i dont really understand this line. 'the last place 5 choices 2'
#help-41
dire siren
violet raven
sorry i was being lazy
dire siren
ah okay
wouldnt it be 4 choices to consider only one repeated digit for this scenario.
5 x 1 x 4 for all combinations with 1 repeated digit
then
5x1x1 for all combinations with 2 repeated digits ?
instead of the quoted
astral umbra
would be 5C2 * 2
picking two numbers out of 5
and then two different possibilities of aab and abb
if we choose a and b
$=\frac{5!}{2! \cdot 3!} \cdot 6 = \frac{5\cdot 4}{2} \cdot 6 = 60$
oh wait
its not * 2
dire siren
would be 5C2 * 2
are you saying this as the final answer to the question?
im questioning it because i found a somewhat elegant way....
dire siren
its not * 2
yeah 🙈 what is tthe correction?
grizzled pagodaBOT
dire siren
so * 6
my final answer is still different than 60.
is there a missing case in yours and would you be able to reiterate it using our set or say it differently than aab aba baa ect?
astral umbra
my final answer is still different than 60.
is there a missing case in yours an...
hmm
on e min
ill try going through all possibilities in python
astral umbra
my final answer is still different than 60.
is there a missing case in yours an...
hold on, they said at least one repeating number?
ah
dire siren
hold on, they said *at least* one repeating number?
yes, so we can have 555
astral umbra
i see
i forgot that
i thought exactly one repeating digit
then every combination except non-repeating should be counted
dire siren
adding those triple digits does make our answers the same though
dire siren
would be 5C2 * 2
could you restate why we use 5C2 and then multiplied by 6?
im sort of confused about the choose 2 part
im still new to combinations and using that function
astral umbra
could you restate why we use 5C2 and then multiplied by 6?
actually, theres a simpler method if its at least
there are 5P3 ways to make a number with non-repeating digits
so answer would be 5^3 - 5P3
dire siren
there are 5P3 ways to make a number with non-repeating digits
is it 5C3 or 5P3?
dire siren
so answer would be 5^3 - 5P3
i did this method with 5P3
dire siren
could you restate why we use 5C2 and then multiplied by 6?
the combination function method is the one that confuses me with the multiplier at the end and how that works.
since you decided in your last message to use 5C3 then there would be a different multiplier again to make the numbers add up and thats the part i guess i dont understand what was done
stoic locust
Only after understanding it
astral umbra
10 days later 💀
amber waspBOT
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willow sluice
is there any way to do this without using tan(x/2)
amber waspBOT
is there any way to do this without using tan(x/2)
willow sluice
<@&286206848099549185>
hearty inlet
is there any way to do this without using tan(x/2)
i guess you could try king's rule
$$ \int_a^b f(x) \dd{x} = \int_a^b f(a+b-x) \dd{x} $$
grizzled pagodaBOT
mayer-vietorUs
willow sluice
i guess you could try king's rule
then add the 2 integrals?
hearty inlet
yes sure
amber waspBOT
@willow sluice Has your question been resolved?
amber waspBOT
@willow sluice Has your question been resolved?
velvet falcon
amber waspBOT
velvet falcon
idk how to do this
oh nvm this is out of my level lol
idk how to diff trig functions yet
.close
south ledge
Do you guys know the solution for this?
amber waspBOT
Do you guys know the solution for this?
quick ridge
72
shrewd elm
unless it's a trick question, chemistry after all is (allegedly) a science
south ledge
How did they get it using permutation and combination? Is it simply 3 x 4 x 6?
restive python
How did they get it using permutation and combination? Is it simply 3 x 4 x 6?
yes
naive totem
3x4x6 = 72 iirc
restive python
fundamental counting principle
south ledge
How about in this type of question?
south ledge
I'm not sure. But I found this one, Idk if it's correct tho
vast spade
I'm not sure. But I found this one, Idk if it's correct tho
it is correct
amber waspBOT
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faint ermine
amber waspBOT
faint ermine
ok ok
so
i dont need help
but
i just wanna see if i'm understanding it correctly
so
im going to explain how |-5| = 5
using this
true jackal
Yeah correct
faint ermine
and you guys let me know if im right or wrong
alright?
Ok so basically what i'm thinking is that |-5| is quite literally the same thing as |x| so in other words: -5 is REPRESENTING 'x'.
this means that when x < 0 or in other words, -5 < 0, the result would be -x!
Given that x = -5, -x would be -(-5) which is hence = 5
correct?
spiral zealot
yeh
violet nymph
Can anyone help me with this i choose choice A but the answer is C
violet nymph
We add equal number to all of these so how can the median change?
haughty token
The position of the median in set B is the same as set A
slate heron
Can anyone help me with this i choose choice A but the answer is C
do you remember how to find median and the range?
haughty token
The position of the median in set B is the same as set A
But remember, all values in set B are 56 higher than values in set A at the same position
spiral zealot
We add equal number to all of these so how can the median change?
they mean the values themselves, not the number of times each value appears
amber waspBOT
@violet nymph Has your question been resolved?
cinder grail
amber waspBOT
cinder grail
any idea about 3
amber waspBOT
@cinder grail Has your question been resolved?
iron void
could someone please explain the answer to iii) im not very confident iwth contour integral s
amber waspBOT
@iron void Has your question been resolved?
trail oxide
because the derivative of ln(z)=1/z, the integral of dz/z should just be ln(z) over that contour. our radius r is 1 in this case (because we're going from -i to i, |i|=1), that's why ln(z) here is ln(1)+i*phi=i*phi. lastly, our contour goes from -i to i, so that's a 180 degree/pi rad angle change (for C1) but since we're going in the negative direction it should be -i*pi
@iron void
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civic spindle
amber waspBOT
https://youtu.be/99y7u8PQ5ks
civic spindle
- Is the reason why completing the square works becuase, is the number that solves the polynomial solved while the problem is still in the form of being factored, and it doesnt actually require any operation or squares done unto X?
- though this reasoning would bring the question up of why they wouldnt of just done that without factoring erm but i guess because itd be hard to do it without factoring first
civic spindle
> - Is the reason why completing the square works becuase, is the number that so...
- Or is it simply because by factoring it into the squared form you can easily solve for the zeroes anyway and without it youd have to use normal factoring which may be harder in some situations?
- As it does get very compressed afterwords.
split sail
completing square says there is only one kind of quadratic equation upto translation and scaling
civic spindle
- elaborate in simple terms on the terminology used and their connotations
haughty token
> - Is the reason why completing the square works becuase, is the number that so...
I can't make sense of this
Not sure what the third phrase refers to
civic spindle
Not sure what the third phrase refers to
- It didnt make sense to me how completing the square would work as all operations seemingly would be reduced to near zero anyway by factoring
It also didnt make sense why it would be done due to the fact that the square wouldnt be removed.
That came up as a logical near impossibility as no matter how you reshape the problem the square persists.
the exception is if they didnt remove it but just solved for the answer without completing it and reformed the equation to work without needing it to be completed until you already have an answer.
which by the way
it appears to be mostly the case as they didnt really delete the square as much as they did make the question as easy as possible prior to squaring the possible answers.
haughty token
I'm really struggling to decipher what the question actually is. Could we maybe start with an example quadratic and let's work our way through using completing the square and why we would do that instead of factorizing?
civic spindle
are they not the same thing?
haughty token
They are different ways of expressing the same quadratic expression
civic spindle
They are different ways of expressing the same quadratic expression
Why was it seemingly explained that completing the square seemingly removes the square or gets rid of it so you dont have to deal with it?
Because right now thats looking deceitful in that it actually seems to just move it until the end when your checking the answer list.
haughty token
> Why was it seemingly explained that completing the square seemingly removes th...
Not sure where you heard that but I'd say the good thing is that it keeps ''x" as a single term in the final expression. Thus, we can solve quadratic equations by just carrying our some inverse operations
$x^2 + 6x + 7 = 0$ doesn't have any trivial factors so we would opt for completing the square which gives us:
$(x + 3)^2 - 2 = 0$
$(x + 3)^2 = 2$
$x + 3 = \sqrt{2}, x + 3 = -\sqrt{2}$
$x = \sqrt{2} - 3, -\sqrt{2} - 3$
grizzled pagodaBOT
StrangeQuarkAL
civic spindle
Not sure where you heard that but I'd say the good thing is that it keeps ''x" a...
And for this example is this how theyd determine 3 as the factor?
From what I know the factoring allows for both addition and multiplication so you can use either. (unsure of the limits yet i havent fully processed this mentally)
civic spindle
> From what I know the factoring allows for both addition and multiplication so ...
If anyone reads this can you explain this process more in detail for me?
gusty plaza
Can someone guide me through number 5? I am confused on how to begin this
gusty plaza
I don’t understand how to begin sorry
tired girder
You start by considering the total distance as x
gusty plaza
Yes
tired girder
Distance = velocity × time
or Time = dist./velocity
avg speed = (total distance)/(total time)
So we first need to find out the total time required
gusty plaza
But we don’t the distance or time
tired girder
x/2 distance covered with speed of 40 mph
gusty plaza
Yes
tired girder
But we don’t the distance or time
We don't actually need the distance, you see it will cut out
So what will be the time ?
gusty plaza
How do we know
tired girder
x/80 right ?
tired girder
or Time = dist./velocity
This relation?
tired girder
We don't need to
Just find out everything in terms of x
Assume that you know 'x' the distance as of now
Okk ?
gusty plaza
Yes
tired girder
So first half travelled in time x/80 hr
What time will be cover the second half , if he travelled x/2 distance more with 60 mph speed ?
gusty plaza
So first half travelled in time x/80 hr
Don’t you mean 40
gusty plaza
I mean x/40 mph
tired girder
Are you getting me ?
tired girder
Can someone guide me through number 5? I am confused on how to begin this
"first half of the distance"
tired girder
Yes first half of the distance she drives x/40 mph
Okk
Then what is our total distance?
x+x = 2x
Right ?
gusty plaza
Yes
tired girder
I was considering total distance x , so taking x/2 there
Anyway , this is fine !
So what is total time ?
x/60 + x/40
,calc 1/60+1/40
grizzled pagodaBOT
Result:
0.041666666666667
This
gusty plaza
,calc 1/60+1/40
Why did you use 1
tired girder
Why did you use 1
No just for calculation
We have x
So average speed = 2x/(x/60 + x/40)
Can you cancel out x , here ?
gusty plaza
You cancel out x by removing it from factoring out the x on the denominator?
gusty plaza
Why did you decide to help me even though I gave you a hard time
Thanks though
I understand now
gusty plaza
That is (2×60×40)/100
Over 100?
gusty plaza
Oh ok I see wait let me try
Thank you good person
You are a good person
May god bless you
Because you are a good person
(You are a good person)
You
Tank you
ok bye
.close
amber waspBOT
tired girder
Thankss !!
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gusty plaza
For number 4, the discontinuities are at -2, -1, 0, and 1 right? (Just want to make sure)
gusty plaza
If not can someone help
mint wraith
yes
gusty plaza
Ok thank you Peter griffin
mint wraith
no problem
gusty plaza
wtf I just searched up Peter griffin in the gif thingy
Don’t do that
Ok bye
.close
amber waspBOT
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gusty plaza
Am I making this graph correct? 11.a.
amber waspBOT
Am I making this graph correct? 11.a.
gusty plaza
Function of hours past midnight
How should I write it then
Or indicate that it is a function of hours past midnight
keen topaz
In 24 hours format
gusty plaza
In 24 hours format
Like right all the numbers on the clock?
keen topaz
Like right all the numbers on the clock?
No from 0 - 23
gusty plaza
Oh ok thanks
keen topaz
You should specify what the x and y axes represent
lavish wind
Graph looks fine
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Available help channel!
safe atlas
What is the rule called whereby the integral of 1/(x^p) converge if p > 1 and diverged if p <= 1?
keen topaz
What is the rule called whereby the integral of 1/(x^p) converge if p > 1 and di...
I think that is the integral test for p series
lusty pine
p series maybe?
fossil lintel
errant sluice
im trying to find the inverse fourier transform of $\frac{p}{p^2+a^2}$ where $a$ is a constant with the same units as $p$. More specifically, i must solve
$$\int ^\infty_{-\infty}\frac{p}{p^2+a^2}e^{ipx/\hbar}dp$$
i've tried using the convolution theorem with $g_1=p$ and $g_2=\frac{1}{p^2+a^2}$ but so far no luck.
grizzled pagodaBOT
arizona
amber waspBOT
@errant sluice Has your question been resolved?
amber waspBOT
@errant sluice Has your question been resolved?
pallid canopy
**arizona**
uh have you used partial fractions and residue theorem?
slate cairn
domain in interval notation
amber waspBOT
domain in interval notation
subtle viper
domain in interval notation
how far are you
slate cairn
idk how to solve it bc you cant take square root of the negtiave 4
subtle viper
which negative 4
I see + 4
The domain is the set of all real values (assuming you deal with a real function) for which the function is defined
slate cairn
bc youd solve the equation as x^2>=-4
subtle viper
bc youd solve the equation as x^2>=-4
you want to know when the value inside the root is >= 0
because then that root exists
so let's solve x² + 4 >= 0
x² >= -4
well x² will always be bigger than 0 for any real x
so x² >= 0 >= -4 is always fulfilled
subtle viper
k stepwise, you want to know when the sqrt(x² + 4) exists right?
slate cairn
ik this is the answer but i cant figure out why
subtle viper
ik this is the answer but i cant figure out why
I think you've given us a wrong image before
because that's not the correct answer
the domain is (-inf., inf.)
slate cairn
oh maybe its not the correct asnwer then
subtle viper
I presume your initial function was this instead
with - 4 instead of + 4
because then the domain would be correct
slate cairn
nvm my answer was wrong
subtle viper
k
slate cairn
the domain is (-inf., inf.)
can you explain this?
subtle viper
can you explain this?
well before I explained that for any real x, the root of x² + 4 exists right
since x² + 4 is always bigger than 0
which also means sqrt(x² + 4) > 0 is always true
therefore you can compute the function for any real x
meaning the domain is all real numbers
Domain = R = (-inf., inf.)
slate cairn
well before I explained that for any real x, the root of x² + 4 exists right
i dont understand what this means
is that whenever its a squared x with addition that the domain is all real numbers?
subtle viper
i dont understand what this means
no the domain are all real x for which the function is defined
meaning you're asking for which x is (2x + 1) / sqrt(x² + 4) defined
well it's only undefined if you try to get the sqrt of a negative number or if you divide by 0
and here for any real x, we know that x² + 4 >= 0
therefore we never take the sqrt of a negative number
and we also don't divide by 0, since x² + 4 > 0 implies sqrt(x² + 4) > 0
meaning the function has a value for any real x
meaning the domain are all real x
slate cairn
so you just dont take the sqrt of the negative number that's why its all real x?
i also need help with this i have no idea how to do it
outer abyss
i also need help with this i have no idea how to do it
remember youre gonna have domain issues when you have negative square roots or denominators that are 0
could either of those be the case here
slate cairn
remember youre gonna have domain issues when you have negative square roots or d...
no?
i actually dont know im rlly confused
theres also this one which also has the exponet
amber waspBOT
@slate cairn Has your question been resolved?
keen pawn
So I''m trying to find a. $\varepsilon$ st $|x^2-a^2|<\varepsilon$
grizzled pagodaBOT
Veni, vidi, perii
keen pawn
I'm basically trying to show x^2's limit is a^2
here , I don't get why |x+a| causes the problems
I mean this is $|x-a||x+a|< \varepsilon$
grizzled pagodaBOT
Veni, vidi, perii
keen pawn
Why does |x+a| cause problems here
I'm trying to wrap my head around \varepsilon before I understand \varespilon-\delta
weak zinc
**Veni, vidi, perii**
Well, remember you want a delta such that when you have |x - a| < delta, you get this (which is the tex above it)
grizzled pagodaBOT
Veni, vidi, perii
grizzled pagodaBOT
Veni, vidi, perii
keen pawn
so. $|x|-|a|<|x-a|<\varepsilon$
grizzled pagodaBOT
Veni, vidi, perii
weak zinc
Maybe not "wrong", but, more to the question, does it help 
grizzled pagodaBOT
Veni, vidi, perii
weak zinc
(keep the absolute values in)
grizzled pagodaBOT
Veni, vidi, perii
weak zinc
**Veni, vidi, perii**
Sure, we can try and use that somehow 
any ideas of how that'd help you? 
(the proof of continuity of x^2 is a tiny bit tricky, I shall say!)
keen pawn
I need $|x-a| <\frac{\epsilon}{|x+a|}$
grizzled pagodaBOT
Veni, vidi, perii
keen pawn
so $|x+a|>1$
grizzled pagodaBOT
Veni, vidi, perii
weak zinc
**Veni, vidi, perii**
\catthink Maybe play around with the $\abs{x + a}$ first, and see if you can try and make use of this? Then see what follows from $\abs{x - a}\abs{x + a}$
grizzled pagodaBOT
@weak zinc
keen pawn
$|x|+|a|\geq |x+a|$
weak zinc
(\geq, triangle inequality doesn't rule out equality)
grizzled pagodaBOT
Veni, vidi, perii
keen pawn
so I know that this is more than 1
weak zinc
Potentially, though maybe not...
keen pawn
I know that this is more than $\varepsilon$ for sure
grizzled pagodaBOT
Veni, vidi, perii
weak zinc
More importantly, can you use anything you have found before to then piece together something from $\abs{x + a} \leq \abs{x} + \abs{a}$?
grizzled pagodaBOT
@weak zinc
keen pawn
**Veni, vidi, perii**
Would this be helpful
weak zinc
Would this be helpful
Not that one, no 
keen pawn
**Veni, vidi, perii**
this I think
grizzled pagodaBOT
Veni, vidi, perii
keen pawn
but that doesn'g make much sense to me
weak zinc
Right, let's take what you've just said, which is very useful 
(you shall see in a bit!)
<@&268886789983436800> please 
keen pawn
so $|x-a| < \frac{\varepsilon}{2|a|+1}$
grizzled pagodaBOT
Veni, vidi, perii
weak zinc
That's very close to what we'd like!
To take a few steps back, us restricting $\abs{x - a} < 1$ allowed us to say that $\abs{x + a} < 1 + 2\abs{a}$, and so, we get that $\abs{x - a}\abs{x + a} < (1 + 2\abs{a})\abs{x - a}$
grizzled pagodaBOT
@weak zinc
weak zinc
Can you then make an additional choice on delta which would make that last part less than epsilon?
keen pawn
As I said, I'm trying to understand $\varepsilon$ first
grizzled pagodaBOT
Veni, vidi, perii
keen pawn
Before I wrap by head around the complete limit defn
weak zinc
that's like the distance you want the function output to be within, whenever your function input is within a distance of delta of a (but not necessarily equal to, as per last time)
keen pawn
I see
So I was just lookig at spivak, he says that |x-a|<min(1,\frac{\varepsilon}{2|a|+1}$?
weak zinc
Yep, that's pretty much it, and what we're very close to getting to
weak zinc
**Veni, vidi, perii**
Here, we implicitly chose that $\abs{x - a} < 1$ (also, if $\abs{x - a} < 1$, you can also then argue that
[
\abs{x} = \abs{x - a + a} \leq \abs{x - a} + \abs{a} < 1 + \abs{a}
]
as we found anyway)
grizzled pagodaBOT
@weak zinc
keen pawn
I see
so we obvisously want the minimum of those two
which is what we found
thus the limit is a^2
Awesome!
Though, this is still hard to wrap my head around. Is this normal
weak zinc
<@788085606483361802>
Yep, and of course, at the final part, we wanna somehow get rid of that 1 + 2|a| too and all
weak zinc
Though, this is still hard to wrap my head around. Is this normal
Yes, it does take a while to get used to limits (and it did for me too 
) It'll settle in eventually though!
weak zinc
keen pawn
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cobalt grail
Need help with how I would substitute x and y. 2^x + 3^y = 5, 8^x + 9^x = 18
cobalt grail
<@&286206848099549185>
pastel silo
oo
cobalt grail
2^x
pastel silo
damn
fading prism
damm
zenith spear
I'm guessing this is a system of linear equations?
zenith spear
oh damn I see
cobalt grail
Original equation was 2^x + 3^y = 5, 2^(x+2) + 3^(y+1) = 18
Bro is everyone as stuck as I am 😭
God help me
half rover
Original equation was 2^x + 3^y = 5, 2^(x+2) + 3^(y+1) = 18
if this was the original, how did you get from this to 2^x + 3^y = 5, 8^x + 9^x = 18
cobalt grail
Would 2^(x+2) be 2^x*2^2 ?
half rover
yeah
cobalt grail
But that doesn't simplify to 8^x?
cobalt grail
That was not how I reached that but regardless, how would I simplify
wild vale
you don't really need to simplify
cobalt grail
Right 4, * 2^x
cobalt grail
So 8^x, isnt that incorrect?
half rover
yes that is incorrect
cobalt grail
So they remain seperate
wild vale
you should have $4(2^x)$ yes
grizzled pagodaBOT
annoying
cobalt grail
So it would be 4 * 2^x + 3^y * 3
amber waspBOT
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amber ginkgo
How do I find the slope of table C at the point with the *? Supposedly it's -1.5 but I have no idea how to get there... I've plotted all the points on a graph but don't know what to do afterwards...
split sail
How do I find the slope of table C at the point with the *? Supposedly it's -1.5...
you do
(the largest acceleration value minus the smallest acceleration value) divided by (the largest displacement value minus the smallest displacement value)
in that case the answer will be 1.52
not - tho
amber ginkgo
you do
(the largest acceleration value minus the smallest acceleration value) di...
Yeah I get 1.5 but according to my teacher it's -1.5. I don't understand how he got to that point. He was talking about like predicting a line, like drawing one that only touches the 20,61 point.
split sail
ah i think its because of the direction the line is going to
amber ginkgo
Tangent line, that's what it was
I don't understand how to do a tangent line. To me it seems like everyone will get a different answer because it's a guesstimate?
amber ginkgo
Is it not an inverse line?
split sail
idts
amber ginkgo
So do I have to do a tangent line? If so, how? Do I need to put in another request specifically about a tangent line?
split sail
i dont think you have to do a tangent line
amber ginkgo
Okay that makes things seem easier but I'm still so confused on how my teacher got -1.5. Is the graph just backwards? I need to plot it differently?
split sail
i think so
its either the graph being backwards or your teacher gave you the wrong answer
amber ginkgo
Okay thank you. My teacher should not be teaching
amber ginkgo
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spark iris
amber waspBOT
spark iris
i dont think we are supposed to help with tests
post test*
split sail
oh
spark iris
i took screenshots
if u want i can show u my time rn
cause that shows 8:21
am
its 4pm now
split sail
its ok
spark iris
i got the answer through guessing but i was wondering if there was a way using algebra or smt?
split sail
So, p(RED) = red/total.
spark iris
yeah
split sail
When you add two marbles, one red and 1 blue p(red) = 7/9.
x should be 21 ish.
Let the initial fraction in algebraic form be
$\frac{x}{n}$ then after adding 1red and 1 blue marble, $\frac{x+1}{n+2}$
You can then find the multiple in which initial n is 2 less than the final n.
grizzled pagodaBOT
Sukiyaki
split sail
if that makes sense.
say your initial n (total number of marbles) in lowest multiple is 5, for the final number of marbles, you can just do some multiplication to find n+2.
spark iris
wdym by You can then find the multiple in which initial n is 2 less than the final n.?
split sail
Lets say you have 10 apples at the end. How many apples would you have at the start if i gave you 2 apples?
10-2
In the case of your probability question, it would be n-2
\begin{bmatrix}
Initial number of marbles&final number of marbles,
\5&5+2
\10&10+2
\15& 15+2
\20&20+2
\25&25+2
\end{bmatrix}
grizzled pagodaBOT
Sukiyaki
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
split sail
Well you just have to find the lowest multiple + 2 of it. If that makes sense, however im sure there was a simpler method compared to mine 😢
spark iris
Well you just have to find the lowest multiple + 2 of it. If that makes sense, h...
so you like guess until you find one that matches 7/9?
using like n+2
spark iris
i dont rlly understand what u did here tho
lusty pine
say there are y blue marbles in the bag
how do you find the probability that you pick a red marble from rhe bag
spark iris
say there are y blue marbles in the bag
how do you find the probability that you...
x/x+y
spark iris
(x+1)/(x+y+2)?
grizzled pagodaBOT
Skill_Issue
lusty pine
cross multiply, expand, profit 🤑
spark iris
so -x+4y=0 and 2x-7y=5
spark iris
ohh thats what its called in english
yeah
spark iris
so y=5 and x=20?
lusty pine
idk i havent calculated it but probably
it should be, if you want to be sure just plug it back in and see weather it works or not
spark iris
it should be, if you want to be sure just plug it back in and see weather it wor...
y could be substitued for x/4 right?
lusty pine
yea
spark iris
wait but for x/x+y why is it that if y=x/4 that all real solutions are possible but if you substitute it in the second equation you get x=20?
lusty pine
wait but for x/x+y why is it that if y=x/4 that all real solutions are possible ...
wdym
you have 2 unknowns and a single equation, you cant find the unknowns
spark iris
wdym
like x/(x+0.25x)=4/5 x can be any but (x+1)/(x+0.25x+2)=7/9 x would be 20 for that
lusty pine
like x/(x+0.25x)=4/5 x can be any but (x+1)/(x+0.25x+2)=7/9 x would be 20 for th...
well you subtituted y=x/4, thats the first equation already
for the first one, subtituting y=x/4 doesent give anything new
spark iris
well you subtituted y=x/4, thats the first equation already
but we didnt use both equations we only used the second one
spark iris
for the first one, subtituting y=x/4 doesent give anything new
wouldnt they both not give anything new?
lusty pine
but we didnt use both equations we only used the second one
where did you get y=x/4? you got it from the first equation
lusty pine
wouldnt they both not give anything new?
no, first wont, but second would since you got the fact that y=x/4
my best guess to answer what you asked is to try to think of it graphically
lusty pine
my best guess to answer what you asked is to try to think of it graphically
y=x/4 has the same graph as the first equation, so it has infinite solutions and wont help
but y=x/4 has a diffrent graph with a diffrent slope, so there is an intersection point between then, or whats called as a solution (here its 5,20)
spark iris
y=x/4 has the same graph as the first equation, so it has infinite solutions and...
arent they both y=x/4?
lusty pine
arent they both y=x/4?
what? no?
spark iris
y=x/4 has the same graph as the first equation, so it has infinite solutions and...
whats the difference between these?
lusty pine
notice how red and orange has the same graph
subtituting red into orange wont give anything, as they are both already the same
its like trying to subtitute y=x into the graph y=x, like it wont give anything new
amber waspBOT
@spark iris Has your question been resolved?
amber waspBOT
amber waspBOT
Available help channel!
woven sundial
Wrote down all information found the ratios, similarities and stuff but still can't figure out the solution on all questions
amber waspBOT
Wrote down all information found the ratios, similarities and stuff but still ca...
@woven sundial Has your question been resolved?
woven sundial
<@&286206848099549185>
amber waspBOT
amber waspBOT
Available help channel!
deft frost
amber waspBOT
deft frost
Im having trouble in understanding where to put the integration constant
In my book they put the c inside the natural log
But I put c on the other side of the equation
Even if I integrated 1/x dx, I would've done it like ln(x)+c instead of ln(cx)
<@&286206848099549185>
knotty reef
Even if I integrated 1/x dx, I would've done it like ln(x)+c instead of ln(cx)
ln(cx) = ln(x) + ln(c) = ln(x) +k
lavish wind
I can tell you that they used the property of logarithms ln(A) + ln(B) = ln(AB)
they wrote the constant as ln(C) instead of just C
it really doesn't make any difference, as it's still an arbitrary constant
but now they have the added benefit of confusing the student.
amber waspBOT
@deft frost Has your question been resolved?
deft frost
but now they have the added benefit of confusing the student.
Hol up
So both answers are correct
Huh
amber waspBOT
@deft frost Has your question been resolved?
deft frost
On which side do I add the constant of integration?
amber waspBOT
On which side do I add the constant of integration?
deft frost
Im always confused if i should add it to the LHS or the RHS
talking about differential equations btw
deft frost
i meant differential equations
cunning birch
both sides work
.
deft frost
both sides work
but sign is opposite in the two cases
cunning birch
if you do + C on one side
then it's the same as doing -C on the other
in any case the C constant is an unknown real number
like here's an example
deft frost
ok if i shift the C to the other side then should i make it -C or let it remain +C
cunning birch
suppose f'(x) = 1, f(0) = 0
really easy example
then by integrating you can either have :
deft frost
yea f(x)=x+c
cunning birch
f(x) + C = x
deft frost
tf
cunning birch
or f(x) = x + C
deft frost
yea
cunning birch
f(x) + C = x
here you would get C = 0
deft frost
wdym
cunning birch
it doesn't matter
cunning birch
"f(0) = 0 "
deft frost
yea thats right
cunning birch
and even if I didn't have an initial value, so what
deft frost
ok if i shift the C to the other side then should i make it -C or let it remain ...
what abt this tho
cunning birch
"there exists a constant C such that f(x) + C = x"
cunning birch
what abt this tho
you can do whatever
create a new constant K = -C or whatever
and you get f(x) = x + K
in the end you can always get back on your feet
amber waspBOT
amber waspBOT
Available help channel!
primal snow
heya! i have a quick question to you all.
$4S^3 + 84S^2 + 80S = 0$
primal snow
i can simply divide with S here, cant i?
to get to a quadratic formula
i have to solve this for S
$4S^2 + 84S + 80 = 0$
so this is what we end up with
earnest sinew
i can simply divide with S here, cant i?
Almost yes
Don't divide by it
I don't know how to say it in English
But if you take S as a common factor
earnest sinew
Yess
rancid raven
And power is 3 there should be 3 solution or root
primal snow
this is not the question guys
we are not allowed to solve the equation in this form
and i am asking if i am allowed to divide with S here legally to get to this equation:
no matter what, i need to get to a quadratic formula
rancid raven
No
primal snow
$S * (4S^2 + 84S + 80)$
grizzled pagodaBOT
sla-ppy
primal snow
this is what i have to do
amber waspBOT
amber waspBOT
Available help channel!
tawdry vigil
amber waspBOT
tawdry vigil
Im having trouble with this question
Should I use a logarithmic function to solve the question?
Would that work?
shy hazel
Would that work?
Yeah
tawdry vigil
Ok can I write it out and you tell me if it's correct
shy hazel
Yea
tawdry vigil
Ok thank you so much
shy hazel
np
amber waspBOT
@tawdry vigil Has your question been resolved?
hard flare
how tf is the answer 0.04??
amber waspBOT
how tf is the answer 0.04??
hard flare
the cube has lengths 20cm btw
amber waspBOT
@hard flare Has your question been resolved?
hard flare
<@&286206848099549185>
mortal dust
shouldn't it reflect the initial displacement of 8 cm downwards? So it should be like -.08 not .04
hard flare
its the y coordinate of the top face not the bottom face
so it starts at y=0.2 then when it gets pushed down by 8 cm shouldnt y(0) be 0.12??
<@&286206848099549185>
hard flare
.close
nova acorn
guys whats (4/3)^8?
amber waspBOT
guys whats (4/3)^8?
split sail
idk
vernal bobcat
,calc (4/3)^8
grizzled pagodaBOT
Result:
9.9887212315196
@nova acorn Has your question been resolved?
nova acorn
,calc (4/3)^8
in fraction tho
vernal bobcat
,w convert (4/3)^8 to fraction
grizzled pagodaBOT
nova acorn
got the right result thanks
nova acorn
,w convert (4/3)^8 to fraction
then multiplied by ½ it is?...
amber waspBOT
@nova acorn Has your question been resolved?
pseudo sail
need help 
amber waspBOT
need help <:blobsweat:584506239661113371>
pseudo sail
when i apply chain rule it keep giving me same result
and when i use integral calculator
mossy meteor
need help <:blobsweat:584506239661113371>
there is a direct result for this problem you can remember that or use by parts
pseudo sail
pseudo sail
yeahh im feeling that pain right now
pseudo sail
do you know where did it come from
mossy meteor
integral(e^ax(cosbx))=((e^ax(sinbx+cosbx))/
(a^2+b^2)
pseudo sail
Do you know integration by parts?
isnt that chain rule
pseudo sail
integral(e^ax(cosbx))=((e^ax(sinbx+cosbx))/
(a^2+b^2)
what if its e^xsin(x)
mossy meteor
another formula there
pseudo sail
does this formula still work
mossy meteor
sinbx-cosbx
maiden kernel
isnt that chain rule
Chain rule is in derivatives
maiden kernel
integral(e^ax(cosbx))=((e^ax(sinbx+cosbx))/
(a^2+b^2)
Isnt integrating by parts possible?
mossy meteor
better to remember and solve fast
pseudo sail
isnt it reverse from chain rule kinda thing
mossy meteor
you apply by parts and you will get the integral again in the expression take that as I
maiden kernel
∫udv=uv- ∫vdu
You can use this if you want to solve it without memorizing
Or do like @mossy meteor said
And memorize that
mossy meteor
better to derive it first
split sail
need help <:blobsweat:584506239661113371>
are you any familiar with complex numbers
pseudo sail
i would rather memorize it
mossy meteor
yes you can use complex number
pseudo sail
the faster the better
mossy meteor
euler formula
many more results are there which you should remember
makes life easy
sterile nymph
If you're familiar with Euler's formula, you can rewrite as Re{e^((1+i)x)} which is easier to integrate
sterile nymph
Oh, haha other people swooped me
mossy meteor
remember this also e^x(f(x)+f'(x))=e^xf(x)
split sail
you swooped me
pseudo sail
okay thanks guys. You are saving my ass from this loop thingey
mossy meteor
e^f(x)(f'(x)g(x)+g'(x))=e^xf(x)g(x)
split sail
okay thanks guys. You are saving my ass from this loop thingey
memorise all standard integrals
you will need them anyway
mossy meteor
if you remeber the 3 formulas i told by parts question become easy
split sail
school college whatever it is
maiden kernel
okay thanks guys. You are saving my ass from this loop thingey
Np i found it funny when i first tried the normal method and was stuck in a loop 😂
pseudo sail
.close
amber waspBOT
amber waspBOT
Available help channel!
dire stirrup
Is this a geometric or an arithmetic sequence
amber waspBOT
Is this a geometric or an arithmetic sequence
knotty reef
Is this a geometric or an arithmetic sequence
Both
It's a agp
dire stirrup
Both
It's a agp
Agp?
knotty reef
Both it's both?
I mean the Denominator is surely in gp for the Numerator well 15 is 3×5
And 45 is 3×15
5 = 3^0 ×5
pseudo crescent
this looks like neither
knotty reef
this looks like neither
The series excluding 3
Is 5 × 3^n-1/2^n
proven vapor
yeah it doesn't look like anything
proven vapor
The series excluding 3
Is 5 × 3^n-1/2^n
n=2 also doesn't satisfy your claim
proven vapor
Chat gpt says it might me neither
!nogpt
amber waspBOT
Chat gpt says it might me neither
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
pseudo crescent
The series excluding 3
Is 5 × 3^n-1/2^n
- this falls under neither
proven vapor
no it would be a GP if that were actually the case
dire stirrup
I'll just put neither
pseudo crescent
no it would be a GP if that were actually the case
you sure?
dire stirrup
Thanks for the help y'all
ivory pivot
Chat gpt says it might me neither
you can use chatgpt for inspiration but you should check all of your work
knotty reef
n=2 also doesn't satisfy your claim
15/4
pseudo crescent
oh... i see
knotty reef
5 * 3^(n-1) / 2^n, they didn't write the brackets
mb bro
amber waspBOT
neat wind
here you go
pallid canopy
help channels are for math questions
pallid canopy
.close
cinder grail
?
spare belfry
Bet, hard af
Sure, I’m curious
Are you having problems with combining them?
Let’s look at a) first
Imagine you have an Apple, and I gave you another.
How many apples do you have?
<@&268886789983436800>
gloomy tide
<@&268886789983436800>
hi I can't tell why you pang
sudden pendant
Have you read discord TOS?
sharp isle
isn't number 1 2a + 2b?
gloomy tide
yeah sorry we can't have you here, come back when you meet the terms of discord
.close
split sail
hi i havent done any work i just wanna know how to do the square root stuff faster
tawny herald
you're trying to find the value of $\left(\sqrt{19}\right)^2$?
grizzled pagodaBOT
PajamaMamaLlama
split sail
you're trying to find the value of $\left(\sqrt{19}\right)^2$?
yea sure
C and D
idk if my teacher would consider C done well enough
i've done D already actually
i just need to redo C
tawny herald
my friend, you don't need to do all that work, by definition the square and square root cancel out :)
tawny herald
THERES A ^2
split sail
ok lets see if i can do the next one on my own
tawny herald
also, this is just a little tip, when you're doing something like B it might be easier just to say that $\sqrt{100}-\sqrt{36}=10-6=4$, you don't need the x and y business :)
grizzled pagodaBOT
PajamaMamaLlama
split sail
also, this is just a little tip, when you're doing something like B it might be ...
teacher doesnt accept direct answers
i know its easier and correct
but i literally got points deducted for saying stuff like 4^4=16
actually let me check
tawny herald
oh, well then yes, listen to whatever your teacher wants
tawny herald
but i literally got points deducted for saying stuff like 4^4=16
well yeah cause that's not true
split sail
well yeah cause that's not true <:helper_laugh:777136834554888194>
but you get the point
tawny herald
but you get the point
yeah no worries, just listen to your prof/teacher
they're the one giving you the grade at the end of the day... no matter how weird the method may be nonetheless
split sail
ok i get to use a calculator for this next one
ill check if theres anything like 8.4 elsewhere
okay i get to use the calculator for all of the next ones you can close this thread
wait this one is confusing asf
The grandmother, who is fond of mathematics, told the following about her and her father's birth years on an online forum: Grandmother's father was born in a year whose square root is a whole number. Grandma, on the other hand, turns 60 in a year whose square root is also a whole number. In what years were grandmother and her father born?
nvm done
close the thread
hexed loom
I wanted to solve this inequality in terms of y
amber waspBOT
I wanted to solve this inequality in terms of y
true jackal
This is correct as long as -x² + 1 is non negative
Btw I think you wanted to write
**-**sqrt(-x^2+1) < y < sqrt(-x^2+1)
split sail
@lusty turret
split sail
:V
you asked for sin(alpha_1) and sin(alpha_2) not alpha_1 and alpha_2
so idk what you're using chatgpt/WA to do
obviously solving for those angles explicitly is obscure
(1)^2 + (2)^2 gives you
$G_2^2 = G_1^2 + G_3^2 - 2G_1 G_3 \sin( \alpha_1)$
grizzled pagodaBOT
!Kiz__
split sail
it's trivial to solve for sin(alpha_1)
and we also had an expression for sin(alpha_2) which u continuously ignored
anyway that's that 
knotty reef
Dam bro used chat gpt
knotty reef
Dam bro used chat gpt <:sully:651816820122189834>
chat gpt 4*
split sail
anyway they probably gave up
knotty reef
<:KEK:586240877358350341> anyway they probably gave up
Gave up on what?
split sail
on the question
knotty reef
on the question
Ohh the one i gave him
Hmm it wasnt that diff rcom ×mvcom = 0 since rcom is in the direction of mcom so angular mom = (Icom)w
knotty reef
Ohh the one i gave him
Hmm it wasnt that diff rcom ×mvcom = 0 since rcom is in ...
Btw mom stands for momentum if u were thinking smthng else
split sail
Ohh the one i gave him
Hmm it wasnt that diff rcom ×mvcom = 0 since rcom is in ...
he's doing his own problem lol
lusty turret
<:breadpensive:556701306169982977> why use chat gpt bro when u can use discord c...
I was using wolframalpha, chat gpt is not good with math
split sail
or was
yeah well u gave it a totally tangential problem to what u had to do
not sure what you were expecting
knotty reef
I was using wolframalpha, chat gpt is not good with math
Tru it's terrible tbh
knotty reef
not sure what you were expecting
He was expecting answers 
lusty turret
not sure what you were expecting
This is exactly why I said before it's so complicated
split sail
it's not complicated
lusty turret
split sail
**!Kiz\_\_**
how is this complicated?
yeah cuz you're solving for x??????
u said you want sin(alpha_1) and sin(alpha_2)
your own solution is only solving for sin(alpha_1) and sin(alpha_2)
knotty reef
This is exactly why I said before it's so complicated
Before , it's so complicated
U missed a comma
split sail
barring the sign disparity 💀 it's almost the same thing
anyway
i can't help ignorance
lusty turret
I just don't understand how it does
knotty reef
i can't help ignorance
Huh? Arnt we helping xylon
lusty turret
Honestly expected to go to Uni not doing math
Yet here I am. Ironically having more issues with this than the others
split sail
Huh? Arnt we helping xylon
ironically there's not much math involved
it's basic trig and that's all of mechanics
in terms of math
knotty reef
Honestly expected to go to Uni **not doing math**
Dam
Why do u not like math it's such a beautiful subject
Btw this is uni physics?
knotty reef
it's basic trig and that's all of mechanics
Wait mechanics comes in uni 
knotty reef
yuhh issa thing for engineers
We are taught this in high school 
I still remember those frightening rotation days (it was 3 days ago)
split sail
i guess u learn it in both places
high school and then you learn more physical applications of it in uni
trusses, etc.
knotty reef
i guess u learn it in both places
Both I'm still in high school
split sail
only xylon can confirm for us
knotty reef
high school and then you learn more physical applications of it in uni
dam I would probably take maths and computing
split sail
knotty reef
knotty reef
Yet here I am. Ironically having more issues with this than the others
If u fear math
Then study olympiad math it will help u understand math more and it's interesting
lusty turret
If u fear math
Then study olympiad math it will help u understand math more and...
I just have gaps in math sadly
Like with pythagoras, since I always get confused with the kathete
I also developed a fear after failing my math exam after studying for 10 hours daily for 2 weeks
But sorry, that I was unable to really understand how to solve it
The only thing I can repay is my appreciation for help 
❤️
knotty reef
I just have gaps in math sadly
Study from the start
knotty reef
I also developed a fear after failing my math exam after studying for 10 hours d...
I mean u gain nothing after doing that u actually lose ur interest in the subject if u start to fear u will just think that u cant do any questions involving math even if u can u
If u are studying physics u won't be able to pass without math as physics is nothing but a application of math it involves math every where
Further when u study center of mass moment of inertia all of them will involve solving integrals and further more in waves there will the general wave eq a second order diff eq
And in heat there is lapace eq a partial diff eq
without maths physics isn't possible
So spend time on it even if a little
lusty turret
I can see what I can do