?
#help-39
cerulean smelt
sacred bough
Subsitute I and I0
cerulean smelt
Subsitute I and I0
yeah its 2
sacred bough
correct
sacred bough
Calculate the logarithm of 2: log 2 ≈0.3010
cerulean smelt
Calculate the logarithm of 2: log 2 ≈0.3010
alr, what next?
cerulean smelt
4.6?
cerulean smelt
3.8010≈3.8≈4.6
where did 4.6 come from
sacred bough
3.8
is also correct
3.8 is approximately equal to 4.6 Hence, the Richter scale measurement for an earthquake with twice the intensity of a tremor measuring 3.5 is approximately 4.6
cerulean smelt
3.8 is approximately equal to 4.6 Hence, the Richter scale measurement for an e...
but 3.8 and 4.6 are kinda different numbers
pearl pondBOT
Available help channel!
silent bramble
yo whatup
silent bramble
lmao im back😂
ok am I trippin but I think theres an error in the solution
question e
answer says .65 but thats the prob of lines 2-4 in use, so it would be 1-.65 for not in use
so 0.35
let me know what you think
actually Im getting both e and f wrong, how would you find probability of not in use
i thought it would just be 1- [prob(in use)]?
merry carbon
Overlap: e.g. at least four lines not being in use means that strictly less than two lines are in use
Wait 
merry carbon
actually Im getting both e and f wrong, how would you find probability of not in...
What did they do for f, and how did you do it?
Also @cinder flower 
silent bramble
merry carbon
Yea see the overlap comment - you gotta be a bit careful
mild niche
according to John Michelle's thoery of blackholes how to calculate the
hot lodge
hot lodge
Sorry
hot lodge
was here first tho
mild niche
ok sry
hot lodge
Noo you have already taken
pearl pondBOT
pearl pondBOT
Available help channel!
midnight haven
how do i integrate sin2x/x
pearl pondBOT
how do i integrate sin2x/x
midnight haven
wrt x
rancid rune
indefinite integral?
midnight haven
yes
rancid rune
no elementary antiderivative
midnight haven
wth
midnight haven
hey can you tell me what exactly is elementary so i dont stare at it for long
rancid rune
hey can you tell me what exactly is elementary so i dont stare at it for long
it's hard to tell
rancid rune
where did u come across this integral of sin2x/x
midnight haven
its not even the question lol i got it while solving some other integral
means theres better method to solve this question
since the way i did it included this
so ill try again i gues
thanks
.close
pearl pondBOT
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carmine root
pearl pondBOT
carmine root
this is not a power series because it isnt x^n but x^2n
or is it not a power series because the 1/x^n is flipped
ok, since it is flipped it isnt a power series
since you basically divide by it
but would the same series but raised to ^2n instead of -2n be a power series
sharp vigil
it's fine for a power series to have a 2n exponent (that's the same as adding only even terms, and letting odd terms be 0), but the negative exponent makes it not a power series
carmine root
but you should calculate it though
since if the qestuon was (2/n*x)^-2n it would be a wpoer seires
right
sharp vigil
yes
pearl pondBOT
Available help channel!
obsidian comet
pearl pondBOT
merry carbon
Hiiii 
Also for those limits, you may wanna use the fact that sqrt{x^2} = |x| 
[and do some factoring! 
]
merry carbon
You can as well (that might be better actually 
)
obsidian comet
i'll try it out but the reason for multiplying with the conjugate, is it because we're dealing with square roots?
ily tyyy
merry carbon
i'll try it out but the reason for multiplying with the conjugate, is it because...
also because too when you do, you also have |x|^2 = x^2, so there are some nice cancellations too 
midnight haven
a) 1/2?
obsidian comet
<:InLove:669265803270553634> also because too when you do, you also have |x|^2 =...
oki so I did it to this point?
$$\frac{x}{|x| + \sqrt{x^2 - x}}$$
jolly parrotBOT
nicoco
merry carbon
oki so I did it to this point?
$$\frac{x}{|x| + \sqrt{x^2 - x}}$$
Yep, perfect
obsidian comet
how should I continue? i get stuck at that part
merry carbon
You can use the fact that as per above, sqrt{x^2} = |x| and consider cases
midnight haven
how should I continue? i get stuck at that part
put the limit +inf hence mod sign already gives + vemod(x) becomes simple x
merry carbon
So then, you can e.g. factor out an |x| in denominator
midnight haven
similarly for -inf limit, mod(x)=-x
midnight haven
So then, you can e.g. factor out an |x| in denominator
mod is sign which depend upon value, if you put +inf means +ve value then there is no meaning of mod,it gives you same mod(x)=x
simple mod(x)={x when x>0 & -x when x<0)
merry carbon
"put +inf" 
merry carbon
a)1/2 and b)-inf
You're also wrong for b
midnight haven
You're also wrong for b
why? whats your answer?
merry carbon
,w lim abs(x) - sqrt(x^2 - x), x to -inf
jolly parrotBOT
merry carbon
(You're not supposed to give answers in this server, fyi)
But anyways, that's why there's the suggestion to factor and consider cases-
midnight haven
oh yes my mistake i took -x+sqrt(x^2-x) instead of -x-sqrt(x^2-x) in denomentore
merry carbon
So then, you can e.g. factor out an |x| in denominator
Anyways, @obsidian comet
midnight haven
You're also wrong for b
part (a) is right though
merry carbon
**nicoco**
If you write this as
[
\frac{x}{\abs{x} \qty(1 + \sqrt{1 - \frac1x}) }
]
you might be happier with it
jolly parrotBOT
@merry carbon
obsidian comet
<@788085606483361802>
yes i got that
but how are we gettting that to 1/2 afterwards?
merry carbon
Well, let's assume we're taking the limit to infinity, so we're dealing with positive x, and so |x| = x
You then, from that, get that the above turns into $\frac1{1 + \sqrt{1 - \frac1x}}$, What happens as $x$ gets larger and larger to that?
jolly parrotBOT
@merry carbon
merry carbon
Yep
A similar argument for -inf: you have x being quite negative, so |x| = -x, and then algebra and all
obsidian comet
thank u chaaart ilysm
merry carbon
ily more
obsidian comet
i'm studying last minute for an exam on saturday
i'll be back with more problems soon lmao
merry carbon
Awwww I'll be looking out for you 
definitely sure I'll catch you along the way 
tysmmm
pearl pondBOT
pearl pondBOT
Available help channel!
vernal grove
pearl pondBOT
vernal grove
For this question
My attempt:
$F_y(y) = P(Y \leq y) = P(X^2 \leq y) = P(-\sqrt{Y} \leq X \leq \sqrt{Y}) = P(X \leq \sqrt{Y}) - P(X \leq -sqrt{Y})$
jolly parrotBOT
Calc III Victim
vernal grove
$F_X(\sqrt{y}) - F_X(-\sqrt{y})$
jolly parrotBOT
Calc III Victim
vernal grove
and then we find the derivative of both sides right
to get
$\frac{1}{2\sqrt{y}} f_x(\sqrt{y}) + \frac{1}{2\sqrt{y}} f_x(-\sqrt{y})$
jolly parrotBOT
Calc III Victim
vernal grove
after plugging in we get
$\frac{1}{2\sqrt{y}} (2(\sqrt{y})e^{-(\sqrt{y})^2}) + \frac{1}{2\sqrt{y}} (2(-\sqrt{y})e^{-(-\sqrt{y})^2})$
jolly parrotBOT
Calc III Victim
vernal grove
which should equal to 0 right?
idk what im doing wrong
Isnt this how the CDF technique works?
this is how they did it in class but I thought for the cdf technique we are suppose to get the derivative
but instead they first integrated..?
im not sure why
oh shit wait since it says 0 < x < inf were we suppose to ignore P(X <= -sqrt{y})
meaning in that case we should have ended with
$\frac{1}{2\sqrt{y}} (2(\sqrt{y})e^{-(\sqrt{y})^2})$
jolly parrotBOT
Calc III Victim
vernal grove
which should = e^-y
pearl pondBOT
@vernal grove Has your question been resolved?
vernal grove
<@&286206848099549185>
potent hedge
Yes exactly
midnight haven
hello
uneven smelt
hello there
midnight haven
im gonna need a variety of help along my revision , is that okay?
plethora of questions
hey esthesia
uneven smelt
here you just ask your questions and pray someone helps
uneven smelt
nope
midnight haven
nope
you are a pending post graduate right , how do you spend your time , if you don't mind me asking
uneven smelt
i play league and dota 2
uneven smelt
indifferent
hm?
uneven smelt
nope
midnight haven
that's nice
uneven smelt
it sure is
midnight haven
<@&286206848099549185>
placid zealot
why are you pinging helpers
woven oak
where is the question
uneven smelt
just ask your question lol
woven oak
just ask your question lol
frr
midnight haven
im gonna need a variety of help along my revision , is that okay?
.
uneven smelt
i think he wants company
placid zealot
oh
midnight haven
i thought you only ask one question per channel
woven oak
i thought you only ask one question per channel
u can more
but stay active all the time so the bot wont close it
woven oak
i thought you only ask one question per channel
u can ask anything even 1+1 i asked once and pinged @ Helpers
oops
sry
uneven smelt
the limit is one channel per person so dont go hogging all the channels
uneven smelt
u can ask anything even 1+1 i asked once and pinged @ Helpers
good
woven oak
bro worst miss ping ever ☠️
uneven smelt
dw i also asked dumb questions
woven oak
dw i also asked dumb questions
i once said if 1/0=0 then im gay
midnight haven
just go ahead
i want to understand the complex
woven oak
they all went trying to prove it ☠️
midnight haven
but idk where to start
midnight haven
yes but there's a lot to it
midnight haven
fair
woven oak
what u study
midnight haven
complex
uneven smelt
i want to understand the complex
what about it?
woven oak
for me i self study calculus and study geometry in school
woven oak
i study it in french 💀
i study geometry at school in arabic and calculus in english
good no geometry questions 👍
midnight haven
what about it?
trigonometry of complex numbers and argument of a complex number and affix of a point
midnight haven
i study geometry at school in arabic and calculus in english
i'm arabic too
woven oak
trig sucks
trig + complex = gg
uneven smelt
trigonometry of complex numbers and argument of a complex number and affix of a ...
any specific questions?
woven oak
any specific questions?
he still finding
wow amazing book has no examples 👍 @midnight haven
midnight haven
trig sucks
trig + complex = gg
bro gets it
midnight haven
any specific questions?
how to find argument of a complex number?
uneven smelt
im guessing its in the form of a+bi?
midnight haven
yes
pearl pondBOT
@midnight haven Has your question been resolved?
woven oak
.reopen
vernal grove
where did the extra ^x go?
pearl pondBOT
where did the extra ^x go?
vernal grove
they bringout the 1/2 so we r left with
e^-x (1/2)^x inside the sum right
cinder flower
(1/2)^(x+1) = (1/2)*(1/2)^x
quartz citrus
e^-x = 1/e^x
vernal grove
1/e^x (1/2)^x
how did they transform this to (1/2e)^x
wait i am an idiot
.close
pearl pondBOT
quartz citrus
pearl pondBOT
Available help channel!
jagged island
why is this the same
pearl pondBOT
why is this the same
merry carbon
Double angle 2sin(a)cos(a) = sin(2a)
thin bane
there is no 2sin on the first step tho
well here
first step you have
cos(a)sin(a)
if 2sin(a)cos(a) = sin(2a)
then whats sin(2a)
thin bane
yup
thin bane
Double angle 2sin(a)cos(a) = sin(2a)
yeah so just divide second step by2
jagged island
bcs sin(x) . cos(x) isn't the same as 2sin(x). cos(x)
thin bane
bcs sin(x) . cos(x) isn't the same as 2sin(x). cos(x)
2sin(x). cos(x) is just 2 times sin(x) . cos(x)
thin bane
jagged island
.close
pearl pondBOT
pearl pondBOT
Available help channel!
hearty burrow
How would I get the answer to #10?
pearl pondBOT
How would I get the answer to #10?
jolly parrotBOT
wanton burrow
@hearty burrow
wanton burrow
uh
hearty burrow
i just dont know how to mf simplify the fractions enough to get to 95pi/6
wanton burrow
no simpylifying
in this problem at all
remember arc length is just
s=rθ
where theta is in radians
what is 150 degrees in radians
hearty burrow
2850
wanton burrow
not quite
hearty burrow
uh oh
wanton burrow
how did u get 2850
hearty burrow
just multiplied theta by radius
hearty burrow
what would it be
wanton burrow
theta/360 * 2pi radius
this works
hearty burrow
but i only get decimals dividing theta by 360
jolly parrotBOT
faiyrose
wanton burrow
$\frac {150}{180} \cdot \cdot \pi \cdot 19$
jolly parrotBOT
Propus
wanton burrow
which beocmes that
hearty burrow
Oh lord
wanton burrow
but thats why
i would say
just make theta into radianss first
actually doesnt matter
$\frac {15}{18} \cdot \pi \cdot 19$
jolly parrotBOT
Propus
hearty burrow
Yes
wanton burrow
$\frac {5}{6} \cdot \pi \cdot 19$
jolly parrotBOT
Propus
wanton burrow
which becomes that
hearty burrow
i knew there was something when i got 6 as an answer
wanton burrow
$\frac {5pi}{6} \cdot 19$
jolly parrotBOT
Propus
hearty burrow
which is just 519pi
hearty burrow
I see thank you
Wait
is question 12 wrong
Once we turn 3pi/4 into degrees wouldnt it be 135 instead of 180
or do we flip it once we cross out the pi after multiplying 180/pi * 3pi/4
nevermind
wouldnt it be 13pi instead of 39pi/4
So my teacher was wrong
so it was laid out already
i just decided to turn it into degrees
hearty burrow
3/4
jolly parrotBOT
faiyrose
hearty burrow
Alright thank u again
pearl pondBOT
@hearty burrow Has your question been resolved?
pearl pondBOT
pearl pondBOT
Available help channel!
subtle vault
pearl pondBOT
subtle vault
im not sure where to start
somber harbor
midnight haven
why not just use Euler's formula
and simplify by exponent rules
,, e^{i\varphi} = \6\cos\varphi + i\6\sin\varphi
jolly parrotBOT
pearl pondBOT
@subtle vault Has your question been resolved?
midnight haven
yo
midnight haven
5% of x is y, and 25% of y is z, how much bigger is z than x
latent quail
!status
pearl pondBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
May I see your attempts?
midnight haven
?
pearl pondBOT
@midnight haven Has your question been resolved?
humble steppe
So I dont understand how to convert this system of linear equations in normal format so I can solve it, I need someone to explain how do i do it. The answer that I put is from chat gpt but I cant trust it since it often gets the answers wrong. So I need to figure out a way how to convert that special system of linear equations into normal format that i can solve
fringe elbow
By normal format, you would need to first bring the equations in the form ax+by=c
So first equation becomes 3x-y = 30
And second becomes -3x + 7y = 6
steady crescent
So I dont understand how to convert this system of linear equations in normal fo...
Just Subtract the first equation from the second
To cancel out the x
Then solve for y and use that to solve for x
pearl pondBOT
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
6
autumn trellis
pearl pondBOT
@humble steppe Has your question been resolved?
compact ridge
.close
hushed heath
pearl pondBOT
hushed heath
I equated horizontal components of U(initial speed) and V, the final resultant speed, and got 10=Vcos(40°), so V=10/cos(40°), so vertical component of V=10/cos(40°) * sin(40°)= 10tan(40°). So now use v=u+at for the vertical velocity components
-10tan(40°)=10root(3)-10t, but i’m not getting correct answer
I’m getting t as 2.57 seconds to 3sf
regal herald
why are you doing 10/cos40 * sin40 may i ask, youre taking a vertical component of a horizontal component
hushed heath
why are you doing 10/cos40 * sin40 may i ask, youre taking a vertical component ...
Wdym
10/cos(40°)=V
So vertical component of V=Vsin(40°)=10/cos(40°) * sin(40°)
=10tan(40°)
hushed heath
should be 5 root (3) no?
No, why?
regal herald
im high as hell (not literally)
hushed heath
Lol, it’s alr
hushed heath
im high as hell (not literally)
(Pity)
@regal herald anyway im pretty sure the ms is wrong cuz they got the exact same equation as mine till the 2nd last line, only the final answer is wrong
Fucking cambridge
worn turret
pearl pondBOT
worn turret
Does anyone understand the part in the yellow box?
I am a bit confused bout the u part
wraith hare
they made a substitution of x = sin(u)
which you can re-arrange to $u = \sin^{-1}(x)$
jolly parrotBOT
lgkoo
wraith hare
$\sin^{-1}$ is the inverse of $\sin$
jolly parrotBOT
lgkoo
wraith hare
also known as $\arcsin$
jolly parrotBOT
lgkoo
wraith hare
surely you've encountered it when doing trig. For example, when doing SOH CAH TOA in a right angle triangle: $\sin(\theta) = \frac{opposite}{hypotenuse}$, so $\theta = \sin^{-1} \left( \frac{opposite}{hypotenuse} \right)$
jolly parrotBOT
lgkoo
worn turret
Oh I got it now, thanks!
pearl pondBOT
@worn turret Has your question been resolved?
pearl pondBOT
pearl pondBOT
Available help channel!
olive zodiac
Where does the 3.1 come from?
pearl pondBOT
Where does the 3.1 come from?
olive zodiac
,rotate
jolly parrotBOT
olive zodiac
But where does the pi ever get mentioned
olive zodiac
Ohhh okay thanks
steel canopy
Np
olive zodiac
.close
pearl pondBOT
pearl pondBOT
Available help channel!
weak lake
i need help with chest area of lines
pearl pondBOT
i need help with chest area of lines
steel canopy
!da2a
pearl pondBOT
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/
weak lake
Im stuck on how to draw them in the sistem
Do i need to get k
To draw them in the system
steel canopy
What is k here??
steel canopy
Ok
weak lake
yea
weak lake
i dont get how should i draw it
humble steppe
.close
pearl pondBOT
pearl pondBOT
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Available help channel!
midnight haven
help
vivid grove
I will assume this is highschool level or so?
By scale factor I presume they meaning scaling on the y-axis.
It seems they want ticks on the y-axis every 10 little square
I will let you take it from there
pearl pondBOT
@midnight haven Has your question been resolved?
pearl pondBOT
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Available help channel!
kindred flame
pearl pondBOT
kindred flame
Can someone explain to me what I’m supposed to do? I’m legit confused and don’t even know if I’m starting off correctly lol
(#6)
sterile crow
Is it specified that's a right triangle? Unless it's right angled you can't do that
kindred flame
yes, its a right triangle, sorry i missed that when copying down the problem
since im using pythagoreon theorem
i know one side is 7m
so can i do (7)^2 + b^2 = b^2 +1?
i just thought of it but idk if that works
sterile crow
(x+1)² = x² + 7²
x+1 is the largest side if 7 is one of it's legs
Solve it, and see if you get integral solution
kindred flame
is x+1 ^ 2 the hypotenuse?
sterile crow
Yes it must be because your question says that 7 is one of the leg of the triangle so hypotenuse could be x or x +1. Since x + 1 is larger so it is it
kindred flame
ok i see
so i did the 7^2 + x^2 = (x+1)^2
then got
49 + x^2 = x^2 + 2x + 1
subtracted 1 from each side
subtracted x^2 from each side
got 2x = 48
x = 24
sterile crow
That's right 👍
sterile crow
Yea correct
pearl pondBOT
pearl pondBOT
Available help channel!
rancid valve
Probability
I'm asked to calculate P(|X_n - C| > epsilon) but I thought we only have bounds for that. Is there an actual method for this? Even to brute force this calculation with programming maybe?
rancid valve
(X_n - sum of n experiments divided by n, C is some constant)
Like that's quite literally Hoeffding's no?
cedar scarab
Is anyone able to point me in a direction here? I've been staring at this thing for 2 straight hours and haven't made any headway.
cedar scarab
I have to prove the left is a subset of the right.
quiet tendon
to prove that one set is a subset of another, show that an arbitrary element of the left set must belong to the right set
if x is an element of (A and B) or (A and C), then either x is in (A and B) or x is in (A and C)
that means that x must be in A
cedar scarab
So far I have that if x is in A and B or x is in A or C, then it is in the left.
warm current
Is anyone able to point me in a direction here? I've been staring at this thing ...
You need distributive law of Boolean Algebra
quiet tendon
and now either x is in A and B or x is in A and C, which means x is either in B or C
quiet tendon
and now either x is in A and B or x is in A and C, which means x is either in B ...
notice that this combined with the fact that x must be in A gives you exactly the right set
cedar scarab
You need distributive law of Boolean Algebra
I have absolutely zero idea what that means.
warm current
For any boolean values $x, y, z$, $(x\wedge y)\vee(x\wedge z)=x\wedge(y\vee z)$
jolly parrotBOT
SWR
quiet tendon
I have absolutely zero idea what that means.
they mean the law that (A and B) or (A and C) = A and (B or C)
cedar scarab
I don't think I'm allowed to use that.
quiet tendon
and now either x is in A and B or x is in A and C, which means x is either in B ...
okay then use this reasoning
cedar scarab
That's the point of the entire proof. To prove that relationship.
warm current
I don't think I'm allowed to use that.
Then your "proof" is just going to be wordy handwaving
warm current
That's the point of the entire proof. To prove that relationship.
No. You're proving for sets. I'm using boolean algebra
cedar scarab
Idk what boolean algebra means.
quiet tendon
it’s like the algebra of logical statements
warm current
Idk what boolean algebra means.
Algebra of boolean values (true or false)
quiet tendon
you can make equivalences between sets and logic
for example, (A intersect B) union C
is the same as (A and B) or C
where those are true/false statements
quiet tendon
and now either x is in A and B or x is in A and C, which means x is either in B ...
again, if you don’t want to use the boolean law, then use this
and verbally explain that reasoning
cedar scarab
How do I use the boolean law in a proof of that very law?
quiet tendon
don’t use the boolean law
cedar scarab
It's not that I don't want to, I just don't think I'm allowed to.
quiet tendon
use the explanation that i’ve referenced 3+ times now
which doesn’t use the boolean law
cedar scarab
Sorry if I'm slow. I've been fighting covid for the past 2 weeks, but this assignment is due today.
warm current
How do I use the boolean law in a proof of that very law?
$A\cap(B\cup C)={x :x\in A\wedge(x\in B\vee x\in C)}$
jolly parrotBOT
SWR
cedar scarab
I'm not really anywhere close to being better, but I paid too much tuition to just not do this homework.
quiet tendon
for this you really just have to verbally explain your logical reasoning
if x is in (A and B) or (A and C)
then no matter what x is in A
warm current
I would go with neil tbh if you know nothing about boolean algebra
quiet tendon
and it must be in either B or C
warm current
(I personally don't like it, but if you're starting from zero, then a wordy understanding is a good start)
You could also use venn diagrams
cedar scarab
So I could say Since x is in A and B, or x is in A and C, x is always in A, so it must be in either B or C to be true?
quiet tendon
You could also use venn diagrams
or truth tables might be the single best way
warm current
or truth tables might be the single best way
also a good choice
quiet tendon
So I could say Since x is in A and B, or x is in A and C, x is always in A, so i...
yes
cedar scarab
I was going to do a truth table last night but the last person said that was a horrible idea
quiet tendon
a truth table for 3 variables isn’t bad
just 8 cases
and if that truth table lets you prove some super useful generic formula
like the boolean distribution law
totally worth the 8 cases
cedar scarab
That was my thought process last night but I was way too delirious to try to argue the point.
quiet tendon
sometimes truth tables and formal proofs aren’t necessary
quiet tendon
So I could say Since x is in A and B, or x is in A and C, x is always in A, so i...
like this reasoning you described should be enough
cedar scarab
Idk what's necessary yet. This is the first week of class so I have no idea how thorough my teacher wants me to be.
quiet tendon
from what i’ve seen from introductory units on set theory
this is sufficient
the only other “proof” would be the case checking if you haven’t already proven the standard formulas like distributive
warm current
agree
cedar scarab
I think this is an introductory class, but my counselor said that there is an alarming rate of students failing this class.
warm current
I think this is an introductory class, but my counselor said that there is an al...
Golden moment to say "sounds like a problem with you, teach" 
cedar scarab
There's like 6 different professors that teach this class, I guess all the students just struggle with it for some reason.
warm current
set theory is when you start to get into truly abstract mathematics.
cedar scarab
I personally think it's the prerequisite class that's the problem since the teacher is extremely hand wavy of everything rather than actually getting into the nitty gritty of why things work.
warm current
It's a real separator for math-minded people
warm current
I personally think it's the prerequisite class that's the problem since the teac...
"why" this works, sadly, is based on topics of boolean algebra, and can be very axiomatic.
cedar scarab
I got an 112% in the class which is already concerning, but I looked at this first homework and none of the problems actually seem to make any sense in my brain.
warm current
I got an 112% in the class which is already concerning, but I looked at this fir...
like what?
quiet tendon
"why" this works, sadly, is based on topics of boolean algebra, and can be very ...
at this level it's probably sufficient to just describe logical reasoning and rather than prove the logic, rely on the fact that someone reading your solution is logical
cedar scarab
For example. My previous teacher said "Images exist. There's ways to do them. Ok onto injections."
quiet tendon
bruh
cedar scarab
We spent all of half a day doing images, and we never did any actual problems.
warm current
yeah quitr a buh moment
cedar scarab
So I have no idea what this question is asking.
warm current
Do you have a book to read? Assigned chapters?
cedar scarab
I do, yeah. I was gonna look at it once I actually got to this question.
warm current
I do, yeah. I was gonna look at it once I actually got to this question.
bruh
Welcome to college
quiet tendon
well the image of a set under a function is the set of all output values produced by taking the elements of the set and evaluating the function at them
warm current
The new standard: you read the material before class, and ask questions during
cedar scarab
I'm procrastinating that question because it looks scary.
I haven't been in class at all, because I have covid.
I'd love to be asking questions if I could.
quiet tendon
well the image of a set under a function is the set of all output values produce...
for example, if i have a function f(x) = x + 1, and the set A = {1, 2, 3}, then the image f(A) = {2, 3, 4}
cedar scarab
for example, if i have a function f(x) = x + 1, and the set A = {1, 2, 3}, then ...
I think that makes enough sense in my head to attempt the problem.
Although I have no idea where this E thing is coming from.
warm current
I haven't been in class at all, because I have covid.
That's a fair point. And lame part of life sometimes
cedar scarab
Covid has quite messed up my past 2 weeks, but such is life.
quiet tendon
in other words, normally you take a single number and plug it into a function to get an output number, but now you can talk about the "image" of a set as plugging in a bunch of inputs and seeing where the outputs go
warm current
I think that makes enough sense in my head to attempt the problem.
The image of a function is the set of all of output values of the function
quiet tendon
Although I have no idea where this E thing is coming from.
E is what they're calling the set of inputs, i called it A in my example
cedar scarab
Find the direct image h(E). Does that mean I take the domain of 0 to 1 and plug it into the composite?
cedar scarab
g o f
quiet tendon
which is
cedar scarab
Does that mean I put g into f, or f into g?
quiet tendon
f into g
cedar scarab
Oh I was gonna do the other
cedar scarab
So h = x^2+4x+4?
quiet tendon
yes
warm current
the notation is a bit annoying imo
lambda-calculus-pilled
cedar scarab
And then 0 to 1 would be a little curve from (0,0) to (1,9)?
quiet tendon
So h = x^2+4x+4?
so now the question is what is all the possible output values when x ranges from 0 to 1
the image is the set of numbers between 4 and 9
cedar scarab
Oh yeah
quiet tendon
it's not (0,0), it's (0,4)
cedar scarab
Is an image a set?
quiet tendon
yes
cedar scarab
Oh ok that explains a lot.
I wasn't actually sure what an image was so I didn't know how to write an answer.
quiet tendon
by the way
cedar scarab
So would it be written [4,9]?
quiet tendon
you can only do this trick by plugging in the interval endpoints 0 and 1 in certain cases
in this case, since your function is strictly increasing on that interval [0, 1] it's fine
then all the possible y values on that interval must be between h(0) and h(1)
but let's say your function started decreasing on this interval and then increased again
you can't just say the image is between h(0) and h(1)
here's your function, notice on [0, 1] your function is only increasing so all possible outputs on this interval are exactly between h(0) and h(1), but if instead you were looking at the interval from -4 to 0
your function doesn't just take on values between h(-4) and h(0)
quartz citrus
For example. My previous teacher said "Images exist. There's ways to do them. Ok...
alternatively for this problem, I think it might be a little bit clearer to see if you first compute f(E) and then to use that to determine g(f(E)) as opposed to taking the composition first and then considering the image
quiet tendon
alternatively for this problem, I think it might be a little bit clearer to see ...
this would be easier to understand, yes
cedar scarab
I'm trying to make sense of what I wrote yesterday for the original proof. Does this make any coherent sense as an entire proof?
quartz citrus
it makes sense but your approach is slightly wrong 
cedar scarab
I wouldn't be surprised. This entire thing is very confusing.
quartz citrus
for the first inclusion, you want to start with x being an element of the LHS
quiet tendon
firstly it seems like for those cases you're showing that an element in the right set is a subset of the left set when what you're trying to show is that the left is a subset of the right? secondly your conclusions like "A and (B or C) = (A and B)" don't really make sense since those aren't true statements
cedar scarab
the wut now
cedar scarab
Can I do the first half the same way I just did the second?
Something like "If x is in A^(B u C), then x is in A and B or A and C"?
quartz citrus
You also flipped the second inclusion as well
cedar scarab
Wut
quartz citrus
you kinda did them both backwards
cedar scarab
I just worked on it with these guys
How is the second one backwards? I went from the left to the right
pearl pondBOT
@cedar scarab Has your question been resolved?
warm current
I would write this a bit clearer. "By the definition of set equality, $A\cap(B\cup C)=(A\cap B)\cup (A\cup C)$ if and only each is a subset of the other", or "... if and only if $A\cap(B\cup C)\subseteq(A\cap B)\cup (A\cup C)$ and $(A\cap B)\cup (A\cup C)\subseteq A\cap(B\cup C)$"
jolly parrotBOT
SWR
warm current
I would write this a bit clearer. "By the definition of set equality, $A\cap(B\c...
@cedar scarab
warm current
The proof is fine though?
Let me look at $(A\cap B)\cup (A\cup C)\subseteq A\cap(B\cup C)$ first, since it's shorter
jolly parrotBOT
SWR
cedar scarab
Ok.
cedar scarab
If it makes sense, I don't mind awkward at the moment. I'm just trying to get the assignment.
warm current
If it makes sense, I don't mind awkward at the moment. I'm just trying to get th...
Hard to say if it makes sense. Proofs like this are always so subjective.
To me, yeah, it's fine, I get what you're saying
But if I wanted to a be a prick about it, I could say "but why must this be true? x is in A, so it must also be in B and C? Why? That's not even valid."
Here's how I would format it: If $x\in (A\cap B)\cup (A\cup C)$, then blah blah blah, therefore, it must be that $x\in A$. At the same time, if $x\in (A\cap B)\cup (A\cup C)$, then blah blah blah, so $x\in B\cup C$ also. Thus, $(A\cap B)\cup (A\cup C)\subseteq A\cap(B\cup C)$.
jolly parrotBOT
SWR
cedar scarab
Here's how I would format it: If $x\in (A\cap B)\cup (A\cup C)$, then blah blah ...
What is the second blah blah blah here in regard to the B u C?
warm current
What is the second blah blah blah here in regard to the B u C?
The first part is you showing that x is in A, and the second part is showing that x is in union of B and C. Once you you've shown both, it must be that x is in the intersection of these sets
cedar scarab
So Since x in the union of B and C, it must be in one of them?
warm current
So Since x in the union of B and C, it must be in one of them?
yeah
cedar scarab
Gotcha.
pearl pondBOT
@cedar scarab Has your question been resolved?
pearl pondBOT
pearl pondBOT
Available help channel!
olive zodiac
Anyone able to explain this
jolly parrotBOT
ember spear
so do you know the formulas for this?
ember spear
Then can you tell them to me?
ember spear
Do you know the meaning of ratio?
olive zodiac
Like the difference
ember spear
No
olive zodiac
Idk then
ember spear
it means the the relationship between two groups or amounts that expresses how much bigger one is than the other
basically the division
olive zodiac
Alright from there what do we do
ember spear
so we do
volume of cone/volume of cylinder
olive zodiac
Then what?
ember spear
$\frac{Vol^m_{cone}}{Vol^m_{cylinder}} = \frac{\frac{1}{3}\cdot B\cdot h}{ B\cdot h}$
jolly parrotBOT
Pro_Hecker
ember spear
Yeah
olive zodiac
Alright
ember spear
You're right it's cuz 1/3 in the formula of cone
mental wigeon
Hello.
mental wigeon
This might sound obvious but I got doubty.
How many even three-digit natural numbers (in base 10) have all their digits distinct from each other?
There are only 4 cases to analyze, right?
quartz citrus
which would be 
mental wigeon
a) n1, and n2 even b)n1 even n2 odd, c) n1, odd n2 even d) n1, n2 odd
quartz citrus
I suppose you could answer it like that
mental wigeon
4 * 4 * 3 + 4 * 5 * 4 + 5 * 5 * 4 + 5 * 4 * 5 = 328
midnight haven
How many even three-digit natural numbers (in base 10) have all their digits dis...
The answer is 9x9x8 right?
fathom saffron
The answer is 9x9x8 right?
even numbers
waxen condor
There are only 4 cases to analyze, right?
,calc 959
rough forge
,w 9×5×9
quartz citrus
mental wigeon
No way, i only counted 328
quartz citrus
4 * 4 * 3 + 4 * 5 * 4 + 5 * 5 * 4 + 5 * 4 * 5 = 328
You're missing stuff
fathom saffron
wouldnt it be 360
mental wigeon
Like what, i literally put all the cases
autumn topaz
what are "n1" and "n2"?
mental wigeon
n1, n2 and n3
quartz citrus
digit 1, digit 2 even
You got 4 * 4 * 3,
you have 5 options for digit 3, then 4 options fot digit 3 then 3 options for digit 2
quartz citrus
no
waxen condor
No way, i only counted 328
8 middle one
mental wigeon
digit 1, digit 2 even
You got 4 * 4 * 3,
you have 5 options for digit 3, then 4...
That looks incorrect
They are different
waxen condor
,calc 958
jolly parrotBOT
Result:
360
you have to account for an even number being used in the first two digits, right?
fathom saffron
the first two digits can be even asw?
waxen condor
Middle one 8 mistake
quartz citrus
That looks incorrect
what about it looks incorrect
waxen condor
you have to account for an even number being used in the first two digits, right...
Ahh true
mental wigeon
The digits are different
fathom saffron
casework: when the units digit is 0 and when it is an even number other than 0
for the first its clearly 9*8
waxen condor
.
fathom saffron
for the second n3 can be 4 things, n1 can be 8 things and n2 can be 8 things
midnight haven
No way, i only counted 328
That is the correct and final answer I think
You need to use permutations
mental wigeon
n1 = 2, 4, 6, 8; n2 = 0, 2, 4, 6, 8; n2!=n1; n3 = 0, 2, 4, 6, 8; n3!=n1 and n3!=n2
That is 4 * 4 * 3 =48
midnight haven
I took multiple cases, in each case the last digit is a different even number
midnight haven
I took an easier approach
mental wigeon
I am using discrete maths
midnight haven
It's correct
mental wigeon
So my approach with 4 cases was enough
midnight haven
midnight haven
This is how I took my cases
The digit at the end is a different even number in each case
There are a total of 10 digits
In the first case, the left most digit cannot be 0 as it has to be a three digit number
midnight haven
And it can't be 2 either cuz repetions are not allowed
mental wigeon
Exactly
midnight haven
So 8 possibilities, and for the middle digit , 0 is allowed but we have already used a digit for the left most digit so still 8 possibilities
The only difference is in the last case
As 0 is the last digit
So you get 9 possibilities for the left most
And 8 for the middle
Yours is the right answer if you ask me
midnight haven
Yeah, no worries
pearl pondBOT
@mental wigeon Has your question been resolved?
mental wigeon
.close
wise kettle
pearl pondBOT
regal herald
what formula do you have linking x and y
regal herald
you can make x or y the subject, sub, differentiate then etc, at least thats one way
sterile tusk
did you implicitly differentiate the circle equation?
that wouldn’t give you what you’re looking for
since it wants the max of x+y not the max of the circle
outer crypt
But what is the max of the circle?
the upper point
sterile tusk
not really what we’re looking for
and you would probably get two critical points as well
one for the min and one for the max
wise kettle
Ohh the upper and lower point
Ok so for this question how do I do it?
Is it partial differentiation
sterile tusk
you can make x or y the subject, sub, differentiate then etc, at least thats one...
^
lagrange multipliers could work too
wise kettle
Differentiate this?
pearl pondBOT
@wise kettle Has your question been resolved?
midnight haven
Differentiate this?
Where did the y come from?
thick thorn
pearl pondBOT
thick thorn
help
fringe elbow
Whats the derivative of tanx?
thick thorn
why you taking u sub of tanx?
thick thorn
Whats the derivative of tanx?
sec^2x
fringe elbow
So why not just put u = tanx?
fringe elbow
Its possible
Okay
The prime mistake you made was that you didn't change the limits of integral on substitution
fringe elbow
Other than that your substitution was also incorrect
u = secx
du = secxtanxdx
So the integral would become just udu
With changed limits
fringe elbow
When you do substitution, you need to eliminate x completely
And change the limits
Do these both, get the answer
cedar scarab
I need some assistance with this question.
pearl pondBOT
I need some assistance with this question.
cedar scarab
My book doesn't really reference explicit bijections specifically, so I am not sure what the question is asking for.
Is this asking me to find a function where, given a domain of (a,b), I need to find a function that yields a codomain of (0,1)?
trim willow
Is this asking me to find a function where, given a domain of (a,b), I need to f...
Range (0,1) not codomain
But yes
cedar scarab
Gotcha. Is there like a good way to do it, or do I just need to explore asymptotic functions?
trim willow
If you think about what the question asks is if (a,b) same length as (0,1) you just need your function to shift (a,b) to (0,1). If not same length you also need a scaling
So a function on the form c+d * x does that
cedar scarab
So a function on the form c+d * x does that
c+d*x like a linear function?
trim willow
Yep
cedar scarab
So to go from 0 to 1 from a to b, it would be something like $y=\frac{b}{a}x$?
jolly parrotBOT
Narutoes
trim willow
If (a,b) same length as (0,1) so say (2,3) what would it be?
pearl pondBOT
@cedar scarab Has your question been resolved?
cedar scarab
If (a,b) same length as (0,1) so say (2,3) what would it be?
It would be 1, but if I specify a y-intercept of 0, then it would span 0,1 no?
trim willow
What is the exact function that does it?
pearl pondBOT
@cedar scarab Has your question been resolved?
storm harness
pearl pondBOT
storm harness
here, why cant i do 1 + ((i)^2)1004+1
i seem to get the wrong answer if i use the same logic for the rest of the brackets except the firstone where its (1 + 1) in the end
tropic saddle
why should you be able to do that
cyan oracle
dont know where to start for this question
pearl pondBOT
dont know where to start for this question
@cyan oracle Has your question been resolved?
faint crypt