they're just numbers
#help-27
winter patrol
describe what you did here
why did you choose to use the number 4
where did that come from
regal berry
because 4x = 2 * 2 *x our b is 2
2^2 = 4
here findind b is so much easier but finding the b in my problem is a bit harder
that is why I asked for help how do i find the b here
regal berry
p = 8/2 = 4
winter patrol
what about
2q = 9
regal berry
q = 9/2
winter patrol
yes
so same idea
also i wouldn't use b like that here, since it normally represents the whole coefficient of x
regal berry
i am trying to find the problem where we left off hold on
winter patrol
2k = 7/2
solving for k isn't that different from what you did just now
regal berry
$2 * (x^2 + 7x/2 + 11/2)$
woven radishBOT
Simon James B
regal berry
ok much better now that i can see it again
confused about the k part
i am so stupid what's happening 
2ab we have 2xb for 7x/2 ahh:(
winter patrol
$2\cdot \what = \frac 72$
woven radishBOT
ℝαμOmeganato5
regal berry
i don't know 😭
3.5 but that is 35/10 to so whatever is easier i have no idea what is happening
winter patrol
no
regal berry
then idk
winter patrol
again recall what you did
for
2p = 8
and 2q = 9
do the exact same thing here
how did you solve for q there?
regal berry
2x = 7/2
x - 7/2 /2
regal berry
2y = 7/2
y = 7/2/2?
winter patrol
don't use y either
regal berry
WHYY
winter patrol
well technically y would be fine here since it hasn't been predefined in the question
but its not a good idea to use variables to represent different things
regal berry
we can do 2* what but it is easier visually to see a letter you know
winter patrol
or things they don't usually represent
winter patrol
but w/e
now simplify the (7/2)/2
regal berry
anyways in our case it is 7/2/2 = 7/2 * 1/2 = 7/4
regal berry
(7/4)^2 ?
woven radishBOT
Simon James B
winter patrol
why 11/4
regal berry
don't we have 11/4 after it in the problem?
winter patrol
no
regal berry
**Simon James B**
$2 * (x^2 + 7x/2 + 11/2)$
woven radishBOT
Simon James B
regal berry
11/2
winter patrol
adding and subtracting (7/4)^2
doesn't impact the 11/2 in any way
regal berry
i did not have the problem in my visual so i was thinking it was 11/4 in the problem not 11/2
winter patrol
you should be writing this down on paper as you're going
regal berry
$2(x^2 + 7x/2 + 49/16 - 49/16 + 11/2)$
woven radishBOT
Simon James B
regal berry
you should be writing this down on paper as you're going
i am doing problems on my whiteboard after
and then on paper
$2[(x+7/4)^2 - 49/16 + 11/2]$
woven radishBOT
Simon James B
winter patrol
its not ideal to just follow on the screen, you keep having to scroll
and misremember values, what you have etc
now simplify that
-49/16 + 11/2
regal berry
$2[x+7/4]^2 -49/16 + 88/16$ i amplified it
woven radishBOT
Simon James B
regal berry
so it would be {-49+88}/16
winter patrol
no
regal berry
why
winter patrol
there'd still be () around the entire thing
expressing 11/2 as 88/16 doesn't change that
winter patrol
first go back put in those ()
regal berry
$2[(x+7/4)^2 - (49/16 + 88/16)]$
woven radishBOT
Simon James B
winter patrol
no
winter patrol
now you added in and additional pair of () that don't belong there
winter patrol
still have additional () that don't belong
regal berry
$2[(x+7/4)^2 - 49/16 + 11/2]$
woven radishBOT
Simon James B
winter patrol
you had this earlier, this was fine
just change that 11/2 to 88/16
don't mess around with any of the ()
woven radishBOT
Simon James B
regal berry
$2[(x+7/4)^2 - {49+88}/16]$
woven radishBOT
Simon James B
winter patrol
no
regal berry
this did not comply well
winter patrol
do this on whieteboard/paper and take a pic
or draw on paint
regal berry
i can't take a picture i am not logged in on discord on my phone anyways
2[(x+7/4)^2 - 39/16] ?
winter patrol
incorrect
regal berry
my head is exploding
winter patrol
you're not being careful with signs
draw your work on paint
or just focus on simplifying
-49 + 88
regal berry
50/16
winter patrol
yes
regal berry
That is what i said
winter patrol
it was not
2[(x+7/4)^2 - 39/16] ?
you're not being careful with signs
you had -39 there
regal berry
- 39/16
regal berry
2(x + 7/4)^2 + 78/32 >0
winter patrol
you're not distributing that 2 corretly
regal berry
78/16
winter patrol
yes
regal berry
Will i ever get to understand this thing like ever💀
winter patrol
would've been more efficient to cancel a factor of 2 directly instead of first simplfying 2 * 39
regal berry
I managed this one with help but i am sure the next one will be a bit easier but still won't get it right
woven radishBOT
ℝαμOmeganato5
winter patrol
doesn't matter if the smiley face is an integer, fraction, decimal or whatever
same approach
divide by 2
square it,
add/subtract
etc
winter patrol
and follow my recommendation of writing the work down as you go
instead of just typing it out
regal berry
and follow my recommendation of writing the work down as you go
I am writing it down when i do it on the whiteboard but here on discord i was not able to while getting help. I am not doing them on my laptop
see you pretty soon. Sadly i am sure of it bec my brain is kinda stupid with math
.close
dense summit
where does the * 1/2 come from???
devout snowBOT
where does the * 1/2 come from???
ancient sluice
d/dx (x²-2x-3) = 2(x-1) so
devout snowBOT
devout snowBOT
Available help channel!
unkempt smelt
I dont understand what I need to do when n= k+1
iron kindle
!status
devout snowBOT
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
ripe grove
I'm assuming your proving the statement by mathematical induction ?
ripe grove
I dont understand what I need to do when n= k+1
You simply plug in n=k+1
devout snowBOT
@unkempt smelt Has your question been resolved?
unkempt smelt
I'm assuming your proving the statement by mathematical induction ?
yes
unkempt smelt
<@936609851302350932> Has your question been resolved?
yes but its not working in this question
ripe grove
Have you considered that what your proving is simply not true ?
Did it pass the n=1 test?
unkempt smelt
Have you considered that what your proving is simply not true ?
It has to be true
ripe grove
Why does it have to be true ?
If I said x+7=x+5 for x is element of all integers you know it's not true
unkempt smelt
Why does it have to be true ?
Because the question says prove for every natural n that this is true
devout snowBOT
ripe grove
Sometimes questions are wrong
unkempt smelt
.reopen
devout snowBOT
✅
ripe grove
Did the n=1 test hold
unkempt smelt
Yes, but not like the common cases in induction, it's a subtopic that when you put n=1 in the general term you get the number for which you have to sum up to this number (inclusive)
ripe grove
Could I see the whole question
unkempt smelt
It's not in English, you have to prove that for every natural n this thing holds.
It is possible by induction or any other way, but I try induction
iron kindle
Did the n=1 test hold
it does hold
its just strangely written
for n=1 you get (2+1)+(2+3)+(2+5)=3+5+7=15 which is equal to 3+8+4=15
unkempt smelt
yeah
ripe grove
Maybe I'm not understanding the notation going on
iron kindle
its $\sum_{i=1}^{2n+1} 2i+1$
woven radishBOT
Bonk
iron kindle
so n=1: $\sum_{i=1}^{3} 2i+1=2+1+4+1+6+1=15$
woven radishBOT
Bonk
ripe grove
O sh that makes sense
iron kindle
they shouldve made that last term (2(2n+1)+1) ngl
took me a little while to find aswell
ripe grove
Yeah I didn't notice that😭
Well I mean then it's reasonably straight forward no ?
its $\sum_{i=1}^{2k+2} 2i+1$
woven radishBOT
Nyxzore
iron kindle
Well I mean then it's reasonably straight forward no ?
most induction is
almost every textbook that doesnt cover induction and uses induction writes: can be proven by induction
unkempt smelt
they shouldve made that last term (2(2n+1)+1) ngl
Did you understand how to do the stage when n = k+1
ripe grove
its $\sum_{i=1}^{2k+1} (2i+1)+2(2k+2)+1$
woven radishBOT
Nyxzore
iron kindle
its $\sum_{i=1}^{2k+1} (2i+1)+2(2k+2)+1$
then it should be from i=1 to n
otherwise you count double
iron kindle
Did you understand how to do the stage when n = k+1
you assume P(k) holds, then use it to show P(k+1) holds
ripe grove
?
unkempt smelt
you assume P(k) holds, then use it to show P(k+1) holds
yes but its not working
iron kindle
so, assume $(2k+1)+(2k+3)+(2k+5)+....+(4k+3)=3k^2+8k+4$ then use it to show $(2k+1)+(2k+3)+...+(4k+3)+(4k+5)+(4k+7)=3(k+1)^2+8(k+1)+4$
woven radishBOT
Bonk
iron kindle
yes but its not working
!show
devout snowBOT
yes but its not working
Show your work, and if possible, explain where you are stuck.
unkempt smelt
devout snowBOT
@unkempt smelt Has your question been resolved?
wet ridge
@unkempt smelt the thing you have to notice is that the only difference in both expression is that when expressing with k we have 2k+1 and with k+1 we don't have it but we have additionally 4k+5 and 4k+7 in the left side and the right side has additional 6k+11 and when you add 4k+5 and 4k+7 and subtract 2k+1 you get 6k+11 which proves it
unkempt smelt
<@936609851302350932> the thing you have to notice is that the only difference i...
Oh thank you, but why do we need to substract 2k+1?
wet ridge
because we have 2k+1 when expression through k but not when through k+1 because there we start with 2k+3
devout snowBOT
unkempt smelt
.reopen
devout snowBOT
✅
unkempt smelt
because we have 2k+1 when expression through k but not when through k+1 because ...
I'm really sorry I don't really understand, can you show me your way written on a page or in the app?
wet ridge
this is what i've written to get there, not sure if it's going to be helpful
hazy cradle
$4k^2 +12k +8$?
woven radishBOT
ЯεтιяεĐ
hazy cradle
I'm really sorry I don't really understand, can you show me your way written on ...
use these formulae
c=1
and take 2i as i+i
devout snowBOT
@unkempt smelt Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
frozen aurora
$\int_0^\infty \ln(v) e^{-v} dv$
devout snowBOT
$\int_0^\infty \ln(v) e^{-v} dv$
woven radishBOT
artemetra
frozen aurora
v cuz this is part of a substition
frozen aurora
**artemetra**
not sure where to take this from here
i know that the answer is the euler-mascheroni constant
this is probably some random special function and its 547252nd representation
acoustic leaf
what definition do you have for the euler-mascheroni constant? this would probably come down to showing equivalence with that defn
frozen aurora
wdym what definition
frozen aurora
**artemetra**
i just plugged that into wolframalpha and recognized the constant
this isn't a textbook question, just something i saw online
now that i look at this tho
https://en.wikipedia.org/wiki/Euler's_constant#Formulas_and_identities
hmm
supple knot
Probably substitute the Taylor series for either log or exponential and ibp the series
frozen aurora
first thing to do is to write this as
but go on
sand dove
$\int_0^1\ln(v)e^{-v}dv - \int_0^1\ln(u) e^{-\frac 1u}\frac{du}{u^2}$
woven radishBOT
rafilou is not not born in 2003
sand dove
I believe the right integral can be simplified into gamma function using IBP
and the left integral, well maybe power series e^(-v) = 1 - v + v^2/2 - v^3/6 + ...
frozen aurora
and this we get from $\psi(z) = \frac{\Gamma'(z)}{\Gamma(z)} = \frac{1}{\Gamma(z)} \int_0^{\infty} \frac{\partial}{\partial z} (t^{z-1}) e^{-t} dt = \frac{1}{\Gamma(z)} \int_0^{\infty} t^{z-1} \ln(t) e^{-t} dt$
woven radishBOT
artemetra
frozen aurora
and the left integral, well maybe power series e^(-v) = 1 - v + v^2/2 - v^3/6 + ...
i see
that makes sense
thanks everyone!!!
.close
devout snowBOT
devout snowBOT
Available help channel!
regal berry
$√x^2 -6x +25 + √y^2 +8y+ 41 <= 9 \newline √x^2 - 6x + 9 - 9 +25 + √y^2 + 8y + 16 - 16 + 41 \newline √(x-3)^2 + (y +4)^2 <=9$ what now
woven radishBOT
Simon James B
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
devout snowBOT
regal berry
.close
devout snowBOT
devout snowBOT
Available help channel!
regal berry
$\sqrt{x^2 -6x+25} + \sqrt{y^2 +8y+41} <=9$
devout snowBOT
$\sqrt{x^2 -6x+25} + \sqrt{y^2 +8y+41} <=9$
woven radishBOT
Simon James B
woven radishBOT
Simon James B
regal berry
$\sqrt{(x-3)^2 +16} + \sqrt{(y+4)^2 +25} <= 9$
woven radishBOT
Simon James B
regal berry
this is where i am stuck. I have to find x and y
regal berry
I can't just add a random value that just comes to mind can i now?
I need a exact value for x and y
regal berry
if x is 10 $\sqrt{(10-3)^2 +16} + \sqrt{(y+4)^2 +25}<=9$
woven radishBOT
Simon James B
regal berry
$\sqrt{49+16} = \sqrt{65}$
woven radishBOT
Simon James B
muted mural
You can do this on paper if you like. It's probably faster while we're investigating.
regal berry
i already do
are these types of problems a harder difficulty or am I the problem?
16 = 4^2 maybe there is some hint there because if we know that sqrt x^2 = |x| maybe there is a way to rewrite the content of our sqrt to be all under one ^2 so that we cancel out the sqrt
muted mural
It's not possible to make this into one root
regal berry
both 16 and 25 can be re-written as 4^2 and 5^2 so i am sure it is something to do with them?
muted mural
Did you get an answer for y when x is 10?
regal berry
if those would be gone we could cancel out the sqrt but because both can be written as ^2 maybe we do something with those idk
muted mural
This particular question has an easy answer but you have to do a bit of work to see it
regal berry
Did you get an answer for y when x is 10?
i do not see it
muted mural
Can you find it approximately? Like you got root65, which is really close to root 64.
regal berry
idk how to approximate a sqrt
muted mural
I'm not taking about anything fancy. Root 64 is 8
Just pretend that root 65 is 8 for a moment.
regal berry
$8 + \sqrt{(y+4)^2 +25} <=9$
woven radishBOT
Simon James B
regal berry
$8= 2\sqrt{2}$
woven radishBOT
Simon James B
regal berry
so do we have $2\sqrt{2} + \sqrt{(y+4)^2 +25} <=9$
woven radishBOT
Simon James B
muted mural
Just move the 8 to the other side
woven radishBOT
Simon James B
muted mural
What does all the stuff under the root have to equal?
regal berry
1?
muted mural
Yeah, or less.
regal berry
yes.. i don't see where this is going
muted mural
There is no value of y that makes that happen.
The square part is always 0 or positive, and then you add 25.
regal berry
and +25 will also never make it 1 or less right
muted mural
So x=10 is not possible.
With that information, you should think about what might be possible.
How did it go wrong?
Sqrt(65) was too big.
So we need a smaller result under the first root.
muted mural
Maybe? Try to make it as small as possible to see what happens
woven radishBOT
Simon James B
regal berry
so the square to be 0 x needs be 3
and the first sqrt would give us 16 => 4
$\sqrt{(y+4)^2 +25}<=5$
woven radishBOT
Simon James B
regal berry
Ahh here the 5 i was talking about 
muted mural
Does that give you a value for y?
regal berry
hmm
let me see
could y be 1
let me try again
if y is 0 we have sqrt 41
it is not less then 5
this is not possible either?
muted mural
y=0 gave you a value under the root that was too large.
Is there a value of y that would give you a smaller result under the root?
regal berry
if y is 1 the root is even bigger
do we go negative
-4!
the root will get 25 and that is =5
so 5 <= 5
muted mural
Does this question as a whole kind of make sense to you?
muted mural
Okay, but you have an answer. Do you think there could by any other answers? It is an inequality after all.
regal berry
well the next one should be 4^2 = 36 and is less then 4
if i can get this sqrt to be equal to 4
i can't find more values
i tried to make the sqrt equal 4 but i failed
muted mural
This is good.
The point is that you made those roots as small as possible, and it only just worked.
regal berry
so the value of y is always going to be -4 here?
there would be no other solutions of y?
muted mural
And you choose x to make the first root as small as possible too.
regal berry
x =3
muted mural
This question is different from most in that the solution process is more conceptual and less immediately algebraic (except for the completing the square that you did to start; that was really good).
Let me break down how I look at this question.
You have two square roots adding up to at most 9.
Square roots bottom out at 0, and only go up.
So my first this is that this might or might not have any solutions.
I see that there are two variables, x and y, and they don't really interact too much. I can pick values independently to test them out.
So I can look at the two roots separately.
I want to keep their values small.
The fact that it's (x-3)^2 instead of x^2 makes it look more confusing, but the range of possibilities is exactly the same.
It's just some real number being squared.
So mentally, I'm looking at
$\sqrt{x^2 + 16} + \sqrt{y^2 +25} \leq 9$
woven radishBOT
Silkster
regal berry
i see it
muted mural
Now I see that making the smallest possible roots makes it only just work out, so that must be the only answer.
regal berry
both my ^2 needs to be 0
so the only value for x and y is the value that makes it 0 in ()
but how do i prove all of this. In the exam i can't just replace it with numbers and proof
there is a proof in my answer sheet if you want to analyze with me
muted mural
I would write $\sqrt{(x-3)^2 + 16} \geq 4$.
woven radishBOT
Silkster
regal berry
slow down a bit 
how did we get to >=4
muted mural
Remember that the square is at least 0, so adding 16, the stuff under the root is at least 16
regal berry
yes
oh i see it
we changed the condition but it's actually the same logic
<= 9 is the same logic as >=4
just different conditions
or not?
muted mural
The part about it being at most 9 is given in the question.
I'm making a separate claim that $\sqrt{(x-3)^2 + 16} \geq 4$.
woven radishBOT
Silkster
regal berry
I am so failing my Sat's 
because we have <=9 our first root is >= 4 and that is true <=9 ?
and we make it 4 because root of 16 is 4?
muted mural
We inspected the first root, noticed that the square is at least 0, so overall the root is at least 4.
Inspecting the second, we see that it's at least 5.
The question is a bit like:
Solve for a and b given
muted mural
$a \geq 4$, $b\geq 5$, $a+b \leq 9$.
woven radishBOT
Silkster
regal berry
i see
i think i understood like 70%. The rest comes just with many more problems like this:(
but still i really am not used with this type of math like just logic and analyzing. Usually it's operations or formulas or completing for algebra. At least how it was for me until today
muted mural
It's a wild world out there. It's a bit like going from "fill in the colours of this drawing" to "here's a blank page and some paints, do whatever you like"
regal berry
It's a wild world out there. It's a bit like going from "fill in the colours of ...
I wrote the proof i will send it in a bit as a photo to see if it's good
maybe my handwritting is ugly but srry
I hope this is right. It is past midnight for me
muted mural
I'm not sure what this is being submitted to, but these two implications can't be done in separately from one another.
muted mural
it's only because one is at least 4 and the other is at least 5 and the total is at most 9.
You need all 3 constraints to pin down x and y.
regal berry
How do i separate 2 conditions in one line
muted mural
with a comma
Math is a language like any other. If you want to say two things, you can say one and then the other. Or in two sentences, or use "and".
regal berry
Now maybe
or we can also start with the original condition and say => to the 2 conditions separated by, => the final answer
muted mural
this part isn't implied. It's a third statement leading up to the conclusion
the less than 9 part is given in the question
regal berry
So we do the orignial question => in the 2 conditions => the final answer?
muted mural
these two statements are ones that you deduced with algebraic reasoning, independent from the question.
There's only one implication
muted mural
it is part of the proof, but you did not deduce those two inequalites from the question
These two came from algebra, not from the question
regal berry
i have to do it from the actual start? before completing squares?
i can't think well it's like 1am💀
muted mural
all I'm saying is that in this line, the first implication should be a comma
because the question doesn't come from anything
regal berry
so all i have to do is add a , before the start
Why did the teacher never show us what is important. Instead she showes things we never use
muted mural
This question is different from most. A lot of kids are probably still struggling with completing the square. It's hard to teach everything. But I don't know about your teacher or class. Maybe she's bad?
muted mural
I think you might have misread this part
They're writing a separate logic step that says:
$a\geq 4$ and $b\geq 5$ $\implies$ $a + b \geq 9$
woven radishBOT
Silkster
muted mural
They they combine that with $a + b \leq 9$ to get $a + b = 9$
woven radishBOT
Silkster
regal berry
thank you so much for the help and time. I think i will go to sleep as it's 1am for me i will learn better tomorrow. As long as i do not get this in my SAT's i am all good 
even tho this problem made me feel stupid
muted mural
Good night and good luck!
devout snowBOT
devout snowBOT
Available help channel!
sweet dawn
Hi, is the way that I'm distributing 2 here (at the end) correct in the context of how the Fundamental Theory of Calculus is to be applied? Thank you!
devout snowBOT
Hi, is the way that I'm distributing 2 here (at the end) correct in the context ...
woven radishBOT
devout snowBOT
@sweet dawn Has your question been resolved?
dapper egret
how do i use factor theorem to get the rest of the factors??
devout snowBOT
how do i use factor theorem to get the rest of the factors??
woven radishBOT
final drift
devout snowBOT
@dapper egret Has your question been resolved?
spring oasis
In isosceles triangle $\triangle ABC$ we have $AB=AC=4$. The altitude from $B$ meets $\overline{AC}$ at $H$. If $AH=3(HC)$ then determine $BC$.
devout snowBOT
In isosceles triangle $\triangle ABC$ we have $AB=AC=4$. The altitude from $B$ m...
woven radishBOT
938c2cc0dcc05f2b68c4287040cfcf71
lost laurel
Hint: trignometry
spring oasis
can you elaborate
stable cedar
just draw the diagram, you get the right triangle ABH
solve for BH
and u know right triangle BHC
all using pythagorean theorem
spring oasis
just draw the diagram, you get the right triangle ABH
lament kraken
!occupied
devout snowBOT
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).
twilit beacon
Someone else is already using this help channel. If you need help with a questio...
okay
lament kraken
I cant rlly help with that tho
lunar harbor
spring oasis
lunar harbor
Same thing as this: #help-27 message
frosty portal
ohhh
u get BH by pythagorus theorem
use that to find the areas of ABH and BHC
and set their sum eqaul to the area of abc
??
lunar harbor
Area is too much effort
Once you find BH, you have the two legs of triangle BHC
and hence the value of BC follows directly
lunar harbor
ok
frosty portal
whts the other way ?
lunar harbor
You could always coordbash
But that’s even more impractical
Stewart’s/law of cosines also works, but again, extremely overkill.
You get the idea
spring oasis
Yeah, but you drew HC=3(AH).
lunar harbor
frosty portal
Stewart’s/law of cosines also works, but again, extremely overkill.
You get the...
i nevere really understood that theorem
frosty portal
wait
spring oasis
AH = HB
lunar harbor
AH = HB
The altitude only bisects the opposite side of you draw the altitude to the base
That’s not the case here
spring oasis
hb = 5?
lunar harbor
hb = 5?
HB isn’t the hypotenuse, AB is.
You legit wrote it that way with your equation
frosty portal
ohhh waiiit waiiit
BH^2 = 4^2 -3^2 = 7
BH = root(7)
this means BC = root(8)=2root(2)
spring oasis
this means BC = root(8)=2root(2)
I see
doing math on midnight is dangerous
we got it
frosty portal
doing math on midnight is dangerous
truth be told
devout snowBOT
lunar harbor
doing math on midnight is dangerous
Mood
It’s 2 in the morning over here and I’m waiting for my water to boil
💀
spring oasis
2am here aswell, happy boiled water, ty for the help
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sturdy zealot
Why isn't the ans (13C1 * 4C2) * (12C1 * 4C2) * 44 ? I understood the solution which they have provided but what is wrong with my solution ??
devout snowBOT
Why isn't the ans (13C1 * 4C2) * (12C1 * 4C2) * 44 ? I understood the solution w...
fossil locust
Why isn't the ans (13C1 * 4C2) * (12C1 * 4C2) * 44 ? I understood the solution w...
you need to find how many ways to choose the numbers for the two pair, and that's (13 choose 2)
the order doesn't matter, say if you choose 4 then 7, or 7 then 4
sturdy zealot
the order doesn't matter, say if you choose 4 then 7, or 7 then 4
oh ok so in my counting i have treated 4 then 7 and 7 then 4 as different , right ?
fossil locust
oh ok so in my counting i have treated 4 then 7 and 7 then 4 as different , righ...
yes
devout snowBOT
@sturdy zealot Has your question been resolved?
orchid glade
given a,b,c are constant and lim(x to a) of f(x) is c. wont lim(x to a) of b*f(x) be bc
devout snowBOT
given a,b,c are constant and lim(x to a) of f(x) is c. wont lim(x to a) of b*f(x...
uneven talon
given a,b,c are constant and lim(x to a) of f(x) is c. wont lim(x to a) of b*f(x...
yes
orchid glade
im incredibly confused because im studying the proof of sin(x)/x as x tends to 0
i cant grasp why it wouldnt be true for degrees
i do the same thing as the radians and get the limit : 180sin(x)/x*pi for (x to 0) = 0
fossil locust
i cant grasp why it wouldnt be true for degrees
the area of the blue sector is only 1/2 * x when x is in radians
1/2 r^2 theta
here's a similar derivation
orchid glade
hmm so if i do take degrees instead of 1, the limit will be 180/pi
thanks!
.close
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fossil locust
nw!
fossil locust
hmm so if i do take degrees instead of 1, the limit will be 180/pi
nearly, it would be pi/180 actually
sin(x degrees) = sin(pi/180 * x radians)
for example, 1 degree = pi/180 radians
because pi radians = 180 degrees
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native stone
i need help with this exercise
native stone
.close
late mason
I need to know the lenght of the red line so i can calculate the yellow, then i would need to calulate the surface area of the thing i marked green but i think i can do that. i am just not sure how to get the length of the red line
devout snowBOT
I need to know the lenght of the red line so i can calculate the yellow, then i ...
sage burrow
!original
devout snowBOT
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.
late mason
I need to caluclate the surface content
of the entire thing, i already calculated the area of the red
solar goblet
is there anything special about the labeled angle?
sage burrow
thats still not the entirel question. given the screenshot it is not solvable.
late mason
I need to get the surface area of pretty much everything
of the entire blue part
I also dont think i can assume ist 3 3 3 because the right side seems longer
fossil locust
I also dont think i can assume ist 3 3 3 because the right side seems longer
that diagram is really unfortunate
they mean the diagonals (which are assumed equal) of the trapezoid are equal to 5,0
because the shorter base is of course 3,0 (it's vertically above)
so you can split the 9,0 into 3,0 3,0 3,0
sage burrow
I also dont think i can assume ist 3 3 3 because the right side seems longer
if you could assume 3:3:3 it would be solvable, but i agree if its not given then you cannot assume it. But then its not solvable.
fossil locust
3,0 = base and 5,0 = hypotenuse
yeah the big assumption is that it's an isosceles trapezoid
otherwise you can't split the remaining 9,0 - 3,0 = 6,0 equally into 3,0 and 3,0
kind cliff
can some1 pls explain when a series is conditionally convergent and when its absolute convergent
devout snowBOT
can some1 pls explain when a series is conditionally convergent and when its abs...
lost laurel
A series is conditionally convergent if it's convergent but when you take the absolute value of all its terms and makes that a series it's not convergent
kind cliff
so if i take the lim (-1)^n An
and it converges
but the lim An does not
it means its conditional?
lost laurel
yes
lost laurel
you need to find the limit or just determine convergence ?
kind cliff
find if its conditionally or absolute convergent
lost laurel
Okay, so check if it's absolutely convergent first
that's easier
chose a convergence test and go with it
kind cliff
how do you know that checking if absolutely convergent firstly is easier
lost laurel
Because I don't have to deal with the $(-1)^{n+1}$
woven radishBOT
math rocks(wai)
kind cliff
so when there is the -1 i should test for absolute firstly
kind cliff
no i just took the limit of the absolut value of the term inside the series
kind cliff
i got e^-3
lost laurel
Yeah, sounds right
kind cliff
so now i do the same with the whole term or i can already determine what it is
lost laurel
well, now you have to apply some other test to determine convergence, a series can not converge absolutely and still converge
kind cliff
is there a test that works for all senarios?
lost laurel
Not really, but I'd use the ratio test here
kind cliff
how do u know that
lost laurel
well, an integral test here would be near impossible, a comparssion test will be kind of hard, but may work
so that leaves root and ratio test
kind cliff
i still didnt learn integral test
i think there is about seven tests without the integral but its kinda hard for me to remember them all
lost laurel
the alternating series test may actually work better here
kind cliff
what about root test
devout snowBOT
@kind cliff Has your question been resolved?
kind cliff
for me it doesnt work even with that
lost laurel
Huh, why not
what limit are you getting as n goes to infty
a non-zero number , right
kind cliff
ye
devout snowBOT
kind cliff
.reopen
lost laurel
yea?
dire hatch
A task I have is to prove/disprove:
If $F\to G$ is valid, is $F\to(G \vee H)$ valid.
But my question is, why can we assume $F\to G$ is valid when a valuation where F is true and G false makes the statement false?
woven radishBOT
Michael
dire hatch
Yeah, it says in the task that they are formulas
dire hatch
and then e.g. F = A, G = A would make F -> G valid
Oh
polar chasm
is this first order or propositional btw?
dire hatch
Sorry, what do you mean with that?
polar chasm
first order logic or propositional logic
dire hatch
Uhh, I have no clue
polar chasm
are there quantifiers such as for all and exists or not yet?
dire hatch
Just following a Norwegian discrete maths book
dire hatch
are there quantifiers such as for all and exists or not yet?
No, it’s introduced in chapter 12 (I’m in chapter 5)
polar chasm
ic, ig it's propositional then
polar chasm
propositional assigns truth and false directly to the variables, while first-order logic is more complicated
dire hatch
I see
polar chasm
first-order logic has some kind of objects (e.g. numbers), functions (e.g. +, *) and relations (e.g. =, isPrime(), isEven()) etc
and truth and false are then assigned to the relations which are applied on objects
and you can also quantify over the object and say that something holds for all of them, or for at least one of them
so e.g. 1 = (2 + 3) would be a formula of first order logic in certain language
dire hatch
Ohh alright, that sounds interesting
uneven talon
I love modal logic
dire hatch
Excited to learn more about this
uneven talon
A task I have is to prove/disprove:
If $F\to G$ is valid, is $F\to(G \vee H)$ v...
Anyways, when we assume that F implies G is valid, then we assume some cases for F and G
Your job is to show that in those cases, F implies (G or H) still holds
dire hatch
Okay, but what must F and G be if my "definition" of valid is the thing?
uneven talon
It's all the cases where F implies G is true
dire hatch
What’s the difference between F being a formula and it being valid when all the valuations make it true
polar chasm
It's all the cases where F implies G is true
valid means true for all interpretations (valuations)
polar chasm
What’s the difference between F being a formula and it being valid when all the ...
wdym?
not every formula is valid obviously
so being a formula and being a valid formula is a difference
uneven talon
valid means true for all interpretations (valuations)
How's this different from saying F -> G is true
polar chasm
How's this different from saying F -> G is true
this would be for a particular valuation
not necessarily for all of them
dire hatch
Like, earlier in the chapter it says:
"If a statement-logical formula F is true for all valuations, we say that the formula is a tautology, or valid, and we write […]"
uneven talon
So we just need to go through each state of F and G and see where this is true
And we get this validity table
polar chasm
So we just need to go through each state of F and G and see where this is true
oh, that's what you meant, yeah, then yes
dire hatch
Hmm, I’m not really sure what I’m asking right now lol
uneven talon
Hmm, I’m not really sure what I’m asking right now lol
Let's go at it this way
Consider F to be a true statement
What values of G cause F -> G to be true
If F is true
dire hatch
Then G must be true
uneven talon
Then G must be true
Yep
Alright now consider when F is false
What values of G cause F -> G to be true
dire hatch
Then G can be either true or false
polar chasm
we are trying to prove that F -> (G v H) is valid. So we have to show that it's true for all valuations. So given an arbitrary valuation, there are few cases:
-
F is true under this valuation, but since F -> G is valid, we know that G must be true as well under this valuation ... (etc)
-
F is false ... (etc)
(this is just the outline of what you're doing now in the language of logic and validity)
the point is that we're essentially working with arbitrary valuation here, in order to show that it works for all valuations
uneven talon
Then G can be either true or false
Exactly
So now that we have all the cases we need for F and G
Let's look at the cases for F -> (G or H)
Ok so let F be true
Since G is true, is (G or H) true?
dire hatch
Yep, it’s true
dire hatch
Then it’s true
dire hatch
And if F is false:
G true gives G or H true, and F -> (G or H) true again
uneven talon
But let's realize something
dire hatch
sorry skipped ahead there
uneven talon
When F is false, it doesn't matter what (G or H) is
dire hatch
Ah yeah true
dire hatch
Yeah
But what about the case that doesn’t make F->G, ie F true and G false?
I still don’t get why we can say that F->G is valid when we have a case where it’s false?
uneven talon
But what about the case that doesn’t make F->G, ie F true and G false?
I still d...
It's because we assume F->G is valid from the start
It's just saying in all the cases where F->G is true, is the other thing also true?
polar chasm
But what about the case that doesn’t make F->G, ie F true and G false?
I still d...
that case leads to contradiction essentially
dire hatch
Okay, so we only consider the valutions of F and G which makes F->G true
dire hatch
It's just saying in all the cases where F->G is true, is the other thing also tr...
Alright
polar chasm
Okay, so we only consider the valutions of F and G which makes F->G true
those are by assumption all the valuations
dire hatch
But then I don’t really get the definiton of "valid"?
polar chasm
the point is that if there was a valuation that makes F -> G false, then that's a contradiction straight away
so there is no such valuation
dire hatch
Like, earlier in the chapter it says:
"If a statement-logical formula F is true ...
Which stated here
dire hatch
so there is no such valuation
Oh shite, I think I get it now
polar chasm
Okay, so we only consider the valutions of F and G which makes F->G true
we are allowed to consider only such valuations, because by our assumption no other valuations exist
uneven talon
It's easy to get it confused, because it seems weird that we just don't consider at all the case where it's false
But math can be real complicated and often times we have to assume something about a statement to get a useful result about something else
polar chasm
we are trying to prove that F -> (G v H) is valid. So we have to show that it's ...
It might be useful to write your proofs as detailed as this for now
explicitly thinking about the valuations
dire hatch
It might be useful to write your proofs as detailed as this for now
Yeah, I think so too
dire hatch
But math can be real complicated and often times we have to assume something abo...
Yeah
Alright, well thank you guys. This makes more sense now
.close
devout snowBOT
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Available help channel!
agile narwhal
can someone help me with quaternions?
devout snowBOT
can someone help me with quaternions?
agile narwhal
im struggling how to do rotations
quick quest
Hi, i dont really know how to find the X values of the asymptotes in a tang problem, fro example one like this
devout snowBOT
Hi, i dont really know how to find the X values of the asymptotes in a tang prob...
quick quest
i assume i need to split the tan into sin/cos but idk
dense rampart
no need
yk how tan(pi/2) is undefined
that^2 is also undefined
tan(-pi/2) is also undefined
everything else is safe
dense rampart
that^2 is also undefined
so you dont have to worry about an extra value that might be undefined, its just pi/2
quick quest
so tan^-1(pi/2)+- is the values? (1.003)
dense rampart
maybe your calculator cant show the word inf or I or that symbol
theres not muh to worry about
pi/2 is where the asymptote is, tan(pi/2) is what y value itd have at the asymptote
quick quest
ok thank you, is their any variable which changes the asymptote?
or is tan just always pi/2
dense rampart
have you learnt graph transformation
quick quest
yes
vital dagger
or is tan just always pi/2
yes unless you have an added constant inside tan
dense rampart
then youd know tan2x is horizontally squished compared to tanx
and tan(x+1) moves the graph left by 1
quick quest
true, thanks alot for the help
dense rampart
np
quick quest
.close
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unique zealot
what integral property am i supposed to use to figure out this qustion (answer is b)
devout snowBOT
what integral property am i supposed to use to figure out this qustion (answer i...
winter torrent
why did you close the last channel and reopen it
tardy edge
what integral property am i supposed to use to figure out this qustion (answer i...
let t = 2x probably
winter torrent
just pick one
tardy edge
and then go from there
fluid sinew
hey
fluid sinew
i need help
vital dagger
?
iron kindle
!da2a
devout snowBOT
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/
jagged harbor
4-9/2 is negative
fluid sinew
why not tho
jagged harbor
-1/2 is not equal to sqrt((-1/2)^2)
jagged harbor
(4 - 9/2)^2 isnt the same as 4^2 - (9/2)^2
this is not the error, sorry
fluid sinew
oh right
dense rampart
(4 - 9/2)^2 isnt the same as 4^2 - (9/2)^2
no he used the a^2 + 2ab + b^2 identity
vital dagger
why not tho
complex numbers
iron kindle
$4-\frac92=-\frac12\neq\sqrt{\left(-\frac12\right)^2}=\frac12$
fluid sinew
its basicaaly the same way that you can prove 8 = -8 by using 64= 64 and rooting both sides
vital dagger
lol 2 typos
fluid sinew
got it thanks
woven radishBOT
Bonk
vast wing
oh i get it now
devout snowBOT
@fluid sinew Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
tropic tinsel
which method of factoring is used here
devout snowBOT
which method of factoring is used here
north roost
completing square
sleek bronze
how to resolve this kind of exercises? the calculation of cn is kinda hard and i dont know how to solve the integral in a)
devout snowBOT
how to resolve this kind of exercises? the calculation of cn is kinda hard and i...
@sleek bronze Has your question been resolved?
devout snowBOT
eternal pike
this me and my firend have been aruging about this qn for the past hour
Is it
-9/4
or
9/4
dense rampart
how do you find slope
eternal pike
well we just needed to make it into
y=mx+b
so
-9x
-4y=-9x+12
then dived by -4
y=9x/4-3
so the slope is
9/4
right
dense rampart
ur slope is correct but y intercept is -3 not +3
dense rampart
yes 9/4
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gaunt bay
in implicit differentiation, when you take the derivative of the term 3y^4, why do you write y prime as i did? should it not just be written as 12y^3?
devout snowBOT
in implicit differentiation, when you take the derivative of the term 3y^4, why ...
quaint citrus
whatever u did in ur image is correct
meager sequoia
Here's an illustrative example
Because y is a function of x.
Pretend $y$ was $x^3$ for a moment
then let $f(x)=3y(x)^4=3x^{12} $
if I differentiate it wrt y only I get
$f'(x)=12y(x)^3=12x^9$
if I differentiate it including the y' instead it is
$f'(x)=12y(x)^3y'(x)=36x^{11}$
Which is correct? Just check by differentiating $3x^{12}$ to get $36x^{11}$
the issue is that $y$ is a function of $x$ and you're differentiating with respect to $x$
gaunt bay
wouldn’t u have to use the product rule to derive 3(y)x^4
meager sequoia
wouldn’t u have to use the product rule to derive 3(y)x^4
I'm writing 3y(x)
i.e "y of x"
i.e explicitly showing y is a function of x, not multiplying
so you would you chain rule
untold shore
hi, i am currently doing some programming in unreal engine and im having problem with some math. currently i am trying to fill in a circle, im doing this by making circles with desired spacing until i hit the desired radius.
My problem: when generating the circles there seems to be a problem with the angle when placing the segments of the circle. im calculating the needed segments by taking the circumference of the current circle, and dividing it by the desired spacing inbetween each segment. i calculate the angle for the current segment by: 2 * pi * currentSegment / amountOfSegments. then i do this for x: cos(angle) * radius. and for y: sin(angle) * radius. i think the way i am calculating the angles might not be correct, because the only side without an offset is the north side(0,+y). im not sure if this is the correct place to ask this question. but i figure i might be doing something wrong in the math area.
for a better overview of the equations?(idk math very well) im using:
segments = circumference / desired spacing
angle = 2pi * segment / segments
x = cos(angle) * radius
y = sin(angle) * radius
sorry if this is not the correct place to ask this, just let me know and i will close the question, i tried to make it as math related as i could
devout snowBOT
hi, i am currently doing some programming in unreal engine and im having problem...
static ember
show a picture maybe
devout snowBOT
@untold shore Has your question been resolved?
untold shore
if thats what u meant by pictures
the first picture shows the north points of the main circles with their colors being green. the second picture shows that when its checking the south side of the circle, it should be 0,-51000 but its south side has an offset of 125. when from my understanding it should be 0,-radius.
blazing condor
devout snowBOT
blazing condor
Is 3.25 correct if not where did I go wrong
devout snowBOT
@blazing condor Has your question been resolved?
lethal pollen
You're correct
blazing condor
R u sure cause when I verify it, it doesn't seem to work?
lethal pollen
R u sure cause when I verify it, it doesn't seem to work?
How are you verifying it?
@blazing condor
blazing condor
I'm taking the first term and adding 3.25 to each and then checking the sum of the first 14 but I don't get 603.75
lethal pollen
I'm taking the first term and adding 3.25 to each and then checking the sum of t...
So you're doing (22+3.25)*14?
blazing condor
No I'm doing (22+3.25) + (25.25+3.25)... For the first 14 terms
But I don't get 603.75
lethal pollen
I mean it's more like
22+(22+3.25)+(22+2(3.25))...+(22+13(3.25))
As said, the first term is 22
lethal pollen
Yea
blazing condor
Alr thanks can you just tell me about one more question and then I'm done
@lethal pollen
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cosmic herald
I am doing problem e. I understand how to get the variables a, b, c, and e (eccentricity (c/a)), but I don't understand what they mean, so I am unable to interpret them in the setting. So my question is: What do these variables mean in this setting of the moon's orbit?
devout snowBOT
I am doing problem e. I understand how to get the variables a, b, c, and e (ecce...
@cosmic herald Has your question been resolved?
cosmic herald
I saw that once at least 15 minutes were up I can use the <@&286206848099549185> sorry if I am misunderstanding this ping
cosmic herald
.close
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prime narwhal
devout snowBOT
prime narwhal
It's the end of the winter break and I don't remember anything
For 2a Ik I do a/asin = b/bsin = c/csin
But how do I get those values
visual hazel
,rccw
woven radishBOT
visual hazel
internal angles of a triangle sum to 180
prime narwhal
internal angles of a triangle sum to 180
Okay, and the 44mm I already have. How do I know if that is a b or c
is it b
Cuz it's across
visual hazel
yes
prime narwhal
yes
So finding any missing angle or side is the same right,m
Just fill in the info
Then go
visual hazel
So finding any missing angle or side is the same right,m
well depends if you have to use sine rule or cosine rule
unless this exercise is only sine then yes