what then now
#help-27
radiant drift
the denominator is real
right
so it has to be
it can be anything
wtf
LINT
PLEASE
restive river
the denominator is real
you can be more specific than 'real'
radiant drift
non zero
restive river
write it in terms of |x|
radiant drift
What a deviant
half minnow
stop this...
arctic field
LOL
devout snowBOT
What a deviant
Helpers are just people volunteering their time to help you. Be polite.
how
devout snowBOT
@radiant drift Has your question been resolved?
untold lark
$a_1+a_2+...+a_{40}=58$ $(a_1,a_2,...,a_{40} ≠ const)$ .$\text{Min , Max }a_1^2+a_2^2+...+a_{40}^2 = ?$
woven radishBOT
mendeleevpro
restive river
What is the point of operator "is subset or equal"?
Seems that it is completely the same just like "is subset" operator.
Can you give an example with difference between these two operators?
I mean if A "is subset" of B, then it could be also equal to B, so using "is subset or equal" operator nothing really changes. It's redundant operator, pointless?
devout snowBOT
What is the point of operator "is subset or equal"?
Seems that it is completely ...
hybrid snow
I think they're legit the same
I like the line under because it differentiates that from the letter C lol
restive river
I like the line under because it differentiates that from the letter C lol
that's true
hybrid snow
restive river
But then we defined a power set, which is a set off all possible subsets of one set.
In power set we do include the set itself, which means it is one of the subsets.
..hm..well that's actually fine, they never said "proper subset"..
i think I get it.. but still some books don't bother to make a difference between these two.
@hybrid snow
thanks for your help
devout snowBOT
@restive river Has your question been resolved?
devout snowBOT
noble mirage
Use substitution method
Yes
Simplify it
Do you know about the quadratic formula?
Yeah so just simplify and use it
x^2 - 6x + 4 = x + 1
=> x^2 - 7x + 3 = 0
Yeah
Yeah you'll get two values for x
devout snowBOT
noble mirage
Anytime
devout snowBOT
Available help channel!
prisma forge
the probability of rolling a 5 is now 30%. the die is rolled 10 times. find: the probability of rolling exactly 8 "5"s.
devout snowBOT
the probability of rolling a 5 is now 30%. the die is rolled 10 times. find: the...
prisma forge
How would I start this problem?
main gull
the probability of rolling a 5 is now 30%. the die is rolled 10 times. find: the...
You still have #help-17 open
brave ravine
devout snowBOT
left robin
put in each x value and see if it equals 0
brave ravine
is there another way to solve
left robin
i think this is the easiest way
brave ravine
<@&286206848099549185>
forest moat
what do you need help with?
devout snowBOT
@brave ravine Has your question been resolved?
robust torrent
can anyone help me read this
devout snowBOT
can anyone help me read this
robust torrent
is it diffrential of x at time t = a function of t and x at time t times differential of t with initial value of x is x_0? i just dont get why didnt they just write x(t) as x_t ?
winter torrent
this is someone who's very insistent on reminding you that x is a function of t
$\dv{x}{t} = a(t, x), x(0) = x_0$
woven radishBOT
Hayley
winter torrent
the change in x is some function of both t and x
you might have like $\dv{x}{t} = x^2 - t, x(0) = 3$ and that would be a differential equation with some solution
woven radishBOT
Hayley
narrow plank
so x is a function? not variable?
correct
x is a function, but can be thought of as a dependent variable
t is the independent variable, x is the dependent variable
winter torrent
yeah, a is a function as well; but that's usually given to you explicitly like I did in the example
robust torrent
oh so in the beginning dx(t) is the same as d(x(t)) ?
devout snowBOT
devout snowBOT
Available help channel!
devout snowBOT
neat night
devout snowBOT
@restive river Has your question been resolved?
narrow plank
@restive river This is it
left robin
cosecant is 1/sine
secant is 1/cosine
any intuition why this is the case? I mean the naming
after all, cosecant sounds like cosine and secant sounds like sine
hollow mantle
cosecant comes from compliment of secant
the names has nothing to do with their reciprocals
devout snowBOT
devout snowBOT
Available help channel!
viral lynx
devout snowBOT
https://i.imgur.com/gEigzI4.png
viral lynx
4 different lines haha
sonic smelt
x = -2 and x = 6 are vertical lines, right?
sonic smelt
You can use a graphing calculator by the way
sonic smelt
Looks correct
viral lynx
okok
I think I can solve this actually, the graphing helped me understand a lot
I assume they want this bit right?
these bits*
sonic smelt
Yes
viral lynx
Okok
sonic smelt
Make sure to split the intervals up
viral lynx
Make sure to split the intervals up
Wym by that sry
Ahh yeye I get you
Ok thanks! I will give it a go now
❤️
.close
devout snowBOT
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woven topaz
does anyone know the how a and b are decided in the product to sum rules?
sonic smelt
I mean you won't mess up if you just remember that each term is sin(smth1)cos(smth2) and alternate the angles
dreamy shore
if you remember formulas of sin(A+B), sin(A-B), cos(A+B), cos(A-B) then these can just be derived
woven topaz
yeah but how do you decide which one is A and which one is B
pseudo basin
does not matter
sonic smelt
Ugh, it doesn't have to be identically the same all the time
pseudo basin
whichever is more convenient
... btw the cos*cos and sin*sin ones are messed up i think
they should be the other way around
or rather
woven topaz
oh i don't plan on using them. Was doing an integral that needed me to change it to be possible as it was a product
pseudo basin
cos(A)cos(B) = 1/2 (cos(A+B) + cos(A-B)) and sin(A)sin(B) = 1/2 (cos(A-B) - cos(A+B))
is what it should be
woven topaz
so i can use either sinAcosB or cosAsinB and not be wrong?
wooden veldt
you pick which one you call A and which one you call B and then use the appropriate formula of the first two
woven topaz
so once im consistent i can just go with either one
devout snowBOT
Available help channel!
vague obsidian
stupid question--why use "greater than or equal to" (≥) when you can use > n-1? Like, instead of x ≥ 4, why not just x > 3?
devout snowBOT
stupid question--why use "greater than or equal to" (≥) when you can use > n-1? ...
pastel pasture
because real numbers are a thing
vague obsidian
wdym
pastel pasture
$x \geq 4$ and $x > 3$ are only equivalent if $x$ is an integer
woven radishBOT
neonperseus
vague obsidian
ohhhhhh
restive river
how should i begin with this question?
devout snowBOT
how should i begin with this question?
restive river
!status
devout snowBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
1
pseudo basin
statusing yourself 
restive river
idk how it works
pseudo basin
!status only makes the bot print this list of responses, it's intended to be used when a helpee isn't saying anything about where they are with the problem
anyway,
restive river
`!status` only makes the bot print this list of responses, it's intended to be u...
oh i thought it would flag the channel
pseudo basin
you might want to consider the expansion of (1 + 2x/3)^n with the binomial theorem
no, what flags the channel as yours is the fact you posted a message here in the first place.
restive river
i see
restive river
you might want to consider the expansion of (1 + 2x/3)^n with the binomial theor...
right, so the first term would be NC0 * 1^n * 3^2
pseudo basin
focus only on the n'th power for the time being
we'll get back to the (3+nx)^2 bit soon
restive river
how do i get the texit command
\left(\begin{array}{c}n\ r\end{array}\right)1^n\frac{2}{3}x^{n-r}
woven radishBOT
todium3301
\left(\begin{array}{c}n\\ r\end{array}\right)1^n\frac{2}{3}x^{n-r}
```Compilation error:```! Missing $ inserted.
<inserted text>
$
l.57 \left
(\begin{array}{c}n\\ r\end{array}\right)1^n\frac{2}{3}x^{n-r}
I've inserted a begin-math/end-math symbol since I think
you left one out. Proceed, with fingers crossed.
LaTeX Font Info: Calculating math sizes for size <14> on input line 57.
LaTeX Font Info: Trying to load font information for U+msa on input line 57.```
restive river
ok so something like this right?
pseudo basin
\binom{n}{r} for the binomial coefficient
restive river
yeah that looiks easier
pseudo basin
also $ at the start and end of it all
pseudo basin
well the full expansion could be written out as $$\left(1 + \frac{2}{3}x\right)^n = \sum_{r=0}^n \binom{n}{r} \cdot 1^r \cdot \left(\frac{2}{3}x\right)^{n-r}$$ if you want
woven radishBOT
Ann
pseudo basin
but that is unwieldy and most of it won't help us
restive river
i had that written down but i dont know how to "reverse engineer" the value of n
pseudo basin
it is better to write it in increasing powers of x
$\paren{1 + \frac23x}^n = 1 + n \cdot \frac23 x + \dots$
woven radishBOT
Ann
pseudo basin
we could write down the next term as (nC2) * (2x/3)^2 but this actually won't matter -- do you see why or should i explain why?
pseudo basin
the RHS only goes up to the x^1 term, yes.
so we do not care about x^2 and up.
now expand (3+nx)^2 in the same fashion.
restive river
ah
restive river
**Ann**
so you just shortcutted and wrote NC1 as n here? sorry it's my first day working with combinations
pseudo basin
yeah i sure did
restive river
ok i understand now, thanks a lot
so for $$\paren{3+nx}^2$$ it would be $$\paren{3+0}^2 + \paren{3+1}^2 \dots$$?
lmao
woven radishBOT
todium3301
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
restive river
now expand (3+nx)^2 in the same fashion.
so i expand the quadratic and get (9 + 6nx + n^2 x^2)
pseudo basin
where are the parentheses
\paren is a custom command i've made for myself
pseudo basin
so i expand the quadratic and get (9 + 6nx + n^2 x^2)
yes that's correct
you can ignore the n^2 x^2 term
so you now essentially have
restive river
wait why are those two the first two terms
pseudo basin
$\paren{1 + \frac{2n}{3}x} (9+6nx) = 9 + 84x + \dots$
restive river
what would happen after the 3rd term then?
pseudo basin
what would happen after the 3rd term then?
wdym
woven radishBOT
Ann
restive river
because there is nothing else to multiply by
pseudo basin
sorry i still don't understand your question
restive river
nevermind, so we ignore everything after the second term because if they were to multiply with the x^0 term it would be x^2 which is already bigger than the given 84x^1 term?
pseudo basin
which is higher degree than the last term of the RHS, 84x^1
restive river
which is **higher degree** than the last term of the RHS, 84x^1
so the degree is the number that the term is raised to? is that the correct way to phrase it?
pseudo basin
the degree is the exponent yes
devout snowBOT
@restive river Has your question been resolved?
junior cairn
I'm not quite sure where to start
devout snowBOT
I'm not quite sure where to start
winter patrol
holding a ball shaped orange may help
junior cairn
I don't have one ;-;
winter patrol
orange?
junior cairn
yeah
north plaza
I'm not quite sure where to start
The first two are obvious, mull over them for a bit.
junior cairn
I'm not quite sure where to start
although for problem a is obvious, I'm not quite sure how to work it out
winter patrol
describe in your own words the shape in a)
north plaza
Yeah.
north plaza
Exactly.
winter patrol
and can you express a half as a fraction?
junior cairn
1/2
winter patrol
that's it for a)
junior cairn
I just need to write as a reason?
junior cairn
my teacher would definitely want to know
winter patrol
well then pretty much like you said
its half of a sphere
and half as a fraction is 1/2
junior cairn
okay all done
honestly wasn't that hard at all (just required using a lot of braincells)
.close
void kiln
$\text{we have :}\ v_n=-4×3^n \text{and}\ u_n=\frac{3}{2+4×3^n}\ -2$
woven radishBOT
IM_YUCF
void kiln
Calculate in terms of n the sum
Help pls
I've noticed that :
$\frac{3}{u_n+2}\ -2 =-v_n$
woven radishBOT
IM_YUCF
void kiln
Calculate in terms of n the sum
How to calculate this pls ?
Anyone pls ?
Here is my work :
$S_n=ln(-v_0)+ln(-v_1)+....+ln(-v_n)
= ln(v_0×v_1×...×v_n)$
And then idk how
woven radishBOT
IM_YUCF
eager lodge
how to simplify $ln(4*3^n)$
woven radishBOT
_wherewolf_
woven radishBOT
IM_YUCF
void kiln
Is that it ?
void kiln
$ln(3^n)=nln(3)$ ?
woven radishBOT
IM_YUCF
eager lodge
yeah
void kiln
And then i just do the sum ?
eager lodge
yes
dusky creek
devout snowBOT
dusky creek
no idea
devout snowBOT
@dusky creek Has your question been resolved?
dusky creek
<@&286206848099549185>
devout snowBOT
@dusky creek Has your question been resolved?
devout snowBOT
timid peak
is Sn the same thing as An
devout snowBOT
is Sn the same thing as An
timid peak
oh ok
obtuse finch
soft star
Old profile iam not playing
sonic smelt
Are you sure point that out helps with solving the problem?
sonic smelt
Yes
torpid cairn
Right expression is taken to be the default definition of the expression in the left
devout snowBOT
devout snowBOT
Available help channel!
rocky trail
weak cove
.close
devout snowBOT
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Available help channel!
restive river
devout snowBOT
restive river
I get that the roots of this function are -1, 0, and -2
but if we look at the graph of this function, this isn't the case
,w graph (pi^x - 1/pi) * x^pi * (1/pi^2 - pi^x)
woven radishBOT
restive river
or is it?
outer marten
its because you are raising (-1)^pi which is not well defined
restive river
so I am correct?
outer marten
I mean technically yes coz only x is required to be a real
restive river
Okay, I have a bit of struggles with finding the first 4 in the sequence, for one, idk how but the answers i'm getting are completely difference, for the subsequence of 2 for a I got -5/12 but i have no clue my thing said its -1/12, I'm not sure why, and then same with the 3rd sequence being -1/240, idk how it got 240, i only get -4/20
devout snowBOT
Okay, I have a bit of struggles with finding the first 4 in the sequence, for on...
patent marsh
So let's work on these one at a time
restive river
okay.
patent marsh
$c_0 = -6\$.
So then for $j = 1$, we get $c_1 = \frac{-6}{(1 + 1)(1 + 2)} = \frac{-6}{(2)(3)} = \frac{-6}{6} = -1$.
woven radishBOT
mellowdramallama
patent marsh
Did you get that for the first iteration?
restive river
yes
patent marsh
ok cool
so we'll do the next one
$c_1 = -1, j = 2 \implies \frac{-1}{(2 + 1)(2 + 2)} = \frac{-1}{(3)(4)} = \frac{-1}{12} = -\frac{1}{12}$
woven radishBOT
mellowdramallama
restive river
wait, i'm a bit confused, how does it get to -1 though?
patent marsh
that's what $c_1$ is. Remember that $c_n$ is dependent on $c_{n-1}$. So $c_2$ is dependent on $c_1$ for $n = 2$, so $c_1 = -1$
woven radishBOT
mellowdramallama
restive river
so its whatever the previous term was? basically?
patent marsh
yep exactly
restive river
oh okay, and then for the 4th sequence, how does the number jump that high on the denominator?
or 3rd
patent marsh
let's work it out
$c_2 = -\frac{1}{12}, j = 3 \implies \frac{-\frac{1}{12}}{(3 + 1)(3 + 2)} = \frac{-\frac{1}{12}}{(4)(5)} = \frac{-\frac{1}{12}}{20}$. $\\$Then use use the rule $\frac{\frac{a}{b}}{c} = \frac{a}{bc}$, so we see $c_2 = -\frac{1}{(20)(12)} = -\frac{1}{240}$
woven radishBOT
mellowdramallama
restive river
oh i see, i mistakenly used -4/20 because for some reason I was adding one each sequence from -6, so the division improves it
for the (-1/2)/20
oops
-1/12
patent marsh
ah I see
yeah you just use only the previous iterations
also you might notice now that we've had two fractions with a one in the numerator, and the output has 1 in teh numerator
so the rest of the iterations will have 1 in the numerator, so you can use that as a litmus test to verify that you have potentially a correct result 🙂
patent marsh
yeah no problem!
restive river
.close
tough plover
Hi
tough plover
@patent marsh I might need some help again
winter torrent
please don't ping specific helpers, even if they helped you before
winter torrent
$a_{100} = 2(100) - 1 = 199$ \
$\underbrace{(1+199) + (3+197) + (5+195) + \cdots}_{50}$
woven radishBOT
Hayley
winter torrent
we sum pairs -- first and last, second and second last, third and third last, etc
tough plover
Hello
tough plover
Is 5000 right ?
winter torrent
i mean evaluate that expression
does it equal 5000?
but also... are you sure about that 99 at the end?
the last term should be 2(100) - 1 = 199
winter torrent
yeah
devout snowBOT
devout snowBOT
Available help channel!
swift knoll
I'm looking to compute the sup-norm of $f_n(x)=\frac{2x}{1+nx^2}$ over $[0,\infty)$. The derivative of $f_n(x)$ is $\frac{2(1-nx^2)}{(1+nx^2)^2}$. Setting it to zero, yields $x=\pm \frac{1}{\sqrt{n}}$, so $x=\frac{1}{\sqrt{n}}$ is a critical point of interest, where we have $f_n\left(\frac{1}{\sqrt{n}}\right)=\frac{1}{\sqrt{n}}$. At $x=0$, we have $f_n(0)=0$. In the limit that $x$ tends to infinity, we have that $f_n(x)$ tends to $0$. Is $x=\frac{1}{\sqrt{n}}$ necessarily a maximum? Why?
devout snowBOT
I'm looking to compute the sup-norm of $f_n(x)=\frac{2x}{1+nx^2}$ over $[0,\inft...
woven radishBOT
sunside_
swift knoll
According to the extreme value theorem, a continuous function on a compact set attains a maximum and minimum on that set, however, here we are dealing with [0,∞), so there's some uncertainty regarding whether or not the function attains a maximum/minimum or not.
Maybe my approach isn't correct...
graceful cipher
<@&286206848099549185> help this man out
devout snowBOT
@swift knoll Has your question been resolved?
eager lodge
I'm not too good at these proofs but
x=sqrt(1/n) is neither a saddle point nor the minimum
so it has to be the maximum
I'm not too sure though
swift knoll
x=sqrt(1/n) is neither a saddle point nor the minimum
how do you know its neither a saddle point nor a minimum?
eager lodge
it is not the minimum because there f(0) = 0
swift knoll
true
eager lodge
if it were a saddle point then there exist a number c such that f(c)>f(sqrt(1/n))
but since f(0) = 0 and f(infinity) = 0
there must exists another critical point c'
but c' doesn't exist in [0,infinity)
it's not a rigid proof but this is my idea
eager lodge
no problem
swift knoll
.close
devout snowBOT
devout snowBOT
Available help channel!
wooden axle
What is the first kind/second kind of discontinuity?
devout snowBOT
What is the first kind/second kind of discontinuity?
tall knoll
removable and non-removable I imagine
late cipher
In the triangle ABC, Seek verification
tall knoll
In the triangle ABC, Seek verification
!help
devout snowBOT
In the triangle ABC, Seek verification
Please read #❓how-to-get-help
main gull
<@&268886789983436800>
Why the mod ping?
neon folio
most unneccesary ping ever
wooden axle
Because there is reason
tall knoll
hong has dumped the question into multiple other channels
wooden axle
most unneccesary ping ever
Open ur eyes first
dire forge
Yes hong please open your own help channel
graceful cosmos
I've never heard of "first kind" or "second kind"
neon folio
Yes hong please open your own help channel
eric he is spammign his question in all channels
wooden axle
Bro delete the question if i had the power i wouldn't have pinged u
graceful cosmos
But there's a few different discontinuities
dire forge
Maybe they mean jump discontinuity vs other kinds?
tall knoll
neither have i but those are the two kinds that I know so let's go with that 😌
tall knoll
asymptote and jump are both non-removable
arctic field
first kind is jump, second kind is not jump
dire forge
First kind is when both limits exist but aren't equal, second kind is when at least one of the limits doesn't exist
tall knoll
cyan obsidian
That's not what the screenshot says, though. (It might have been what its author intended to say ...)
devout snowBOT
@wooden axle Has your question been resolved?
wooden veldt
👻
feral scarab
how do I do part a)
devout snowBOT
how do I do part a)
feral scarab
feral scarab
so what would we do now
eager lodge
let the 3 boys together called B and girls called g
how many ways are there to arrange 1 B and 4 g's
feral scarab
so 5! ways?
eager lodge
yep
for every way we also consider the three boys
how many ways can the three boys be arranged?
feral scarab
so that would be 5! * 3!
rose flower
devout snowBOT
rose flower
would i use sec beta
as u
4secbeta
like the triganometric
@restive river hello
rose flower
wdym?
wooden wraith
you said as u, like a u-sub?
but it's x = 4 sec(beta)
you substitute it directly in for x
wooden wraith
yeah that should work
devout snowBOT
devout snowBOT
Available help channel!
teal bloom
devout snowBOT
teal bloom
Anyone care to explain how to integrate this?
graceful cosmos
There's a nice pattern when you have an odd power on sin or cos
Pull out as many sin as you can, leaving only one sin left. You'll have:
∫ sin(t)sin²(t) dt
Use pythag to convert the sin² to cos²
Then u = cos(t)
devout snowBOT
@teal bloom Has your question been resolved?
teal bloom
So like this?
devout snowBOT
teal bloom
devout snowBOT
Available help channel!
rough sable
Anyone know Financial Sequences and Series?
devout snowBOT
Anyone know Financial Sequences and Series?
rough sable
I’ve been given homework and there is one question that I don’t really understand
I’ve proved the loan rate and the monthly payment
But I’m unsure how to find the interest and time saved after the lump sum payment has been made
I’ve got the answer to the time and money saved but I wanna learn how to get to that
devout snowBOT
@rough sable Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
restive river
devout snowBOT
https://media.discordapp.net/attachments/923256452783673384/1133864217062166558/...
restive river
what am i doing wrong here
no idea how khan academy ended up with the 21 but I for the life of me cant get it
magic pine
when you add -7x to the top
you didn’t multiply it to the + 3
you did x * -7x, instead of (x + 3) * -7x
restive river
you did x * -7x, instead of (x + 3) * -7x
but thatll just be
-21x then
how am i supposed to do 12+21x
magic pine
also
ok
what i’m saying
ok
try writing 2x^3 - x^2 - 12
as
2x^3 - x^2 + 0x - 12
then redo the -7x step
restive river
Ok one sec
restive river
try writing 2x^3 - x^2 - 12
as
2x^3 - x^2 + 0x - 12
ohhhh
so i should just drop down the 12+21x and continue dividing
magic pine
21x - 12, but yes
even if there’s no term with x, you still have to include that in your calculation
left robin
hey
left robin
$p,q\in\mathbb{R}$ $1\leq p<q\$
$f:[1,\infty)\to\mathbb{R}\$
such that $f$ is integradable on each $[1,b]\in [1,\infty)$
woven radishBOT
martin3125
left robin
that is nice and all, but we want another thing to be true
$\int_1^{\infty}|f(x)|^p dx$ exists, but $\int_1^{\infty}|f(x)|^qdx$ does not exist
woven radishBOT
martin3125
left robin
any ideas?
so sad that there we have absolute values here, otherwise it would be easy
supple knot
$\int_1^{\infty}|f(x)|^p dx$ exists, but $\int_1^{\infty}|f(x)|^qdx$ does not ex...
you're told this is true? there exists a function like this
left robin
i have to find one, yes
and since i cant find one i thought, yeah why not ask chatgpt?
it gave me 1/x since the one integral is infinity so it exists and the other is infinity so it doesn't exist
hmmm
good bot
supple knot
i have to find one, yes
can you screenshot the exact problem
topaz beacon
i feel like this is false
left robin
topaz beacon
is this german?
left robin
yep
high summit
supple knot
The function 1/sqrt(x) for 0<x<=1 and 0 otherwise is L1 but not L2.
so you have to shift/scale your function to the interval to [1, b]
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brave ravine
devout snowBOT
patent marsh
so logically there's only one answer that fits here
what are your powers of 2?
like 2, 2^2, 2^3, etc
blissful cloak
here, log_2(6) is the same as 2^x=6 correct?
brave ravine
yeah
blissful cloak
so what answer choice plugged into 2^x=6 will most likely satisfy the equation?
blissful cloak
yep
brave ravine
what abt this
blissful cloak
do you know change base formula?
floral plover
another way to look at this would be using log rules
6 is 2 times 3
log_2(2*3) = log_2(2) + log_2(3) = 1 + log_2(3), you can then approximate the 3 to a 2, that gives you 1 + log_2(2) = 2
blissful cloak
brave ravine
oh yeah i have that
blissful cloak
use it here
brave ravine
so just apply that?
blissful cloak
yep
brave ravine
ok
brave ravine
another way to look at this would be using log rules
6 is 2 times 3
log_2(2*3) =...
uhuh
i dont get that
blissful cloak
its just another way of solving the problem i would focus on the problem at hand
blissful cloak
wdym?
blissful cloak
yeah
brave ravine
how to ask
brave ravine
4=2^x means that x=2
but this doesnt mean that the whole equation equals 2?
blissful cloak
well lets say log_2(4)=x. if we convert it to exponential form we get 2^x=4. we know 4=2^2 so we can say 2^x=2^2. now we just get rid of base 2 and we get x=2
im not entirely sure what your asking but i hope that clears it up
brave ravine
i did
blissful cloak
and?
brave ravine
well idk what to do from there
blissful cloak
show your work
brave ravine
log5(7)/log5(14)
blissful cloak
that isnt how you use the quotient rule
blissful cloak
blissful cloak
yes, because 7/14 simplifies down to 1/2
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Available help channel!
restive river
devout snowBOT
restive river
I need help solving this problem.
midnight bane
the area of a figure similar figure is the similar figures scalefactor sqaured
restive river
the area of a figure similar figure is the similar figures scalefactor sqaured
yeah but what is the scale factor?
midnight bane
let's say A and B are squares, A with side length 3 and B with side length 6
the scale factor here would be 2
restive river
yeah
midnight bane
any side length of A multiplied by the SF will give you the corresponding side of B
As area is 9
restive river
so the scale factor is 2
midnight bane
Bs area is 36
restive river
so sf^2 is how many times the area is greater
midnight bane
you can that that area of A times SF^2= area of B
midnight bane
9*4=36
restive river
so the scale factor is w/275
so its C
answer to the question
no its A
okay got it
thanks dude
.close
restive river
How is this wrong?
devout snowBOT
How is this wrong?
restive river
pseudo basin
your fraction bar got too short and shriveled up all the way into being under the radical.
restive river
your fraction bar got too short and shriveled up all the way into being under th...
could you explain please
pseudo basin
on paper you have $16 \pm \sqrt{\frac{256-200}{10}}$ and $16 \pm \sqrt{\frac{56}{10}}$ when you were supposed to have $\frac{16\pm\sqrt{56}}{10}$
woven radishBOT
Ann
pseudo basin
your fraction bar should be nice and long enough to cover both the stuff on top of it and the stuff below it
restive river
How is this wrong?
i see but isnt that what i did here anyways?
pseudo basin
if you choose not to take heed of that, then it is a matter of time before you royally fuck up with it
anyway
your fraction can be simplified
sqrt(56) = 2 sqrt(14) so you can cancel out a factor of 2 from num and denom...
restive river
sqrt(56) = 2 sqrt(14) so you can cancel out a factor of 2 from num and denom...
ah so like uhhhh
top would have 8 and btotom 5
i can simplify the sqrt(56) too
pseudo basin
(8 ± sqrt(14))/5 is what you would end up with
restive river
(8 ± sqrt(14))/5 is what you would end up with
how does sqrt 56 go down to 14
sqrt(56) can be simplified to 2√14 in radical form.
So uh
Do uou just simplify the whole thing then it turned into 1?
And that’s how 16 turned into 8 as well
Along with 5 on the denominator
If so that would make sense
ill just assume that then
thank you for your help
it is very much apprecaited.
.close
mint orbit
Hi there I need some help with a proof in the sandwich theorem. lets say we have a function xsin(1/x). lets observe the limit as x approaches 0, which would make the limit 0. We know sin(1/x) oscillates so we know
-1 <= sin(1/x) <= 1
-x <= xsin(1/x) <= x
-|x| <= |xsin(1/x)| <= |x|
-|x| <= xsin(1/x) <= |x|
I am confused on the very last 2 lines of this. Specfically how we got rid of that absolute value. I know we need to otherwise its not the original function and were changing the function but I don't get how to prove that.
devout snowBOT
Hi there I need some help with a proof in the sandwich theorem. lets say we have...
wicked turtle
is x assumed to be positive?
if so, then why do you need the abs vals
if not, then the second inequality is wrong
mint orbit
We do because if we used x by itself
and we look at it visually
on a graph which I verified and also on an answer book
that the sandwich theorem would not hold.
wicked turtle
is x assumed to be positive?
^
wicked turtle
then the second inquality is wrong
because it says -x <= x, and that's false if x is negative
mint orbit
x itself is not negative
the negative number comes from the value that the function oscillates which is [-1,1]
wicked turtle
you just said you're approaching from both sides
if you approach from the left then x is negative
mint orbit
What are you exactly trying to say?
wicked turtle
that the second inequality is wrong
mint orbit
And what makes u say that
wicked turtle
i just told you what makes me say it
wicked turtle
because it says -x <= x, and that's false if x is negative
^
mint orbit
Yeah the second inequality doesn't work
is my exact point
hence the need for the absolute values
It exists in nature.
mint orbit
Its an exception wit sandwich theorem.
Uhhh no, because its the process as how I got to where I got
wicked turtle
you can't get to a true thing from a false thing, it's not valid reasoning
mint orbit
Its implied that its wrong since we hadda do extra stuff to make it fit the condition for sandwich theorem
forget about that
I am concerned about the last 2 lines
wicked turtle
the third one is true but kind of stupid, because 0 is a better lower bound than -|x|
the fourth one is correct
mint orbit
Here is my issue
with the third and fourth line
I don't understand the transition
as to how we got |xsin(1/x)| --> xsin(1/x)
I don't understand how we proved that.
wicked turtle
there is no transition from the 3rd to the 4th
mint orbit
I know we must do that otherwise we are changing the original function
wicked turtle
the 4th doesn't follow from the 3rd
mint orbit
Well mk, but how we get rid of the |xsin(1/x)|
wicked turtle
to me the simplest argument is as follows:
mint orbit
how do we get rid of the absolute value there
wicked turtle
|sin(1/x)| <= 1
multiply both sides by |x| to get:
|x sin(1/x)| <= |x|
this is exactly equivalent to the 4th inequality
mint orbit
mhmmmmm.
wicked turtle
because in general, |a| <= |b| if and only if -|b| <= a <= |b|
mint orbit
because in general, |a| <= |b| if and only if -|b| <= a <= |b|
mhmmm.
yeah.
Hi u there?
Pls lmk if ur here.
mint orbit
because in general, |a| <= |b| if and only if -|b| <= a <= |b|
I don't get this @wicked turtle
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gray berry
isn't this incorrect? shouldnt the integral be 6e^(1/2) not -6e^(1/2)
gray berry
so would it be a positive or negative?
gray berry
it doesnt really
midnight bane
I think thats why your teacher was careless
midnight bane
yeah
devout snowBOT
@gray berry Has your question been resolved?
lunar vigil
I have to know if the function is injective or not, idk how, but when i try to find it, i am getting function is injective and also not injective, can anyone help me identify where i am wrong
devout snowBOT
I have to know if the function is injective or not, idk how, but when i try to f...
@lunar vigil Has your question been resolved?
lunar vigil
<@&286206848099549185>
<@&286206848099549185>
<@&286206848099549185>
<@&286206848099549185>
timber junco
please do not spam ping
lunar vigil
please do not spam ping
its been half an hour, thought of pinging 3 times before i leave
sorry
anyone ?
lost laurel
I'm getting x1=1/x2 toowhich would suggest it's not injective
but the graph suggests otherwise
supple knot
its been half an hour, thought of pinging 3 times before i leave
That just makes helpers less likely to help
lunar vigil
I'm getting x1=1/x2 toowhich would suggest it's not injective
ohh
lunar vigil
but the graph suggests otherwise
hmm
odd elbow
Hi
woven radishBOT
_basudev
odd elbow
I tested out some example... and this was true
So, is this always true for p >= 0?
.close I get it
devout snowBOT
magic pine
you can say the first implication, the second is not so, take n = k = 2, and p >= 2
odd elbow
ye
odd elbow
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✅
woven radishBOT
_basudev
odd elbow
**\_basudev**
.
magic pine
that’s fine
odd elbow
Integer
odd elbow
magic pine
2^2 does not divide 2
odd elbow
Yws
magic pine
do you have a question this is all stemming from
pseudo basin
XYPROBLEM
odd elbow
I managed to get upto here
I think I did smth worng
Hold up...
Ye everything is fine...
.close
hexed inlet
devout snowBOT
weak cove
!status
devout snowBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
So far I have figured out there were 630.57 rotations my diagram is wrongr
But I don’t know how to apply that into finding how high above the ground the bike was
hexed inlet
```
What step are you on?
1. I don't know where to begin
2. I have begun but got...
2
2
devout snowBOT
@hexed inlet Has your question been resolved?
devout snowBOT
@hexed inlet Has your question been resolved?
devout snowBOT
@hexed inlet Has your question been resolved?
hexed inlet
.close
devout snowBOT
devout snowBOT
Available help channel!
zealous ether
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zealous ether
i considered the product being 25,75,125,and 175
25: 5 * 5 * 1
75 = 5 * 5 *3
125 = 5 * 5 * 5
175 = 5 * 5 *7
then computed the probability of 25, 75, and 175
which is individually (1/6)^3 * 3 and since there's 25,75, and 175 i'd have 9 * (1/6)^3
polar wharf
175 = 5 * 5 *7
Dice only go up to 6 usually
zealous ether
Dice only go up to 6 usually
okay i got the answer
this is like the 10th question i do something totally bs
smh
thank you
zealous ether
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zealous ether
.reopen
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✅
restive river
You've learnt permutation combination?
zealous ether
these are the three group
first case: i consider D, B, and C together which is (1/3)^3 * 3! because they can occupy any group
second case i consider B in first group and second group CD which is (1/3^3) * 3!
final case: i consider BC in one group and D in another group which also gives (1/3^3) * 3!
zealous ether
You've learnt permutation combination?
i can't extensively use it but anyway that's what i have
zealous ether
idk if this is rude but i don't want to know what you did
restive river
I just took two cases and divided by total number of cases
restive river
Oh okay nvm
Idk what you did tbh
Different education systems, different ways
Lmao just ping the helpers
restive river
I did a different method
restive river
i know what you did
I didn't even tell you-
zealous ether
your method involves finding cases where diana isn't with bruce and clark
and then subtract that by 1
zealous ether
okay then i guess what you did is
total ways: 3*3 * 3 = 27
number of cases where diana is with one of her brothers is 3*2 * 2 = 12
number of ways where all of them are together are 3
12 + 3 = 15/ 27
restive river
The two cases I took was selecting two people to go together, multiplying them by the choice of group they had + choosing all three of them and they just had 1 group choices whole divided by total number of combinations
restive river
12 + 3 = 15/ 27
Exactly
restive river
Yeah
zealous ether
but now i want to know what i did wrong lol
restive river
final case: i consider BC in one group and D in another group which also gives (...
<@&286206848099549185> what is wrong here?