,tex .demoivre
#help-27
supple knot
woven radishBOT
riemann
grizzled roost
Hmm maybe Dedekind criterion might work but I have trouble understanding the things I should verify
Yes, I meant that I don't know what do do next, because having the n inside the trigs is annoying
What does it mean when a series verifies that its partial sums are bounded
supple knot
What does it mean when a series verifies that its partial sums are bounded
If you're quoting a text, can you just share the whole context
grizzled roost
grizzled roost
Yeah that works
The only thing is to verify that exp(that thing) is bounded
I intuitively know that all terms of that series are steps of equal length that change direction uniformly to eventually draw some kind of circle, so that should be enough. Proving it seems tougher
Oh wait it's a lot easier it's just a geometric sum
I think that's it
Thanks
.close
fallen mason
devout snowBOT
fallen mason
This might a silly question
But for this problem would I just draw curves for where the direction of these fields are heading through said points?
Im not sure if I worded that question good or not 😅
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void canyon
I feel like this should be realitvely easy but the ogive data seems to be quite extensive and difficult to put into box plot. Just need some guidance.
devout snowBOT
I feel like this should be realitvely easy but the ogive data seems to be quite ...
@void canyon Has your question been resolved?
void canyon
<@&286206848099549185>
arctic wing
I feel like this should be realitvely easy but the ogive data seems to be quite ...
all you need is to find the first quartile, second quartile (median) and third quartile on the ogive and graph accordingly into a box plot
void canyon
yeah i know that but i dont have a full grasp on this ogive idea
arctic wing
ahh okay, hmmm
void canyon
im not sure how im supposed to get those summary stastics you listed out from the ogive data
not sure whether or not to look at the cholesterol (x-axis) or cumulative(y-axis)
arctic wing
im not sure how im supposed to get those summary stastics you listed out from th...
i see! so look at everything as 100%
- first quartile is
25%or1/4thus you find it on the cumulative's (y-axis) and find it on the curve. you go horizontally from25%to pinpoint its specific coordinates, essentially - second quartile is
50%or2/4(aka the median) - third quartile is
75%or3/4
arctic wing
oh yeah the y-axis goes from 0-100 that makes sense
yes exactly!
sometimes the y-axis might not be 100 but you just make to sure to apply the same concept anyway
arctic wing
this might sound dumb but is the minimum 150 or just 0
not dumb at all, good on you for confirming! and yes it would be 0
void canyon
0 ok got it
arctic wing
some graphs starts from the x-axis instead and in that case it might be 150 or something
arctic wing
if the line wasnt at 0 but instead 150 then it would be 150
exactly!
void canyon
maximum should be 450
what about outliers?
can you see that straight from the ogive graph or is that just calculated after getting the q1, q2, q3 and the rest of the summary stats
arctic wing
maximum should be 450
yeah, i think so
there's a formula to outliers, i'll have to find it, one moment
void canyon
its q1+1.5IQR and q3-1.5IQR
but im just asking
like sometimes some types of graphs allow you to see the outliers straight on it but when the other types of graphs dont, then it requires this formula
arctic wing
full notes on it (from a textbook)
arctic wing
like sometimes some types of graphs allow you to see the outliers straight on it...
correct!
arctic wing
so ogive does not show outliers straight on it
not at all
we have to identify it and calculate it
arctic wing
pretty straightforward
you're getting along well
arctic wing
but thank you this really watered it down for me
glad to be of support, best of luck and strength with everything else!
restive river
How would I do 3 b.
devout snowBOT
How would I do 3 b.
arctic wing
How would I do 3 b.
have you found the derivative of f'(x) aka the first derivative?
restive river
No
restive river
Would the equation be =-2 (-3 + 1)2 + 3
arctic wing
Would the equation be =-2 (-3 + 1)2 + 3
oh wait sorry, please ignore what i said about f'(x), i misread...
and yes you are correct, it would be that!
y(-3) = -2((-3)+1)^2 +3
arctic wing
Or is that not necessary
foil is necessary because it is a quadratic function!
arctic wing
Would the answer be -1?
i haven't done the maths but have you checked your answer with a calculator?
oh wait but you already plugged in the number so foil won't be necessary
if it was with x then foil would be necessary
restive river
I used photomath and it got -5 but I didn't see foil or anything like that in their solution so idk
arctic wing
I used photomath and it got -5 but I didn't see foil or anything like that in th...
i also got -5
restive river
oh wait but you already plugged in the number so foil won't be necessary
I'm so confused wait what
Oh I did it wrong
arctic wing
I'm so confused wait what
because for this section of equation (-3+1)^2 → (-2)^2 → -2 • -2 = 4
there is no x for you to distribute as normally you would do
(x+1)(x+1)
restive river
Ohh
restive river
Yeah it does
arctic wing
Yeah it does
great! best of luck and strength with the rest!
!!
devout snowBOT
devout snowBOT
Available help channel!
vast mist
devout snowBOT
rugged sparrow
you sure?
vast mist
i dont know what the question wants
sand dove
The 4 inequalities enclose a region that is a quadrilateral
A quadrilateral has 4 corners, how can you express the corners in terms of equalities/inequalities?
vast mist
umm
sand dove
So a quadrilateral has 4 sides right?
vast mist
yes
sand dove
And a corner needs to be on how many of those sides?
vast mist
4?
sand dove
A single corner is on all 4 sides at once?
vast mist
no
vast mist
i need to search which one is not on the side?
vast mist
1
sand dove
Only 1?
rugged sparrow
Hint:||Search for a point that does not satisfy at minimum one of the given inequalities||
vast mist
what
sand dove
How could we know that A is still not a corner?
short iron
[\int{e^{-x} * e^{2x}}dx]
devout snowBOT
\[\int{e^{-x} * e^{2x}}dx\]
woven radishBOT
dopediscorduser
short iron
Where do I even start with this?
woven radishBOT
Dyssrupt
pseudo basin
^
red turret
use the 1st one
pseudo basin
inb4 prohibited
short iron
[y' +2y = e^{-x}]
[Q(x) = e^{-x}]
[P(x) = 2]
[u(x) = e^{\int{\text{P}(x)}dx} = e^{\int{2}dx} = e^{2x}]
[\text{Plug in values to general solution equation}]
[y = \frac{1}{e^{2x}} \int{e^{-x} * e^{2x}}\text{ dx}]
[y = \frac{1}{e^{2x }} \int{e^{2x - x}}\text{ dx}]
[y = \frac{1}{e^{2x }} (e^{2x - x} + c)]
[y = \frac{e^{2x - x} + c}{e^{2x }}]
devout snowBOT
\[y' +2y = e^{-x}\]
\[Q(x) = e^{-x}\]
\[P(x) = 2\]
\[u(x) = e^{\int{\text{P}(x)}...
woven radishBOT
dopediscorduser
short iron
Where am I going wrong with solving this linear differential equation?
red turret
whats 2x - x = ?
lean bluff
X
red turret
asked the op
lean bluff
2x is basically x x so if you minus x from 2x you get x
devout snowBOT
@short iron Has your question been resolved?
supple knot
Where am I going wrong with solving this linear differential equation?
,tex .exp rules
woven radishBOT
riemann
zenith jacinth
2x is basically x x so if you minus x from 2x you get x
short iron
Yes sorry the term should be simplified to e^{x}
Is that correct though? It can't be simplified anymore from
[y = \frac{e^{x} + c}{e^{2x }}]
woven radishBOT
dopediscorduser
devout snowBOT
@short iron Has your question been resolved?
supple knot
Is that correct though? It can't be simplified anymore from
Why do you think it can be simplified further
full prawn
assume we got the following equation:
devout snowBOT
assume we got the following equation:
full prawn
$3x^2 + px + 2 = 0$
woven radishBOT
Seed
full prawn
How can we use CAS to tell us what values the variable p has to be, in order for the equation to have 1, 2, or 0 answers?
I am able to do the proccess without CAS, but the question explicitly asks for you to use CAS and only CAS
restive river
you can find a discriminant equation and graph it
in terms of p
then, where the graph is > 0, or = 0, or < 0, you know that at those p's, the original equation has 2, 1, or 0 solutions
That would be done with geogebra
full prawn
I struggle to find the way of doing this in CAS specifically, as I do not believe CAS draws any graphs in the first place
This would've been less challenging to do using Geogebra itself, yes, but CAS sort of behaves differently
restive river
geogebra draws graphs though, no?
full prawn
geogebra draws graphs though, no?
yes, geogebra does draw graphs
but CAS basically acts as a seperate application within geogebra
restive river
if you want, you can just write (discriminant equation in terms of p) > 0 into the CAS and it'll spit out the interval for which p makes the discriminant > 0, that is your case for 2 solutions
,w discriminant 3x^2 + px + 2 = 0
woven radishBOT
woven radishBOT
restive river
boom, that's p such that the original equation has 2 solutions
those two inequalities
you can do the same for = 0 and < 0
full prawn
You're right, I think it should be done using that relatively cumbersome method
Currently pressing the "x =" button, in which I get no results. Pfttt.
restive river
you don't need the sqrt surely
full prawn
you don't need the sqrt surely
Removing the squareroot sign seems to be doing the job. Fantastic!
Thanks a lot, @restive river
I would've prefered to take the approach of solving it algebraically tbh, using CAS to solve this (using this method, at least) seems to require some reshapes of the formula and writing several lines
I'll close this channel for now, thanks again
.close
restive river
Ping
because you've multiplied every term by 3, rather than just multiplying once
if I had a x b, then 3 times that would be 3 x a x b, not 3 a x 3 b
also do the squaring first, then the x3
Nvm
.close
devout snowBOT
restive river
because you've multiplied every term by 3, rather than just multiplying once
MAY GOD BLESS U and i think its also coz the q said to write 3(N) as a product of prime fsctors (prime fsctors of N)
Anywayye
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devout snowBOT
Available help channel!
delicate forge
devout snowBOT
delicate forge
this truth?
wooden veldt
That be the truth brother
delicate fox
differential geometry - https://i.imgur.com/qiGkHxt.png the instructions are "express using $\Gamma^{k}{ij}, S^{i}{j}, b_{ij}, g_{ij}$ and simplify as much as possible"
devout snowBOT
differential geometry - https://i.imgur.com/qiGkHxt.png the instructions are "ex...
woven radishBOT
nadav
delicate fox
alr ty
devout snowBOT
@delicate fox Has your question been resolved?
runic shoal
hey
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
devout snowBOT
@runic shoal Has your question been resolved?
restive river
what is [x^2]
[] is floor
Thats GIF?
Cant be wait
What does it mean to find [x²]
Oh floor
runic shoal
I tried everything but I could not solve it
I even used tartaglia formula (which Im not allowed to use)
runic shoal
3x^3 - 72x + 1 = 0 (x>1)
<@&286206848099549185>
storm crater
,wolf 3x^3 - 72x + 1 = 0
devout snowBOT
@runic shoal Has your question been resolved?
wooden veldt
write down general formulas for the sum of n, 2n, and 3n terms in an AP
ancient ravine
do you how to wait
fathom fiber
this is not human
i'm feeling really dumb
this is the most cursed thing i have ever seen in my entire life
how are you supposed to even solve this thing?
wait 2 seconds
the equation of an A.P. is of the form :
a_n=a_1+(n-1)*d
With that, we can easily conclude that the first n A.P. terms are of the form :
a_1, a_1+d, a_1+2d, ... a_1 +(n-1) d
Are you able to continue from there?
if yes
To sum the x first terms of an A.P. you just sum every term
x = a_1+a_2+a_3+... a_x
The second sum is a bit trickier, but you can start with the same idea, and you end up with
y = (a_1+a_2)+(a_2+a_3)+... a_x+a_{x+1}
z = (a_1+a_2)+(a_2+a_3)+(a_3+a_4)+... (a_{x-1}+a_x)+a_x+a_{x+1}
And there you have it! So if you remember the first equation of the sum of n A.P. terms :
z=a_1+(n-1)d
this is for the third sum
here
i hope you got it
@restive river
barren garden
if you have xsin^4(x^5)
and you need to differentiate
can you factor out the x
or you use product rule and chain rule
devout snowBOT
if you have xsin^4(x^5)
and you need to differentiate
can you factor out the x
o...
wooden zodiac
You differentiate w.r.t x, so ofc u can't act like x is a constant
It's a product of two functions hence product rule
barren garden
It's a product of two functions hence product rule
so it'd be xcos^4(x^5) +xsin^4(5x^4) ?
wooden zodiac
sin^4(x^5) is a composite of three functions
So we actually have f(x)g(p(l(x))
Take derivative of g(p(l(x))) set it equal to u(x), and use it in the product tule formula f'(x)u(x)+f(x)u'(x)
devout snowBOT
@barren garden Has your question been resolved?
supple knot
,tex .diff rules
woven radishBOT
riemann
supple knot
chain rule
barren garden
chain rule
thanks
btw is there an easy method to memorise the derivatives of trig functions?
supple knot
do a lot of problems
barren garden
do a lot of problems
what does this circle mean?
supple knot
what does this circle mean?
function composition
supple knot
**riemann**
use one of the last two rows here
restive river
it means degrees i think
devout snowBOT
@barren garden Has your question been resolved?
devout snowBOT
upper berry
need help on part a
what I don't understand is if P(x) ^ Q(x) is false, that means there are different cases. so there could be a case where P(x) is false and Q(x) is false which would make the implication false. But there is also a case where P(x) is true and Q(x) is false which would make the implication true
so like how can i answer this when i dont know what the actual truth values of P(x) and Q(x) are
devout snowBOT
@upper berry Has your question been resolved?
upper berry
<@&286206848099549185>
devout snowBOT
@upper berry Has your question been resolved?
restive river
If u have
lyric hornet
can you send an image?
main gull
I’m trying to figure out how to show my question
A picture would be the best
main gull
What's the context?
pulsar phoenix
Do you want to simplify
restive river
Yes
lyric hornet
PEMDAS
pulsar phoenix
Tes^
pulsar phoenix
Yeah
pulsar phoenix
BEDMAS
lyric hornet
Then how come my answer sheet says 0.5
well then your answer sheet is wrong
pulsar phoenix
Yes
restive river
It’s the teachers work
Textbook says it’s 0.5 too
How does that entire expression at the front just become 0? Doesn’t sin and cos oscillate forever
lyric hornet
well don't care about sin and cos
look at that e^(-b)
as b->inf
e^(-b)->0
doesn't matter what sin and cos are :)
we know they're between -1 and 1
lyric hornet
honestly I think you're instructor may have made an arithmetic mistake tbh
lyric hornet
hmm 
ah no you wrote the problem wrong lol
supposed to be (0-1) not (0-1)
this makes the second term negative
and minus a negative
restive river
Oh my got
lyric hornet
same thing as adding a positive :)
devout snowBOT
lyric hornet
Thx so much
devout snowBOT
Available help channel!
old flume
I need to find 2 pairs of opposite rays
devout snowBOT
I need to find 2 pairs of opposite rays
old flume
I got it, but I am able to use E? is e a point?
devout snowBOT
@old flume Has your question been resolved?
old flume
<@&286206848099549185>
devout snowBOT
@old flume Has your question been resolved?
vast violet
devout snowBOT
vast violet
they say simplify expressions and only want the positive exponents
Wat am i doing wrong 😭
Oh my god
I just realized
🤦🏻♂️🤦🏻♂️🤦🏻♂️
vast violet
Yes i turn them to radical right?
quaint cove
16^(1/2) ≠ 8
quaint cove
And it won't be x²
quaint cove
2*1/2 = 1
quaint cove
get sq root basically
Square root of 16 is 8?
vast violet
4
Idk what was going through my head
I was doing 16^1/2 as 8 thinking i just needed half of 16
quaint cove
What is the square root of 64?
vast violet
8
quaint cove
What did u write
quaint cove
💀
vast violet
i give it another shot hopefully all will be good
quaint cove
Good luck
quaint cove
(y/x)² looks better
main gull
Unrelated but your y took like half the page lmao if it helps, I suggest using printer paper because it has no lines because I know that fraction lines and the lines on the paper make it hard
quaint cove
devout snowBOT
@vast violet Has your question been resolved?
plush light
devout snowBOT
plush light
calacumus 
dry oxide
calacumus👍
plush light
wjat
plush light
$\frac{e^x - 1}{x} + 1$
woven radishBOT
dabbingpotato
plush light
uh
timid whale
hmm
plush light
i don't think this the way
plush light
no
plush light
how do you tell if its a standard limit
timid whale
theres some basic limits
which youre tought
like sinx/x
this is exponential limit
timid whale
ok l hospital
it is a 0/0 form
so you can differentiate
what do you get
you get e^x+1
e^x when x tend to 0 is 1
1 +1 is 2
restive river
can someone double check if this is correct please last try and i dont wanna restart lol thanks
devout snowBOT
can someone double check if this is correct please last try and i dont wanna res...
supple knot
can someone double check if this is correct please last try and i dont wanna res...
!show
devout snowBOT
can someone double check if this is correct please last try and i dont wanna res...
Show your work, and if possible, explain where you are stuck.
supple knot
Yea that was hard to follow but I think it's right
restive river
Yea that was hard to follow but I think it's right
yea my bad i do half the math in my head n half on paper i needa start doing a better job thank you
.close
hard warren
devout snowBOT
sonic smelt
Look at what du is equal to
hard warren
so where does dw go?
sonic smelt
(1 - 1/w)dw = du
cos(w - lnw) = cos(u)
So (1 - 1/w)cos(w - lnw)dw = cos(w - lnw) * (1 - 1/w) dw = cos(u) du
hard warren
oh wait if you were to solve for dw either way it would be dw= du/(1-1/w) so that would cancel out 1-1/w and just leave du
sonic smelt
Yes
hard warren
is that generally what to do when doing u substitution?
when doing u sub, is it generally to cancel out a term in the integral
sonic smelt
Of course
devout snowBOT
devout snowBOT
Available help channel!
topaz wyvern
is this correct?
devout snowBOT
is this correct?
topaz wyvern
it is a parabola
scarlet shale
yes, mark the axes tho
devout snowBOT
@topaz wyvern Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
heavy wedge
I don’t get it
devout snowBOT
I don’t get it
dreamy gorge
use the exponent rules
heavy wedge
use the exponent rules
In which order?
dreamy gorge
i dont think it matter here
ex 1 for the 4x^3
itll become 4^1/2 * x^3 * 1/2
and then ofc you simplify it to get rid of expnents and so on and so forth
heavy wedge
No for question 1 d)
dreamy gorge
no
dreamy gorge
you see how 1d is raised to the 1/2
it will become 4^1/2 * x^3/2
and you can simplify from there
because it is multuplying 4 * x^3
heavy wedge
How have u split it up
dreamy gorge
because it is multuplying 4 * x^3
thats how u split it
heavy wedge
Can u pls use @woven radish I don’t understand from text
dreamy gorge
idk how that works lol
heavy wedge
Is the answer 2x square root x?
dreamy gorge
yea
tacit swan
heavy wedge
I searched that up… how Tf can I get to that
tacit swan
dreamy gorge
because it is multuplying 4 * x^3
by simplifying this lol
heavy wedge
Where did the square root come from
dreamy gorge
an exponent raised to 1/2 is equal to square root
dreamy gorge
use the fractional exponent
heavy wedge
I’m way too stupid for this
heavy wedge
the more u do the easier it is
Exponent is indices?
heavy wedge
it will become 4^1/2 * x^3/2
Where did the 3/2 come from?
heavy wedge
itll become 4^1/2 * x^3 * 1/2
4^1/2 = 2
(2x^3) ^1/2?
Wait I’ve got half of it now
Done
Finished
.close
quasi finch
Help
quasi finch
Question : If tan x = 1/root of 3 , then sin 6x?
So in this case I want to make sin 6x from sin (3x+3x)
And I got sin 3x = 5 root of three/9
After that I want to find cos 3x using the formula : 4 cos^3x - 3 cos x
red turret
Question : If tan x = 1/root of 3 , then sin 6x?
just find x from your first equation
why go through so much hassle
quasi finch
This is the cos 3x if I use pythagoras theorem
But this is the cos 3x if I use the cos 3x formula (cos 3x = 4 cos^3x - 3 cos x)
Which cos 3x is correct?
quasi finch
How to know the one that's in the right range of x without using calculator?
supple knot
is cos(x) positive or negative in the range 30deg < x < 90deg ?
quasi finch
Positive
supple knot
good. now answer the question for cos(3x)
quasi finch
Wait, is this the right cos 3x?
supple knot
i didn't check all your algebra
but since you have different signs for the same number, the correct answer is usually chosen based on the range
quasi finch
Wait, is this the right cos 3x?
Because I've tried using that cos 3x (the positive one), and the final answer isn't correct
And, when I use the negative one, the answer is correct
That's why I'm confusing right now
wheat pawn
there's 2 angles with the same trigonometric function value and sign within 0º<=x<360º; There's an additional two that have the same value but opposite sign.
You need additional information to determine which of the two is. In this case, they are telling you it's the one in the first quadrant
quasi finch
And, when I use the negative one, the answer is correct
Can you explain to me why when I use the negative one, the final answer for sin 6x is correct?
Because as far as I know the negative one is outrage of x, but why the final answer for sin 6x is correct when I use the negative one?
Btw, my statement about "Because as far as I know the negative one is outrage of x" is correct, Is it?
@wheat pawn
wheat pawn
the negative what, sorry?
quasi finch
But this is the cos 3x if I use the cos 3x formula (cos 3x = 4 cos^3x - 3 cos x)
I mean, this one @wheat pawn
wheat pawn
are you allowed to use a calculator, or do you need to get the exact values without computing the angle?
quasi finch
No, I'm not allowed to use a calculator
I just need to get the exact values without computing the angle
coral tulip
Which qstn are you talking about?@quasi finch
coral tulip
Question : If tan x = 1/root of 3 , then sin 6x?
This one?
wheat pawn
Question : If tan x = 1/root of 3 , then sin 6x?
Okay, let's start by the beginning.
You get given tanx, not sinx
wheat pawn
so you actually got sinx=1/sqrt3?
quasi finch
Yes
wheat pawn
Okay.
Since you know the formula for sin3x, i assume you also know the one for sin2x, correct?
quasi finch
Yep, 2sinxcosx
wheat pawn
okay. Since you got sinx, i assume you know how to get cosx
quasi finch
Use the pythagoras theorem?
wheat pawn
that's one of the ways. So you do know.
Now:
Let's call 3x = y
Let's call 2y = z
compute siny = sin3x from the formula you've given in MSPaint
compute cosy = cos3x with pythagoras
compute sinz = sin2y = sin6x with the formula you've given me last
quasi finch
compute siny = sin3x from the formula you've given in MSPaint
compute cosy = cos...
sin 3x =5 root of three/9
cos 3x = root of 6
sin6x = 10 root of 2/27
But actually, the correct answer from the answer key is -10 root of 2/27
quasi finch
compute siny = sin3x from the formula you've given in MSPaint
compute cosy = cos...
I think the problem is from the cos 3x, because if I use the negative root of 6/9 (from the original formula of cos 3x), the final answer for sin 6x will be negative too, which is the correct answer
But the problem is, -root of 6/9 is outrage of x
wheat pawn
keep in mind that when obtaining the cosine of 3x, you're gonna get two possible values.
At the start, you're told that 30º<x<90º
That means that 90º<3x<270º
Which means that the cosine of 3x will be the negative one
wheat pawn
you can restrict more the value of x, since you know that 1/sqrt(3) is less than 1/sqrt(2), which means that x is also x<45º
that brings the range to 30º<x<45º, which means 90º<3x<135º, which will also mean that 180º<6x<270º, so the angle will be on the third quadrant, and thus, both sine and cosine of 6x will be negative
quasi finch
keep in mind that when obtaining the cosine of 3x, you're gonna get two possible...
Tysm, I just realized the "90º<3x<270º"
wheat pawn
But the problem is, -root of 6/9 is outrage of x
x is not the same as sinx.
-sqrt(6/9) = -sqrt(2/3) which is approx. -0.81
the angle with a sine of -0.81 would be -54.7º = 305.3º (fourth quadrant)
quasi finch
Ahh I see
wheat pawn
6x is about 211º, and sin6x should be about -0.5 (rounding, you should get the actual value yourself), so you can check your answer
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dreamy gorge
devout snowBOT
dreamy gorge
i know how to solve both
but
for the first we use dot product, and for the second we use cross product. Why don't we use only dot product for the second one?
because I thought when finding angles, we have to use dot product
devout snowBOT
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kind sable
e^y=x^2-4x+4
=>e^y=(x-2)^2
=>y=ln((x-2)^2)
All steps correct??
devout snowBOT
e^y=x^2-4x+4
=>e^y=(x-2)^2
=>y=ln((x-2)^2)
All steps correct??
frosty nebula
e^y=x^2-4x+4
=>e^y=(x-2)^2
=>y=ln((x-2)^2)
All steps correct??
Yeah this is correct
frosty nebula
Its not y=ln(x-2)^2 right?
Nope. From property of logarithms, we know $\ln((x-2)^2) = 2\ln(x-2) \neq (\ln(x-2))^2$
woven radishBOT
thedude365
devout snowBOT
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dusty stone
Can someone help explain why this equation having no real roots means that the determinant of the matrix can’t be -1?
devout snowBOT
Can someone help explain why this equation having no real roots means that the d...
dusty stone
Pls ping if you have an answer
devout snowBOT
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devout snowBOT
@dusty stone Has your question been resolved?
wheat pawn
Pls ping if you have an answer
where's the actual exercise 8?
dusty stone
Mb here
wheat pawn
what kind of transformations have you studied?
i assume rotations, reflections and scalings?
Anyways. You're given that a reflection matrix A has detA = -1
det N = (k+1)(k+2)
Hence, if the matrix represents a reflection,
(k+1)(k+2) = -1
k^2 + 3k + 2 = -1
k^2 + 3k + 3 = 0
Since this equation does not hold for any real k, there's no k that will hold that detN = -1
Since detN cant be -1, N cant be a reflection
dusty stone
i assume rotations, reflections and scalings?
Yeah
dusty stone
Anyways. You're given that a reflection matrix A has detA = -1
det N = (k+1)(k+2...
Ah I see thanks
.close
ornate fable
dense jay
!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
still havent figured it out
dense jay
do you have any ideas at all?
dense jay
base charge is $29
every gb above 5 is +$6 (d-5) would be a valid way you could express the gb s above 5
can you think of a way to put that together?
woven radishBOT
AℤØ
dense jay
just ignore that
winter zenith
But this is the cos 3x if I use the cos 3x formula (cos 3x = 4 cos^3x - 3 cos x)
i dont understand ser
how to solve
dense jay
i dont understand ser
you'll have to open a new channel
ornate fable
so would it be p(d) = 29+6(d-5) ?
dense jay
looks good to me
ornate fable
thank youu
devout snowBOT
@ornate fable Has your question been resolved?
marsh yacht
I need to find the domain of f, in a compound inequality form but I am not sure when or how to use the greater than or equal to or the regular greater than etc.
devout snowBOT
I need to find the domain of f, in a compound inequality form but I am not sure ...
marsh yacht
I also cannot send pictures
devout snowBOT
@marsh yacht Has your question been resolved?
slim hornet
stuck on this one https://gyazo.com/35719fbb39578081b6f01f5210177616
slim hornet
there's a point of discontinuity at x=1 but i dont know how to express that with a table
do we use the point of discontinuity or the actual point
sharp palm
The black dot means the actual value at x = 1.... the white dot (or circle, whatever) is where x = 1 discontinues on the y scale
slim hornet
right\
sharp palm
If f(x) is a piecewise function, I would say that f(1) = 7
slim hornet
but then when it comes to using limits for that
and it's a similar style
pnt of discont and an actual point
sharp palm
The limit of f(1) would definitely be 4
sharp palm
Correct, I would agree
slim hornet
gotcha tysm
sharp palm
It's ambiguous
If it was f(3+) it would be 0 and if it was f(3-) it was 2... but since those are different the limit doesn't exist for f(3)
devout snowBOT
sharp palm
You're welcome 🙂
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Available help channel!
vast violet
Help pls
vast violet
Another scenario i deal with that i need to make it in a form that like ax^2+bx+C
devout snowBOT
@vast violet Has your question been resolved?
devout snowBOT
@vast violet Has your question been resolved?
dreamy gorge
devout snowBOT
dreamy gorge
i know volume is the integral of the bounds by the cross sectional area
and the area of this cross section is 1/2 * b * h
I have a relation for b but how do I find one for height?
rapid merlin
Are you sure that this all that got in the question
I mean I can't draw the question in my head depending on that
dreamy gorge
Are you sure that this all that got in the question
I mean I can't draw the ques...
this is the entire question
finding moments while avoiding the question
i tried to draw it out but its so hard to visualize
thats like my current sketch
its a triangle so im assuimg to find necessary componets i need to use pythagorean theorm i just dont know how
OH
dreamy gorge
Are you sure that this all that got in the question
I mean I can't draw the ques...
ITS ISOSCELES LMAO
the two legs are the same
overthinking it for no reason lol
we ball
ggs
.close
lapis jolt
devout snowBOT
lapis jolt
i need to graph those subsets in plane R2
something like this
but i dont really get how to do it with x and y
i got it lmao
.close
devout snowBOT
devout snowBOT
Available help channel!
torpid elbow
devout snowBOT
devout snowBOT
@torpid elbow Has your question been resolved?
gilded coyote
I'm trying to understand the exponent rules more cleanly. When some online math educators (like khan) show exponentiation, they do something like:
a^2 = a * 1 * a
Is the actually what's happening? Do the laws of exponents tell us that we begin all exponentiation by first multiply the base number by 1? This doesn't seem right for some reason. It obviously works, but it feels wrong.
It feels as if a^0 should equal a; a^1 should equal a*a. This obviously isn't how it works, but I'm wondering what's actually happening when we're raising something to a power.
I've been out of school for over a decade, so I'm relearning the basics, and trying to actually understand what's going on rather than just regurgitating formulas.
devout snowBOT
I'm trying to understand the exponent rules more cleanly. When some online math ...
gilded coyote
If I didn't represent my question clearly, just let me know.
I should note that from what I remember in middle school, they'd always say "exponents tell you how many times to multiply the base times itself."
Using that language, a^2 would be multiplying a times itself twice. a * a * a. Which is a^3, not a^2.
Is there a different way of wording it that's closer to what's happening?
empty flame
$a^n=aaa.*a..$ n times where n is a natural number ie a number like 1,2,3,4,5...
woven radishBOT
calculus is fun
amber plume
I should note that from what I remember in middle school, they'd always say "exp...
its easy
actually
empty flame
so its just a shortcut to simplify writing
empty flame
instead of writing 100 2s to multiply them all you can just say 2^100
amber plume
is a
the exponent
defines how many times the number has to be written
@gilded coyote are you even there?
gilded coyote
Yes, I'm just reading
amber plume
ok
see
a^1 = a
a = a
hence
a is the number of times it can be represented as a integer
if you are revising i believe that you must know integers right
gilded coyote
Is it sort of like saying
amber plume
@gilded coyote understood?
empty flame
Yes, I'm just reading
is the concept clear
gilded coyote
whoops, mistyped
amber plume
is the concept clear
i am asking that too
gilded coyote
I think I understand.
amber plume
so
u can contact anyone antime (not me because i am not alsways ther)
but yeah
this server is for that only
bye
.close
@gilded coyote u can close it if you want
pale bolt
.close
neat bridge
devout snowBOT
neat bridge
wym
neat bridge
the question is about the area of the graph until t
that gets us the distnace yes
neat bridge
look at part a
tropic zealot
how can I prove that this is true?
where U_n is number of unlabeled tree with n vertices
devout snowBOT
how can I prove that this is true?
where U_n is number of unlabeled tree with n ...
tropic zealot
$U_n < \binom{2n-2}{n-1}$
woven radishBOT
Choram
tropic zealot
I have no Idea where I should start
narrow grove
what is $U_n$ ?
woven radishBOT
exophades
tropic zealot
it's number of non-isomorphic unlabeled tree with n vertices
narrow grove
induction is the firsst thing that comes to mind
tropic zealot
hmm... I tried but induction step was very complicated
narrow grove
I kind of found the solution online
and the catalan number is
This number is equal to U_n in your problem
tropic zealot
This number is equal to U_n in your problem
umm actually it is not
catalan number is number of unlabelled 'binary' trees
U_n has different values
it's OEIS A000055
tropic zealot
in what way is it different
U_n is number of any unlabelled trees but catalan number is number of unlabelled binary trees
narrow grove
U_n is number of any unlabelled trees but catalan number is number of unlabelled...
I see
tropic zealot
For example, first 10 values of U_n is 1, 1, 1, 1, 2, 3, 6, 11, 23, 47
tropic zealot
apparently there is no closed formula for it
sadly no
tropic zealot
hmm..
narrow grove
tough shit really
narrow grove
I think I found something
a guy in the comments answered the question
he said it's at most $n \cdot 4^n$ don't ask me why
woven radishBOT
exophades
narrow grove
so we just need to show that $n \cdot 4^n < \binom{2n-2}{n-1}$
woven radishBOT
exophades
tropic zealot
so we just need to show that $n \cdot 4^n < \binom{2n-2}{n-1}$
actually it is $n \cdot 4^n > \binom{2n-2}{n-1}$
woven radishBOT
Choram
narrow grove
actually it is $n \cdot 4^n > \binom{2n-2}{n-1}$
why
tropic zealot
but it is true that $U_n < \binom{2n-2}{n-1} < n \cdot 4^n$
woven radishBOT
Choram
narrow grove
well it's confusing because he said the number of unlabeled trees is at most n4^n. "at most"" usually means the bound is attained
narrow grove
**Choram**
but yeah that's probably what they meant
tropic zealot
hmmm...
devout snowBOT
@tropic zealot Has your question been resolved?
tropic zealot
<@&286206848099549185>
devout snowBOT
@tropic zealot Has your question been resolved?
storm crater
https://mathoverflow.net/questions/352972/bound-on-the-number-of-unlabeled-tree-...
hey, don't forget
!nosols
devout snowBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
storm crater
narrow grove
this one is pretty hard, I know the rules but..
narrow grove
when it's tough it's tough
narrow grove
that's the "fun", right
it's fun until it's not fun anymore
devout snowBOT
@tropic zealot Has your question been resolved?
tropic zealot
Actually this is not homework
My friend told me that this was true and I tested with my computer
But I have no idea how to prove this is true
storm crater
https://mathoverflow.net/questions/352972/bound-on-the-number-of-unlabeled-tree-...
Did you read this?
narrow grove
My friend told me that this was true and I tested with my computer
if he just tested it with random values of n that doesn't mean it's true
tropic zealot
Did you read this?
Yes
storm crater
if he just tested it with random values of n that doesn't mean it's true
Hey, I think you are just not a physicist 👨🔬
devout snowBOT
@tropic zealot Has your question been resolved?
sour gull
Hi
trim minnow
get his ass out of here
acoustic bridge
...
devout snowBOT
@tropic zealot Has your question been resolved?
brisk lily
Is it ok if I ask help for an assignment
devout snowBOT
Is it ok if I ask help for an assignment
red turret
yeah, its alright.
just post your question.
@smoky gyro why did you react with that?
devout snowBOT
@brisk lily Has your question been resolved?
gaunt flame
Ive searched youtube videos but i cant find anything that explains how to do this
devout snowBOT
Ive searched youtube videos but i cant find anything that explains how to do thi...
winter patrol
what were you looking up
low coyote
So 7ⁿ means the n-th term is 7ⁿ
So what is the first term, second term, third term...
gaunt flame
Geometric and aeithmetic nth term
winter patrol
the type of sequence doesn't really matter
given the general expression for the nth term
sub in the value(s) of n to get those terms
gaunt flame
Is the answer 7,14,21,28
gaunt flame
Welp
low coyote
What is the difference between 7n and 7ⁿ??
gaunt flame
What do you mean
restive river
put n = 2 :)
gaunt flame
But the question asked to write down the first four terms
How do i find out those terms with only knowing the sequence is 7n
restive river
is the serie a gp or ap
low coyote
So 7ⁿ means the n-th term is 7ⁿ
THIS
restive river
Ive searched youtube videos but i cant find anything that explains how to do thi...
i kinda thought the black things a machine gun
winter torrent
to be clear, $7^n$ means $\underbrace{7\cdot7\cdots7}_{n\text{ times}}$
woven radishBOT
hayley!
devout snowBOT
@gaunt flame Has your question been resolved?
late egret
hello if i factor a quadratic trinomial do i also need to use the quadratic formula?
devout snowBOT
hello if i factor a quadratic trinomial do i also need to use the quadratic form...
eager lodge
winter torrent
qf is a way to factor a trinomial but it's kind of a pain
late egret
okay thanks i was just making sure if using qf is good before i make my calculator program run trinomials
devout snowBOT
Available help channel!
restive river
How did pisagor find pythagorean triplets
devout snowBOT
How did pisagor find pythagorean triplets
livid geyser
he willed them into existence
cinder mesa
trial and error?
supple knot
About else
about what?
anyway, you're asking a historical question
https://www.popularmechanics.com/science/math/a37269363/babylonian-pythagorean-triples/
maybe try looking for a history discord server
devout snowBOT
@restive river Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
forest geode
!help
forest geode
A sector of a circle has a radius of 13.2m and an angle of 181° at its centre.
Calculate
a. The sector’s area.
b. (i) The arc length
(ii) The perimeter of the sector.
(a) Sector Area = 181/360 * pi * 13.2^2
= 275.216082825m^2
(b) Arc Length = 181/360 * pi * 26.4
= 41.6994064886m
(ii) p = Arc Length + 2r
p = 41.6994064886 + 2 * 13.2
p = 41.6994064886 + 26.4
p = 68.0994064886
