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#help-0
lone heartBOT
Available help channel!
night lodge
lone heartBOT
night lodge
where does the 1/2 come from
ah 9^1/2 = 3
not entirely sure how im supposed to find that out tho?
alpine sable
not entirely sure how im supposed to find that out tho?
Remove the log. You send the base to the right-hand side here, so 9 raise to the power y. Which can be re written as 3 to the power 2y.
Bases are equal now.
So, 2y = 1.
y= 1/2.
Just practice the questions. You'll get a hang of it.
proven leaf
not entirely sure how im supposed to find that out tho?
$n^{\frac{1}{2}}=\sqrt{n}$
ocean sealBOT
XxMrFancyu2xX
lone heartBOT
proven leaf
ty both of u
yw! 
lone heartBOT
Available help channel!
potent flame
I only got 2 are there more than 1 answers?
lone heartBOT
I only got 2 are there more than 1 answers?
Show your work, and if possible, explain where you are stuck.
potent flame
I got the answer but Im not sure if there is more than one for this question
alpine sable
how did you get x=2?
potent flame
simplified the left side of the log then just continued with solving it and got 2, and-18 but -18 does not make the equation true
so idk if 2 is the only answer i put or -18 also
alpine sable
yes, you are right
potent flame
so i only put 2?
alpine sable
x>0 is assumed
potent flame
what that got to do
alpine sable
you cant take logs of negative numbers
lone heartBOT
@potent flame Has your question been resolved?
night zephyr
Hello! I need help with this question where do I start
lone heartBOT
Hello! I need help with this question where do I start
night zephyr
Im not quite sure what to do, as I cannot find it in any of my homework
hasnt been quite 15 minutes but <@&286206848099549185>
proven leaf
hasnt been quite 15 minutes but <@&286206848099549185>
lol ok I can help, is your goal only to sketch?
night zephyr
-3 and 0
proven leaf
yep ok good, so because $\sqrt{0}=0$ those will be zeroes of root f(x) as well :))
ocean sealBOT
XxMrFancyu2xX
night zephyr
like this?
proven leaf
that is not $\sqrt{f(x)}$
ocean sealBOT
XxMrFancyu2xX
night zephyr
that is not $\sqrt{f(x)}$
im not sure,
uhhh do I take f(x) = (x + 3)(x - 0)
no
ahh
my thinking behind that was if its sqrt root i need to take that point and square root it
every point where the line passes through
night zephyr
**XxMrFancyu2xX**
I don't quite understand this part sorry
The domain for y = f(x) is (x, infinity) and the range is (y equal to and greater than -3)
sorry i should say -infinity to infinity for the domain
Mr. Fancy?
tawdry urchin
if you take a square root of a negative number, it will be complex, and therefore unrepresentable on your graph
so any value > 0 will not satisfy your function
so your domain will be from 0 to inf
night zephyr
okay
tawdry urchin
do you know if you have to take plus-or-minus when you take sqrt?
night zephyr
im still lost sorry, I just not sure what exactly what to do. I know my zeros are -3 and 0
tawdry urchin
because i know some teachers like to get rid of the negative solution
i don't think the zeroes matter?
night zephyr
we didn't even go over this question, well i don't remember it so im a little lost as to how to convert the graph from y = f(x) to y = sqrt f(x)
night zephyr
Mathematics 30-1
tawdry urchin
which country?
night zephyr
Its not public school.
night zephyr
aight
tawdry urchin
so do you know that $\sqrt{4} = \pm{2}$
ocean sealBOT
Dork9399
tawdry urchin
so therefore you have to take whatever you have above the y-axis, and also put it below the y-axis
tawdry urchin
wait, let me make a graph real quick
night zephyr
here is the original if you wish
night zephyr
aight
tawdry urchin
now as we discussed, for the square root, everything where x<0 doesn't matter because this is a normal plane, not a complex plane
night zephyr
okay
night zephyr
yes
tawdry urchin
so firstly, our domain is obv x>0, since x cannot be less than 0
night zephyr
right
tawdry urchin
also, when we take sqrt, we have to take plus or minus
here is a sketch of the sqrt function(red
night zephyr
okay
tawdry urchin
so your range will be from $\sqrt{2}$ to $-sqrt{2}$
ocean sealBOT
Dork9399
night zephyr
sorry my power cut out and my computer crashed
night zephyr
**Dork9399**
okay yes so far makes sense
night zephyr
alpine sable
would this be non linear ?
lone heartBOT
would this be non linear ?
placid zinc
It's linear if it's of the form
y = mx + b
alpine sable
It's linear if it's of the form
y = mx + b
so thats not in that form
im trying to follow this
placid zinc
The z makes me sus.
alpine sable
Okay, fair. So then this one is non-linear
thent his is also non linear since 100 i just a constant with no variable
alpine sable
thats right
alpine sable
ye
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
Hello I could use some help in trig
lone heartBOT
Hello I could use some help in trig
alpine sable
cos theta / csc theta -1 * csc theta +1 / csc theta +1
The first thing i did was combie the bottom into a id and got the top / -cot^2
i think thats right so far
hello...
anyone
.close
fallen verge
Thats a plus/minus symbol
Hmm idk if it has a specific name
Yes
For example
If you have a problem like x^2=4, both -2 and 2 are solutions
So you can say x=±2
lets say you just have b-3=2, can you solve for b?
How did you do that?
lone heartBOT
fallen verge
Youre welcome
opal merlin
I’m confused where to even start
keen mason
Have you solved 4th order polynomials before?
alpine nacelle
if you're thinking about rational roots theorem, then for all rational roots p/q written in the form such that p and q are relatively prime, p divides the constant term, and q the leading coefficient
keen mason
which is p and which is q?
P is the constant in the question (-20) and q is the leading co-effecient
1
proven leaf
that is not all the possibile cases
opal merlin
it would be plus or minus 1,2,4,5,10,20
opal merlin
what do I do with that
lol
wait how can I figured out the end behavior of the graph
proven leaf
wait how can I figured out the end behavior of the graph
what's the parity of this function?
opal merlin
wdym
proven leaf
is it even or odd?
opal merlin
even
opal merlin
the main thing that determines if it’s even or odd is the highest exponent
so the x^4 is even?
proven leaf
well the entire function is even but x^4 also is
because $x^4$ will dominate the $x^3 \gg x$
ocean sealBOT
XxMrFancyu2xX
opal merlin
so what determines if it will be up down
proven leaf
the coefficient of the largest exponent 
opal merlin
oh right
proven leaf
so we have a positive even highest exponent, what does that tell us about our end behavior? :))
opal merlin
up up
proven leaf
yep!
proven leaf
it would be plus or minus 1,2,4,5,10,20
already did ^
opal merlin
don’t I have to solve?
proven leaf
yep
test small numbers first especially considering you have small coefficients
I would probably test a number like 1 first
proven leaf
yep!
gusty gorge
test by plugging in
synthetic division if it comes out to zero
otherwise you're wasting a lot of time calculating terms that you'll toss
lone heartBOT
lone heartBOT
Available help channel!
barren scroll
lone heartBOT
fallen verge
So 30' is how many degrees?
lone heartBOT
Please read #❓how-to-get-help
olive shell
??
olive shell
How
alpine sable
just go to any empty one and send a msg
olive shell
Already read it it says go to zero to ask
barren scroll
A minute is 1/60 of a degree
can i just divide the 30/60
alpine sable
Already read it it says go to zero to ask
no just go to any channel
they used 0 as an example
lone heartBOT
@barren scroll Has your question been resolved?
tardy stag
can i just divide the 30/60
yeah
grizzled echo
cerulean garnet
channel is taken
wheat isle
For 4e
proven leaf
to find the slope of the tangent of the point at $a$ we need $\left.\frac{\mathrm{d}}{\mathrm{d}x}\right|_{x=a}$
plugging in zero would give the minimum/maximum i.e. points with slope=0
wheat isle
dx/dx?
proven leaf
d/dx*
wheat isle
oh
ocean sealBOT
XxMrFancyu2xX
proven leaf
dx/dx lol 
wheat isle
wheat isle
plugging in zero would give the minimum/maximum i.e. points with slope=0
So that wouldn’t give us the y value?
proven leaf
ok hang on first what is f'(x)?
proven leaf
oh ok for e
i though you were doing d and got a really wrong answer
anyways
i digress
wheat isle
lol
wheat isle
Alright I’ll do that now
wheat isle
Oh
ohh ok
What would happen if we plugged that into the derivative instead of the original function?
proven leaf
we'd get the slope of the function at t=2 which is our next step :))
proven leaf
v(2)=6 but yes
proven leaf
ok good, we have our point!
now what is the slope of the function at t=2?
you already did this 
wheat isle
now what is the slope of the function at t=2?
44
proven leaf
yep! 🙂
ok now we have the slope and the point
do you know any linear equation that takes these two inputs and gives a line 
proven leaf
yep :))
wheat isle
but we need a y value for that unless we’ve already found that 
proven leaf
so you have x1,y1 and m
wheat isle
Oh we do have y1?
proven leaf
what you think we did for? 😂
proven leaf
now Bob's your Uncle!
lone heartBOT
lone heartBOT
Available help channel!
frosty solstice
wo functions f1, f2 : A → B are equal if and only if they agree on each element of the
domain, i.e., f1(a) = f2(a) for all a ∈ A.
(a) Show that if f : A → B has an inverse g : B → A, then this inverse is unique. It therefore makes
sense to speak of the inverse of a function, and to write f −1 for the inverse going forward.
(b) Show (by example) that a function f : A → B may have several distinct left inverses.
(c) Show (by example) that a function f : A → B ma
pls help
ivory fern
wo functions f1, f2 : A → B are equal if and only if they agree on each element ...
Which definition of inverse are you using?
frosty solstice
the inverse of f: A--> B may be g: B --> A
ivory fern
But how do you define it?
frosty solstice
what do you mean?
ivory fern
What condition must an inverse of f hold?
frosty solstice
a = f(b)
b = f(a)
this one?
ivory fern
a = f(b)
b = f(a)
this one?
No
frosty solstice
im afraid i dont understand your question
ivory fern
Doesn't your book say something like this?
Definition. Let f: A--> B be a function. g is an inverse of f if...
ivory fern
it does not
I will assume that you should use the following definition: g is an inverse of f: A -> B if g(f(a)) = a for all a ∈ A and f(g(b)) for all b ∈ B
frosty solstice
okay
makes sense
I'll email my professor tomorrow and ask him if it's okay but i see no reason for it to not be
ivory fern
wo functions f1, f2 : A → B are equal if and only if they agree on each element ...
To prove (a), you have to show that g is the unique inverse in case it exists. In general, an object k is the unique one which holds some property P if any object x that holds the property P equals k
So in this case, you have to show that if h is some inverse of f, it equals g
frosty solstice
is this answer correct
Suppose f : A → B has an inverse g : B → A, and let h : B → A be another inverse of f. We want to show that g = h.
To show that g = h, we need to show that g(b) = h(b) for all b ∈ B.
Let b ∈ B. Since g and h are inverses of f, we have:
f(g(b)) = b and f(h(b)) = b
Now, consider the composition of functions f(g(b)) and f(h(b)). We have:
f(g(b)) = f(h(b))
Since f is a function, it means that g(b) = h(b) for all b ∈ B. Therefore, g = h, and the inverse is unique.
ivory fern
Suppose f : A → B has an inverse g : B → A, and let h : B → A be another inverse...
No, that is not correct. f(g(b)) = f(h(b)) does not imply g(b) = h(b)
That applies only in the case that f is injective
frosty solstice
hmm
ivory fern
I will assume that you should use the following definition: g is an inverse of f...
Try to modify the proof using the other condition, g(f(a)) = a for all a ∈ A
frosty solstice
The function f: A → B is injective and has inverse functions g: B → A and h: B → A.
To show that g = h, we need to prove that g(b) = h(b) for all b ∈ B.
Let b ∈ B. Since g and h are inverses of f, we have:
f(g(b)) = b and f(h(b)) = b.
Now, consider g(b) and h(b). We want to show that g(b) = h(b).
Assume, for the sake of contradiction, that g(b) ≠ h(b).
Since f is injective, we know that if f(a₁) = f(a₂), then a₁ = a₂ for any a₁, a₂ ∈ A.
Considering f(g(b)) = b and f(h(b)) = b, if g(b) ≠ h(b), then f(g(b)) ≠ f(h(b)).
However, this contradicts the fact that both f(g(b)) and f(h(b)) equal b. Therefore, our assumption that g(b) ≠ h(b) must be false.
Consequently, we can conclude that g(b) = h(b) for all b ∈ B, and thus g = h.
@ivory fern
ivory fern
The function f: A → B is injective and has inverse functions g: B → A and h: B →...
That is correct if you know that f is injective
ivory fern
wo functions f1, f2 : A → B are equal if and only if they agree on each element ...
But that is not a hypothesis
However, there is a theorem which says that a function with an inverse is bijective (and therefore injective), which perhaps you can use
frosty solstice
f: A → B has an inverse g: B → A and another inverse h: B → A, then f is an injective function.
does this work?
ivory fern
However, there is a theorem which says that a function with an inverse is biject...
It does, if you have this theorem
frosty solstice
what exactly is the theorem
ivory fern
Was it proven previously?
ivory fern
what exactly is the theorem
A function is invertible (has an inverse) if and only if it is bijective
lone heartBOT
@frosty solstice Has your question been resolved?
desert prism
lone heartBOT
desert prism
would I set f(x)=g(x)
then isolate for a and then sub it back into f(x) and then isolate for b and solve?
tardy stag
you need the function and its derivative to be continuous
just f(x) on its own won't be enough to find both a and b
desert prism
oh ok
so i take the derivative of both sides and i end up with 2a=-8/sqrt(2+b)
multiply each side with the denominator i assume?
tardy stag
sure
tardy stag
go to the next equation :P
or you can try to get the sqrt(2+b) on its own and square both sides
chrome monolith
Help
plucky token
lone heartBOT
@chrome monolith Has your question been resolved?
lone heartBOT
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Available help channel!
modern maple
How do I solve example 3
lone heartBOT
How do I solve example 3
marble coral
y = ax + b
a = 3 right?
tardy stag
they give you a chart so you might as well use it
you know one of the points, go ahead and draw that
and then you know slope is rise/run, right?
tardy stag
okay so can you draw a line of slope 3 coming from that point?
then see what value it has for x=3 to find y
tardy stag
✅
tardy stag
the horizontal axis
modern maple
I mean what does the - beside the x mean
surreal meadow
modern maple
Idk how to do the problem
Oh wait does it mean
Y needs to be 0?
So it’s on the black line
tardy stag
✅
modern maple
I’m not sure about these
tardy stag
Not allowed to graph it
make a chart instead
do like
x y
4 6
5 8
6 10
or extend it backwards if you need to
lone heartBOT
lone heartBOT
Available help channel!
quasi kettle
lone heartBOT
quasi kettle
Anybody know why this keeps happening? Am I using the options wrong?
tardy stag
you're grepping stdin
you probably want to give it a filename to look through or use -r (recursively search the current directory)
quasi kettle
Supposedly h is a no file name option but I don’t know if the syntax is correct
How do I get out of the blank line with the blinking cursor?
tardy stag
ctrlC should stop the process
quasi kettle
Thank you!
tardy stag
-h means don't print a filename with the output, let me get an example
quasi kettle
Ahh okay
tardy stag
quasi kettle
Ahh so h doesn’t affect the redirection just what is printed
tardy stag
correct
quasi kettle
You are the best! Thank you Hayley
tardy stag
quasi kettle
.close
plucky tree
am i totally stupid or does this not make any sense
lone heartBOT
am i totally stupid or does this not make any sense
carmine reef
Without a diagram it definitely doesn't make any sense
plucky tree
thats all there is to the question
vapid shuttle
that is not true
what are p and t
random letters?
no
they come from a diagram that you aren't including
what are angle 1 and angle 7?
vapid shuttle
what are these questions from?
plucky tree
a quiz
vapid shuttle
we can't help you with your quiz anyways
plucky tree
it says tests or exams!
vapid shuttle
are you allowed outside help with this quiz in your class?
plucky tree
yes its online
vapid shuttle
it being online doesn't mean your teacher said you could get outside help with it
plucky tree
no but she explicitly said if you don’t understand anything to use the resources around you
vapid shuttle
I'm not so sure that this is what she meant by that. But anyways, either there is a picture above or below this question that is meant to be part of it, or the question is not solvable and whoever made the quiz made a mistake with this question.
alpine sable
This may be aweird one but does anyone know why im getting an error
alpine sable
with this matrix
tardy stag
first row has 7 elts, second row has 6
or 6 and 5 whatever
point is they're different
alpine sable
ye your right lol
lone heartBOT
@alpine sable Has your question been resolved?
heady finch
22nd question please
lone heartBOT
22nd question please
heady finch
I got this
heady finch
But the answer key says (-∞, -3) U [1, ∞) - {4} U {-2}
vale wigeon
anyway (x+3)^2021 is an odd exponent
heady finch
those x's do not look like x's at all lol
Aight
vale wigeon
so the curve should cross, not touch, at x=-3
heady finch
Ah okay
vale wigeon
also keep in mind that (a) your inequality is weak and (b) -3 and 4 should not be part of the solution set nmw
heady finch
so the curve should cross, not touch, at x=-3
Wait I don't get this
If we put a value between 2 and 3 such as 2.5 in place of x, wouldn't the LHS be positive
vale wigeon
why are you concerned about values between 2 and 3?
did you maybe mean between -3 and -2?
heady finch
Ah sorry no I meant 1, 4
vale wigeon
and now that's irrelevant to the issue i pointed out.
heady finch
Wouldn't (x-4)^2022 be positive for any real value of x
vale wigeon
it would be positive for all x except specifically x=4.
vale wigeon
so the curve should cross, not touch, at x=-3
.
this is the issue with your wavy curve
heady finch
Aight
vale wigeon
it is drawn correctly to the right of -3 but not to the left
heady finch
I see
heady finch
it is drawn correctly to the right of -3 but not to the left
So it's supposed to be above the x axis right
vale wigeon
yes, exactly.
heady finch
I still have a doubt tho
If we take any value between -∞ to -3 wouldn't the expression be negative
Cus (x-1)^2019 has an odd exponent and would be negative
vale wigeon
and (x+3)^2021 would also be negative.
alpine sable
Hello! Can I have some help please? it's about Numeric and Geometric patterns. I need some help understanding the formulas again 😅
alpine sable
So if there are 3600 meerkats, and 470 are added each year, that means after one year there will be 3600 + 470 = 4070 meerkats.
I need to figure out a formula where m = meerkats and n = years, to find out how many years I will need for the population of 3600 to double
minor needle
That's arithmetic progression
alpine sable
There are many names for it lol
And many different formulas depending on the country too
minor needle
So what's your general formula
alpine sable
Tn = 4n + 1 I think
That's the only one in the book that they explain
And that's for fences and sticks, so | - - - | - - - |
minor needle
Maybe you can think about something like $T_n = a_1 + (n-1)d$?
ocean sealBOT
modus7591
alpine sable
Please can you explain that?
minor needle
but in fact here we even don't need a formula, logical thinking should be enough
alpine sable
Sure, but I need to use the formula because it's half my marks
And if I get it wrong then questions following that will be wrong too
minor needle
if at the beginning there are 3600 meerkats and after each year amount of meerkats increases by 470
so it goes like
1st year: 3600 + 470 = 4070
2nd year: 4070 + 470 = 4540
3rd year: 4540 + 470 = 5010
and so on
notice that you can rewrite it as
1st year: 3600 + 470 * 1 = 4070
2nd year: 3600 + 470 * 2 = 4540
3rd year: 3600 + 470 * 3 = 5010
...
n-th year: ???
alpine sable
Wait
Ohhh ok
Yes that makes sense
But I really do need to understand the formula I have here
It's literally half my marks in the exam
minor needle
but 4n + 1 is just usage of the formula
haven't you got general formula in the book?
minor needle
send it if possible
alpine sable
They use T_n
Ok
I'll just take pics
Those are the examples they give me
That is apparently the formula for the meerkats
Wait a minute
If m = meerkats, and n = years
And the end part of the sum is exactly as you explained it...
Ohhh I've got it!
So m is the total of meerkats from the sum
With the sum just being mixed about a little
alpine sable
.close
lone heartBOT
Available help channel!
alpine sable
i dont understand (b)
lone heartBOT
i dont understand (b)
vale wigeon
do you know what population density is
queen river
They actually defined it for you
alpine sable
oh do i have to look at what population density is and then move forward
okay make sense
tysm
.close
wise snow
lone heartBOT
wise snow
I am trying to write 3 trigonometry related questions with this diagram
I want one question to be finding the area D
and then two other sort of precursor questions to that
thoughts?
lone heartBOT
@wise snow Has your question been resolved?
lone heartBOT
Available help channel!
craggy pendant
sin2x < root3/2
lone heartBOT
sin2x < root3/2
craggy pendant
is x (pi/6 +2kpi, pi/3 + 2kpi) correct?
vale wigeon
is x (pi/6 +2kpi, pi/3 + 2kpi) correct?
should be x ∈ (π/6 + 1kπ, π/3 + 1kπ), no?
craggy pendant
um
i dont even know what that 2kpi means excatly
but my teacher said to add 2kpi always
vale wigeon
well in the literal sense 2kπ is just the product of 2, k and π
k here ranges over the integers
and usually you should write that explicitly
the addition of these things is how you account for periodicity of trig functions
and hopefully you do not do it blindly like your teacher is trying to make you
craggy pendant
not really
vale wigeon
fairly important thing to be missing
a function f is said to be periodic if there exists some positive P such that f(x+P) = f(x) for every x
or to put it another way if the graph of f can be translated left or right by some nonzero distance and end up a copy of itself
any such P is called a period of your function
with the smallest one called the fundamental period or "the period" for short
sin and cos are probably the first periodic functions you learn about
they both have period 2pi
craggy pendant
okay my friend just told me that its always 2kpi for sin and cos
vale wigeon
because, yknow, 2pi means going once around the circle
jeez.
ok.
so you want to listen to your friend who again makes you blind
craggy pendant
probably for now
i havent really listened in class and its hard for me to understand complex things in english
.close
charred plank
Hey all I'm trying to prove that the only normal sub-groups of $S_n$ are $1,A_n,S_n$ for $n \geq 5$
So far I know that assuming there's another nomral sub-group denote K, $K\cap A_n$ should be normal too. But since $n \geq 5$ I can conclude that the only normal sub-groups of $A_n$ is 1. Therefore $K \cap A_n = 1$ I also know that according to that (proved earlier) that if $|K| > 2$ I get that $K\cap A_n \neq 1$ therefore $|K|=2$ and I'm kinda stuck at this point. Any help?
ocean sealBOT
meitar5674
lone heartBOT
@charred plank Has your question been resolved?
lone heartBOT
@charred plank Has your question been resolved?
lone heartBOT
@charred plank Has your question been resolved?
bronze helm
Slightly confused as to how a qq plot works.
Suppose if the sample data is [1,2,3,4,5], do we then consider 1 to represent the 20th percentile of the sample date, 2 is the 40th percentile of the sample data, etc…
Now when plotting sample quantile against theoretical quantile. Do I plot ‘1’ against the 20th percentile of the theoretical distribution?
lone heartBOT
Slightly confused as to how a qq plot works.
Suppose if the sample data is [1,2...
@bronze helm Has your question been resolved?
tiny onyx
Hi guys, I am now currently studying sequential circuits and I've got acquainted with SR latches, D latches and D flip flops.
Now I am supposed to study finite state machines (FSM), so Moore Fsm and mealy FSM
But I don't get what the hell is a moore fsm...
rancid trail
I think the answer will be F, because by applying triangular law of vector addition, it will become a regular hexagon. But I want to write it mathematically. How do I do it?
alpine sable
you could draw it and cancel opposite forces
if you want to do it algebraically, convert polar to cartesian
rancid trail
Wtf is polar? Like, I haven't drawn any bears?
rancid trail
you could draw it and cancel opposite forces
So, the answer is F?
alpine sable
So, the answer is F?
no
alpine sable
Wtf is polar? Like, I haven't drawn any bears?
basically using sin and cos to convert an angle to a coordinate
rancid trail
no
Is it 0???? Because I drew the diagram and the head of the last vector touched the tail of the first vector.
alpine sable
yes, you can pair each vector up with its negative
rancid trail
Alright
Now I will try to convert i.t.o. sin and cos, i.e. polar form
Well I turned my work in, and it seems that I don't need it to prove algebraically. Thank you for your help @alpine sable
.close
pseudo flume
can anyone help me with this
lone heartBOT
can anyone help me with this
alpine sable
is [x] the integer part of x?
pseudo flume
yeah
alpine sable
write f as a piecewise function to get rid of [x]
then it should be routine to get the range of each part
sharp thorn
Hi
sharp thorn
$\int \frac{1}{x^2-9}dx$
ocean sealBOT
bettim
sharp thorn
Here now I would write the denominator as (x-3)(x+3)
Which comes first (x-3) or (x+3)
upbeat hornet
Which comes first (x-3) or (x+3)
Doesn’t matter
sharp thorn
Okay
Because i did something similar and it gave me a wrong answer because i took it in the wrong order
Thank you
.close
coral crag
factorise x^2-55x+750=0
lone heartBOT
factorise x^2-55x+750=0
crimson carbon
Find some values alpha, beta such that alpha+beta=-55, and alpha * beta = 750
if that's not really doable (in the case that you'll possibly have complex roots, i.e. is irreducible over reals, prime coefs, and simply non integer coefs js pose challeges)
just use the quadratic formula
pseudo flume
factorise x^2-55x+750=0
split -55x into -25x and -30 x
coral crag
just use the quadratic formula
that is harder
coral crag
split -55x into -25x and -30 x
thx
crimson carbon
eh not necessarily
crimson carbon
split -55x into -25x and -30 x
ye but do you understand why you do this
you can't have someone pull smth outta their bum and then accept it
unless you do understand
lone heartBOT
@coral crag Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
limpid cypress
Let A be a set with 10 elements, B be a set with 2 elements, and C be a set with 5 elements. Let f be any function from A to B, and g be a function from B to C. Let h(x) = g(f(x)) = (f ∘ g)(x). How many different functions are there? I really do not get the answer ?
The answer is C(5,2)*(210 − 2) + 5 = 10225
lone heartBOT
@limpid cypress Has your question been resolved?
limpid cypress
<@&286206848099549185>
raven girder
Does l'hosptal allow me to just derive the whole thing?
lone heartBOT
Does l'hosptal allow me to just derive the whole thing?
raven girder
ohh ok thanks
proven leaf
$\lim_{x\to c}\frac{f(x)}{g(x)}=\lim_{x\to c}\frac{'f(x)}{g'(x)}$
If $f'(c)$ and $g'(c)$ exist and $f(x)$ and $g(x)$ are differentiable
needs to be a fraction of two functions
ocean sealBOT
XxMrFancyu2xX
lone heartBOT
raven girder
.reopen
lone heartBOT
✅
raven girder
I'm not sure what to do when I have a sum like this
can I split into 2 limits or do I have to reform this?
proven leaf
$\frac{1}{x\sin(x)}-\frac{1}{x^2}=\frac{x^2-x\sin(x)}{x^3\sin(x)}$
ocean sealBOT
XxMrFancyu2xX
raven girder
got it thanks
x - sinx / x^2 sinx works too right
or why did you choose to mulitply with another x
proven leaf
because I used $\frac{a}{b}-\frac{c}{d}=\frac{ad-bc}{bd}$
ocean sealBOT
XxMrFancyu2xX
proven leaf
and x^2 times x is x^3
proven leaf
yes lol please don't use $\frac{a}{b}-\frac{c}{d}=\frac{a-c}{b-d}$
raven girder
what?
ocean sealBOT
XxMrFancyu2xX
raven girder
yes lol please don't use $\frac{a}{b}-\frac{c}{d}=\frac{a-c}{b-d}$
what is this formula
is it another one
ocean sealBOT
XxMrFancyu2xX
raven girder
ah now I get it LOL
proven leaf
ok so now how do you evaluate this limit? $\lim_{x\to0}\frac{x^2-x\sin(x)}{x^3\sin(x)}$
ocean sealBOT
XxMrFancyu2xX
raven girder
I derive upper and lower function
proven leaf
yep! and what do you get?
raven girder
sec im not so fast
proven leaf
dw :))
proven leaf
but is numerator?
proven leaf
numerator is 1
not quite
proven leaf
also I think you did ur bottom derivative wrong
raven girder
isn't sin(x)' = cos(x)?
proven leaf
$\frac{\mathrm{d}}{\mathrm{d}x}[x^3\sin(x)]=x^2(3\sin(x)+x\cos(x))$
ocean sealBOT
XxMrFancyu2xX
ocean sealBOT
proven leaf
ah
very well
bottom checks out then sorry for confusion 
yep we get another 0/0
l'Hôpital's Rule to save the day 
raven girder
wtf
proven leaf
you have another indeterminate form...
raven girder
does lhospital always work?
proven leaf
**XxMrFancyu2xX**
as long as these conditions are met ^
raven girder
I mean does it always lead to a result
proven leaf
oh and if the limit of indeterminate
raven girder
,w lim x->0 1/(x sinx) - 1/x^2
ocean sealBOT
raven girder
proven leaf
,w lim as x to 0 of (sinx)/(2sinx+2xcosx+2xcosx-x^2sinx)
ocean sealBOT
proven leaf
raven girder
proven leaf
sorry man gonna have to differentiate again maybe their might be a more elegant way but honeslty idrk
proven leaf
you can stop now :))
raven girder
jfc
🎉
proven leaf
thanks sir
lone heartBOT
@raven girder Has your question been resolved?
glad basalt
conditons for l'hospital rule is 0/0 or inf/inf
0/inf and inf/0 also applies i think(not sure)
raven girder
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wide plaza
lone heartBOT
lone heartBOT
@wide plaza Has your question been resolved?
wide plaza
<@&286206848099549185>
<@&286206848099549185>
bro what the hell
ive been waiting for 30 mins
really no one?
vernal current
Hi
lone heartBOT
@wide plaza Has your question been resolved?
tacit arch
this is more of a CS question
try CS server in #old-network
or also try #discrete-math
tacit arch
ive been waiting for 30 mins
in either case, don't be entitled
wide plaza
ok
ivory pumice
I am currently stuck on question 2(bottom). This question involves the Witch of Agnesi shown above. The following is known -
The witch is made from a circle shown in the figure.
Point E is the center of the circle.
The radius of the circle is a.
The x-coordinate of point P is x, and the y-coordinate of point P is y.
The distance between the origin and point B is d.
The angle d makes with the x-axis is theta.
I must show that d = 2a/sin(theta). Looking at it it makes intuitive sense, but I can't seem to prove it.
ivory pumice
What I have tried -
I've tried using the Pythagorean Theorem by acknowledging that x is equal to the x-coordinate of P, and that the height of d is always 2a. I have attempted to define x in terms of a by the equation x = a cot(theta). However, when attempting to evaluate the resulting expression via the Pythagorean Theorem, I come to a dead end as there is a root that cannot be simplified.
Another thing i tried was to turn 2a/sin(theta) into 2a csc(theta) to remove the quotient, however this leads to a similar dead end.
thorny patio
So do you have it given that the lines form a rectangle?
The one that d would be the diagonal of
@ivory pumice
If so the result is easy from there
lone heartBOT
@ivory pumice Has your question been resolved?
wheat isle
lament forge
well u = 5x+4, and y = (5x+4)^7
wheat isle
I still don’t understand where y=u^7 comes from
lament forge
you're just taking y = (5x+4)^7, and replacing the 5x+4 with u
which you can do because we decided that u = 5x+4
wheat isle
oh okay
I think I get it now
I think the notation confuses me a bit. Does du/dx mean you are differentiating u with respect to x? Or is it the other way around
lament forge
du/dx is differentiating u with respect to x
wheat isle
Ah okay
wheat isle
du/dx is differentiating u with respect to x
And for notation like y’ or u’ does it tell you what it’s being differentiated with respect to?
naive oar
hi
naive oar
hello i need help with a question for linear algebra over matricies
lone heartBOT
@naive oar Has your question been resolved?
true sand
Yee
You need to make a matrix and calculate the inverse
You can make a augmented matrix and use the identity matrix to find the inverse
The method listed wants you to do a coefficient matrix tho
Then multiply both sides by the inverse of the first matrix with the first row 3,-1,1
The left side simplifies to x,y,z. Because $I_n *B = B$
ocean sealBOT
Differential Equations
naive oar
so this is the ax=b form, how would i do coefficient matrix
true sand
The matrix on the left is the coefficient matrix
lone heartBOT
@naive oar Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
high wolf
lone heartBOT
high wolf
Can someone help me solve this mb
placid zinc
∂/∂x of both sides
Keeping in mind that z is a function of x
This means y is a constant, and something like xz needs the product rule
lone heartBOT
@high wolf Has your question been resolved?
toxic kraken
2x+3y=13 2x+y=7 elimination answer x=2 y=3
lone heartBOT
2x+3y=13 2x+y=7 elimination answer x=2 y=3
sonic ridge
yes
toxic kraken
Bruh that fast
sonic ridge
you can always check by plugging in the x and y's back into the original equations
see if LHS = RHS
twin yoke
hey there, im struggling with the following calculus problem
twin yoke
so what ive tried so far was to parameterize our path in terms of two variables u,v
i got the paramterization s(u,v) = (u,sqrt(1-u),v)
taking the derivatives w/rt to u and v to get our normal vector i get that ds/du = (1,-1/2sqrt(1-u),0) and ds/dv = (0,0,1)
taking the cross product to get normal vector yields this mess
heres where im certain i made a mistake, taking the magnitude of this, evaluating the vector field with such paramterization, and trying to integrate is insanely difficult
can i get some advice and potentially some help?
lone heartBOT
@twin yoke Has your question been resolved?
fading moth
ah, i don't think you want to take the magnitude
you want to take the dot product of the vector field and the cross product vector
you were thinking of this formula
where f is a scalar field
lone heartBOT
lone heartBOT
Available help channel!
marsh gulch
Can someone explain me why λ becomes negative and is just only multiplying Px?
https://cdn.discordapp.com/attachments/838616759559913483/1119103785390854164/image.png
tacit arch
Can someone explain me why λ becomes negative and is just only multiplying Px?
...
What's the definition of p
What's the first line supposed to read. The handwriting isn't great
marsh gulch
What's the definition of p
price
marsh gulch
What's the first line supposed to read. The handwriting isn't great
The problem is max that
tacit arch
The problem is max that
Are $p_x, p_y$ two different variables?
ocean sealBOT
rie.mann
marsh gulch
Are $p_x, p_y$ two different variables?
Yes
They are functions
Price of X and Price of Y
P(x) P(y)
tacit arch
Can someone explain me why λ becomes negative and is just only multiplying Px?
...
is the second line supposed to read $\alpha = 10 ...$
ocean sealBOT
rie.mann
tacit arch
what does alpha: even mean
marsh gulch
Lagrange
tacit arch
so yes
marsh gulch
It is assumed to be an economic maximization using Cobb-Douglas
marsh gulch
marsh gulch
do you know partial derivatives?
Yes
tacit arch
can you calculate this partial derivative
marsh gulch
Yes in the first part, the problem is Idk why the derivate of λ is just P(x)
tacit arch
only one of these terms depend on x
marsh gulch
Income and Price of Y becomes 0?
tacit arch
if you say so
marsh gulch
tacit arch
I and y are independent of x
so when you calculate partial derivative of those 3 terms, only 1 remains
marsh gulch
Ah, I see...
What if i want to do a partial derivate of λ?
All of those is just erased?
tacit arch
no
tacit arch
only one of these terms depend on x
this is lambda * (something that doesn't depend on lambda)
so when you differentiate wrt lambda, you treat that (...) as a constant
tacit arch
yes
rotund junco
Help part 2
lone heartBOT
Help part 2