-sqrt45/4)^2
That’s not an answer
You are asked to find solutions
sweet ingot
And kinda weird to write (…+/-…)^2
silver sinew
what would you write
sweet ingot
(…+…) * (… - …)=0
silver sinew
ah yes
i just hate doing it the long way
anyways
thank you very much for that quick check
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lost raptor
Is the answer to this that because w is an element of span(s), it is a linear combination of v1, v2 and v3. So hence, the set {v1,v2,v3,w} must be dependent?
rare dock
i think there is some relevant information cut out at the bottom
rare dock
yea, that’s right then
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hard birch
The perimeters of triangles AA1A2, BB1B2, and CC1C2 are 21 cm, 6 cm, and 73 cm, respectively. Calculate the perimeter of triangle ABC.
near mirage
The perimeters of triangles AA1A2, BB1B2, and CC1C2 are 21 cm, 6 cm, and 73 cm, ...
What have you tried?
near mirage
The perimeters of triangles AA1A2, BB1B2, and CC1C2 are 21 cm, 6 cm, and 73 cm, ...
And what can you say about these two lines
hard birch
What have you tried?
i honestly have no clue where to start i just marked that aa1 aa2 and so on are equal
hard birch
same lenghti
near mirage
same lenghti
So think of it like, C1M gets moved to there
Like you move C1M to C1T where T is the intersection point of the circle and the BC
near mirage
The perimeters of triangles AA1A2, BB1B2, and CC1C2 are 21 cm, 6 cm, and 73 cm, ...
You move the sides that are inside of the big triangle and rotate them so that they land on the big triangle
I hope this makes sense?
near mirage
The perimeters of triangles AA1A2, BB1B2, and CC1C2 are 21 cm, 6 cm, and 73 cm, ...
You rotate C1M to be on the big triangle
Same for C2M
And so on
near mirage
Idk what you drew
near mirage
The perimeters of triangles AA1A2, BB1B2, and CC1C2 are 21 cm, 6 cm, and 73 cm, ...
C1M to C1T
hard birch
t is a newq point yes?
near mirage
Not really
near mirage
I'm moving C1M to C1T because they are equal length
sharp hemlock
ah, disregard then
near mirage
like that??
What did you draw?
hard birch
What did you draw?
bro idk i moved it
sharp hemlock
ohhhh I understand now
near mirage
I think we need a paper and pen
zinc light
All the black lines can be moved to their opposite blue line
near mirage
All the black lines can be moved to their opposite blue line
Exactly
To the blue line closer to the circle
sharp hemlock
zinc light
The perimeters of triangles AA1A2, BB1B2, and CC1C2 are 21 cm, 6 cm, and 73 cm, ...
Just rotate the black line around till it's on the blue straight line
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zinc light
Np :)) lolol
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thick hedge
I'm having trouble understanding this proof
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I'm having trouble understanding this proof
thick hedge
why does the defn of the direct sum imply the only way to write 0 as a sum of elements is to take each element to be zero
fast peak
what is the definition of direct sum you are working with
thick hedge
fast peak
well 0+0+0...+0 is certainly one way to write 0 as the sum v_1+...+v_m
and by the first bullet point it has to be unique
so thats also the only way to write 0 as the sum v_1+...+v_m
thick hedge
that follows from this?
thick hedge
as the only properties that a subspace can surely have are these
0+0+0.... must be one of the ways
but why can't I write it as say 1 -1
fast peak
ignoring the issue that 1 might not be in your subspaces
the first bullet point says that by definition for a direct sum you are only allowed one way to write 0
thick hedge
what if 1 and -1 are
thick hedge
I don't follow
fast peak
if you can write it as 1-1 then you dont have a direct sum
I dont know how to write it clearer. maybe someone else does
thick hedge
if you can write it as 1-1 then you dont have a direct sum
ok, that was my question
thank you
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hallow walrus
can someone help me through this? I don't fully understand the question..
