#help-13
cedar kilnBOT
opaque root
You can’t find a value for x if you don’t create an equation
Oh wait
I read wrong the picture lol
Did not see the equal sign 
Ok so, have you tried anything here?
@gritty drift
gritty drift
<@1244911422576660536>
not yet
opaque root
Start by gathering all terms in one side
You can do this by applying the same operation to both sides of the equation
gritty drift
You can do this by applying the same operation to both sides of the equation
x^2-5x-2x^2-x = 0?
gritty drift
Now operate common terms
-x^2+6x=0 ?
opaque root
-5x-x is not 6x
gritty drift
oh -6x
wraith daggerBOT
Samuel
gritty drift
Now factor $-x^2-6x$
-x(x+6) = 0?
opaque root
Nice
Now, when you have a product
AB=0, A=0 or B=0
In your case A=-x and B=x+6
Now you solve both equations and you get your 2 solutions
cedar kilnBOT
If you are done with this channel, please mark your problem as solved by typing .close
gritty drift
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cedar kilnBOT
cedar kilnBOT
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azure shadow
I have a question on inner products. My math professor has taught me that for a vector space (real or complex) the inner product <u,v> contains linearity in the 1st slot, and conjugate linearity in the 2nd slot, but my Physics prof has said that it has linearity in the 2nd slot, (still dealing with possible complex vector spaces), just looking for some clarity on this apparent contradiction
azure shadow
Im obviously leaning towards to what the mathematician has said, but my physics prof said he would take a mathematician's approach when teaching inner product spaces
dawn junco
for a vector space (real or complex) the inner product <u,v> contains linearity in the 1st slot, and conjugate linearity in the 2nd slot, but my Physics prof has said that it has linearity in the first slot, (still dealing with possible complex vector spaces), just looking for some clarity on this apparent contradiction
you said the same thing twice
crimson delta
different conventions, both valid. just be sure to be consistent in a given context and dont switch
azure shadow
oh whoops lol
ill change it now
So if the convention is linearity in the 2nd slot there would be conjugate linearity in the 1st?
crimson delta
yes
azure shadow
Yikes, two exams covering the same thing in different ways and likely marking it differently
ok well thanks for the clarity (despite the critical typo)
.close
cedar kilnBOT
cedar kilnBOT
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merry heath
what does the highlighted thing mean?
cedar kilnBOT
what does the highlighted thing mean?
wanton isle
cedar kilnBOT
merry heath
.reopen
cedar kilnBOT
✅
merry heath
what does n and r stand for?
regal garden
r things to be selected from n....
velvet hemlock
cedar kilnBOT
cedar kilnBOT
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maiden juniper
hello
tranquil gulch
You don't meet all the requirements.
You've marked something to the right of x=-4, which is not possible, because the first one says that it must be smaller than -4 or equal to -4..
maiden juniper
i think i got it now?
wait i think now
@tranquil gulch excuse me good sir i think i got it now
tranquil gulch
<@526810534004260904> excuse me good sir i think i got it now
The first requirement is that x is smaller than or equal to -4. You still have an area to the right (larger) than -4.
maiden juniper
god am i that dumb
tranquil gulch
So everything you mark must be to the left of the line x=-4
tranquil gulch
No?
So first mark the area that satisfies the first requirement, then the second, then the third. Then look for the area that all three requirements have.
maiden juniper
So first mark the area that satisfies the first requirement, then the second, th...
so this is the first mark
heres the 2nd
3rd?
tranquil gulch
so this is the first mark
That little part on the bottom right, you've missed that.
maiden juniper
That little part on the bottom right, you've missed that.
this?
maiden juniper
and then everything else was right on the first requirement
oh
so i got them all?
tranquil gulch
No, the second requirement has the whole bottom right part missing.
that triangle
maiden juniper
this?
tranquil gulch
Why'd you mark that upper part?
maiden juniper
Why'd you mark that upper part?
oh this one?
tranquil gulch
yes
tranquil gulch
You don't need to mark that 🙂
tranquil gulch
👍
tranquil gulch
Oh, sorry, didn't see that, you did not have do that actually.
For the third one, you've missed this little triangle.
tranquil gulch
For the third one, you've missed this little triangle.
for the 2nd one this should be unmarked
for the 3rd one it should be marked
maiden juniper
for the 2nd one this should be unmarked
for the 3rd one it should be marked
what the heck is the second one
this>
?
tranquil gulch
Ok, now look: what's marked on all 3 requirements?
tranquil gulch
Does 1 meet requirement 1 and 2 meet requirement 3?
maiden juniper
Does 1 meet requirement 1 and 2 meet requirement 3?
yes but theres an extra
this?
tranquil gulch
yes but theres an extra
If x has to be equal to or smaller than -4, is that the area to the left or to the right of the line x=-4?
maiden juniper
If x has to be equal to or smaller than -4, is that the area to the left or to t...
its smaller than -4 or equal to it?
tranquil gulch
its smaller than -4 or equal to it?
that is what it says
maiden juniper
that is what it says
so its right!!
maiden juniper
You can't have marked this area, because that is larger than -4, right?
😭
so its just this?
tranquil gulch
can this be marked if y is larger than 3x + 5?
maiden juniper
can this be marked if y is larger than 3x + 5?
yes
upper ruin
Why?
maiden juniper
the green one
upper ruin
Correct
upper ruin
can this be marked if y is larger than 3x + 5?
Does this black triangle belong to the green region?
maiden juniper
Does this black triangle belong to the green region?
yes it does since its all in three inequalities?
cedar kilnBOT
@maiden juniper Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
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quaint iris
help don't know anything about this please someone solve this <@&286206848099549185>
cedar kilnBOT
help don't know anything about this please someone solve this <@&286206848099549...
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
@quaint iris Has your question been resolved?
unborn gull
prove that if $\sum_{n \geq 1}{U_n}$ is convergent if and only if $\sum_{n \geq 1}{2^n U_{2n}}$ is convergent
wraith daggerBOT
💎𝔞𝔷𝔢𝔡𝔡𝔦𝔫𝔢💎
cedar kilnBOT
@unborn gull Has your question been resolved?
grand shale
prove that if $\sum_{n \geq 1}{U_n}$ is convergent if and only if $\sum_{n \geq ...
cauchys condensation test
and its not true always
u_n needs to be non increasing
unless this is something completely different
im assuming thats 2^n in the base
red coyote
I have to find an approximate value of the integral shown below with an error less than 1/1000.
I've tried to set up a Taylor/Maclaurin series but I don't know what to do when it's divided by x^2.
Can someone help? (the answer is supposed to be 29/30)
red coyote
.close
cedar kilnBOT
cedar kilnBOT
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cerulean prairie
im having problems with this equation
cedar kilnBOT
im having problems with this equation
cerulean prairie
I used the Method of Undetermined Coefficients but for the 2nd part the 1/sen is giving me a lot of trouble
dire geode
I used the Method of Undetermined Coefficients but for the 2nd part the 1/sen is...
!show
cedar kilnBOT
I used the Method of Undetermined Coefficients but for the 2nd part the 1/sen is...
Show your work, and if possible, explain where you are stuck.
cerulean prairie
dire geode
Maybe try variation of parameters with cos(x) and sin(x)
cedar kilnBOT
@cerulean prairie Has your question been resolved?
upper ruin
yes it does since its all in three inequalities?
Bruh...
cerulean prairie
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cedar kilnBOT
cedar kilnBOT
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crimson sedge
Hello! working through this problem and I admittedly still don't really know how to remove exponents from both sides
crimson sedge
lyric widget
Close! It's true that the square root of 9a^2 / 3 is what you wrote down. But it's not just the square root that x could be, x could also be negative
When you square 3a/sqrt(3), you get 9a^2 / 3, which is good
But if you square -3a/sqrt(3), you also get 9a^2 / 3
So therefore -3a/sqrt(3) is also a valid solution
crimson sedge
ooop i forgot to right that down
crimson sedge
Hello! working through this problem and I admittedly still don't really know how...
though i did include it up here
lyric widget
Is 0 a critical point?
lyric widget
(if you were really careful then you'd also get that sqrt(a^2) = |a|. This doesn't really matter though, because you have a plus or minus anyways, and that makes the |a| pretty much pointless)
crimson sedge
lyric widget
i think if i sub in 0 for A then it is = 0
The value of f is zero at x=0, but that doesn't mean x=0 is a critical point. A necessary (and insufficient) condition for a critical point is that f'(x)=0. And f'(0) = -9a^2, which is nonzero since a is nonzero
lyric widget
Don't feel sorry for learning
crimson sedge
i'm kinda of confused on where else it could be then
lyric widget
Do you need a third critical point?
crimson sedge
Hello! working through this problem and I admittedly still don't really know how...
i think so
lyric widget
Why do you think so?
crimson sedge
because i answered with +-(3a/sqrt(3)) and got told it was wrong
lyric widget
The derivative of a third degree polynomial has degree 2, so therefore the derivative has at most 2 zeros. Therefore the original function can have at most 2 critical points
crimson sedge
i only see two on the graph and it lines up with what i answered but i got told it was wrong so i'm not really sure what to do
lyric widget
because i answered with +-(3a/sqrt(3)) and got told it was wrong
I don't know what happened then because that should be the correct answer
crimson sedge
??
lyric widget
It says to use a comma to separate answers so maybe they want you to write
3a/sqrt(3),-3a/sqrt(3)
lyric widget
well that's awkward
crimson sedge
man i hate this math program 😭
prof tells us not to simplify it
ah well thanks for the help
lyric widget
I wouldn't blame yourself for that one
you did well
I wish you luck on your math journey
crimson sedge
Thank youuu
lyric widget
^^
analog summit
hello, what is the limit when x--->0 of f(x) = 1 when x = k.pi with k element of Z and f(x) = 0 when x different from k.pi?
analog summit
is there a limit?
digital cliff
if k is an integer i would assume its just 0
analog summit
but then x = 0 = 0.pi if k=0?
mental trail
hello, what is the limit when x--->0 of f(x) = 1 when x = k.pi with k element of...
as x is close to 0 but not equal to 0, the f(x) picked up is always gonna be 0
and the limit of 0 is 0
analog summit
so it's not f(0)?
mental trail
hello, what is the limit when x--->0 of f(x) = 1 when x = k.pi with k element of...
here, you can see f is not continuous at 0
mental trail
as x is close to 0 but not equal to 0, the f(x) picked up is always gonna be 0
because of what we said here
potent fable
Quick question: How do you know when to use natural logarithms? Is it every time you have something to the power of x in an equation?
dreamy void
Quick question: How do you know when to use natural logarithms? Is it every time...
Usually, you can apply natural log on equations that have a power to the x, but not all of them
potent fable
Usually, you can apply natural log on equations that have a power to the x, but ...
Could you give an example of when not to?
And also why, of course.
wraith daggerBOT
bacc (unhelpful)
dreamy void
If I apply any log on both sides, I cannot really simplify it
wraith daggerBOT
bacc (unhelpful)
dreamy void
the right side expression, I wouldn't know how to simplify it
but that's also not an example you would encounter usually in school
wraith daggerBOT
bacc (unhelpful)
potent fable
Hmm what does g(x) mean?
potent fable
Oh so g(x) is the second defined function
dreamy void
is a possible
you could have a simple case where f(x) = g(x) = x then you simply have a^x = b^x
potent fable
**bacc (unhelpful)**
What would this be? f(x)*ln(a)=g(x)*ln(b)?
dreamy void
What would this be? f(x)\*ln(a)=g(x)\*ln(b)?
ya
potent fable
Hm thats interesting lol I'm actually learning this 2 years earlier but I'm really into maths so
So if you have an addition or subtraction in an equation with exp(x), you cannot use ln?
potent fable
**bacc (unhelpful)**
Like this
dreamy void
you can
the real question is
is it useful
does it get you somewhere
we apply things on things basically to simplify things
but i can ensure that such equations are really rare to encounter as the above
potent fable
**bacc (unhelpful)**
Wouldn't it just be
-x*ln(3)=ln(5) though
dreamy void
**bacc (unhelpful)**
the real reason why we apply log on equations as these is, so we can bring down the power
potent fable
Because you get x*ln(3)=2x*ln(5)
dreamy void
Wouldn't it just be
-x\*ln(3)=ln(5) though
How did you get this?
potent fable
the real reason why we apply log on equations as these is, so we can bring down ...
Oh I thought it was to get an answer
dreamy void
Oh I thought it was to get an answer
your question is like asking when do I take the square root, or when do I multiply by some number?
potent fable
How did you get this?
x*ln(2)=x*ln(3)*x*ln(5)
Whoops I missed the 3
dreamy void
no
potent fable
your question is like asking when do I take the square root, or when do I multip...
Basically
Like how do you know if you should use ln
dreamy void
[ \textcolor{green}{\ln (ab) = \ln a + \ln b} \textbf{ not } \textcolor{red}{\ln (a +b) = \ln a \ln b} ]
wraith daggerBOT
bacc (unhelpful)
potent fable
\[ \textcolor{green}{\ln (ab) = \ln a + \ln b} \textbf{ not } \textcolor{red}{\l...
But it's an addition in between them, so why is it ln(3*5) and not ln(3)+ln(5)?
dreamy void
But it's an addition in between them, so why is it ln(3\*5) and not ln(3)+ln(5)?
log is not linear
potent fable
So what if it was subtraction
wraith daggerBOT
bacc (unhelpful)
potent fable
**bacc (unhelpful)**
Hm but wouldnt the two x's be outside, making it 2x*ln(3+5)
dreamy void
nope
wraith daggerBOT
bacc (unhelpful)
potent fable
Yeah thats what I meant
potent fable
**bacc (unhelpful)**
But in this example, a is 3 and b is 5?
potent fable
a^x not a^x + b^x
So why wouldnt this be true
potent fable
Is it even more complicated with a sum of 2?
potent fable
Unsolvable?
potent fable
**bacc (unhelpful)**
But symbolab says that this is unsolvable.
wraith daggerBOT
bacc (unhelpful)
dreamy void
a = 2
b = 15
f(x) = g(x) = x
potent fable
**bacc (unhelpful)**
Isn't that only for the same base? Like (3^x)*(3^y)= 3^(x+y)
wraith daggerBOT
bacc (unhelpful)
potent fable
**bacc (unhelpful)**
I don't think I learned the first one in school...
That's strange
I might've missed it
Well anyway thanks for your help, I just learned a lot!
Have a good one
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
lusty scaffold
which would be the top and bottom function?
cedar kilnBOT
which would be the top and bottom function?
dire geode
Depends on the question
lusty scaffold
it’s finding the area bound by the two graphs
dire geode
Then it doesn't matter. The area is always be positive
If you get a negative, just flip the sign at the end
lusty scaffold
so when i’m setting up the function does it not matter which function i’m subtracting by?
dire geode
If the question is finding the area between two curves, it doesn't matter for the reason I said above. If the question is to find the integral, then it does matter
lusty scaffold
this might sound dumb sorry but like what’s the difference between finding the integral and finding the area
dire geode
Integral is signed area. Regions underneath the x axis count negative towards the integral
E.g. sin(x) between pi and 2pi
,w int pi to 2pi of sin(x)
wraith daggerBOT
lusty scaffold
it’s asking to find the area so then it wouldn’t matter which graph is on top then?
upper ruin
$\int top - bottom = \int \lvert bottom - top\rvert = \int \lvert top - bottom \rvert$
wraith daggerBOT
Alberto Z.
upper ruin
If you use abs values the order doesn't matter, otherwise you have to put the top one first, and subtract the bottom
lusty scaffold
got it so if i find a negative area depending on which function is on top and on bottomjust take the abs value of it
upper ruin
Pay attention, the area is not the abs value of the result of the integral without abs, but instead it's the integral of the abs value of top-bottom
upper ruin
$\int \lvert stuff \rvert \neq \left\lvert\int stuff\right\rvert$
wraith daggerBOT
Alberto Z.
upper ruin
Not here, please read #❓how-to-get-help
quasi jungle
Oh..
upper ruin
Nothing against you of course, it's just to keep things in order
fierce laurel
cedar kilnBOT
fierce laurel
I do not see how this address range is correct
it should be 0x800000 to 0xBFFFFF
these are the same (in orange) so they do not count
cedar kilnBOT
@fierce laurel Has your question been resolved?
fierce laurel
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meager vapor
how do I rationalize this
cedar kilnBOT
how do I rationalize this
meager vapor
Is that a fraction btw?
Yea
opaque root
You are looking for the reciprocal?
meager vapor
Yes
opaque root
You have a cube root numerator
And a cubic root denominator
That is equal to cubic root the whole fraction
Do that and simplify
meager vapor
That is equal to cubic root the whole fraction
So what do I multiply top and bottom by
opaque root
Nothing
You have this
(numerator)^(1/3)/(denominator)^(1/3)
That is equal to (numerator/denominator)^(1/3)
meager vapor
So I need to mult all terms by 3/1?
opaque root
No
meager vapor
I swear on a similar problem I multiply fraction by common term
opaque root
$\frac{\sqrt[3]{25x^5y}}{\sqrt[3]{6xy^3}} = \sqrt[3]{\frac{25x^5y}{6xy^3}}$
wraith daggerBOT
Samuel
opaque root
$\sqrt[3]{\frac{25\cancel{x^1}x^4\cancel{y}}{6\cancel{x}\cancel{y}y^2}} = \sqrt[3]{\frac{25x^4}{6y^2}}$
wraith daggerBOT
Samuel
meager vapor
$\sqrt[3]{\frac{25\cancel{x^1}x^4\cancel{y}}{6\cancel{x}\cancel{y}y^2}} = \sqrt[...
i defintekly did this problem wrong
this is what my tewacher got on i
opaque root
What is the original problem?
meager vapor
What is the original problem?
thwe fraction next to 6c
opaque root
Everything looks right there
meager vapor
Everything looks right there
my teacher got that
meager vapor
How did you get your first pic
I thoght I had to simplfiy
opaque root
You do, but u only simplified the numbers
meager vapor
so how do you raionakliuze
opaque root
The way your teacher did is written out there in your picture
opaque root
**Samuel**
The way to do from here is multiplying numerator and denominator
By (36y)^(1/3)
$\frac{\sqrt[3]{25x^4} \cdot \sqrt[3]{36y}}{\sqrt[3]{6y^2} \cdot \sqrt[3]{36y}} = \frac{\sqrt[3]{900x^4y}}{\sqrt[3]{216y^3}}$
wraith daggerBOT
Samuel
meager vapor
why 36
opaque root
Because 36 is 6^2
And in the denominator you have 6 already
You need 6^2 to reach 6^3
Because u have a cubic root
Same for y
You have y^2
So you need y to get y^3
That is why 36y
$\frac{\sqrt[3]{900x^4y}}{\sqrt[3]{6^3 y^3}} = \frac{\sqrt[3]{900x^4y}}{6y}$
wraith daggerBOT
Samuel
opaque root
What complement
meager vapor
oof I mneant rationalization
opaque root
You want to eliminate the root from denominator
So is your job to find out which number os variable u have ti use to get rid off it
If you have cubic root of x in the denominator
U need x to be x^3 not x
So u will use cubic root of x^2
Because cubic root of x * cubic root of x^2 is cubic root of x^3 which is x
And to not alter the actual fraction u multiply both, numerator and denominator
vapid otter
cedar kilnBOT
vapid otter
stuck on (c)
i really kind of got it but the last part it weird
"How can you approximate the resulting change in area...."
<@&286206848099549185>
cedar kilnBOT
@vapid otter Has your question been resolved?
vapid otter
<@&286206848099549185>
cedar kilnBOT
@vapid otter Has your question been resolved?
red yarrow
Im really confused on how solve this equation fully, comapring it to another persons work
red yarrow
surreal cave
well what specific part are you confused about?
cedar kilnBOT
@red yarrow Has your question been resolved?
red yarrow
how to put u back into the integral
and why 8/9 is only added to the end and not in the beginning of inputing the bounds
civic gazelle
Tom and Alex are playing a game where they take turns rolling a fair six-sided dice. The game starts with Tom rolling the dice, and the player with the higher number wins the round. The first player to win three rounds wins the game. After the first two rounds, Tom has won one round and Alex has won one round. If Tom rolls a 5 in the third round, what is the positive difference between Tom's expected profit and Alex's expected profit, assuming the winner of the game receives $$12$ and the loser loses $$2$ for each round they lost?
wraith daggerBOT
ZiXO
cedar kilnBOT
@civic gazelle Has your question been resolved?
civic gazelle
<@&286206848099549185>
cedar kilnBOT
@civic gazelle Has your question been resolved?
silent badger
hi hello this is URGENT. I am doing a lab where we vary the radius of a string which rotates in horizontal circular motion. Then using a video recorder, we can find how long the length of a period is. My teacher said that when we curve straighten, we will get the value of some constant. The thing is, I have no idea what constant!! My question is, what constant is represented by the slope PLEASE HELP ITS 12 AM 🙏
dry temple
the slope of what
silent badger
my teacher said the slope of the period over the radius is supposed to represent something
dry temple
period / radius?
silent badger
yes
it is supposed to represent some kind of constant, I was thinking either mass or the centripetal acceleration, but i have utterly 0 idea !!
Sorry it should be period^2 / 2 because we curve straigten
straighten*
dry temple
yea i got no clue, gl
silent badger
NOOOO (I appreciate the effort)
cedar kilnBOT
Available help channel!
unique crane
What am I doing wrong for this problem? I have no idea.
cedar kilnBOT
What am I doing wrong for this problem? I have no idea.
unique crane
cedar kilnBOT
@unique crane Has your question been resolved?
unique crane
<@&286206848099549185>
solemn quail
The base is the difference between the two x values
cedar kilnBOT
@unique crane Has your question been resolved?
compact quest
cedar kilnBOT
compact quest
i dont get the undelined part
can someone give me example?
<@&286206848099549185>
hollow trail
so we have $e^{i \theta} = \cos \theta + i \sin \theta$. note that this implies $e^{i \theta}$ is periodic with period $2\pi$
wraith daggerBOT
cloud
hollow trail
,, \frac{\theta_0 + 2k\pi}{n} = \frac{\theta_0}n + \frac{2k\pi}{n}
wraith daggerBOT
cloud
hollow trail
if we plug in k = 0, 1, 2, ... n - 1 then we will get distinct values out
but if you plug in $k = n$, then it will just be [ \frac{\theta_0}{n} + 2\pi ] which will get the same result as $k=0$
wraith daggerBOT
cloud
hollow trail
so every other value of k, we can express it as (the expression with 0 <= k <= n -1) + (some multiple of 2pi)
compact quest
.close
cedar kilnBOT
Available help channel!
nimble estuary
does the author mean V_p instead of V_q? Also isnt it true that any radius which guarantees that both neighborhoods are disjoint sets works just as fine as d(p;q)/2?
solid juniper
does the author mean V_p instead of V_q
it's fine
with no subscripts it would be fine
or if it was V_p it would also be fine
nimble estuary
yes ik the naming doesnt matter
but he is using subscripts to clarify things
thats why i found it a bit wierd
solid juniper
it's like
for a different q, V_q might be different
it's a neighborhood of p but the "dependence" (in the sense of what makes you choose it) is more on q
it also depends on p sure
nimble estuary
yes because the radius which is chosen depends on both q and p
solid juniper
but whatevs
nimble estuary
if q changes d(p;q)/2 may change which will change both V_q and W_q
solid juniper
V_(q,p) might be a more descriptive name but that's kinda excessive
solid juniper
Also isnt it true that any radius which guarantees that both neighborhoods are disjoint sets works just as fine as d(p;q)/2
yea that's kinda arbitrary
nimble estuary
also there is no problem in K being contained in a union of neighborhoods of finitely many points of K
because K is compact and it is contained in the union of neighborhoods of all points of K thus there is a finite subcover
so any radius will work but the only restriction is that $W=\cup_{i=1}^nW_{q_i}$ and $V=\cup_{i=1}^nV_{q_i}$ are disjoint
wraith daggerBOT
pirateking0723
nimble estuary
then the theorem will follow after noting that V is a subset of K^c and thus p is an interior point of K^c
is what i said correct and sufficient as a proof ?
cedar kilnBOT
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nimble estuary
<@&286206848099549185>
nimble estuary
<@&286206848099549185>
cedar kilnBOT
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dusk hemlock
Can someone explain how the conclusion follows from the last inequality
vast pike
Can someone explain how the conclusion follows from the last inequality
what are K-classes ?
dusk hemlock
it's just a set of K objects, for example cats dogs etc...
cedar kilnBOT
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civic gazelle
Tom and Alex are playing a game where they take turns rolling a fair six-sided dice. The game starts with Tom rolling the dice, and the player with the higher number wins the round. The first player to win three rounds wins the game. After the first two rounds, Tom has won one round and Alex has won one round. If Tom rolls a 5 in the third round, what is the positive difference between Tom's expected profit and Alex's expected profit, assuming the winner of the game receives $$12$ and the loser loses $$2$ for each round they lost?
wraith daggerBOT
ZiXO
worldly chasm
!show
cedar kilnBOT
Show your work, and if possible, explain where you are stuck.
@civic gazelle Has your question been resolved?
worldly chasm
Why is P(5) = 1/5?
worldly chasm
Do you remember the definition of expectation?
civic gazelle
i actually don't
but what i did is this :
2/3 x 3/4 + 1/6 x 1/2 + 1/6 x 1/4
civic gazelle
Do you remember the definition of expectation?
but i think i know what you mean
is it considering scenarios where each possibility happens and their possibility of happening ?
worldly chasm
Yes
civic gazelle
ok so : now the score is 1-1 after 2 rounds and tom just rolled a 5 in round three if he wins this round he would just need to win the next round to win the game which have a probability of 1/2, but if tom loses the next round it would be a tie and he would need to win one more round which also have probability of 1/2.
so tom wins this round when he rolled a 5 he needs to win next round : 1/2
tom wins this round and draws the next making it a tie 2-2 then he would need to win one more round : 1/2 * 1/2
probability that tom wins the game 1/2+ 1/2*1/2 = 3/4
worldly chasm
So assuming tied games are null and just repeated, the probability of going from n vs m to n+1 vs m is 1/2 and the probability to go to n vs m+1 is also 1/2 by symmetry.
cedar kilnBOT
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unique pelican
,tex [\lim_{x\to 0}\frac{x^{1/5}}{\ln^{5}x} = \frac{\lim_{x\to 0}x^{1/5}}{\lim_{x\to 0}\ln^{5}x} = \frac{0}{\lim_{x\to 0}\ln^{5}x} = 0]
am i allowed to apply the limits like this
wraith daggerBOT
caotin
rare vault
yes, assuming the denom isnt 0 (and the limits exist)
unique pelican
it goes off to -inf
mental trail
if the limit of the denom is 0 or doesn't exist then you couldn't do it
rare vault
I didn't actually read the functions in your problem, i answered for general f(x)/g(x), but that should answer you right?
unique pelican
the limit of the denominator is -inf. im wondering if that changes things.
i applied the limit just for the top, which seems illegal to me
this limit does exist (because i was asked to show it), but the method im confuised about
i want to know if there are any other ways to find this limit without applying LH. because that is not possible in this case. the denominator will still contain natural logs
im thinking a substitution. let x = e^t, but what does the limit tend to now that t is there? theres some holes in my knowledge of limits
cedar kilnBOT
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@unique pelican Has your question been resolved?
short stratus
im thinking a substitution. let x = e^t, but what does the limit tend to now tha...
t tends to negative inf
unique pelican
whats the reasoning behind that
cedar kilnBOT
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upper ruin
The task is "verify if this function is injective and find its image. In case it is, find the inverse". I'm wondering if there is some quicker way to prove injectivity rather than making all the cases depending on the branch where x1 and x2 live (when doing f(x1) = f(x2) => x1 = x2)
pastel vault
The task is "verify if this function is injective and find its image. In case it...
nope, you have to consider each part of the piecewise function
I mean it's not that bad though if you know the shape of the graph
you can justify it by taking the derivative and checking that f'(x) >= 0 or f'(x) <= 0 for all x in the domain, I guess
cedar kilnBOT
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upper ruin
you can justify it by taking the derivative and checking that f'(x) >= 0 or f'(x...
Yeah, the problem is that I have to do it without derivatives, so I guess I really hav to do all the painful work 
upper ruin
I mean it's not that bad though if you know the shape of the graph
Yeah, but I don't think I can rely just on graphs
I mean, it would be too easy
pastel vault
oh jeez then
tidal anchor
I need help with this i don’t know how to solve it
cedar kilnBOT
I need help with this i don’t know how to solve it
crimson sedge
,rotate
wraith daggerBOT
tidal anchor
Thank you for willing to help me
wraith daggerBOT
faiyrose
flint condor
Simplify to get r by itself
cedar kilnBOT
Simplify to get r by itself
flint condor
Better picture
I need to get r by itself and then I start solving equations using what I come up with. I’m just confused about what to do with pi and the V as I don’t know if they should go on the numerator or denominator.
.close
cedar kilnBOT
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frail root
cedar kilnBOT
frail root
working on it from that tysm
dusk goblet
or wait
nevermind
i just looked at your picture
@frail root
the whole distance is 20 but you use that later
let x be the distance from the pole to the man
then let y = distance from man to shadow tip
frail root
20 is the pole and man right
dusk goblet
20 is the pole and man right
well that’s irrelevant rn
we are going to plug it in after differentiating
frail root
ok
dusk goblet
can you draw another picture
with what i described
no 20 is necessary
just 16 for the height
6 for the other height
then x and y as described
frail root
frail root
yup
frail root
that's a bit fast just a sec
dusk goblet
the 20 is irrelevant actually
dusk goblet
dy/dt = 3/5 dx/dt
^
frail root
it says 24/5
dusk goblet
huh
dusk goblet
oh wait
that’s just dy/dt
that’s the shadow from the man
not the shadow from the pole
so we need dy/dt + dx/dt
9/5 + 3 = 24/5
frail root
why do they add?
dusk goblet
isn’t it common sense? the rate at which the shadow moves from the pole is the same as the rate at which the shadow moves from the man but the man is moving from the pole
maybe that was worded poorly
superposition principle i guess
from physics
like
if i’m in a car that’s moving idk 10 mph
crimson sedge
Can i get help solving this from the beginning
Given 4cotθ + 3 = 0° < θ < 180°
use a sketch to determine the value of cosθ without using a calculator
mossy cloud
Can i get help solving this from the beginning
Given 4cotθ + 3 = 0° < θ < 180°...
cot ?
or cos
worldly chasm
cotan
crimson sedge
given cot, find cos
worldly chasm
@crimson sedge isolate cot theta, and then use sohcahtoa
mossy cloud
given cot, find cos
you know the formula of cotan ?
worldly chasm
remember that cot = 1/tan
crimson sedge
<@456226577798135808> isolate cot theta, and then use sohcahtoa
i got cotθ = - 4/3
what do i do from there
worldly chasm
cot theta = -3/4
mossy cloud
then cos theta = -3/4sin theta
worldly chasm
I don't know if that's the best way to explain it
mossy cloud
then you gotta know your trigonometry formulas
worldly chasm
@crimson sedge you have a right triangle embedded in the unit circle, where the opposite side is 4 and the adjacent side is -3 (3 units left instead of right)
(we know it's this and not -4 opposite and 3 adjacent because that would put theta out of the range required)
then you use the pythagorean theorem to get the hypotenuse
and then use the definition of cosine
crimson sedge
hyp = 5
worldly chasm
yes
worldly chasm
cos = a/h
cedar kilnBOT
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Available help channel!
junior rapids
<@&286206848099549185> can someone show me how to solve this
junior rapids
its actually x^2n
sharp saffron
!status
cedar kilnBOT
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
sharp saffron
How are you supposed to do the euclidian division of two polynomials?
junior rapids
i don't know how to do it with powers like that
its my first time doing this type of exs
sharp saffron
Can you at least write the definition of euclidean division?
junior rapids
P(x)=b(x)*q(x)+r(x)
and you keep doing it until deg(r)<deg(of the divisor )
deg(R)*
sharp saffron
Yes
cedar kilnBOT
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cedar kilnBOT
@junior rapids Has your question been resolved?
wraith daggerBOT
ZiXO
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
ivory agate
absolutely lost
cedar kilnBOT
absolutely lost
pulsar lily
if u = 1-x, then x = 1-u
you make the appropriate substitution for all instances of an x
lofty cargo
I think integration by parts should work right?
cedar kilnBOT
lofty cargo
sure yeah that's easy as well
ivory agate
integration by parts is like a later chapter so im not sure the textbook would want us to use it yet
.reopen
cedar kilnBOT
✅
undone epoch
It is defined.
lofty cargo
It should be cos(x^8) right? https://en.wikipedia.org/wiki/Leibniz_integral_rule
cedar kilnBOT
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untold trench
how do i find the formula that leads to the function of many zero, zero as in where the line meets the x axis
dire geode
!original
cedar kilnBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
@untold trench Has your question been resolved?
crimson pollen
cedar kilnBOT
crimson pollen
can someone help me w 70 im so lost
i have to find the tangent line to the point (-3, 3/2) but idk how😭
what's the first step
do i have to find the derivative of the given equation first ?
would it be (27/9)x^-2 ?
or 3x^-2
wait why
cerulean sail
Chain rule ⛓️💥
do you know how to differentiate 27/u with respect to u?
How about x^2 + 9 wrt x?
cedar kilnBOT
@crimson pollen Has your question been resolved?
limpid brook
!
ornate sand
robbed my channel 🙁
limpid brook
i know u set y as 48
ornate sand
factor
limpid brook
oh
woven crescent
personally
i would just use subsitution for the x^2 terms
and solve using the quadratic formula
limpid brook
can u explain further.....
ornate sand
z=x^2
woven crescent
then you will have:
0 = u^2 - 5u - 44
use the quadratic formula on this new equation
then you will get your answers in terms of u
however
you will then plug in x^2 for u, and solve for x
limpid brook
oh!
ornate sand
sqrt the answer and add +/-
limpid brook
for: 0 = x^4 - 5x^2 - 44
ok and what abt this part
the other way that i originally started to do
woven crescent
wdym? like factor it?
honestly i never really thought about factoring anything past cubic
woven crescent
well isnt there another way of solving b)
i just gave you one lol
woven crescent
then you will have:
0 = u^2 - 5u - 44
^
limpid brook
well ya thats one way
woven crescent
this is the transformed version of: 0 = x^4 - 5x^2 - 44
woven crescent
well ya thats one way
its kind of the best way, it works fine
limpid brook
mhm
hexed vortex
yeah thats the best way to go about it
limpid brook
alr ty
limpid brook
lol we never rlly went over it in class so hopefully it doesnt go on the test
woven crescent
and use one more way
you could do the same thing and sub in u, except
you factor instead of plugging it into the quadratic formula
limpid brook
well ya
ik the answer is decimal so ik factoring wouldnt even rlly work
soo
like it would be bad
bc of all the decimals
but anyways thanks tho
hexed vortex
you could still complete the square to get a factored form
woven crescent
you could still complete the square to get a factored form
thats just asking for pain
cedar kilnBOT
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cedar kilnBOT
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Available help channel!
harsh sierra
cedar kilnBOT
harsh sierra
?
gleaming silo
my bad
harsh sierra
Hi I am having trouble figuring out how to solve this
I found slope of F(a) to be -20a using derivative and g(b) slope as -2b+4
I am unsure as to where to go next
cedar kilnBOT
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harsh sierra
<@&286206848099549185>
cedar kilnBOT
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cedar kilnBOT
@harsh sierra Has your question been resolved?
quaint iris
help someone has chegg premium? cause i really need the answer for this one
quaint iris
oooook
dire geode
!1c
cedar kilnBOT
Please stick to your channel.
dire geode
.close
wicked inlet
Can someone give me the answer for this please
cedar kilnBOT
Can someone give me the answer for this please
wicked inlet
dire geode
Can someone give me the answer for this please
!noans
cedar kilnBOT
Can someone give me the answer for this please
The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.
cedar kilnBOT
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@wicked inlet Has your question been resolved?
peak minnow
would like some hint on this
cedar kilnBOT
would like some hint on this
hushed spoke
can you derive the expression of electric filed on axis due to one ring?
peak minnow
E = Kqz/(R^2 + z^2)^3/2?
hushed spoke
you could write the net electric field on point P now
peak minnow
you could write the net electric field on point P now
yeah i have that , do i equate them to make them 0?
hushed spoke
you can basically comment on the magnitudes of Electric fields due to ring one and two
peak minnow
oh wait , the question was easier than i thought , idk what i was thinking about
peak minnow
you can basically comment on the magnitudes of Electric fields due to ring one a...
E1 = E2 , yeah?
hushed spoke
yes
peak minnow
also can electric field go negative?
like if i have a negative charge and a positive charge , is net electric field
E1 + E2 or E1 - E2
hushed spoke
like if i have a negative charge and a positive charge , is net electric field
E...
you should analyse the directions that electroc field takes if you do those cases
if you have a neg and a postive charge case, you will notice that the direction of EFs due to both will be in the same direction
hushed spoke
ty for the help
yw:)
peak minnow
if you have a neg and a postive charge case, you will notice that the direction ...
this is the question i was doing
q1 q2 q3 are positive and q4 are negative , so i just did E1 + E2 + E3 - E4
(im bad at these btw)
hushed spoke
q1 q2 q3 are positive and q4 are negative , so i just did E1 + E2 + E3 - E4
did you vector summate?
peak minnow
no
hushed spoke
also dont put +/- here
peak minnow
the direction is due to point P
hushed spoke
you vector summate everything
peak minnow
we need to find net electric field on P
hushed spoke
you cannot just add their magnitudes
because EF is a vector quantity, and does not follow rules of scalar addition
you have to think in terms of vectors, using +/- for magnitudes to find resultant can be really detrimental
peak minnow
you have to think in terms of vectors, using +/- for magnitudes to find resultan...
hmm
hushed spoke
you should revisit vectors and see if what i'm saying makes sense
cedar kilnBOT
peak minnow
.reopen
cedar kilnBOT
✅
peak minnow
@hushed spoke ok last question , physics makes my brain not brain
when Z = infinity , what is the magnitude of electric field (still ring of charge)
so im thinking , it would be 0
$$E = \frac{KqZ}{\sqrt{R^2 + Z^2}^3}$$
wraith daggerBOT
JustToPro
peak minnow
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
shrewd epoch
cedar kilnBOT
shrewd epoch
Please help with this question
Ik that for all n being odd it is possible, but what about when n is even?
fallen moat
cool, so
when n = 1
1 + 2 + 3 + 4 + 0 + 1 (mod 5)
when n = 2
1 + 4 + 4 + 1 + 0 + 1 (mod 5)
when n =3
1 + 3 + 2 + 4 + 0 + 1 (mod 5)
when n = 4
1 + 1 + 1 + 1 + 0 + 1 (mod 5)
and it repeats every 4 times
see if this works for you first, if you still need help, i can explain
fallen moat
Cheers!
cedar kilnBOT
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merry heath
cedar kilnBOT
merry heath
can someone explain what is going on here
past wave
do you know what | means?
merry heath
do you know what | means?
is it probability of A given B?
crimson sedge
bruh lemme finish
crimson sedge
is it probability of A given B?
Yup
past wave
bro you go ahead
past wave
i thought | means or so yeah
crimson sedge
damn
merry heath
okay chat
crimson sedge
lemme go ahead
crimson sedge
.
(i)
the value of P(A/B) = 1
this happens only when
P(A intersection B) = P(B)
merry heath
I have a question about this question in general
is this something I can do on the spot or is it memorization based
merry heath
alright