nobody knows because you don't know what a represents
#help-33
main idol
knotty trellis
If there is some more context to it (maybe at the beginning of the page?), send it all
lime rampart
I'd prefer you to share your thoughts and then we'll see why you say each answer is what you say it is.
static quarry
the other three questions are so vaguely worded that they raise more questions than they ask
normal fog
hybrid gull
small berry
What have you tried so far?
marsh citrusBOT
@normal fog Has your question been resolved?
smoky fractal
Hi guys... Anyone mind helping me out?
marsh citrusBOT
Hi guys... Anyone mind helping me out?
wary lichen
!da2a
marsh citrusBOT
Asking the actual question right away is more likely to get responses.
Asking "Can I ask...?" or "Does anyone know about...?" doesn't give people enough information to decide whether they can help, and answering can feel like a promise to help with the actual question, which they might find themselves unable to.
wary lichen
Okay, remember that acceleration, velocity and position are all the antiderivative of the previous.
smoky fractal
Yeah
cunning fiber
Can anyone help me out here please?
wary lichen
As such, a moment of instantaneous rest is just when velocity equals 0.
Now we know that the acceleration is
a(t) = 36 - 6t
v(t) ?
What about velocity
<@&268886789983436800>
thanks
@smoky fractal
marsh citrusBOT
@smoky fractal Has your question been resolved?
elfin badger
marsh citrusBOT
elfin badger
Hi shouldn't the bit in yellow be -3y/x
cunning fiber
Hi shouldn't the bit in yellow be -3y/x
no
the integrating factor is $e^{\int p(x) \dd{x}}$, not $e^{\int p(x)y \dd{x}}$
elfin berryBOT
Civil Service Pigeon
cunning fiber
this should be clear if you consider how the integrating factor helps you force a form related to the product rule
a y in the exponent would mess with this
[note that p(x) is the "coefficient" of y in a sense]
marsh citrusBOT
@elfin badger Has your question been resolved?
cedar badger
can someone help me understand this problem?
marsh citrusBOT
can someone help me understand this problem?
cedar badger
Im confused on how to find the value for c
vast falcon
C is the rightward shift
void dawn
C represents the horizontal shifts
in the parent function: f(x) = cosx , its peak is on the y axis
what do you see in this graph?
uh lmk if im wrong or smth lmao this is my kinda first time helping
vast falcon
To find $C$, look at the x-coordinate of any maximum point on the graph. In a $y = \cos(x)$ function, the peak is normally at $x=0$. If the peak has moved, that movement is your $C$.
elfin berryBOT
Ajay
vast falcon
uh lmk if im wrong or smth lmao this is my kinda first time helping
What you've said is correct
cedar badger
To find $C$, look at the x-coordinate of any maximum point on the graph. In a $y...
so like the peak would be at the values 0 and 2pi?
vast falcon
Not quite—if the peaks were at 0 and 2pi, then C would be 0
take a look at the grid lines between 0 and pi/2
cedar badger
i meant at the x-cordinate of 0 and 2pi
vast falcon
still no
cedar badger
oh
vast falcon
Notice the peak (the highest point) isn't sitting on the vertical y-axis
It's shifted slightly to the right.
There are two grid squares between 0 and pi/2. The peak is sitting exactly on that first grid line, which represents x = pi/4
If the peak was at x=0, then C would be 0. If the peak was at x=pi, then C would be pi. Since this peak is a little bit to the right of zero, we have to use that specific fraction.
cedar badger
.close
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strong dagger
im not seeing how 3 couldnt hold given 1 and 2 hold could someone give me some hints
marsh citrusBOT
im not seeing how 3 couldnt hold given 1 and 2 hold could someone give me some h...
static quarry
ah wait sorry i misread, let me rethink
strong dagger
oh hm
is this something that breaks only in 3 dimensions and higher
cuz you know how you can have different limits depending on which curve you approach the point at
maybe not idk
wait no what I said doesnt make sense
the limit wouldnt even exist in the first place
regal coral
i posted the answer but i saw you asked for hints only so i removed it
wet holly
||I think choose f(x) contradicting hypothesis 2 in here?:https://proofwiki.org/wiki/Limit_of_Composite_Function||
strong dagger
i posted the answer but i saw you asked for hints only so i removed it
ye I saw lol
regal coral
whoops
wet holly
Eh I'll leave it as a spoiler just in case
Well the page straight up has a counterexample but if you just read where the proof does work and try to come up with the counterexample yourself then my spoilered answer could count as a hint
regal coral
ok for a hint, make f(x) constant
static quarry
ok for a hint, make f(x) constant
won't g(f(x)) be constant if you do that?
regal coral
yes
regal coral
||I think choose f(x) contradicting hypothesis 2 in here?:https://proofwiki.org/...
|| yeah, in fact, you have to have to contradict both hypotheses ||
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shut lark
marsh citrusBOT
shut lark
I got 30, i don't know the answer but i'm fairly sure it's correct? just that I have no clue how i'm meant to solve questions like it
cobalt sedge
just find the rate at which they do the work
shut lark
10A + 42B = 48B
A = 6/10 B
(Trial and error)
A 6/10 * 30 = 18 Work units
B*30 = 30 Work units
which is 48 so idk
shut lark
just find the rate at which they do the work
like how
cobalt sedge
yk B needs 48 days to finish
shut lark
yeah
cobalt sedge
so if A did 10 days of work and B needed 42 more days to finish, that means A works 6/10 times as fast as B
shut lark
yesyesyes
cobalt sedge
or A needs 80 days to do the whole job
cobalt sedge
48 * (10/6)
cobalt sedge
A works 6/10 times slower, so A needs 10/6 times more time
shut lark
right
cobalt sedge
Aight, so you have B being able to finish in 48 days and A in 80 if they work individually
shut lark
Aight, so you have B being able to finish in 48 days and A in 80 if they work in...
right
cobalt sedge
so, in 1 day, B does 1/48 of the total task, and A does 1/80th of the task
shut lark
yes
cobalt sedge
or together, they are able to finish 1/48 + 1/80 of the work
shut lark
yes
cobalt sedge
which is 1/30
shut lark
how did you do that so quick
neat grove
for part b
marsh citrusBOT
for part b
neat grove
i thought of using like
the formula i wrote on the write to find all the values of q
but there shld be a quicker way no?
marsh citrusBOT
@neat grove Has your question been resolved?
thin dock
$\dfrac{d}{dz} e^{y'''} = \sin(y') x^5 \ln(z), z = y'',$ find $y=y(x,z)$
elfin berryBOT
しもた
marsh citrusBOT
@thin dock Has your question been resolved?
marsh citrusBOT
thin dock
.reopen
marsh citrusBOT
✅ Original question: #help-33 message
stoic saddle
where did you get this question from
thin dock
where did you get this question from
my own exercise
i wonder what are the methods would people use with this PDE
marsh citrusBOT
@thin dock Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
✅ Original question: #help-33 message
@thin dock Has your question been resolved?
marsh citrusBOT
@thin dock Has your question been resolved?
faint breach
If A-G=1/2 and G-H=2/5
A is arithmetic mean
G is geometric mean
And H is harmonic mean
faint breach
Then find values of those two numbers
stoic saddle
what two numbers
vernal forge
Then find values of those two numbers
of the numbers of which we are taking the means?
$$
\begin{cases}
\frac{a+b}{2}-\sqrt{ab} = \frac{1}{2}\
\sqrt{ab}-\frac{2}{\frac{1}{a}+\frac{1}{b}}= \frac{2}{5}\
\end{cases}
$$
elfin berryBOT
artemetra
vernal forge
this is equivalent to
$$
\begin{cases}
\frac{a+b}{2}-\sqrt{ab} = \frac{1}{2}\
\sqrt{ab}-\frac{2ab}{b+a}= \frac{2}{5}\
\end{cases}
$$
elfin berryBOT
artemetra
vernal forge
note that you know b+a and ab as 2*A and G^2
$$
\begin{cases}
A-G = \frac{1}{2}\
G-\frac{G^2}{A}= \frac{2}{5}\
\end{cases}
$$
faint breach
Yes
elfin berryBOT
artemetra
marsh citrusBOT
Then find values of those two numbers
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
faint breach
$$
\begin{cases}
A-G = \frac{1}{2}\\
G-\frac{G^2}{A}= \frac{2}{5}\\
\end{cases}
...
From here
vernal forge
ok well solve it in terms of A and G
vernal forge
then solve for a and b
still temple
two variables and two equation are solvable
still temple
what happened here?
still temple
nah, where did a come form
what happened after upper step
,, \frac{G}{2G+1} = \frac{2}{5}
elfin berryBOT
firestepper
still temple
this is what it turns to
marsh citrusBOT
still temple
Same for b
right
marsh citrusBOT
Available help channel!
buoyant jetty
marsh citrusBOT
elfin berryBOT
Renato
spark otter
what have you tried
spark otter
even + odd = odd
yes, either even + odd = odd or odd + even = odd
buoyant jetty
yes, either even + odd = odd or odd + even = odd
help
buoyant jetty
thats my progress
spark otter
I mean you have to choose such a function, so why not start by choosing what f(1) and f(2) must be
you saw that exactly one of them must be even, the other will be odd
buoyant jetty
5 x 4 x ?
spark otter
why 5?
spark otter
n <= 8
spark otter
close but not exactly
buoyant jetty
?
spark otter
right now you chose the value of the odd number and the value of the even number
but we still don't know which of f(1) or f(2) is odd
spark otter
ok... say you choose odd = 3
and even = 6
does that mean you chose f(1) = 3, f(2) = 6
or f(1) = 6, f(2) = 3?
buoyant jetty
2 x 4 x 4 x ?
spark otter
now we're good
so now we assigned values to f(1) and f(2)
we can either start by choosing f(3), f(4), f(5)
or choosing f(6), f(7), f(8)
one is slightly easier
buoyant jetty
f6 f7 f8 is easier
spark otter
mmh, how many ways to assign them values?
buoyant jetty
is not easy
spark otter
how many choices for f(6)?
buoyant jetty
6
buoyant jetty
5
buoyant jetty
4
spark otter
ok
so now, we're left with 3 unassigned values
that we need to assign to f(3), f(4), f(5)
buoyant jetty
hard
spark otter
really?
buoyant jetty
2 x 4 x 4 x 6 x 5 x 4 x ?
spark otter
2 x 4 x 4 x 6 x 5 x 4 x ?
for now yes
spark otter
that we need to assign to f(3), f(4), f(5)
but this really isn't hard
say we're left with 2,5,7
do we really have a lot of choices for f(3), f(4), f(5)?
buoyant jetty
im not following
spark otter
remember that f is bijective
buoyant jetty
do we really have a lot of choices for f(3), f(4), f(5)?
just one way of placing each
spark otter
and that we need f(3) <= f(4) <= f(5)
spark otter
just one way of placing each
yeah
if we're left with 2,5,7
we have no choice but f(3) = 2, f(4) = 5, f(5) = 7
and same thing for any other triple left
spark otter
how so
elfin berryBOT
Result:
3840
Where would the overcounting happen
buoyant jetty
the ordering
spark otter
which one?
f(1) .... f(8) are all distinguishable
so it's normal for there to be ordering
buoyant jetty
ok
buoyant jetty
and same thing for any other triple left
hardest shit I have done in a while
counting is hard
noticing it was injective as well was key
I appreciate it
ty for the help
.close
marsh citrusBOT
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echo scaffold
Can I have some help on 23,37,38. For 23 I just don’t know what to do next and for 37 and 38 I don’t know how to find the domain and range
marsh citrusBOT
Can I have some help on 23,37,38. For 23 I just don’t know what to do next and f...
twin cloud
Can I have some help on 23,37,38. For 23 I just don’t know what to do next and f...
can you write cos(x) in terms of sin(x)
echo scaffold
can you write cos(x) in terms of sin(x)
I don’t know how
Like I could do a transformation but I don’t think that works for this question
echo scaffold
Is it the square root of 3
twin cloud
close
its (square root of 3)/2
echo scaffold
Ohhh yea cus we need to include the radius
stoic saddle
close
its (square root of 3)/2
sqrt(3)/2
twin cloud
ye
echo scaffold
Ok for this one I feel like I am doing it wrong and I also do not know what is half of pi/3
twin cloud
Ok for this one I feel like I am doing it wrong and I also do not know what is h...
where is pi/3
still temple
,rccw
elfin berryBOT
twin cloud
half of 3pi/2 is just 3pi/4
twin cloud
Ok for this one I feel like I am doing it wrong and I also do not know what is h...
swap the range and domain as it's its inverse
echo scaffold
Oh yea besides that is it correct
twin cloud
wait
echo scaffold
I think I did it in a weird way I took domains and ranges from the inverse and transformed those
twin cloud
are you sure its 3π/2 αηd not π/2
twin cloud
no worries
echo scaffold
Are these correct now?
still temple
Are these correct now?
again domain and range swap inverse trigonometric functions give output as an angle
still temple
Are these correct now?
als in 38 how does horizontal shrink make [-1,1] -> [-1.5,1.5] you multiply -1, 1 by 1/2 -> [-0.5,0.5]
and where does 4.5pi come from 
i think you confused into where to apply factors
?
marsh citrusBOT
@echo scaffold Has your question been resolved?
austere knot
I'm working on this problem, but I don't know what to do next. I have to get rid of the 2pi/150 somehow... but how? What's the easiest way of doing so?
marsh citrusBOT
I'm working on this problem, but I don't know what to do next. I have to get rid...
gloomy merlin
I'm working on this problem, but I don't know what to do next. I have to get rid...
Use arccos
river solar
noble geyser
Wth happened
noble geyser
That is clearly not true
river solar
Wdym
dim forge
Arc cos 3/5 is not 53 degrees it is nearly 53 degrees
noble geyser
Its not even in degrees
river solar
Back in hs
noble geyser
Its in radians
river solar
Gng I forgot a dot
austere knot
I got 53 as my answer, too (the problem says to round to the nearest whole second).
dim forge
Not ug math yk
I was just taking a piss
river solar
Just convert it?
austere knot
dim forge
river solar
Oh no I was saying it to the guy who said I did not write in degree
noble geyser
I got 53 as my answer, too (the problem says to round to the nearest whole secon...
Thats not good it should be in radians
"Here, t is entered in radians"
austere knot
Thats not good it should be in radians
arccos(-3/5) in radians is approximately 2.214...
noble geyser
arccos(-3/5) in radians is approximately 2.214...
That is true
Now multiply by $150/2\pi$
elfin berryBOT
Roy
noble geyser
Yes
But dont forget, the 2.2 value you got for arccos is not the first time
It also shouldnt be right
austere knot
Huh, that's strange. I'll close this, but thanks for the help!
noble geyser
K
austere knot
.close
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zealous halo
Proof for :-
If X :=(xn) is a bounded sequence of real numbers , then every subsequence of X is bounded.
Proof :
Since X is bounded , there exists M>0 , such that |xn| ≤M for all n ∈N .
Suppose there exists a subsequence X":=(x_k) of X , such that (x_m)>M for some m ∈S.
where S is the set of all indices of sequence (x_k).
Since xn≤M , it is impossible to find a natural number n such that xn= x_m for m ∈ S.
marsh citrusBOT
Proof for :-
If X :=(xn) is a bounded sequence of real numbers , then every subs...
zealous halo
Proof for :-
If X :=(xn) is a bounded sequence of real numbers , then every subs...
Thus X" cannot be a subsequence of X
So , for every subsequence of X, we have it's terms≤M. So that the subsequence is bounded .
crystal lintel
this is kinda convoluted
like no need to use a contradiction or whatever you tried towards the end
the subsequence’s terms are also bounded by M. that’s all you need to observe really
zealous halo
like no need to use a contradiction or whatever you tried towards the end
I wanted to write a fully Rigorous proof
Obviously it is quite intuitive
stoic saddle
fully rigorous ≠ needlessly obfuscated
rule of thumb: don't do a proof by contradiction where a direct proof does the job
crystal lintel
zealous halo
It's just an idea
Somebody could have come up with an easy one , no doubt
But I want to check it it's correct
Kindly help
stoic saddle
it seems fine logically speaking
crystal lintel
i suppose its correct but i still don’t like it
stoic saddle
but it bears repeating that a proof by contradiction is just overkill here
zealous halo
Is the set S defined correctly, and m associated with it
zealous halo
i suppose its correct but i still don’t like it
Can u provide an easy proof
crystal lintel
your subsequence is notated a little weirdly
stoic saddle
Can u provide an easy proof
i think i gave you one when you were first here with the same question, and you didn't answer clearly when i asked if it was formal enough for you
zealous halo
i think i gave you one when you were first here with the same question, and you ...
Yes , I have your proof
You argued about the indexes , that subsequence have indexes subset of set of natural numbers , something like this
zealous halo
Is the set S defined correctly, and m associated with it
@stoic saddle can u answer this.
zealous halo
your subsequence is notated a little weirdly
Pls elaborate
stoic saddle
im gonna let layla handle the rest of this
crystal lintel
darn i was hoping you would handle the rest of this
zealous halo
darn i was hoping you would handle the rest of this
Shes angry with me ,
crystal lintel
a sequence (x_k) normally just looks like x_1, x_2, …
usually you write it like (x_{n_k}), so that k can still just range over 1,2,3,… but the n_k’s are the indices from the ambient sequence used for the subsequence
zealous halo
I thought , after all they are just numbers , so i simply used x_k
tacit fjord
Can u provide an easy proof
Let M>0 be a bound for X.
Then for any s in X, |s| < M.
Let Y be a subsequence of X.
Every element of Y is also an element of X.
Therefore for any s in Y, |s| < M.
It follows M is also a bound for Y.
Hence Y is bounded.
This proves all subsequences of X are bounded.
crystal lintel
damn you could be in a circus with how stilted that proof is
zealous halo
Let M>0 be a bound for X.
Then for any s in X, |s| < M.
Let Y be a subsequence o...
Thanks
tacit fjord
Its just a direct proof. Not necessarily particularly well written
ornate ginkgo
tacit fjord
at the end of the day, your proof could be a 2-3 liner. depends what your course expects
All elements of a subsequence are also elements of the sequence. Therefore any bound for elements of the sequence will also be a bound for elements of the subsequence.
Hence subsequences of a bounded sequence are bounded.
crystal lintel
I thought , after all they are just numbers , so i simply used x_k
yea but like if you have the sequence (x_n) already, that means x_1, x_2, etc. are already there.
the sequence (x_k) is the same thing. it’s the sequence with elements x_1, x_2 etc
zealous halo
Yes , go on
crystal lintel
you could, i guess, say that this sequence is not indexed over 1,2,3,4,… but that’s just awkward
crystal lintel
a sequence (x_k) normally just looks like x\_1, x\_2, …
usually you write it li...
that’s what this notation is for
zealous halo
Simply Your point is , x_nk is used in books , that's why I should use it
Maybe it's better
crystal lintel
hm i will not say it’s “because it’s used in books”
it’s because it’s more correct i guess
static shore
I think the general idea is that a sequence is a function whose domain is N.
therefore, if suddenly you have a subsequence whose domain isn't N it may feel weird, because a subsequence is also a sequence but it's no longer indexed by all of N.
zealous halo
it’s because it’s more correct i guess
More "notationally" correct?
crystal lintel
yea but also for this to make sense you need index the sequence (x_k) with something other than N
and that’s not typical for a sequence
zealous halo
I think the general idea is that a sequence is a function whose domain is N.
the...
Yes , we are choosing certain natural numbers indices from n , but after all they are countably infinite
tacit fjord
you'll just be better understood if u write something like
Let $(n_k)$ be an indexing sequence for the subsequence $(x_{n_k})$
elfin berryBOT
zealous halo
you'll just be better understood if u write something like
Let $(n_k)$ be an in...
That's what we are discussing.
tacit fjord
Or just: let (x_n_k) be a subsequence.
zealous halo
In books too, they have used this notation
tacit fjord
oh and i wouldnt reuse the n
crystal lintel
and that’s not typical for a sequence
like a sequence is a function from N to R at the end of the day. and that’s what will be used for all the theorem statements and stuff
zealous halo
But after all it's just indices , numbers... So i just choose k
zealous halo
yea but also for this to make sense you need index the sequence (x_k) with somet...
In my proof , I choose those specific numbers having index m
crystal lintel
so if you’re using a sequence that is indexed with something else… we’ll idk i think you should just avoid it
zealous halo
So for a subsequence of say (x_t), i should use notation something like
(x_t_u)
crystal lintel
i will write a proof just for fun
suppose the sequence (x_n) is bounded by M, so that |x_n| < M for all n in N. let (x_{n_k}) be a subsequence of (x_n). then for all k in N, we have |x_{n_k}| < M (this is because n_k = n for some n in N). qed
tacit fjord
So for a subsequence of say (x_t), i should use notation something like
(x_t_u)
do people reuse the t there?
i mean, u can, but might slightly confuse, no?
zealous halo
I was giving an example sir
I would not extend this discussion further .
Things are sorted
Thank u all
.close
marsh citrusBOT
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fringe bobcat
Hi, I need help understanding the proof/ trick for proving lim(1/an) = 1/a if lim(an) = a and a is non zero. I posted an extract from Abbott. I understand the tricks used for other algebraic properties, this one just feels out of nowhere.
marsh citrusBOT
Hi, I need help understanding the proof/ trick for proving lim(1/an) = 1/a if li...
static quarry
which line is the first part that seems out of nowhere?
fringe bobcat
"The trick is to look far enough out into the sequence.."
In my mind, to find an upper bound, what makes sense is to find the smallest absolute value of bn that isn't equal to 0, because that's what makes sense to me as an upper bound, so the inequality agrees somewhat with tht notion. I just don't get why we are looking far enough to get closer to b than 0
static quarry
what you said is correct, but "the smallest" element of a set only makes sense in general if the set is finite, so you have to argue why this set is finite
so you have to make some kind of argument similar to abbott's using the fact that b_n -> b and that b is nonzero
fringe bobcat
Ok that makes sense, if it was finite id be able to just pick the element and be on my way
Wait so is what abbott trying to do essentially is find a lower "bound" for members of the sequences after a certain n?
static quarry
yep, that's right
getting a lower bound for the denominator gives you an upper bound for (1 / denominator)
fringe bobcat
okayy this is starting to make a bit more sense
i'm gonna sketch it out a bit and i think itll click after that properly
but thank you so much
static quarry
sure, yw
just open a new channel if there's still any confusion after you review
marsh citrusBOT
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limber crow
Need bel
marsh citrusBOT
Show your work, and if possible, explain where you are stuck.
limber crow
tired sigil
Are those tangents
tired sigil
Looks right
limber crow
i get it as wrong when i input the answer
online
What about these wxy?
for a it's 130 degree 9', convert to decimal - 360 = answer
For beta = 79 degree 50' - 180 = answer
Idk the name of the symbol next to G but i think it's 44 degree 47' - 180 = answer?
Theta is the sum of interior angles - remain angles.
@tired sigil
marsh citrusBOT
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marsh citrusBOT
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wispy summit
Find nonzero vectors $u, v, w$ such that $u \times v = u\times w$ but $v \ne w$
What I've tried: I know that $v$ and $w$ need to be two different vectors but if you take the cross product of either one with $u$ they should result in the same value...
I am not sure how to get two separate vectors that result in the same value when you take the cross product of them and another vector... I know for the dot product if the result is 0 there are two possible values in both directions of the line perpendicular to the original vector but I don't understand how this applies to cross product
(Sorry, I am just learning about the cross product)
marsh citrusBOT
Find nonzero vectors $u, v, w$ such that $u \times v = u\times w$ but $v \ne w$
...
elfin berryBOT
AN
main idol
you can just plug a general v=(v1, v2, v3) and w=(w1, w2, w3) into u x v = u x w and get 3 equations by equating components for 6 unknowns in v and w.
can probably just pick v3 = w3 = 0
hot rivet
u×v - uxw = 0
Cross products are commutative right?
No
Not commutative
Distributive over addition
jagged relic
The result of the cross product of u and v is orthogonal to both and its length is proportional to the area of the parallelogram formed by u and v
main idol
oh yes that's much smarter
jagged relic
As long as u and v stay in the same plane and the area of their corresponding parallelogram stays the same, the cross product will stay the same
wispy summit
u×(v-w) = 0
ohh nice
so just simplify down to that
and then any two vectors on the same line should work
thank you ❤️
hot rivet
welcome
wispy summit
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drowsy pasture
How do I do part b? I got (9pi - 16) / 2 but was hoping someone could check for me. Used trig sub sin^(2)(theta/2) = (1 - cos(theta) / 2
marsh citrusBOT
How do I do part b? I got (9pi - 16) / 2 but was hoping someone could check for ...
@drowsy pasture Has your question been resolved?
drowsy pasture
<@&286206848099549185>
cunning fiber
,w 1/2 (integral of (2-sin(x/2))^2 dx from -2pi to 0) - 1/2 (integral of (2-sin(x/2))^2 dx from 0 to 2pi)
elfin berryBOT
cunning fiber
How do I do part b? I got (9pi - 16) / 2 but was hoping someone could check for ...
!show
marsh citrusBOT
How do I do part b? I got (9pi - 16) / 2 but was hoping someone could check for ...
Show your work, and if possible, explain where you are stuck.
marsh citrusBOT
@drowsy pasture Has your question been resolved?
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cunning heron
Where I am stuck is on the definitions.
Lets take the added graph as an example. The notes mention that there are vertical asymptotes at x=-3, x=-1, x=2.
That is my confusion. I was taught (or at least, how I understood it) that if the limit taken from the left and the limit taken from the right are equal, you speak of a removable discontinuity, and not of a asymptote.
Can someone explain why x=-3 and x=-1 are counted as asymptotes if they equal when approached from the left and the right?
jagged relic
The limits there are not a number, you can't really say they are equal
dim forge
Asymptote is where graph approaches a constant value but dosent reach it
devout mauve
no
just because the limits are both infinity doesnt mean that they "equal" in that sense
it really should be "if both limits are equal and finite numbers"
cunning heron
Ah, so to check if I understand.
Since the limit when approaching x=-3 is ∞ (and -∞ for x=-1), we call it an asymptote? since ∞ is not a finite number
devout mauve
yes
jagged relic
Yes
cunning heron
And a removable discontinuity would be when the limit is a finite number?
jagged relic
For a discontinuity to be removable you would have to be able to plug it with a value for the function
A function cannot give you the value "infinity"
(at least not a real-valued function which is what you're dealing with)
cunning heron
removable discontinuity: you can grab a pen, put down a dot at a value, and complete the line
asymptote: You can't do that
Does my monkey brain have that right?
broken hazel
guys what shape is tis
jagged relic
removable discontinuity: you can grab a pen, put down a dot at a value, and comp...
That's the intuition, yes
jagged relic
guys what shape is tis
cunning heron
Thanks al lot for the explanation @jagged relic @devout mauve
I feel like I understand my mistake 🙂
.close
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modern breach
marsh citrusBOT
modern breach
10 and 16
modern breach
I am clueless here
spark otter
ok
spark otter
for 10
stoic saddle
I am clueless here
do you know any algebraic identities involving squares and addition
modern breach
for everyone's convenience
Thanks
stoic saddle
@spark otter you arent about to spoil are you
modern breach
idk
stoic saddle
modern breach
Is there a way to solve these
modern breach
do you know any algebraic identities at all
Oh u mean those formulas
Yep I do know
stoic saddle
so you know how to expand (x+y)^2 yes?
modern breach
Mhm
stoic saddle
ok
then i suggest thinking about this but with three terms
(x+y+z)^2, how will this expand?
stoic saddle
ok then tell me: how does (x+y)^2 expand
modern breach
X square + 2xy+ y square
modern breach
okay
stoic saddle
also don't put capital x
anyway ok that's good.
now then, can you expand (x + (y+z))^2 for me, and keep all (y+z) as-is?
that is, don't try any more further algebraic steps until i tell you to
i specifically put brackets around (y+z) so you should treat them as a single unit
modern breach
the question is x+y+z=9 and xy+yz+zx=26 ..
stoic saddle
forget the question
modern breach
Okay:)
stoic saddle
i am trying to teach you algebra
modern breach
Okay okay
stoic saddle
since you say you are not able to expand brackets with 3 terms (which will be sth to fix later) i am trying to take you through the "apply the 2 term thing twice" route
stoic saddle
extremely so, i am afraid.
modern breach
damn
stoic saddle
(x + y)^2 = x^2 + 2xy + y^2
this is already known yes?
modern breach
uhm
stoic saddle
you know this identity yes or no
modern breach
yes
stoic saddle
ok
modern breach
I was told those were formulas
stoic saddle
now go CAREFULLY replace every single y in it, with (y+z).
DON'T try to expand more brackets. ONLY replacement.
modern breach
like a+b whole cube a-b squares and all
cosmic mason
for 16 just add all equations
stoic saddle
for 16 just add all equations
that's helpful but we'll get to that once we're done with Q10 ig
cosmic mason
that's helpful but we'll get to that once we're done with Q10 ig
okii
modern breach
now go CAREFULLY replace **every single y** in it, with **(y+z)**.
DON'T try to ...
I didn’t understand it
stoic saddle
you did not understand my instructions?
modern breach
now go CAREFULLY replace **every single y** in it, with **(y+z)**.
DON'T try to ...
no specifically this one
stoic saddle
i dont know what part of "replace every single y with (y+z) and do nothing else" is unclear
cosmic mason
hmm if u r in high school u can directly use this identity ig
stoic saddle
hmm if u r in high school u can directly use this identity ig
sure but op said he didnt know it
and i am trying to at least teach him like
how to reconstruct it for himself
modern breach
hmm if u r in high school u can directly use this identity ig
I got it know
stoic saddle
or maybe you're a memorizer, idk.
cosmic mason
sure but op said he didnt know it
ohh right
modern breach
so can’t I use it
modern breach
hmm if u r in high school u can directly use this identity ig
..
modern breach
😭
stoic saddle
memorize 29 trillion formulas and dont even try to understand shit. just mug up and mug up and puke it out on the big exam.
sure.
ok.
(x+y+z)^2 = [x^2 + y^2 + z^2] + 2(xy+yz+zx)
LHS and second term of RHS are known. stuff in [] is your goal. substitute known values and you're nearly there.
cosmic mason
or maybe you're a memorizer, idk.
hmm no they actually teach it to us in high school n ask us to remember it
u cant derive everything from scratch during the main exam
stoic saddle
remembering these is a good idea. it's like multiplication tables.
but you CAN'T go around not even knowing where these things come from
modern breach
i m frm Nepal
stoic saddle
or being UNABLE to even reason it out
ok you are from nepal and that changes what exactly
modern breach
nothing
stoic saddle
that's right\
if you try to get by with just memorization you will remain in the "suck at math" pit forever
stoic saddle
(x+y+z)^2 = [x^2 + y^2 + z^2] + 2(xy+yz+zx)
LHS and second term of RHS are know...
i basically laid the entire solution out here
hot rivet
Alr got it
stoic saddle
after kind of giving up on trying to take OP through like
extending the 2 term "square of a sum" formula
hot rivet
So you are trying to derive it
stoic saddle
i was trying to teach OP to fish instead of giving him a fish
hot rivet
So you are trying to derive it
I mean explaining how to
hot rivet
i was trying to teach OP to fish instead of giving him a fish
Rightt
OP doesn't have the fishing gear
modern breach
(x+y+z)^2 = [x^2 + y^2 + z^2] + 2(xy+yz+zx)
LHS and second term of RHS are know...
the xy yz zx
right
Wid 26
?
stoic saddle
don't drop the plus signs i am begging you
nobody will understand that your spaces mean plus if you dont write plus
modern breach
oh okay
stoic saddle
xy+yz+zx is GIVEN AS 26, yes.
stoic saddle
that's your right hand side. did you also work out what's on the left?
modern breach
ohhhhh
hot rivet
Right
modern breach
81
hot rivet
Yup
hot rivet
Sure
hot rivet
That's what's asked right?
hot rivet
Fair enough
modern breach
16
modern breach
yes
hot rivet
Write them out
hot rivet
What do you first observe?
modern breach
42 ?
hot rivet
Ok so we have
hot rivet
3a+3b+3c+3d
modern breach
?
hot rivet
Take 3 common
hot rivet
Sure
modern breach
hot rivet
Ok so 1
modern breach
Yes
hot rivet
Ok
So see if you were given the actual amount
He bought it for
Would you have been able to solve it?
modern breach
oh okay
hot rivet
Since you know there is an answer and the amount is not given, it should be same for any amount
So pick a random amount and solve
You'll get correct answer
hot rivet
Right
modern breach
85
hot rivet
Can you show the full page
modern breach
Wait lemme do it properly
hot rivet
Alr
modern breach
hot rivet
Why are you Subtracting 17.5?
hot rivet
Well he made a loss because he earned less than he bought it for
hot rivet
It doesn't mean he earned in negative
hot rivet
The answer is 20
Should be
modern breach
20 percent gain
hot rivet
Yeah
modern breach
okay
hot rivet
2nd?
modern breach
uhm
modern breach
it looks like geometric sequence typa
modern breach
Do you know what the ......... means?
no
hot rivet
Well let's just focus at the numerator
modern breach
okay
hot rivet
3+6+9+.......+2022
modern breach
yes
hot rivet
Yeah
modern breach
ohh
hot rivet
3+6+9+.......+2022
This means sum of multiples of 3 from 3 to 2022
modern breach
ohh
hot rivet
Till 2022
modern breach
uhm I got the numerator
modern breach
ohhh I get it
hot rivet
3(1+2+3+......+674)
hot rivet
Yupp
modern breach
okay thanks a lot
hot rivet
Also check just in case if the ends are matching
modern breach
U mean the answer
hot rivet
No like
hot rivet
Yupp
hot rivet
Solved
modern breach
Yes
hot rivet
Alr
modern breach
Thanks
cunning fiber
!done
marsh citrusBOT
If you are done with this channel, please mark your problem as solved by typing .close
cunning fiber
.solved
marsh citrusBOT
modern breach
.
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autumn phoenix
Could anyone help me with 28 I’m stuck on finding what the failure cases are 😭
autumn phoenix
And is 27 a correct way
cunning fiber
Could anyone help me with 28 I’m stuck on finding what the failure cases are 😭
In the future, please use the ,rotate command.
,rotate
elfin berryBOT
cunning fiber
marsh citrusBOT
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bright patio
need help guidance regarding how to approach calculus 2 with a mindset that doesnt consume time but also gets me to solve questions rather than being fixated in different types of solving methods, but i dont wanna lose out on terminologies like what is called what, which mathematcions name is prefixed to a type of equation so that i dont get confused when writing in exam, context is that, a teacher i went to taught me how to solve things but no geometrical intuition, neither in depth, just enough to pass the exam, now when i open pyqs and books i get overstimulated between terminologies.
for example, in reduceable higer order diff equation, its also called converting cauchy euler equations into linear constant coefficient ordinary differential equations using substition.
marsh citrusBOT
need help guidance regarding how to approach calculus 2 with a mindset that does...
bright patio
one confusion im going through is that, why in the book, the example is in series?
im super bad at math, so please be soft on me
marsh citrusBOT
@bright patio Has your question been resolved?
marsh citrusBOT
@bright patio Has your question been resolved?
bright patio
.close
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brazen oracle
can somebody teach me
marsh citrusBOT
can somebody teach me
whole thorn
no
red phoenix
?
red phoenix
ello
red phoenix
can somebody teach me
what
static shore
hi OP, do you have a more specific math question for the channel?
red phoenix
hi OP, do you have a more *specific* math question for the channel?
who is op
stoic saddle
OP stands for Original Poster.
red phoenix
o ok
whole thorn
op is too tuff to respond
scarlet whale
did anyone here pick maths A aka math edexcel igcse 4MA1 when he/she was in school and if so pls dm me
marsh citrusBOT
did anyone here pick maths A aka math edexcel igcse 4MA1 when he/she was in scho...
main idol
did anyone here pick maths A aka math edexcel igcse 4MA1 when he/she was in scho...
this isn't a math question
knotty trellis
did anyone here pick maths A aka math edexcel igcse 4MA1 when he/she was in scho...
if you have a math question regarding edexcel igcse 4M12EMDSAA you can just ask it
There'll most likely be someone capable of helping you with it
scarlet whale
Okk I have a lot of doubts in alot of topics 😭
My friend needs help with some stuff
Like algebraic proof
scarlet whale
this isn't a math question
I know i understand it isn't quite right
main idol
Okk I have a lot of doubts in alot of topics 😭
no one can help if you don't ask an actual math question
scarlet whale
gojoisthegoat123
static shore
do you maybe have a specific question that you're confused with (or your friend is), so that we can run you through an example and you can then try the rest?
scarlet whale
no one can help if you don't ask an actual math question
Ok he needs help with like the whole bok
scarlet whale
do you maybe have a *specific* question that you're confused with (or your frien...
He's asking how to study for a exam that's in 3 months
Cover the whole portions
And rn his main difficulty is algebraic proof
He doesn't understand it seems
static shore
I think that discussion is best had in #study-discussion, as mentioned by Ann.
main idol
help channels are for math questions
marsh citrusBOT
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cloud canopy
I am confused by these note from my teacher, its domain and range without graphing but the terminology he uses confuses me and like how would i go about answering thse cause it doesnt make sense
marsh citrusBOT
I am confused by these note from my teacher, its domain and range without graphi...
main idol
which terminology words are confusing
stoic saddle
for (d) why is he writing "square" instead of "root" 💀
cloud canopy
which terminology words are confusing
I understand it now, but im not sure what VA
cloud canopy
for (d) why is he writing "square" instead of "root" 💀
i said the same thing 😭
cloud canopy
I understand it now, but im not sure what VA
whats vertical asymptole
Thats the only part the isnt understanding now
static shore
a vertical asymptote is where the value of a function tends towards positive or negative infinity (i.e., increases or decreases without bound).
a function is never defined at its vertical asymptote.
foggy basalt
helloooo! I'm a boy who just finished the high school this year and I wanna help, cheap, everyone at math, as much as I can!!!
cloud canopy
a vertical asymptote is where the value of a function tends towards positive or ...
So basically its an x value a function cannot use
static shore
in simple terms, yes. and in algebra that definition suffices.
cloud canopy
in simple terms, yes. and in algebra that definition suffices.
thank you so much! i understand now 🙂
static shore
but, not all unusable x-values take the form of vertical asymptotes.
cloud canopy
Wait
cloud canopy
but, not all unusable x-values take the form of vertical asymptotes.
thats confusing can you elaborate
static shore
consider the function $f(x) = \frac{(x-3)(x+2)}{(x+2)}$. \
this function is not defined at x = -2, yet if you graph the function you will not find that the function blows up to infinity in either direction.
elfin berryBOT
ʚ littledove ~ Hyposelenia ɞ
cloud canopy
consider the function $f(x) = \frac{(x-3)(x+2)}{(x+2)}$. \\
this function is not...
oooh
thats awful
but i understand it
cloud canopy
**ʚ littledove \~ Hyposelenia ɞ**
so how would i solve this 😭 if it does show up
static shore
instead, what you will get is simply a "hole" at x = -2, indicating that the function is not defined there.
otherwise, the function behaves exactly like f(x) = x-3.
cloud canopy
instead, what you will get is simply a "hole" at x = -2, indicating that the fun...
ooooooh
okayyy
that makes so much more sense
static shore
so how would i solve this 😭 if it does show up
what do you consider "solving" a function to be?
static shore
just to aid your visual intuition, here is the function graphed on Desmos and highlighted is the special point x = -2.
(if you are graphing this yourself on default Desmos settings, you will have to hover over the point to see that it is undefined. this circle will not show up normally.)
cloud canopy
just to aid your visual intuition, here is the function graphed on Desmos and hi...
i hope i never see this
but i likely will
thank you so much
cloud canopy
just to aid your visual intuition, here is the function graphed on Desmos and hi...
and the = with the / in it means it cannot equal that right
and why is x+3 equal to zero
static shore
I'm sorry, do you mean $\neq$?
elfin berryBOT
ʚ littledove ~ Hyposelenia ɞ
cloud canopy
**ʚ littledove \~ Hyposelenia ɞ**
yes
static shore
this means "not equal to", as in x is allowed to be anything except those specific values.
static shore
and why is x+3 equal to zero
as for this, I unfortunately do not get what you mean. I don't remember using an x+3 anywhere.
cloud canopy
as for this, I unfortunately do not get what you mean. I don't remember using an...
like if you look at the orgininal picture
static shore
if it was used in your example question, then I assume it is in the denominator of a fraction. if so, recall what the denominator of a fraction cannot be.
cloud canopy
if it was used in your example question, then I assume it is in the *denominator...
it cant be x right
static shore
no. it can be x. it's just that if the denominator of a fraction is a lone x, then x cannot be a particular value.
in short, recall what number you cannot divide by.
cloud canopy
in short, recall what number you cannot divide by.
you cannot divide by 0
static shore
exactly so. now, the denominator of a fraction is what you are dividing by. so, if you cannot divide by 0, then whatever is in the denominator cannot also be 0, since if the denominator of a fraction is 0, then you end up with a division by 0.
so any value of x that makes a denominator 0 is excluded from the domain of your function out of necessity, and the function is undefined wherever x is one of those values.
cloud canopy
exactly so. now, the denominator of a fraction is what you are dividing by. so, ...
But in that example, it isnt zero no?
its x+3
static shore
the whole denominator is x+3, yes. you are dividing by x+3, and you know you cannot divide by 0. so if x + 3 happens to be 0, then you have a problem.
that is why x cannot be any value that makes x+3 = 0.
cloud canopy
that is why x cannot be any value that makes x+3 = 0.
how do i know if x+3 = 0
static shore
that value happens to be x = -3, so x cannot be -3 (which is where that $\neq$ sign comes into play).
elfin berryBOT
ʚ littledove ~ Hyposelenia ɞ
cloud canopy
oh
static shore
how do i know if x+3 = 0
when stating a domain, you are not asking how you would know if something will end up making the function undefined.
you are straight up defining the domain as (your valid domain), excluding any values that can cause issues like this.
so it isn't so much as "how would I know if x + 3 would end up being 0", but rather "x + 3 is in the denominator of a fraction, so it cannot be 0. what are the value(s) of x that can make this happen?". your job is then to find all values of x to exclude this way, and then exclude them.
with my example, we have (x+2) in the denominator. since we are dividing by (x+2) and we know we cannot divide by 0, we then also know that x+2 cannot result in 0, so x cannot be anything that makes x+2 be 0. and the way we find out what values of x does that is to set the denominator to 0 and solve for x using regular algebra, which I hope you are familiar by now.
cloud canopy
I am very familiar with regular algebra.
cloud canopy
with my example, we have (x+2) in the denominator. since we are dividing by (x+2...
This is making a lot of sense, its clicking
static shore
think of domain exclusions as preventative rather than curative.
as in, domain exclusions are seen rather as "this function cannot have these values and I am stating this now" rather than "oh no! someone put this value in and my function breaks! what should I do?".
(unless you are a programmer, I suppose; then, well...)
but I suppose they are ultimately two sides of the same coin. if you find out later that some values end up breaking your function, then you would note them down to exclude them next time.
either way, my point is that "how do I know when some x makes it undefined" is probably not a helpful question to ask more than "what are some of the common functions that have restricted domains so that I can exclude values of x that make them undefined".
static shore
for basic algebra, I can think of three functions off the top of my head that have restricted domains: the tangent function (x cannot be pi/2 + kpi for integer k), the square root function (or any even root, x cannot be negative), and the denominator of a fraction (x cannot be 0).
(all mentions of x assume a lone x. adjust if x is accompanied by other numbers.)
cloud canopy
either way, my point is that "how do I know when some x makes it undefined" is p...
so like because we cant divide by 0 id just exlude the x=3, and like another example is we have a negative square root, which is impossible so i dont include it in my function
static shore
the first statement is correct, provided you know that you are excluding x = 3 because x = 3 makes the denominator of the fraction 0.
the second statement, I don't quite understand. if I assume you meant that if you have values of x that makes the radicand of a square root negative, you would exclude all such values, that is also correct.
cloud canopy
the first statement is correct, provided you know that you are excluding x = 3 b...
So lets say inside the square root its x-5. You can’t take the square root of a negative → exclude x < 5.
Is that correct>
?*
turbid mica
yes
cloud canopy
I also apologize if I take some time to reply to messages.
alright i understand the terminology and domain exclusions now, no further questions. thank you so much!
static shore
I'm glad to have helped!
cloud canopy
I'm glad to have helped!
for d on the xample
example
he stated -1 >= to 0
Which I understand
But how did he turn it into a positive one?
static shore
add 1 to both sides.
marsh citrusBOT
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wooden shard
i have no idea how to start
marsh citrusBOT
i have no idea how to start
limber wigeon
i have no idea how to start
hint: what would minimizing/maximizing the mean entail?
wooden shard
hint: what would minimizing/maximizing the mean entail?
can you reword that idk what you mean
wooden shard
hint: what would minimizing/maximizing the mean entail?
oh like avrage
uhh
it goes up
right
it goes down/up
limber wigeon
well like the histogram can represent values in a possible interval right
wooden shard
well like the histogram can represent values in a possible interval right
yeah
limber wigeon
like for data set A, there are 3 integers between 20 and 30
so what would the minimum be?
for that specific part
limber wigeon
no, like if you have three integers between 20 and 30, what is the smallest possible value their sum can be?
wooden shard
no, like if you have three integers between 20 and 30, what is the smallest poss...
60
limber wigeon
yeah, so do that for each bar in data set A to get the total minimized mean of A
take the smallest possible value in each range, then multiply that by the frequency
limber wigeon
yeah, so do that for each bar in data set A to get the total minimized mean of A
(then divide by the total number of items for the mean ofc)
mean is just sum divided by amount
limber wigeon
then you would do the same for B, but maximize instead of minimize