#help-28
full forumBOT
gleaming turtle
(ps. sprendinių nėra = no solutions)
tender nacelle
You use the discriminant, negative discriminant means there are no roots ("solutions")
gleaming turtle
You use the discriminant, negative discriminant means there are no roots ("solut...
in the top right where D=0 it says sprendinių nėra
which means no solutions
tender nacelle
well because that's asking for ax^2+bx+c > 0
The D = 0 case means that ax^2+bx+c reaches 0 exactly one
but if its a downwards parabola, it'll never surpass it
Hence the "no solutions"
gleaming turtle
can you explain in laymans terms?
doesnt the discriminant just determine how the parabola opens
sick vortex
do you know the quadratic formula?
gleaming turtle
yes
sick vortex
,, x_{1,2} = \frac{-b \pm \sqrt{\color{red}b^2 - 4ac}}{2a}
glossy valveBOT
mmmm7
sick vortex
think about what red = 0, red > 0, or red < 0 means in this case
gleaming turtle
oh yeah
sick vortex
u get it now?
gleaming turtle
yeah but why does it get flipped depending if its ax^2+bx+c>0 or ax^2+bx+c<0
if its no solutions regardless
sick vortex
wdym flipped?
b^2 - 4ac = 0 gives you one solution
b^2 - 4ac > 0 gives you as you can see tell from the +-
and b^2 - 4ac < 0 gives you 2 complex solutions
so no real solutions
because you'd be dealing with sqrt(negative number)
owing to that you can draw a horizontal line and make it so that
it either intersects it twice
once or never
then you can read off the interval where ax^2 + bx + c > 0
frigid carbon
yeah but why does it get flipped depending if its ax^2+bx+c>0 or ax^2+bx+c<0
Let y= quadratic if the graph is above y=0 then there is no soln for
quadrtic<0
here graph is above x axis so no soln for negative value(<0)
gleaming turtle
ok just to clarify what difference does it make if its y>0 or y<0?
long helm
unique perch
no
unique perch
hint: e^2x - 1 = (e^x)^2 - 1
long helm
ohh
unique perch
actually nvm u sub works
long helm
really?
unique perch
yeah
unique perch
hint: e^2x - 1 = (e^x)^2 - 1
you should let u = e^x instead
long helm
why?
unique perch
then your u' is e^x
unique perch
and you dont have to deal with e^2x
unique perch
yea that looks correct
wait
where's your du here?
did it get kidnapped by some cambodian scam center?
long helm
did it get kidnapped by some cambodian scam center?
bahahaha
unique perch
other than that everything else is correct
unique perch
open another channel
full forumBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
verbal sky
sorry didnt see
unique perch
@long helm if you're done with this question close the channel
long helm
<@1384969590106230894> if you're done with this question close the channel
ohh okiee
.close
pallid urchin
why is the quadratic equation positif when the descriminant delta is negative
onyx glen
what do you mean by "the quadratic equation is positive"
i think you may be misconceiving something
pallid urchin
say we have x squared -ax +1
onyx glen
x^2 - ax + 1
pallid urchin
yeah
onyx glen
use ^ for exponents on discord generally
onyx glen
can you show the full question, just for the record
i dont want to guess at what your goal was & i wanna make sure we both understand how to say things properly
pallid urchin
im js tryna affirm an info i used on a test
onyx glen
the info needs to be cleared up before it can be affirmed or denied
pallid urchin
x^2 - ax + 1
if this is strictly positif
then the descriminant is negatif strictly right
onyx glen
right, but this should be made a bit more precise and general:
given a quadratic function f(x) = ax^2 + bx + c,
the discriminant D = b^2-4ac is negative if and only if the function f(x) is sign-constant, which itself happens if and only if y=f(x) never touches the x-axis
"sign-constant" means either always positive, or always negative (based on the sign of a)
so in your case, a=1 so "sign-constant" means "always positive"
cerulean yoke
help
cerulean yoke
HELP
PLS
I EG U
BEG U
JUST HELP
THIS ONE I MEAN
PLEASE
I BEEN ON THIS FUCKING QUESTOIN 10 TIMES
rough tundra
rough tundra
well for an n-sided polygon the sum of interior angles is (n-2)*180 degrees
low needle
count the angles
fickle adder
how many sides are there..
fickle adder
it literally tells you
cerulean yoke
LAST QUESTION
low needle
count the green things
cerulean yoke
IDK
fickle adder
no
cerulean yoke
8?
gritty rose
uhhh mental breakdown <@&268886789983436800> ?
fickle adder
its in the damn question this is impressively low amounts of effort man
cerulean yoke
iS IT 8?
fickle adder
it is 8
cerulean yoke
SO IS THE ANSWER 8?
low needle
the amount of sides man
cerulean yoke
so if the sum is 180 * (n-2)
WHAT DO I DO WITH THAT
austere cove
@cerulean yoke please calm down
low needle
n = 8 put it in the formula
low needle
only 50 more seconds if you calm it down
cerulean yoke
have no clue...
austere cove
and? I've been on the question I'm currently doing for an hour.
sometimes, you make progress better if you calm down and think things through
austere cove
no one here is going to give you the answer, you're going to need to apply yourself a little.
low needle
yes and you just calculate it
cerulean yoke
calculater?
low needle
idc how just calculate
cerulean yoke
1080?
austere cove
you can use a calculator, or a pen and paper, it's up to you.
austere cove
it is 1080
low needle
if youre confidnet you woudnt ask
austere cove
good job
neon basin
calculater?
no, calculate now
cerulean yoke
Took me 1hr for it
neon basin
I'll see myself out
low needle
Founder of Air france.
Working for Alaska airlines Board of directions.
cerulean yoke
Founder of Air france.
Working for Alaska airlines Board of directions.
roblox airlines
u know im 14...
im practily involved around it
gritty rose
no, calculate now
torn sand
im practily involved around it
if you want to understand why that formula for the sum of interior angles works, consider decomposing your polygon into triangles.
full forumBOT
@cerulean yoke Has your question been resolved?
verbal sky
full forumBOT
grave elm
cos(theta) = adjacent / hypotenuse = 1 / AC
from this, it follows just by rearrangement
rigid yacht
I keep getting this instead of -4. Where is the mistake?
full forumBOT
I keep getting this instead of -4. Where is the mistake?
gritty rose
,rotate
glossy valveBOT
gritty rose
I keep getting this instead of -4. Where is the mistake?
you did $\sqrt{4x^2} = 2x$ but that's only true when $x > 0$
glossy valveBOT
riemann
rigid yacht
you did $\sqrt{4x^2} = 2x$ but that's only true when $x > 0$
Why would x have to be positive when (-a)^2 = (a)^2?
Oh I see now that's why it doesn't work.
.close
full forumBOT
full forumBOT
Available help channel!
fallen ivy
Until when is algebra 1?
full forumBOT
Until when is algebra 1?
gritty rose
wut
iron sand
Until when is algebra 1?
until you pass the exam 
full forumBOT
@fallen ivy Has your question been resolved?
slate glacier
You'd have better response at #math-discussion , the help channels are for asking help in solving questions only
fallen ivy
No1 talks there
slate glacier
Maybe try #study-discussion
full forumBOT
@fallen ivy Has your question been resolved?
full forumBOT
@fallen ivy Has your question been resolved?
warped frost
unless you have a specific topic you don't get, it's unlikely anyone can give you any specific answers other than to revise and understand the material.
wary condor
Until when is algebra 1?
you are currently in algebra 1, nenni.
i think algebra 2 starts with complex numbers and polynomial expansions? not very sure.
full forumBOT
hollow timber
Hey I need help really quick.. I am studying for my test and I am doing a review sheet
I am confused on
sleek mortar
I am confused on
Simplify
warped frost
!occupied, btw
full forumBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
warped frost
it's still not open yet
full forumBOT
Available help channel!
coarse flax
Hello! I'm a Calculus BC student studying for a test tomorrow that will be 3 questions. I've been working on my homework from yesterday to review for the test but I've been struggling a lot. Can anyone help me understand how to start this problem and how to approach this kind of problem? We're working on real analysis right now and we're writing proofs and tomorrow's test is 3 questions, most likely with at least 2 of them being proofs. Any help is appreciated. Thank you!
hybrid yacht
Hello! I'm a Calculus BC student studying for a test tomorrow that will be 3 qu...
are you allowed to prove from scratch those things that you cannot argue
slate violet
How are calc BC students doing real analysis?
hybrid yacht
thats another question on its own
coarse flax
are you allowed to prove from scratch those things that you cannot argue
I think that I'm not allowed to argue using that even if I were to prove it from scratch
slate violet
Nah, you just need the maximum of the absolute value of the first N terms
Then all the other terms are bounded by some max and min
coarse flax
So far in class we've really only used the N-epsilon definition of sequence convergence, triangle inequality, the max function, and cauchy convergence and since we only do proofs ocassionally I'm not too sure how to do that with a proof by contradiction
hybrid yacht
ok yeah i think direct might be the move
coarse flax
By the way the solution key shows this but I don't really understand it
hybrid yacht
first lets convince ourselves its true
coarse flax
okay
coarse flax
Okay
hybrid yacht
a_m is below one of the numbers in that list
that means a_m is below M (the maximum)
coarse flax
okay
hybrid yacht
and that's for all "big enough" m
coarse flax
Sorry, what do you mean by "big enough" m? Are you talking about the m'th term?
hybrid yacht
yeah
coarse flax
Okay
hybrid yacht
it says m > N
coarse flax
And N is some natural number
hybrid yacht
im trying to strip away the formal language
hybrid yacht
so then all the numbers in the sequence are either the first few terms or any of the other ones
the other ones are all below M
coarse flax
Okay
hybrid yacht
the first few are at most M by definition
coarse flax
Okay
hybrid yacht
does that help
coarse flax
Yes, thank you. So would that be part of what is meant by Cauchy?
slate violet
Nah, you just need the maximum of the absolute value of the first N terms
either the maximum is in the first N terms, or it's in the other terms (N + 1, N + 2, ...)
hybrid yacht
cauchy means that the next term is "almost the same as" the previous term
slate violet
if it's in the first N terms, we just choose the maximum absolute value
if it's in the later terms, well, we can set n = N + 1 to show that $|a_{N + 1} - a_m| < \epsilon \implies a_{N + 1} - \epsilon < a_m < a_{N + 1} + \epsilon$ for all $m > N$
coarse flax
so will it be the max{M, and the other one} for the maximum of that sequence?
hybrid yacht
the other one is below M
coarse flax
okay
hybrid yacht
you can write that and it will work
glossy valveBOT
south
coarse flax
Yes, thank you very much
hybrid yacht
theres only one thing missing
cauchy has for all epsilon > 0
which means it works for any choice
coarse flax
okay
coarse flax
okay
hybrid yacht
you can use whatever number, but choose a number for this
coarse flax
Do certain values for epsilon make it more convinient later on on the proof?
coarse flax
okay
coarse flax
Does 3/10 work well for most things?
coarse flax
Okay
I think I'm starting to get what each piece of the question means but how do we put it all together? Also how would you go about doing scratch work for this problem?
hybrid yacht
start by citing the definition of cauchy
then, pick specific epsilon (a number)
use the version of triangle inequality that gets the inequality in the right direction
coarse flax
Okay
hybrid yacht
you should be able to get that the "far away" terms are bounded
coarse flax
Yes
hybrid yacht
thats the hardest part
the close terms, those are bounded by the maximum among them
coarse flax
How would I show that the far away terms are bounded?
hybrid yacht
you should be able to get that the "far away" terms are bounded
oh yeah you do need to fix one of n or m to N+1 or something
because the cauchy definition involves pairs of n and m
coarse flax
Okay
hybrid yacht
How would I show that the far away terms are bounded?
triangle inequality
one of them will get you an upper bound
you will need to play around with that, because there are a bunch of versions of it
coarse flax
Okay, thank you! I'll try to set up my scratch work based off of that.
Also, do you have any reccomendations on how to start a proof? Usually the quizzes and tests we have are timed and we only have around 30 minutes in total (I usually lose points because I run out of time). How would I start to think of this and are there key words/key ideas to focus upon?
lime ether
Also, do you have any reccomendations on how to start a proof? Usually the quiz...
do more problems
hybrid yacht
for questions of this nature, begin by writing down relevant definitions
before attempting the proof
weary star
I have a doubt in trigonometric identities
hybrid yacht
the path tends to become clearer
coarse flax
Okay, I'll try to review all the definitions in depth
hybrid yacht
so you will need to memorize formal definitions of cauchy, convergence etc
slate violet
I have a doubt in trigonometric identities
!help
coarse flax
Thank you
full forumBOT
I have a doubt in trigonometric identities
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
weary star
!help
full forumBOT
To ask for mathematics help on this server, please open your own help channel or help thread. See #❓how-to-get-help for instructions.
full forumBOT
lime ether
for a good source of problems you can go use the beginning of carothers real analysis for similar problems
full forumBOT
✅ Original question: #help-28 message
coarse flax
I still have these questions and I don't really get them
lime ether
have you tried anything here?
coarse flax
For 5, I don't really have an idea on what to do, I might try restating some definitions. For 6, I think I might be able to start by supposing instead that a doesn't equal b
lime ether
For 5, I don't really have an idea on what to do, I might try restating some def...
no i wouldn't do that they gave you the suggestion
for 6
coarse flax
Okay
coarse flax
Should I try to use the definition of sequence convergence and use it on x_n converging to a and x_n converging to b?
Oh wait they sort of suggested that too
oops
lime ether
yea the third one hint is the best one
coarse flax
Also would I need to use N_1 and N_2 for this?
lime ether
it doesn't involve assuming a \neq b though 🤔
lime ether
Also would I need to use N_1 and N_2 for this?
yes
then take the max
you don't need to assume a \neq b
coarse flax
Okay
coarse flax
I don't know that
lime ether
try proving it
coarse flax
Okay
coarse flax
coarse flax
<@1284998264566976523> are you stuck or something?
Sorry I was typing on my computer so it took my a while to figure out how to take a photo
lime ether
if a \neq 0 then |a| > 0 so taking eps = |a| gives the contradiction
use the third hint to arrive at a similar statement
lime ether
do you know that if |a| < eps for every eps > 0 then a = 0
and use this
coarse flax
Okay, I'll try that, thank you
coarse flax
I got until here for the scratch work but I'm not really sure what to do beyond htis
this
coarse flax
Yeah, I'm not really sure how to incorporate it
lime ether
what inequality can we invoke here?
coarse flax
Triangle inequality?
lime ether
perfect
remember that we have control over |x_n - a| and |x_n - b|
we should always keep those in the back of our minds
which is how we come to think of using the triangle inequality here
coarse flax
would |x_n-a| + |x_n-b| be greater than or equal to |x_n-a+x_n-b|?
coarse flax
|a-b|?
lime ether
we want |a - b| < eps to use the theorem i gave earlier
no
$|a - b| = |(a - x_n) + (x_n - b)| \leq |x_n - a| + |x_n - b| < \dots$
glossy valveBOT
knief
lime ether
what should the last inequality be
coarse flax
epsilon?
lime ether
yes
so how can we bounded |x_n - a| and |x_n - b|
so that they sum to be less than epsilon
coarse flax
would |x_n-a|<3/7*epsilon work?
lime ether
they will
coarse flax
Wouldn't epsilon/2 + epsilon/2 be epsilon?
lime ether
yes and we have the <
coarse flax
Okay
lime ether
|x_n - a| + |x_n - b| < eps/2 + eps/2 = eps
coarse flax
Sort of. Would I try to simplify one side of the equation until I get a contradictory statement?
lime ether
we don't need contradiction here
lime ether
do you know that if |a| < eps for every eps > 0 then a = 0
we are using this
coarse flax
Okay
coarse flax
I think I got it. Thank you
lime ether
ok
👍
my hint for 5 would be it suffices to show that l = lim(s_n - t_n) <= 0 so try assuming l > 0 and then contradict s_n <= t_n
coarse flax
Okay, thank you very much!
lime ether
no worries
coarse flax
I'll try to work on the rest of the questions. Thank you for explaning a lot of it
lime ether
you're welcome
coarse flax
.close
full forumBOT
full forumBOT
Available help channel!
odd galleon
how are you able to derive this I thought because e^0=1 its not written in an indeterminate form
grave elm
how are you able to derive this I thought because e^0=1 its not written in an in...
it's limit to infinity, not to 0
so it would be e^inf/2 = inf
so its inf/inf which is indeterminate
full forumBOT
full forumBOT
Available help channel!
lucid lily
i have this graph. is it only concave down at (x3, +infinity)? I said this because the derivative of the f’(x) graph (so f’’(x) basically) seems to only decrease here. i believe the right answer had 2 different intervals though so im missing one. did i do this right?
full forumBOT
i have this graph. is it only concave down at (x3, +infinity)? I said this becau...
@lucid lily Has your question been resolved?
twin wolf
,rccw
glossy valveBOT
lucid lily
i have this graph. is it only concave down at (x3, +infinity)? I said this becau...
nvm i think its concave down at (x1, x3) u (x3, +inf)
hard quartz
What did I do wrong?
$\x=2\x^2=2^2\
\sqrt{x^2}=\sqrt{2^2}\
x=\pm2\x=2 \text{ or } x=-2\Rightarrow 2=-2 \to \gets$
glossy valveBOT
fort craft 🇵🇸
sudden condor
What did I do wrong?
$\\x=2\\x^2=2^2\\
\sqrt{x^2}=\sqrt{2^2}\\
x=\pm2\\x=2 \text...
going backwards instead of forward
hard quartz
going backwards instead of forward
Elaborate please.
sudden condor
Elaborate please.
the process you did is the reverse of solving x^2 = 2^2
and I'll add that we know that x is already positive so how can x be evaluated as negative afterwards ?
hard quartz
the process you did is the reverse of solving x^2 = 2^2
and I'll add that we kno...
So what if I had wrote this:
$\x=a\x^2=a^2\
\sqrt{x^2}=\sqrt{a^2}\
x=\pm a \x=a \text{ or } x=-a\Rightarrow a=-a \to \gets$
glossy valveBOT
fort craft 🇵🇸
sudden condor
So what if I had wrote this:
$\\x=a\\x^2=a^2\\
\sqrt{x^2}=\sqrt{a^2}\\
x=\pm a \...
given no constraints this falls into we already know that x = a
so how did we find x=-a ?
hard quartz
given no constraints this falls into we already know that x = a
so how did we ...
Don't we get the negative from the plus or minus sign?
forest trail
Don't we get the negative from the plus or minus sign?
I think what qimmah is trying to say is this:
At the last line you have:
"x = a or x = -a"
Which is actually still perfectly fine, but here's the thing - how do you then conclude what x is from this statement?
We can't say "x = -a" just because.
The word "or" here simply means it could be one or the other, or both.
hard quartz
I think what qimmah is trying to say is this:
At the last line you have:
"x = a ...
well you don't conclude what x is. a is a non-zero real number. you just write what x is in terms of a.
forest trail
well you don't conclude what x is. a is a non-zero real number. you just write w...
Well, when you say a = -a, you are certainly concluding what x is.
"you just write what x is in terms of a"
How can you write what something is if you can't conclude what it is inherently?
frigid carbon
going backwards instead of forward
lmao
hard quartz
I have no idea what you talking about.
heavy gorge
I think if x is a then x can't be -a at the same time
frigid carbon
I think if x is a then x can't be -a at the same time
unless a = 0
hard quartz
unless a = 0
nope. I defined a as a non-zero real number, outruling the possibility of a being 0.
forest trail
I have no idea what you talking about.
Uh let me put it this way.
When you are solving an equation x^2 = 100, we are essentially asking "for what values of x when squared gives us 100?".
In that case, the answer is both x = -10 or x = 10, which makes sense because both values satisfy the equation.
However, your question is slightly different:
You are saying "Given that x = a, what can we say about x?".
So, we're not trying to find a 'value' for x since we are already given the value of x. That means when you get statements like:
"x = a or x = -a"
You must choose the one that fits the situation best; in that case, it is x = a.
There is nothing in the statement "x = a or x = -a" that implies that x must be both values.
hard quartz
Uh let me put it this way.
When you are solving an equation x^2 = 100, we are es...
Perfect. Thank you.
.close
robust fox
full forumBOT
unreal wren
!status
full forumBOT
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
1
unreal wren
1
Here's a small exercise to help you notice a patern
What is $U_{3}$ in terms of $U_1$ and $V_1$?
Wait sorry
glossy valveBOT
Matcha
full forumBOT
@robust fox Has your question been resolved?
half sorrel
Name three things you are people grateful for today.
full forumBOT
Name three things you are people grateful for today.
unique perch
- You closing the channel and move this to a discussion channel
- Same as 1
- Same as 2
onyx glen
Name three things you are people grateful for today.
!redir
full forumBOT
Name three things you are people grateful for today.
This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.
onyx glen
.close not a math question nor any hint at such
full forumBOT
onyx glen
you're posting in the wrong channel mate
fallen ivy
Wow... your positivness today...
for real..
restive geyser
for fake...
fallen ivy
You guys… as always are so negative and have bad energy.
full forumBOT
Available help channel!
cosmic tusk
School calculators are sold by one company only in packages of 11 and packages of 15. What is the largest number of calculators you could purchase where it would still be necessary to open a package?
cosmic tusk
i need help with this question for an extracurricular
queen crater
That's called the Frobenius number if you want to look it up
slate violet
School calculators are sold by one company only in packages of 11 and packages o...
it's way more fun if you think about it as McDonald's nuggets though
but yes, that is the proper name of the theorem
restive sapphire
https://artofproblemsolving.com/wiki/index.php/Chicken_McNugget_Theorem
Could u give me a hand explaining that to me
I don’t get why the largest number isn’t just infinity ( ik it’s not a number I’m just trynna explain what I’m having trouble with lmao)
restive sapphire
Ahhh
queen crater
At this point you can make any number 4+2n or 5+2n by just adding 2
That covers all integers >=4
restive sapphire
Gotcha
queen crater
For 11 and 15 it'll be a lot more, but the same logic applies because they are coprime
full forumBOT
@cosmic tusk Has your question been resolved?
cosmic tusk
thanks guys
cosmic tusk
I also need help with this question for the same extracurricular: find the number of five-digit numbers less than 40 000 in which the three three-digit numbers formed by consecutive digits are all divisible by either 17 or 23.
onyx glen
!status
full forumBOT
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
got a feeling like this might not have any more sophisticated solution than simply listing out all possible sequences of 3 digits and then looking at how they fit together if at all
102 115 119 136 138 153 161 170 184 187
204 207 221 230 238 253 255 272 276 289 299
306 322 323 340 345 357 368 374 391
408 414 425 437 442 459 460 476 483 493
506 510 527 529 544 552 561 575 578 595 598
612 621 629 644 646 663 667 680 690 697
713 714 731 736 748 759 765 782 799
805 816 828 833 850 851 867 874 884 897
901 918 920 935 943 952 966 969 986 989
and ig you also have 017 023 034 046 051 068 069 085
full forumBOT
@cosmic tusk Has your question been resolved?
fallow ridge
Cam anyone up here help me in this question. Professer tried to explain it but i didnt get it
fallow ridge
https://artofproblemsolving.com/wiki/index.php/Chicken_McNugget_Theorem
what is this bruh?
gritty rose
this is the standard explanation
copper tangle
Honestly this is partially a history question, because you need to know what Euclid's proof is.
Actually it's not stated correctly
Well, cuz it's false...
nvm
covert heath
this is the standard explanation
@fallow ridge 3b1b does a casual explanation here
linked it cuz its fun
full forumBOT
@fallow ridge Has your question been resolved?
marsh vault
Honestly this is partially a history question, because you need to know what Euc...
Hopefully that has been explained in class; otherwise it would be a bit of a mean question.
full forumBOT
@fallow ridge Has your question been resolved?
fallow ridge
- how can he say that there exists at least one additional prime number not included in the list? 2) Why have he added one into the product of all prime number? 3) What is he actually trying to do or prove?
queen gull
Cam anyone up here help me in this question. Professer tried to explain it but i...
Euclied is trying to prove there are infinitly many primes
To do that, he assumes there is a finite number of them and he labels them
So this finite list includes all prime numbers
This number N is not divisable by any of the primes in the list
So it has a prime factor which is not in the list
restive geyser
For which there are two options (for N, or if you're reading from Riemann's citation, for q):
one - it does have a prime factor that isn't in this list - which is a contradiction, because we assumed this list were complete
two - it itself is prime - but then it should've been in the list, so again a contradiction
queen gull
In both cases it has a prime factor
restive geyser
The question as phrased isn't true, because that's only the second option, not the first one
full forumBOT
@fallow ridge Has your question been resolved?
fallow ridge
The question **as phrased** isn't true, because that's only the second option, n...
meaning q is a prime number?
how?
restive geyser
where did I say q
restive geyser
So this finite list includes all prime numbers
Is up to this point clear to you, first off?
fallow ridge
_where did I say q_
in solution euclid have assumed q
restive geyser
The name of the new number is not important
fallow ridge
then what is?
restive geyser
What it represents is
restive geyser
meaning q is a prime number?
But you've not mentioned q before here, and since i haven't got what you're reading here, I have no context for whatever's being defined as q
restive geyser
this is the standard explanation
Though... Do you mean the q here?
fallow ridge
this is the standard explanation
here is the solution by euclid
restive geyser
For which there are two options (for N, or if you're reading from Riemann's cita...
Then read from here
Both are contradictions
But BOTH are needed for the proof
Because that's the whole point of a proof by contradiction
fallow ridge
one - it does have a prime factor that isn't in this list - which is a contradic...
why cant it have prime factor within list?
restive geyser
"because we assumed this list were complete"
restive geyser
To do that, he assumes there is a finite number of them and he labels them
Literally the first step here
Might I recommend revising what proof by contradiction entails:
e.g. https://youtu.be/MfTmjQnGOA8
fallow ridge
This number N is not divisable by any of the primes in the list
hmmm @restive geyser we assumed a prime number "q" in which we added 1. so isn't there possibility that when we added 1 it would have maybe became a non-prime number? or even if it is a prime number so it will not have a number which is factor of it. right? but what do i get to know by getting the conclusion that q have no prime factor within list?
fallow ridge
Might I recommend revising what proof by contradiction entails:
e.g. https://yo...
alright
restive geyser
No, you've misunderstood what q is
restive geyser
Is up to this point clear to you, first off?
I reclaim my time and re-ask you this
fallow ridge
i mean q is sum of all prime numbers + 1
restive geyser
No, you've still misunderstood it
fallow ridge
I reclaim my time and re-ask you this
thats what i am asking. my question is part of the first point
restive geyser
That product already can't be prime (if that list has at least 2 numbers) because we can write it as a product of prime factors
But we're not examining this product specifically - we're looking at the number one more than it
The cited example of the proof calls this q = P + 1; your original question calls this number N
Either way, its nature is contradictory
Either it is prime - CONTR. because it then should have been in our list of primes that we thought was complete
Or it has a prime factor not in our list - CONTR. because then we still have some prime number not in our list
restive geyser
Cam anyone up here help me in this question. Professer tried to explain it but i...
The question as stated here says only the first part (that this new number N is prime), but neglects the second case, hence the answer being "False"
fallow ridge
ok so second case is wrong or you can say not asked in the question. And about the first case - if q is a prime number P+1 so in this scenraio if its a prime number than it should have been within the finite set
that means there is no finite rather infinite prime numbers
fallow ridge
The question _as stated here_ says only the first part (that this new number N i...
are you in universty man by the way?
restive geyser
I've finished an undergraduate degree in mathematics, yes
fallow ridge
I've finished an undergraduate degree in mathematics, yes
ok. Thanks for helping
appreciated everyones concern
.closed
.close
full forumBOT
full forumBOT
Available help channel!
noble citrus
dy = sinx/cos^2x dx
full forumBOT
dy = sinx/cos^2x dx
rough tundra
and you have to solve for y(x)?
rough tundra
yes integration
rough tundra
have you learned how to do integration?
noble citrus
i know the power rule for the integration
thats it
i know all my derivitave rules tho
and anti derivitaves are like the exact oppsite
im js like confused on how to start
ivory cairn
it's a trig identity
sin x / cos x = tan x
1 / cos x = sec x
rough tundra
you sure you haven't done anything like this before?
ivory cairn
then you probably know a function whose derivative is that....
noble citrus
my teacher said its like a puzzle
fathom saddle
It's actually pretty reasonable to guess the integral here. You want to think of a function whose derivative is sin(x)/cos²(x)
forest trail
it's a trig identity
sin x / cos x = tan x
1 / cos x = sec x
Isn't this a little overkill? Why not just ||use u-substitution?||
ivory cairn
they don't know u-sub yet.
fathom saddle
OP, double check to see if you can use u-sub haha
hot herald
Isn't this a little overkill? Why not just ||use u-substitution?||
no, usub is more complex here
noble citrus
it's a trig identity
sin x / cos x = tan x
1 / cos x = sec x
oo
so i like split the denominator
forest trail
no, usub is more complex here
Well I mean what are the chances that tan(x)sec(x) is not in OP's derivative list? It's not a standard integral where I come from
hot herald
they mentioned they know the common derivatives
thus knowing the integral of that is implied
forest trail
I also agree - this is kind of unreasonable as the first ever integration question even if there is a known integral/derivative for it. So would it not be better to route to u-sub, which is a fundamental process for integration?
noble citrus
is the answer sec x
hot herald
yes
noble citrus
it makes like sense
ivory cairn
Well I mean what are the chances that tan(x)sec(x) is not in OP's derivative lis...
it's a standard derivative of a typical trig function.
It's not beneficial to jump to u-sub if they don't know that method yet.
hot herald
practice, recognition of common derivatives
hot herald
pretty much, yeh
hot herald
is the answer sec x
also don't forget the constant of integration
noble citrus
also don't forget the constant of integration
oh shoot
sec x +c
ok that is all
thank you
.close
full forumBOT
full forumBOT
Available help channel!
full forumBOT
Available help channel!
neon rivet
σ
x
glossy valveBOT
h
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
neon rivet
also Im not sure why I got this wrong
I used this method
and if we can use our calc to find population SD, whhy are we given this?
slate violet
and if we can use our calc to find population SD, whhy are we given this?
cause your calc is automatically doing these steps for you
neon rivet
yea if the calc is doing for me, why are we learning how to do it by hand
from the slides shown
because in the exam we will also use calculators
slate violet
that's not our problem then.....
onyx glen
i mean you DO need to know the process for it right
cause otherwise this entire SD thing is just gonna be a completely black box to you
ocean crescent
Four million 500-kilowatt windmills in the states listed in the table could generate 91% of the total electrical use. If this were done, how many windmills would be in North Dakota? (Hint: It is not 11% of 4 million.
full forumBOT
Four million 500-kilowatt windmills in the states listed in the table could gene...
gritty rose
.close
full forumBOT
ocean crescent
.close
full forumBOT
Available help channel!
turbid tide
Im trying to find the first and second derivative, am I doing the first one right?
gritty rose
,w diff x*sqrt(x^2+16)
glossy valveBOT
unreal wren
Im trying to find the first and second derivative, am I doing the first one righ...
Do you know the product and chain rule?
unreal wren
Im trying to find the first and second derivative, am I doing the first one righ...
Cause this is wrong
turbid tide
unreal wren
Oh yesh
onyx glen
this actually equals op's answer does it not
unreal wren
I'm so sorry, it's correct
Well now @turbid tide you can try taking the second derivative
turbid tide
Cause this is wrong
Ohhh I see I just needed to simplify
turbid tide
Well now <@1425737018180239383> you can try taking the second derivative
And then i need to find the critical points of the second derivative
unreal wren
And then i need to find the critical points of the second derivative
You mean "finding the critical points of f(x) using it's second derivative" right?
turbid tide
Yes
unreal wren
Yes
Well recall the definition of a critical point
We actually use the first derivative to compute it
So, do you mind showing the original question?
turbid tide
full forumBOT
@turbid tide Has your question been resolved?
onyx glen
And then i need to find the critical points of the second derivative
this form you've got it in is definitely not that great for finding concavity, even if correct
gonna say you need to assemble these into one fraction at least
with denom (x^2+16)^(3/2)
turbid tide
Okay
onyx glen
,rccw
glossy valveBOT
glossy valveBOT
onyx glen
ok looks like your 2nd derivative is also correct but unsimplified
wide crag
turbid tide
Wait i think I got the critical numbers
But now I need to find the derivative of this
turbid tide
?
full forumBOT
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
onyx glen
Wait i think I got the critical numbers
But now I need to find the derivative of...
i think you're cooked here as far as an exact value goes
!xy though
full forumBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
onyx glen
ill be busy soon tho
onyx glen
no instructions for how many decimal places to go for...
wait
hold on a bit. what am i saying
5^(-x) * ln(5) = 1
divide both sides by ln(5)
get 5^(-x) = 1/ln(5) = log_5(e)
you're not cooked at all
1/log_a(b) = log_b(a)
turbid tide
.close
tired blade
why is the angle between Y' and W 20 degrees
full forumBOT
why is the angle between Y' and W 20 degrees
tired blade
can someone explain the geometry applied here
green badge
This uses similar triangles
umbral dome
,tikz \draw[->] (0,0) coordinate(O) -- (2,0) coordinate(X) node[right]{$x$};
\draw[->] (O) -- (0,2) coordinate(Y) node[above]{$y$};
{[rotate=20]
\draw[->] (0,0) coordinate(O) -- (2,0) coordinate(X') node[right]{$x'$};
\draw[->] (O) -- (0,2) coordinate(Y') node[above]{$y'$};
}
\draw pic[draw, angle radius=5]{right angle=X--O--Y} pic[draw, angle radius=7]{right angle=X'--O--Y'} pic[draw, "\ang{20}", angle eccentricity = 2.3]{angle=X--O--X'} pic[draw, "?", angle eccentricity = 2]{angle=Y--O--Y'};
glossy valveBOT
cloud ☁
green badge
^^
tired blade
,tikz \draw[->] (0,0) coordinate(O) -- (2,0) coordinate(X) node[right]{$x$};
\dr...
sorry I can't decipher this
umbral dome
you have the original x and y axes, the new x' and y' axes, the 20 degree angle, and the right angles between x and y and between x' and y'
that is enough to determine the angle between y and y' using a bit of algebra
tired blade
that is enough to determine the angle between y and y' using a bit of algebra
okay thank you
tired blade
that is enough to determine the angle between y and y' using a bit of algebra
is this angle 60 right? I'm trying to decompose the P vector onto the y' and x' axis
umbral dome
yes
tired blade
the 60 degree angle is between P and the y axis
it makes sense to me though, the opposite is the component along the x', so this gotta be sin
umbral dome
P does not point along the y' axis
umbral dome
that is an artefact of you drawing all diagonal lines at a 45 degree angle regardless of their actual direction
tired blade
that is an artefact of you drawing all diagonal lines at a 45 degree angle regar...
btw does this pattern have a name because I come across it a lot and I don't want to waste time doing this geometry every single time
umbral dome
it's a rotated coordinate system
tired blade
it's a rotated coordinate system
oh like this one? the angle between y and y' is the same as theta?
umbral dome
yes
tired blade
yes
are the two triangles formed by x-y and x'-y' congruent
i want to know how you can justify this with similar triangles
wait do we consider y and x equal in magnitude
full forumBOT
@tired blade Has your question been resolved?
gentle hollow
hi, is this even right, or are there better ways to do this
full forumBOT
hi, is this even right, or are there better ways to do this
unreal wren
You could just use the chain rule honestly
Doing the derivative this way will be quite simple but the expanding and simplifying will take ages
sacred yarrow
.solved
full forumBOT
warped spire
full forumBOT
Please stick to your channel.
sacred yarrow
yeah, just stick to your channel, Ann is trying to help you rn
full forumBOT
Available help channel!
warm temple
someone please help 🙏
restive geyser
someone please help 🙏
!status
full forumBOT
someone please help 🙏
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
1
i really dont understand the concept of transversals
and cant seem to find much info online
restive geyser
A transversal point of an equivalence class would be a singular point in that class
A transversal would be a set where each of its elements belongs to exactly one of these classes
It helps first to figure out what this equivalence class actually looks like
Graphically, can you describe this equivalence relation?
warm temple
well it would be straight lines going out of the center point
restive geyser
ye
Let's take each line and collapse it onto a single point that can define that class
warm temple
and the equivalent classes from what i understand are either (-p, q) (p, -q) or (p, q)
since if theyre both negative it just goes into k
restive geyser
I'll give one for free: (x, y) where x² + y² = 1, and y > 0
warm temple
so an upper semicircle?
restive geyser
yee
warm temple
ok wait let me see if i understand this right
restive geyser
(noting also that we haven't included the y=0 relation, but we can just add that point to the set)
warm temple
and the equivalent classes from what i understand are either (-p, q) (p, -q) or ...
where would p, -q go? if the semi circle is for y>0
or did i not get this right at all
restive geyser
and the equivalent classes from what i understand are either (-p, q) (p, -q) or ...
No I don't think this is quite right
(-p, q) for one is where (p, q) reflects to on the y-axis
restive geyser
well it would be straight lines going out of the center point
But for two, you'd already said this here
(-p, q) isn't even on the same line as (p, q)
warm temple
(-p, q) isn't even on the same line as (p, q)
wouldnt (-p, q) just be negative x axis but positive y?
restive geyser
Yes, but since when was it on the same "straight [line] going out of the center point" as (p, q)?
restive geyser
where would p, -q go? if the semi circle is for y>0
You've even drawn these on different lines: these points are not in the same equivalence class
warm temple
i tried to draw the different cases
restive geyser
What different cases?
warm temple
equivalent classes of
[(m, n)]
[(-p, q)]
[(l, -o)]
restive geyser
each blue line (and the highlighted red line also) is a singular equivalence relation
We can uniquely define each one of these with a point on each line; for the sake of normalising, we can have those points be a distance 1 away from the origin (hence the x^2 + y^2 = 1 condition I set)
warm temple
oh i see
so no matter what each of the equivalent class graphically straight lines reach positive y
restive geyser
Now if I only have that condition, then I'm gonna have two points for each class
For every (x,y) point I have there, I'm gonna get (-x, -y) there too
So I can further restrict that y > 0, i.e. the second condition I set
warm temple
that makes sense
what about the quotient set? how do i find that
i know its the set of every equivalance class but how do i write that?
restive geyser
Well, the difference between the quotient set and a traversal is just what elements it contains
A transversal contains exactly one point from each class
A quotient set contains each class
It suffices then that if we can write each class using the defined point, we should be done
restive geyser
equivalent classes of
[(m, n)]
[(-p, q)]
[(l, -o)]
And seeing this, I think you should already have the notation down
warm temple
It suffices then that if we can write each class using the defined point, we sho...
so would [(x,y)] (x,y) being from R x R work?
restive geyser
(x,y) being from the transversal we've just defined
warm temple
so [(x,y)] from x^2 + y^2=1 y>0?
restive geyser
yes (you should know how to define a set, right?)
(Like, with set-builder notation)
warm temple
dude genuinely thank you so much
restive geyser
(and also)
restive geyser
(noting also that we haven't included the y=0 relation, but we can just add that...
You need to tweak the answer to deal with this class too
warm temple
y=0 relation like [(x, 0)]?
restive geyser
ye
0 isn't greater than 0, so atm we haven't included it yet
But it is in our relation
warm temple
x² + y² = 1, y=>0 perhaps?
restive geyser
again, though, we can use set-builder notation just to union a singleton set as an add-on to the sets we've made, so this should be the easy part
restive geyser
x² + y² = 1, y=>0 perhaps?
Now that would make both (-1,0) and (1,0) in the transversal
We only need one of them
warm temple
ah
warm temple
the U looking thing right
restive geyser
ye
restive geyser
Almost
[(x,0)] isn't clear - you need a class that's generated by a defined, not undefined, point
Think of it like, the point we use acts as the class's nametag
warm temple
since our radius is 1 we can just do [(1,0)]?
restive geyser
ye
restive geyser
Your "unioning" doesn't look right
restive geyser
X/~ = {[(x,y)] : (x^2 + y^2=1 y>0) U [(x, 0)] }
And similarly here btw
warm temple
Your "unioning" doesn't look right
well (1, 0) isnt a group
warm temple
And similarly here btw
oh i see
restive geyser
What's the set that contains just the point (1,0)?
restive geyser
What's the set that contains the number 23?
warm temple
{23}
restive geyser
Good
You just add the curly brackets in
Now what's the set that contains the point (1,0)?
restive geyser
No you're replacing the brackets there
warm temple
{(1, 0)}
warm temple
okay okay
restive geyser
Union this with the other set
warm temple
X/~ = {[(x,y)] : (x^2 + y^2=1 y>0) U {[(1, 0)]} }
restive geyser
waiiit
{[(x,y)] : x^2 + y^2=1, y>0**}**
This is one set
{(1,0)} is the other set
warm temple
ohhh ok
restive geyser
{set 1} union {set 2} needs the braces in the same places
warm temple
X/~ = {[(x,y)] : (x^2 + y^2=1 y>0) } U {[(1, 0)]}
restive geyser
{set 1} U {set 2}
restive geyser
{[(x,y)] : x^2 + y^2=1, y>0**}**
Check the formatting here
warm temple
oh wait
an equivalent class is just a set
X/~ = {[(x,y)] : (x^2 + y^2=1 y>0) } U [(1, 0)]
but for the transversal it would be
T = {(x,y) : (x^2 + y^2=1 y>0) } U {(1,0)}?
restive geyser
Check the formatting here
By this I mean, your way of writing the conditions is off
Also, both of these are sets, but of different things
T is a subset of X, i.e. comprised of elements of X
X/~ is a subset of the powerset of X, i.e. it is comprised of subsets of X
To this end, the only difference between the traversal and the quotient set is the []s
warm temple
To this end, the only difference between the traversal and the quotient set is t...
is it like this in every case? where the quotient set is just the traversal set but with equivalent classes?
restive geyser
Well, the difference between the quotient set and a traversal is just what eleme...
Well, yh - see here
warm temple
ok so the strategy for finding traversals is imagining the equivalent classes and it as a graph of sorts?
restive geyser
Well, the idea behind understanding an equivalence relation is precisely to understand what an equivalence class looks like
A transversal is just a set defined by collapsing each class to a single elements and then collecting those elements up
In this case, this was done by projecting each class onto a unit circle (and then making adjustments, like taking y>0, and then adding an extra point)
This is gonna have to come with practice, ultimately
warm temple
do you have any recommendations of where to practice?
warm temple
why is this subject so hard to study 😭
well thank you so much for all the help
o/
.close
full forumBOT
full forumBOT
Available help channel!
digital nymph
what's up with this
full forumBOT
what's up with this
digital nymph
if i solve according to this board
then i get
i ask chatgpt and it tells me yp is this instead
but the final solution isn't even the same as the one in my textbook
umbral dome
then i get
you did not use the product rule when differentiating yp
umbral dome
Bro help me in my maths
this channel is currently occupied. pleas open your own (see #❓how-to-get-help )
umbral dome
Help me in maths
again, this is not your channel. please open your own #❓how-to-get-help
full forumBOT
@digital nymph Has your question been resolved?
digital nymph
you did not use the product rule when differentiating yp
ok, i put it in the original equation. now i got 2Ax-2A=xe^-x
what now
umbral dome
well that means your guess was wrong
umbral dome
so make a different guess. in particular, if you have (some polynomial) * e^(ax) then you should always guess (polynomial of same degree) * e^(ax)
digital nymph
i ask chatgpt and it tells me yp is this instead
ok, so it is this then
full forumBOT
@digital nymph Has your question been resolved?
full forumBOT
full forumBOT
Available help channel!
heavy gulch
Uh I don't even know how Part A is supposed to help me with part B. Am I dumb?
hallow walrus
Uh I don't even know how Part A is supposed to help me with part B. Am I dumb?
What did you get for part A
kindred grove
looks good, now the idea is to plug in that matrix^n from part A in the series
delicate torrent
How can I prove that OI, NQ and MP all meet at H? ABCD ise an inscribed quadrilateral where AC is perpendicular with BD at I. M, N, P, Q are midpoints of AB, BC, CD, DAA
delicate torrent
Note that I am working with Euclidean geometry, not some coordinated geometry
full forumBOT
@delicate torrent Has your question been resolved?
delicate torrent
<@&286206848099549185>
hot frigate
Let's see
hoary ember
with some angle chasing you can see yhat MNPQ form a rectangle and H is the center of it, but not sure where this comes into pkay