well that's fine then
#help-13
dawn junco
nocturne compass
dawn junco
yes, it's essentially $\alpha\int_0^{\frac\pi\alpha}\sin(\alpha x)\dd x$ then
wraith daggerBOT
_aplatypus
timber turtle
can someone help me with a?
cedar kilnBOT
can someone help me with a?
vestal bear
log_e is just ln
fallen moat
can someone help me with a?
what have you tried?
timber turtle
what have you tried?
nothing
i dunno where to start
i guess i should rewrite it as ln(a) - ln(b)?
timber turtle
by inverting both of them?
vestal bear
what do you mean by invert
fallen moat
do i switch it around and make it ln(b) - ln(a)
but how
timber turtle
but that will just be a different answer
timber turtle
🤔
timber turtle
-1??
vestal bear
yea
timber turtle
wait how though
vestal bear
you factor out a -1
vestal bear
then you should be able to get it back into log base e
timber turtle
yeah ok
vestal bear
you can do it without switching it to ln too
but i figured it looked better using ln
hidden hound
cedar kilnBOT
hidden hound
how do you factorise this
what would be the first step?
taking the entire equation to one side?
vestal bear
start by getting rid of fractions
vapid sand
taking the entire equation to one side?
start by making the LHS one whole fraction
hidden hound
start by making the LHS one whole fraction
how would I do that
vapid sand
do you know how to normally add fractions?
hidden hound
do you know how to normally add fractions?
yeah getting the same denominator by multiplying ig
wait would i do lcm
vapid sand
just do that
hidden hound
@vapid sand what would be my next step
i've pretty much gotten rid of fractions
hidden hound
and its all smooth sailing from there
I would just cross them out now
all the x's
right?
vapid sand
yea
signal bison
Y'all want me to send the sol?
vapid sand
no its fine
signal bison
vapid sand
because you have to factorise the numerator for this, you cannot just cancel them out when they're in additon
,rotate
wraith daggerBOT
vapid sand
yea what he did
hidden hound
ohhh
no wonder
so what I did first to get the same denominator was correct
I just had to pretty much get rid of it
then substitute values/move them around
until i got the value of x
vapid sand
mhm
boreal trail
cedar kilnBOT
boreal trail
i get that but whats x=-8
if u sub into x+2y=4 u get that
but what even is it?
cuz to get answer u sub y=6 (aka x) into the f(y) = 16-12y+y^2
vestal bear
i am confused on your confusion
boreal trail
i am confused on your confusion
why did they get x= -8
where i circled
whats the point if thge goal is to find (6, -20)
livid hound
based on what the question is asking,
there wasn't much to gain from determining x
vestal bear
oh i read the rest of it
yeah i dont get why they added that either
i assumed there would be reason guess not
vestal bear
yeah right
boreal trail
vestal bear
i didnt look at the full thing lol
boreal trail
im just confused why they did this, theres no point?
cedar kilnBOT
silent finch
Yes, you know there are n choose 2 1/(4x^2), so you have the equation 2+3/4*n choose 2=17 3/4. From here you get n=7
(2x)^2
I’ll clarify
So firstly there is 2 as a constant term right?
@crimson sedge
Ok
Is that the only constant term?
no when you expand
When you expand everything there is 2 times 1 right?
One step at a time
silent finch
When you expand everything there is 2 times 1 right?
Do you understand?
foggy mason
If i do a two path test, and the limit does not exist for both paths, can i conclude the limit DNE?
tropic oxide
the nonexistence of a limit along ONE path should be enough to conclude the multivar limit doesn't exist.
drowsy hare
cedar kilnBOT
drowsy hare
I get that I must find the limits of the function when f(pi) and f(-pi). However what is that I sub into the limit in order to either get f(pi-) = f(pi+) = f(pi)?
The rules of the limits state that what I sub in must be less than pi so how would they ever be equal to each other?
<@&286206848099549185>
<@&286206848099549185>
cedar kilnBOT
@drowsy hare Has your question been resolved?
drowsy hare
<@&286206848099549185>
wet haven
<@&286206848099549185>
What do you need help with
drowsy hare
hey
wet haven
Yo
drowsy hare
the question at the top
wet haven
Ok
drowsy hare
im not too clear on how to solve it, all I know is it uses the convergence of fourier series
drowsy hare
I posted it in the more advanced sections and have still not got a response
So I dunno if anyone is even online to help right now
flint plinth
I get that I must find the limits of the function when f(pi) and f(-pi). However...
the first thing to check is whether in fact f(pi-) = f(pi+) = f(pi). Is that the case here?
drowsy hare
the first thing to check is whether in fact f(pi-) = f(pi+) = f(pi). Is that the...
I'm not sure but it either has to be either i or ii from this
flint plinth
I'm not sure but it either has to be either i or ii from this
right, that's what i'm getting at. You need to see which case you're in
drowsy hare
but i don't know how to check that
flint plinth
well let's take x = pi, what is |sin(x/4)|?
drowsy hare
1/pi^1/2
drowsy hare
it should be the same
flint plinth
well the function is defined as |sin(x/4)| for -pi <= x < pi, note that the -pi is included in this interval but pi is not
but i guess that doesn't really matter here
,w plot |sin(x/4)| from x=-pi to x=pi
wraith daggerBOT
flint plinth
so the value at -pi is |sin(-pi/4)|, which is |-1/sqrt(2)|, which is 1/sqrt(2), right?
now you just need to check the left and right limits, and from the graph it's pretty clear what those are
drowsy hare
I don't fully get what you are saying to do tho
flint plinth
find f(x0), f(x0-), and f(x0+), where x0 = -pi
then you will know whether you are in case (i) or case (ii) of the dirichlet theorem
f(x0) is 1/sqrt(2)
what are f(x0-) and f(x0+) ?
drowsy hare
what should i sub in?
flint plinth
x0 is -pi
you're looking for the left and right hand limits of the periodic function, at x = -pi
to get the periodic function, you take the graph in the screenshot above and you extend it periodically
drowsy hare
so i assume that it will continue as it is?
flint plinth
you'll take that graph and replicate it at every multiple of 2pi
flint plinth
what means -2pi
drowsy hare
flint plinth
yes P here is 2pi
but i don't get what you mean by "that gives me 1"
what gives you 1?
drowsy hare
since the interval range becomes -pi to pi then surely I go back an interval of pi?
so its -2pi
flint plinth
what is -2pi?
that's where there will be another minimum of the function, is that what you mean?
drowsy hare
yeah its the next x value
so then sin(-2pi/4) = 1
for my limit coming from the left
flint plinth
why are we looking at x=-2pi?
the question is what happens at x=-pi
that's what is stated in the question
drowsy hare
yeah but i cannot find which condition it fits without doing the limit, but the limit cannot be the same as Xo
flint plinth
also, even if you want the function value at x=-2pi, you don't get that by plugging x=-2pi into |sin(x/4)|, because that formula is only valid for -pi <= x < pi
beyond that interval, you periodically replicate the function
that's not the same as just computing |sin(x/4)| for all x
drowsy hare
oh thats true
flint plinth
because the period of |sin(x/4)| is 4pi, whereas your function's period is 2pi
drowsy hare
what should i do a limit of then as it must be to the left and right of -pi
flint plinth
what you want to do is look at the plot from -pi to pi, then for x values less than -pi, you "wrap around" to pi, and similarly for x values greater than pi, you "wrap around" to -pi
I would plot it explicitly using wolfram but i'm not sure how to tell it to periodically extend
drowsy hare
so there is no 2pi technically then? its just pi, -pi , pi, -pi?
flint plinth
to find the value of the function at an arbitrary value of x, you add or subtract multiples of 2pi until you get a number in the range [-pi, pi). So in the case of x = 2pi, you'd subtract 2pi to get x=0
i.e. the value of the function at x=2pi is the same as the value of the function at x=0
drowsy hare
so its not representative of the value 2pi but 0 repeated?
so 0, pi, -pi, 0, pi ,-pi, 0
as the interval does not actually include the value 2pi and fourier assumes that the function is periodically extended?
flint plinth
here we go
this took a bit of work, i finally used matlab to plot it
this shows three periods of your function:
the blue is the range [-pi,pi)
the darker red is [-3pi, pi)
the lighter orange on the right is [pi, 3pi)
drowsy hare
so I would sub in the next value at after one period length for the limits?
flint plinth
yea, to see what happens with the left limit at -pi, you would look at values of x that are just slightly smaller than -pi, and that is the same as looking at values of x that are just slightly smaller than pi (because you add 2pi to get back in the original range)
drowsy hare
so i would do abs(sin(-3pi/4)) and abs(sin(pi/4))?
flint plinth
-3pi/4 and pi/4 are both within the interval [-pi, pi), you would not make any adjustments to them (no adding or subtracting 2pi)
drowsy hare
but to see the limit as it approaches -pi?
for -pi- and -pi+
would that work or is it the same as saying Xo again?
which the limit forbids
@flint plinth
drowsy hare
.close
unique wind
n
untold torrent
its correct
crimson sedge
I don't get it
cedar kilnBOT
I don't get it
crimson delta
chain rule
crimson sedge
.close
cedar kilnBOT
crystal raptor
what a chain rule hater
slate lintel
why can we treat it as such
we can 
cedar kilnBOT
Available help channel!
crimson sedge
⇐⇒
crimson sedge
what does this mean?
crimson sedge
It is a biconditional
so in this context
it means that only if the lim = 0, then it converge
bold hinge
No
It's a two part statement
You have to read it in both directions
- The alternating sum converges only if the limit is 0
- The limit is 0 only if the alternating sum converges
mild sail
cedar kilnBOT
mild sail
the explanation makes no sense
how is choice A different from choice B?
is choice B saying that the x intercept is 3 away from the LoS in both sides?
why isnt it positive btw
cedar kilnBOT
@mild sail Has your question been resolved?
sweet umbra
isnt there only one such permutation (the identity permutation)?
sweet umbra
e.g. the permutation just switching 1 and 2
do you mean f(1) = 2, f(2) = 1?
crimson delta
yes
cedar kilnBOT
cedar kilnBOT
Available help channel!
crimson sedge
cedar kilnBOT
crimson sedge
im depressed this is supposed to be the easy question of the homework
i wrote and started simplifying the characteristic equation for A but
i feel like its going nowhere
crimson sedge
is there a way to write lambda
white delta
Its obv
crimson sedge
explain
crimson sedge
wait what
white delta
But we want it to get this as 2 dimentional
crimson sedge
how do you tell what the dimension will be
without simplifying to its root
abd seeing the multiplicity
white delta
H= 6
white delta
without simplifying to its root
What
OK i dont speak very well english but let me write il mathematical language then send you a pic
white delta
i didnt read that the eigen value was 5
You got it now ?
Didnt know that this was called eigen value in english lol
I mean theres nothing else to write imo
wraith daggerBOT
cedar kilnBOT
lone ferry
what formula did you use?
also please only ping helpers after 15 minutes, thank u
i got that too
rounded to nearest whole number
cedar kilnBOT
@crimson sedge Has your question been resolved?
twilit knot
I'm sorry but I'm not helping a spammer which is insulting me
fleet eagle
You are loser
twilit knot
Elo?
Tell me your elo
Sir calm yourself
It's 2am
1999
Ironically
Max 1208
And u?
Im doing some work
But tmr sure
Well
What r u trying to prove
Go study compound interest
What version of stockfish do u prefer
crimson sedge
1v1 me
twilit knot
You started asking for help
With compound interests
Then massed ping us
Insulted us
And now dare to call us shit
cunning forum
And now dare to call us shit
Bad attitude person asking for help?
You’re not obligated to
if it gets worse ping mods
crimson sedge
some worse than others 😂
twilit knot
if it gets worse ping mods
I mean if he's like this daily
twilit knot
some worse than others 😂
Speaking truth
crimson sedge
I’d suggest neutral101 read <#486128019652476939>
bro you really think the reason he acting like this because he didn't realize it was against the rules
cunning forum
bro you really think the reason he acting like this because he didn't realize it...
no
I think he’s doing this because he’s a troll
twilit knot
I think he literally expected helpers to appear instantly
cunning forum
I guess we all have bad days
True, but out of every 100 bad attitude people asking for help that I’ve encountered, 99 are just trolls
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
$\frac{1! \times 2! \times 3! \times ... \times n!}{2^{n-2} \times 3^{n-3} \times ... \times (n-1)} = 120$ Determine n
wraith daggerBOT
imperiling
leaden otter
Does the denominator strike a bell?
crimson sedge
Strike a bell? Hmm
leaden otter
You can rearrange it to form (1!)(2!)...(n-1)!
crimson sedge
I don't see how though
leaden otter
See how many times each number from 1 ro n-1 is multiplied in (1!)(2!)...(n-1)!
crimson sedge
1 - (n-1) times
2 - (n-2) times
3 - (n-3) times
...
(n-1) - once
leaden otter
And what is the denominator
leaden otter
1 - (n-1) times
2 - (n-2) times
3 - (n-3) times
...
(n-1) - once
Isn't this also true for the denominator?
crimson sedge
Isn't this also true for the denominator?
Well, I dont know how u rearranged the denominator to form 1!.2!.3!...(n-1)!
leaden otter
Take a 1 to form 1!, take a 1 and a 2 to form 2! and so on all the way to taking 1,2,3,..., n-1 together to form (n-1)!
So wait, numerator is (1!)(2!)...(n!)
And the denominator is all but without n!
crimson sedge
Oh
Wait, let me see if I get it
I think I got it
oh Im so dumb
Thank you, Euclid
.close
old monolith
"Sketch the region D = ···. Then set up the integral for both orders of integration"
old monolith
Is there a difference between an interated integral and a double integral?
And beyond that - this is just asking me to compute the bounds and set up the integral in both directions?
sinful summit
Is there a difference between an interated integral and a double integral?
The double integral makes sense depending on what you are calculating, whereas the iterated integral is just a method of calculating the double integral.
for example, given $D = {(x, y) \in \mathbb{R}^2 : a \leq x \leq b, g_1(x) \leq y \leq g_2(x)},$ $$\iint_D f(x, y) ,dx,dy$$ this make sense and tells something. Bu this $$\int_a^b \left( \int_{g_1(x)}^{g_2(x)} f(x, y) ,dy \right) ,dx.$$ is just $$\iint_D f(x, y) ,dx,dy \stackrel{calculation}{=} \int_a^b \left( \int_{g_1(x)}^{g_2(x)} f(x, y) ,dy \right) ,dx.$$
wraith daggerBOT
adzetto
drifting marlin
best practice would be to use the un-rounded value
cedar kilnBOT
@solemn pulsar Has your question been resolved?
mossy mango
heres a nice surface area problem for sir stone
Mr. Tearfox Ou has n towers shaped like rectangular prisms. Each tower has a 1 by 1 base. The first tower has height 1, the next has height 2, up until the nth tower which has height n. Mr. Tearfox Ou randomly arranges these n towers on his table in a line. Over all arrangements of these rectangular prisms Mr. Tearfox Ou could make, what is the average surface area
mossy mango
how do i solve this
sinful summit
heres a nice surface area problem for sir stone
Mr. Tearfox Ou has n towers shap...
Start by determining the surface area for a single tower with height $i$ ($A_i$) and and generalize that to the sum form
wraith daggerBOT
adzetto
mossy mango
Start by determining the surface area for a single tower with height $i$ ($A_i$)...
expand sir....
im pretty sure @inland fossil would be interested too...
inland fossil
im pretty sure <@831591156919173141> would be interested too...
mister tearfox hu is my teacher hu...
sinful summit
expand sir....
Let $A_i$ denote the surface area of the $i$-th tower. For each $i \in {1,2,\ldots, n}$, we have $A_i = 2 + 4i$. Then the total surface area $A$ of all the towers is $\displaystyle A = \sum_{i=1}^{n} A_i = \sum_{i=1}^{n} (2 + 4i) =?$
wraith daggerBOT
adzetto
cedar kilnBOT
@mossy mango Has your question been resolved?
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'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
<@783697943176675349>
stop acting like ur tob
inland bone
i'm not too sure how to start this problem
cedar kilnBOT
i'm not too sure how to start this problem
lone ferry
set something as a variable
adn then use pythagorean theorem to get equations
here which segment would be the most beneficial if you knew it
lone ferry
so what if you set mn as x
inland bone
so a^2+c^2=b^2-x?
lone ferry
theres 3 triangles
try to use the relationship between those triangles
3 right triangles
pythagorean theorem
inland bone
sorry i still don't get it 😅
lone ferry
if x is equal to MN, what is KN equal to
lone ferry
sorry i still don't get it 😅
no worries! we'll walk through it together :)
inland bone
kn=b-x
lone ferry
right and what is b
inland bone
26.4
lone ferry
so kn = 26.4-x
now that we know KN and a, what can we solve for
using the pythagorean theorem
inland bone
ln
inland bone
ln...?
lone ferry
yup
then you can set them equal to each other to get x
does that make a lil more sense?
inland bone
i think so! let me try it
inland bone
ping me when youre done!
wait i'm a little confused, how do i solve the equation?
i end up having to do the quadratic formula and i'm getting a bunch of random numbers and sqrts 😭
i'm doing 24^2-(26.4-x)^2=11^2-y^2
cedar kilnBOT
@inland bone Has your question been resolved?
inland bone
i set mn as y
lone ferry
oh
if you set mn as y, then make sure to keep that
because tehre's x and y in ur equation right now
there should only be one variable, which should represent MN
ur equation is right, just make sure the variable names are consistent
inland bone
wait so they're both supposed to x?
lone ferry
yes
inland bone
OHHHH wait
inland bone
i get it
lone ferry
👍
inland bone
in my mind x was kn
lone ferry
ohh
inland bone
ping me when ur done
i got 4.58
lone ferry
i got 4.58
👍
inland bone
thank you so much for helping me!! 🙇♀️
cedar kilnBOT
cedar kilnBOT
Available help channel!
naive ether
Hi
fleet solstice
Hello! What’s your question
(Please try to give as much info as possible about the problem and what steps you’ve done beforehand)
cedar kilnBOT
@naive ether Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
crimson sedge
Show that it is true
(with using mean value teo)
$$ \sin x < x \quad \forall x > 0 $$
wraith daggerBOT
.vucic
dire geode
What class is this for
crimson sedge
Calculus
crimson delta
compare their derivatives
crimson sedge
but it want us to prove with mean value teo
dire geode
but it want us to prove with mean value teo
Can you screenshot the problem
cedar kilnBOT
@crimson sedge Has your question been resolved?
flat oracle
crimson sedge
I already asked to bing AI
but there is a part which still confuse me therefore I need other perspective to approach this problem
but anyways
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
cedar kilnBOT
Number 3 and 4 please
crimson sedge
I solved the 4th one though. I just need help for the 3rd
crystal pelican
I solved the 4th one though. I just need help for the 3rd
try squaring both sides
crystal pelican
yeah you can move it to the other side, then i think if you square both sides it makes the problem easier to do
crimson sedge
yeah you can move it to the other side, then i think if you square both sides it...
Ah this didn't worked
<@&286206848099549185>
thin roost
I guess this works
lunar lynx
,rotate
frank tangle
its the boundary condition
something like that
sqauring
you get some eqn < 4sin^4 y
looking at some eqn
you see its minimum value is 4
which is max value of 4sin^4 y
crimson sedge
Yess, done
cedar kilnBOT
Commands:
clopen: .close, .reopen, .solved, .unsolved
consensus: .poll
factoids: .tag
help: .help
Type .help <command name> for more info on a command.
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
crimson sedge
.reopen
cedar kilnBOT
✅
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
minor walrus
a) Sketch the graph of y=2 cos x for 0° ≤ x ≤ 360°.
cedar kilnBOT
a) Sketch the graph of y=2 cos x for 0° ≤ x ≤ 360°.
twilit knot
a) Sketch the graph of y=2 cos x for 0° ≤ x ≤ 360°.
Do you know how to graph a normal cos x?
minor walrus
no
minor walrus
okay
twilit knot
This is a normal cos x
starts at 0,1 and so on
you need to memorise this in order to sketch more complicated graphs
This is cos(x) which can be seen as 1cos(x)
amplitude of 1
meaning it goes up and down 1
your graph is 2cosx
meaning it's amplitude is now 2
it goes up 2 and down 2
twilit knot
This is the graph you're looking for.
more info here: https://www.mathsisfun.com/algebra/amplitude-period-frequency-phase-shift.html
but I'll explain it in more basic terms
you said what does the x mean?
minor walrus
ah yeah
twilit knot
x is what you put in
the inputs
cos(x) means you take the X value and do some stuff to it and get a Y value
to plot it you put the input
X=0
and get a result
minor walrus
oooh
high kiln
more info here: https://www.mathsisfun.com/algebra/amplitude-period-frequency-ph...
more generally these are called function transformations, if you want to read up on them more
cedar kilnBOT
@minor walrus Has your question been resolved?
celest heath
Can someone check if this is correct
cedar kilnBOT
Can someone check if this is correct
celest heath
I got it using the combinations formula
celest heath
yea
thin roost
Looks gud
silent finch
Does sets not count order?
celest heath
no just 8 and 5
thin roost
,w 8 choose 5
silent finch
Ig idk what sets of 5 pictures means
celest heath
Ig idk what sets of 5 pictures means
like imagine u have 8 people and 5 spots on a team how many ways to make that team
zinc hamlet
help pls
cedar kilnBOT
help pls
Please read #❓how-to-get-help
zinc hamlet
huh
silent finch
like imagine u have 8 people and 5 spots on a team how many ways to make that te...
Yea ik I thought it was permutations
zinc hamlet
im new so idk?
celest heath
im new so idk?
put question here #help-0
thin roost
im new so idk?
celest heath
,w 7 choose 11
wraith daggerBOT
celest heath
.close
shell arrow
I'm reading a book on number theory. It says that you can look at positive integers as multisets made out of the primes that make the number up, for example, $63 \equiv {7, 3, 3}$, or $n = 63$ then $N = {7, 3, 3}$ (notation used in book). Theorem 1.5.1 from the book states the following: "Let $a, b$ be two integers. Then $a \mid b \Longleftrightarrow A \subset B.$"
But isn't this false? Shouldn't it be $A \subseteq B$? If the integers $a$ and $b$ are equal, so are $A$ and $B$. But $A \subset B$ would mean that $A$ is a strict subset, so $A \neq B$.
shell arrow
wraith daggerBOT
___aether
crimson sedge
I would assume that the author does not distinguish between $\subset$ and $\subseteq$
wraith daggerBOT
toby____
shell arrow
Oh, I see. Is that common?
crimson sedge
its quite common in algebra
oak moat
Hi, Im not sure how to solve this exercise, specially when they involve functions like the one they gave me. So I have $F:\mathbb{R}^2 \rightarrow \mathbb{R}$ a differentiable function so that $F(x+y+z,x^2+y^2+y^2+z^2)=0$ with $z=z(x,y)$ a differentiable scalar field. Knowing that $z(1,-1)=1$ and that the Taylor Polynomial (Order 1) for F centered at $(1,3)$ is $P(x,y)=-x+y-2$ I have to get $\nabla z(1,-1)$
wraith daggerBOT
neo6448
cedar kilnBOT
@oak moat Has your question been resolved?
toxic vapor
this is very frustrating. Does anyone know what formatting I need for webassign here?
toxic vapor
not really a "math" help so i apoligize if it goes against the rules
I tried without the equal signs as well and that didnt work
dire geode
(x(theta), y(theta))
there shouldn't be equal signs
nor should there be "x" or "y"
toxic vapor
yeah idk what the issue is here, ill bring it up to the prof on a weekday
dire geode
(x(theta), y(theta))
parens around the two equations?
toxic vapor
this worked as the last try haha
question shouldve indicated that I have to write them as x= and y= but i got it finally
thanks still <3
.close
minor orbit
cedar kilnBOT
minor orbit
This is my first time graphing something like this, not sure where I went wrong
I assume it has to do with the last function because I was a bit confused about how to graph that one
minor orbit
Would I start it from 2 with an open circle?
cedar cypress
Yeah
minor orbit
.close
carmine terrace
Three points are on a same line: (3,-5), (-a+2,3), (2a+3,2). What is a?
carmine terrace
Help
cedar cypress
if ABC are on the same line,
slop of BC=slope of AB
carmine terrace
if ABC are on the same line,
slop of BC=slope of AB
ik
cedar cypress
then use it
carmine terrace
but I dont know how to find a
cedar cypress
but I dont know how to find a
by literally using what i said above
carmine terrace
Find the slope <@798555088250470460>
so using (3,-5) and (-a+2,3) I got slope = -7/1+a
carmine terrace
a/8
carmine terrace
so I was kind of right before
cedar cypress
you got the denominator correct first
and then the numerator
but anyway
the slope is -8/a+1
carmine terrace
ok
carmine terrace
So y=mx+b?
carmine terrace
and equate
didn't we already find the expression for slope?
@cedar cypress
do I put one of the points (3,-5), (-a+2,3), (2a+3,2) into y=mx+b?
.close
celest heath
Can someone check
cedar kilnBOT
Can someone check
carmine bronze
Can someone check
👍
celest heath
thank you
carmine bronze
Do you know how to do matrix multiplication?
celest heath
Do you know how to do matrix multiplication?
nah
celest heath
https://www.youtube.com/watch?v=2spTnAiQg4M
🙏
celest heath
You should probably learn that first.
ok i think i got it
so now we just multiply -2 with -2 and 9 with 8 as the first one?
celest heath
Do you know how to do matrix multiplication?
is the first option for the question correct?
carmine bronze
is the first option for the question correct?
Yes.
celest heath
Yes.
wait r u sure because when i multiply the first row with second problem i am not getting -90 as the final number
wait nvm
i am
thanks
.close
celest heath
Would this be 0 or inconsistent?
cedar kilnBOT
Would this be 0 or inconsistent?
vernal shell
Would this be 0 or inconsistent?
the fourth column is full of zeros, so x4 doesn't affect the system, it could take any value as it's not restricted
celest heath
the fourth column is full of zeros, so x4 doesn't affect the system, it could ta...
so would I just put 0?
vernal shell
x4 isn't restricted, so why would it be exactly 0? 🤔
celest heath
x4 isn't restricted, so why would it be exactly 0? 🤔
wait would it be x4=t?
since there is a 1 in x3 so only one free variable?
vernal shell
since there is a 1 in x3 so only one free variable?
yes
crude lagoon
what is the difference between $Axx^2$ and Ax^2$
cedar kilnBOT
what is the difference between $Ax*x^2$ and A*x^2$
wraith daggerBOT
dios
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
crude lagoon
where A is a constant
dire geode
what's the context
wraith daggerBOT
dios
dire geode
well $Ax \cdot x^2 = Ax^{1 + 2} = Ax^3$
wraith daggerBOT
dios
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
rie.mann
crude lagoon
ok
dire geode
you have an x^2-3 term which can be factored as (x+sqrt(3))(x...)
so the product of those two will need to be split
crude lagoon
you have an x^2-3 term which can be factored as (x+sqrt(3))(x...)
$x+sqrt(3)(x)$?
wraith daggerBOT
dios
wraith daggerBOT
dios
wraith daggerBOT
rie.mann
crude lagoon
i didnt know that worked for imperfect squares
i thought that property was only for the diff of 2 perfect squares
dire geode
$3 = \sqrt{3}^2$
wraith daggerBOT
rie.mann
crude lagoon
but i have $(x^2-3)$
wraith daggerBOT
dios
wraith daggerBOT
dios
crude lagoon
$3 = \sqrt{3}^2$
are my factors $x^2(x-sqrt(3))(x+sqrt(3))$
wraith daggerBOT
dios
crude lagoon
do i seriously have to deal with square roots here
@dire geode before i get into it are those the factors? sorry for ping
dire geode
are my factors $x^2(x-sqrt(3))(x+sqrt(3))$
if you multiply this out do you get your starting expression?
crude lagoon
no
dire geode
,w expand x^2(x-sqrt(3))(x+sqrt(3))
wraith daggerBOT
cedar kilnBOT
@crude lagoon Has your question been resolved?
cedar kilnBOT
crude lagoon
.reopen
cedar kilnBOT
✅
limber snow
Is this correct
cedar kilnBOT
Is this correct
crimson sedge
Looks good to me
limber snow
Looks good to me
constructing right inverse ^
is it suppose to be similiar to left inverse?
crimson sedge
cedar kilnBOT
bold hinge
Lets back up for a second
Do you agree that the coefficients of ANY polynomial are symmetric, polynomial functions of its roots?
crimson sedge
Do you agree that the coefficients of ANY polynomial are symmetric, polynomial f...
Yes
bold hinge
Great. So does the sum product thing make sense?
The constant term of a polynomial is up to sign the product of roots.
The n-1th degree term is up to sign the product of roots
crimson sedge
The constant term of a polynomial is up to sign the product of roots.
The n-1th...
I don’t get it
bold hinge
Its a good exercise to derive vieta's formulae on your own
Expand:
(x-x_1)(x-x_2)(x-x_3)(x-x_4)
You will notice a pattern in the coefficients of this expansion
cedar kilnBOT
@crimson sedge Has your question been resolved?
orchid summit
I think it is the second option but please correct me thank you
orchid summit
<@&286206848099549185> ty
indigo eagle
🤷🏽♀️ I can’t give you the answer
lone ferry
can you tell me the difference between combinations, permutations, and the fundamental counting principle?
orchid summit
I think I got
Permutation is a r-permutation of a set of "n" elements in an ordered selection of r elements from the set of n elements. While combination is the number of combinations of n elements taken r at a time.
lone ferry
did you copy paste that 😅
orchid summit
The fundamental counting principle is used to determine the total number of outcomes when there are multiple independent events occurring
orchid summit
did you copy paste that 😅
No I wrote it in my online notes I can show u
Can u tell me now?
I mean there are 6 ways of rolling a dice
And 2 of flipping a coin
So 6*2 = 12
So it should be option B???
@lone ferry Don’t leave me hanging I’m gonna get super confused 😭😭
lone ferry
sorry sorry 😭 give me a second
lone ferry
why do you think its option B
orchid summit
I just explained
orchid summit
I mean there are 6 ways of rolling a dice
☝️
lone ferry
right but are the two events depdent on each other
orchid summit
right but are the two events depdent on each other
That isn’t told
It just said that this is this and this is this
lone ferry
yeah they are two independent events
orchid summit
They specify when the things are dependent
lone ferry
i think you are right
lone ferry
yup 👍
orchid summit
.close
random kelp
how do you work out (x+3)/5tan(x+3) ?
cedar kilnBOT
how do you work out (x+3)/5tan(x+3) ?
random kelp
because I dont really know if you can divide (x+3) with the tan(x+3)
untold torrent
what are you trying to "work out"
of course you can't cancel it out
the x+3 in the denominator is the argument of tan
$\frac{x+3}{5\tan(x+3)}$
wraith daggerBOT
redstoneplayz09
untold torrent
so what's the question? what are you trying to do with this expression?
dire geode
how do you work out (x+3)/5tan(x+3) ?
,tex .original
wraith daggerBOT
rie.mann
random kelp
dire geode
The limit is important to the question
random kelp
it is
dire geode
Try factoring the numerator
random kelp
i did
random kelp
**redstoneplayz09**
which leads me to this
ik its (x+3)(x+1)
but they obviously want me to do some cancellation but im not sure if its possible
untold torrent
try solving $\lim_{x \to 0} \frac{x}{\tan x}$ first
wraith daggerBOT
redstoneplayz09
random kelp
hint: ||split up tan(x) into sin(x)/cos(x)||
xcotan(x)?
random kelp
whats the point of converting back into cot or tan
then its (x)(cos(x))/(sin(x))
random kelp
thats my hint for u to solve limit
did i get it correct??
random kelp
solve the limit
well i got (x+3)(x+1)cos(x+3)/5sin(x+3)
random kelp
just offset by 3
wdym by 'offset'
dire geode
the entire function becomes DNE
Nope
random kelp
5sin(-3+3) = 0
dire geode
x+3 goes to 0 as x approaches -3
.
random kelp
i understand but that just makes the entire function 0/0
dire geode
,w plot x/sin(x) for -1<x<1
wraith daggerBOT
dire geode
,w plot x/sin(x) for -1<x<1
Have you learned the limit of this function near x=0?
random kelp
Have you learned the limit of this function near x=0?
is this the squeeze theorem
no wait thats sinx/x
random kelp
Have you learned the limit of this function near x=0?
no
dire geode
no wait thats sinx/x
Yes
x /sin(x) and sin(x) / x have the same limit as x goes to 0
https://www.khanacademy.org/math/ap-calculus-ab/ab-limits-new/ab-1-8/v/sinx-over-x-as-x-approaches-0
cedar kilnBOT
@random kelp Has your question been resolved?
random kelp
x /sin(x) and sin(x) / x have the same limit as x goes to 0
so i essentially have to take the reciprocal?
regardless that wont work because the denominator would be 0 as (-3)+3 = 0
dire geode
regardless that wont work because the denominator would be 0 as (-3)+3 = 0
Watch the Khan video