what other information do they give you
#help-0
upbeat gorge
Maybe your calculator is in radians even though you mean degrees
unkempt viper
what other information do they give you
none, just the lengths of the 2 sides
ionic jewel
ill assume its right angles thn
so you know they are similar triangles
i.e. multiplying all the side lengths of one tringle by a constant gives you the side lengths of the other triangle
so you need to multiply the top triangle by 78/26 to make them match
so therefore
$\frac{78}{26}(9x+16) = 10x-65$
ocean sealBOT
ʎuunq
latent thistle
can someone help me with ii)?
i know this is physics, but no one answered me in the physics server im posting here
also left hand side is cut off, its supposed to be 25
not 5
alpine sable
can someone help me understand B and C?
dV/dT is the change in volume over the change in time
how do i know if it is focusing on whether the volume is increasing or the pressure?
shell widget
suppose you are given a function y = f(x). dy/dx means the change in y as we change x. So here we are changing the pressure, and by doing so, the volume changes, so we have dV/dP
and it says that dV/dP is proportional to the reciprocal of the square of the pressure
We have $\dv{V}{P} ∝ \frac{1}{P^{2}} \implies \dv{V}{P} = \frac{k}{P^2}$
ocean sealBOT
¿dnS
alpine sable
right
shell widget
now it says that the change in pressure is positive
since we are increasing pressure
and it says that the change in volume is negative, since the volume is decreasing
that means the ratio dv/dp is negative
the ratio dv/dp is equal to k/p^2, so k/p^2 must be negative, but p^2 is positive, so we must have that k is negative
alpine sable
oh, i see so as long as pressure is positive, i will get a decreasing rate and it will be (-dV)/(dP)
shell widget
np
static peak
hello does anyone know how to simplify this? p is a constant
shell widget
best we can do is (1/p) * ln[((x_1)^p + (x_2)^p)]
static peak
hello thanks for the reply, why is bringing out 1/p allowed?
is it because of properties of log?
jagged imp
yes. $\ln(a^b)=b\ln(a)$
ocean sealBOT
112213122111112112111
static peak
alright thank you so much!!
steady scroll
I don’t understand why square root of 10-x becomes -1/2 square root of 10-x
Was it that square root was actually -1/2 exponent also?
static peak
derivative of 10-x is -1
static saffron
Given a function $f(x,t)$, find the partial derivatives with respect to x and t for the function $f(\frac{u+v}{2},\frac{v-u}{2c})$ where $u=u(x,t)$ and $v=v(x,t)$
ocean sealBOT
ǝʇʇopɹǝp
static saffron
i am kinda stuck since both arguements are dependent on both variables, i know i need to use the chain rule here. But i dont think i ever used it on a such a problem
so, how would i find the partials here?
vale wigeon
you basically have three functions composed together
in order from the outside in
- the function sending (x,t) to (u,v)
- the function sending (u,v) to ( (u+v)/2, (v-u)/(2c) )
- f itself
i believe the gradient of the whole thing is just (grad f)^T * (jacobian of function 2) * (jacobian of function 1)
vale wigeon
yeah
paper minnow
hi, is there a way to estimate critical points for t distribution when alpha is outside your range of values? I have to find a t such that P(T>t)=0.45 but my t distribution table only goes up to an alpha of 0.4, any ideas? Thanks
rich basin
@cold void Do you still need help with finding the area?
alpine sable
@novel field the first line is not equivalent to the second line
verified him?
@novel field what is unclear about what i said
fuck you too
moron
vale wigeon
????? what's going on
rigid smelt
umbral mango
fuck you too
??
rigid smelt
just be nice lol, and they were right, dont question others' authority as it can be very disrespectful. You should rather ask why they came up to that impression
vale wigeon
your work has several typos
umbral mango
Shouldn't it be $$ \frac{1}{4} (x^2+4x-4+4-2) $$ for the second line ?
vale wigeon
line 2: x^2 + 4x + 4 - 4 - 2
line 3: 1/4 ( (x+2)^2 - 6 )
ocean sealBOT
>_< nɹᴉM ¡
vale wigeon
if you fix these typos then your work becomes correct
alpine sable
@umbral mango what
umbral mango
<@344647286426566657> what
don't be rude please
alpine sable
they wasted my time so i let them know what i thought of them
you would too if you had any respect for yourself
rigid smelt
doesnt matter, just let it pass
quartz tusk
normal fractal
Help me with my homework? Prove that no three positive integers a, b, and c satisfy the equation a^n+ b^n= c^n for any integer value of n greater than 2.
normal fractal
I’m gonna fail
eager spade
please confirm that that isnt actually your hw 
eager spade
let it go Andy it's a troll lmao
normal fractal
I don’t get it
novel monolith
Given points A, B and C, how would one find D from C if C->D had to be 1?
I found out I can sub out a ton of calculations with this solution, but I don't know linear algebra
vale wigeon
are A, B and C given as coordinates?
novel monolith
yes
vale wigeon
you may have zero, one or two possible locations for D
i'll call the coordinates x_A, y_A, x_B, y_B etc
i'll call the coordinates of D just X and Y so that they stand out
what you have, essentially, is that D lies on the circle of radius 1 centered at C
thus $(X - x_C)^2 + (Y - y_C)^2 = 1$
ocean sealBOT
uu∀
vale wigeon
and you will also need an equation for the straight line joining A and B
which is a bit annoying to write out
novel monolith
funnily enough, the unknown point on a circle given a line intersection was exactly what I was trying to figure out, you have nice intuition
give me a moment to wrap my head around what you said
I don't mind if you send me to a resource that has it already written out
vale wigeon
wait, so this is a restatement of your original problem?
novel monolith
no it's the same problem, but the linear system of AB constrained by CD = 1 was what I was gunning for
vale wigeon
well, you'll need to write out the equation of line AB, and then substituting that into the circle equation will give you a quadratic in X
(or in Y if your line turns out to be vertical)
so solve that, get the value(s) for one coordinate, say X
and check if it falls between the x coords of A and B
if it does it's on the segment, otherwise it isn't
novel monolith
okay I'll give that a go, thank you so much for your help!! 🙂
I realise I have no idea where to start subbing the line equation into the circle equation
bleak meadow
Hey, since it's easter I decided to refresh my brain with Maths, my weakest and most disliked subject
However, I want to finally understand math
And to do that I went onto a revision page where I sadly start with my weakest subject in Math, Fractions/Ratio/trigonometry
anyone mind helping with this
plucky crow
alpine sable
,w integral of (1+x)^3
ocean sealBOT
ocean sealBOT
stark flicker
How do you reduce a quintic to brioschi form?
alpine sable
You do that when you have to solve a pair of linear equations
I mean
You gave the situation in your question itself
cloud matrix
i mean
give me an example
because i didnt understand what theyre trying to say in that paragraph
alpine sable
Take any 2 linear equations
alpine sable
Now if you multiply the first equation with 5 and second one with 3 and subtract the 2
You eliminate x and get the value of y
cloud matrix
yes
isnt that multiplying with any row or column with a non zero number?
like
Ri --> kRi
or
Ci --> kCi
we are not adding anything here
@alpine sable
soo many bunchos wtffff
mortal mica
bunchoooooooooooooooooo
cloud matrix
help
limpid spade
May I eat u
limpid spade
Whtatae your query4
cloud matrix
right up thrre
spare skiff
Initial velocity = 50ms at angle 35 to horizontal, how far will it travel before hitting the ground?
alpine sable
what have you tried so far?
spare skiff
i just need the general formula for it
alpine sable
uh.
alpine sable
$y=y_0+v_{0y}t-\frac12 gt²\ x=v_{0x}t$
where $v_{0x}=v_0\cos(\theta)$, $v_{0y}=v_0\sin(\theta)$, $\theta$ is the angle formed with the horizontal, $v_0$ the initial velocity, $g$ the gravitational constant, $y$ the height after $t$ time, $y_0$ the initial height and $x$ the distance.
alpine sable
How did they arrive at this step?
have you tried expanding out cos(45°-v) and cos(45°+v)?
sand kiln
Can somebody explain to me how this works?
alpine sable
have you tried expanding out cos(45°-v) and cos(45°+v)?
Yes
@alpine sable what did you get?
after some algebraic manipulation it shouldn't arrive anywhere but 2sin(45°)sin(v).
[cos(45)cos(v) + sin(45)sin(v)] - [cos(45)cos(v) - sin(45)sin(v)]
sin(45)sin(v) + sin(45)sin(v) => 2sin(45)sin(v)
Is this correct?
@alpine sable
2(1/√2) sin(v) => (2/√2) sin(v) => 2sin(v)/√2
√2*√2*sin(v)/√2 => √2*sinv
QED?
bronze dust
hello
i wanted to ask if sines and cosines are just ratios of triangle sides then why are they negative sometimes
wind hare
i wanted to ask if sines and cosines are just ratios of triangle sides then why ...
they arent just ratios of triangle sides
wind hare
they are part of the unit circle
they just happen to be great at calculating triangles
alpine sable
Is this correct?
yes. good job.
wind hare
in the broader picture sin and cos has very little to do with triangles
wind hare
sorry i dont understand
bronze dust
so these values are true for just unit circle??
wind hare
the unit circle is a tool
used for a lot of things
some of the things its used for is triangle calculations
in which case you only use positive values
bronze dust
so when we say sin 150 degrees
we mean what is the y coordinate at unit circle when terminal side is rotated by 150 degree
wind hare
positive and minus denotes which route you are taking on the circle
if you say sin 150 it means you are going counter clockwise around
if you said sin -150 it means you are going clockwise around
if you put sin(180) and sin(-180) into a calculator you will see it gives the same result
because even though they went the opposite direction they ended the same place (other side of the circle)
wind hare
for same reason
bronze dust
sine is not ratio?
bronze dust
it is a coordinate not ratio?
wind hare
sine is not ratio?
when you are just gettting introduced to the whole thing, its easiest to just say its a ratio to not cause confusion, because sin can be very complex when you first learn about it
its not a coordinate
to explain properly what it is would take some time
which is why most teachers just say its a triangle ratio and leave it at that until highschool
bronze dust
😕
wind hare
just google unit circle and sinus and you should easily find some webpages that will teach you about it
wind hare
😕
think of it like this
lets say your teacher showed you his computer and said "this is a calculator"
and then you found out it has world of warcraft on it, why does a calculator have a game on it
thats because the computer is much more than just a calculator
but to explain everything a computer is when you just need a calculator is complex and confusing
bronze dust
okk
wind hare
if you are really interested theres a shitload of resources online that teach about it
but othervise they will expand your knowledge about sin and cos in high school
bronze dust
i am in college
bronze dust
i was revisiting my high school maths textbook
i decided i will properly study maths now
wind hare
ok im not sure how your countrys education work but in this case i would highly advise you to start learning about sin and cos
it is critical to almost all college level math
bronze dust
in high school teacher told us to memorise all identities and formulas and solve question
wind hare
they only used rote memorization and not understanding?
wind hare
what part are you stuck at
round hawk
i have no idea how to do part (b)
But for part (a), is it combination (12,6) minus 2?
austere slate
can someone help
why is the cosx cancelled
im trying to look it up but its confusing me
alpine sable
But for part (a), is it combination (12,6) minus 2?
yeah that seems correct.
austere slate
never mind my question lol
alpine sable
i have no idea how to do part (b)
well, you now have only 5 places to sort out, give this a try first.
round hawk
Every time i do probability questions ill doubt my answers lol
alpine sable
a and b were combinatorics questions, but no worries
vestal quartz
In series... when we compare a serie to a riemann serie and use n^a (Un) to see its convergence
Is there a specific rule to find the a
??
nocturne gazelle
If f:[0,1]^2 -> R is a bounded function s.t f(x1,y1)>-f(x2,y2) whenever x_1>x_0 and y_1>y_0, is it always integrable?
i think it should be just trying functions
is there way to prove this properly
<@&286206848099549185>
@vale wigeon sorry for the ping
nocturne gazelle
lol what
fallen fox
Let $A$ be a set and $f:A\rightarrow A$ an injective map. Suppose $f(A) \subseteq C \subseteq A$, then prove that there is a surjective map from $C$ onto $A$.
I wanted to know if my proof is correct.
Suppose not. That is $\forall $ functions $g:C\rightarrow A ; ; \exists ; a\in A$ such that $g(c)\neq a$ for any $c\in C$.
Let $g$ be a restriction on $f(A)$ that is $g|_{f(A)} = a ; \forall ; a$ such that $f(a)$ exists. But this means that some element in $C\backslash f(A)$ must also have an image in A. Therefore there are multiple $c\in C$ such that $g(c)=a$ for some $a\in A$. Which is a contradiction. Thus, $g$ is surjective, proving my claim.
ocean sealBOT
Irish
gray gorge
I don't think the statement you're trying to prove is true though
But maybe I'm just smol brain rn
I'll think about it
spring harbor
Can someone give me a function that's divergent to +infinity and -infinity?
Like the one that jumps between negative and positive values
Not sure what it is called
nocturne gazelle
wait do i just need to show all monotone functions are integrable and im good
coral pagoda
Can someone give me a function that's divergent to +infinity and -infinity?
[f(x)=\begin{cases} x^2 ; &x\in \mathbb{Q} \
-x^2 &x\notin \mathbb{Q}\end{cases}]
That will do it
lean galleon
What's the q domain again
ocean sealBOT
dackid
coral pagoda
Q is rational numbers
spring harbor
\[f(x)=\begin{cases} x^2 \; &x\in \mathbb{Q} \\
-x^2 &x\notin \mathbb{Q}\end{cas...
Thank you, is there a way to put it in desmos and graph it?
coral pagoda
I'm not sure how desmos will handle this one tbh 🤔
alpine sable
,w graph f(x)=\begin{cases} x^2 ; &x\in \mathbb{Q}
-x^2 &x\notin \mathbb{Q}\end{cases}
ocean sealBOT
Requested by ⃟⃟#8027
coral pagoda
What you are asking is to plot a graph that is discontinuous everywhere
spring harbor
Yeah I knew it's very unlikely but I thought it might be possible
Is it possible for only natural numbers though?
1,2,3,4,5..
coral pagoda
What do you mean?
spring harbor
Well basically I am trying to represent geometric rows when q =< -1
coral pagoda
I don't know desmos well enough to know if it can handle these funky restrictions
spring harbor
When q is =<-1 it jumps from positive to negative to positive and so on I believe
q represents t2/t1
coral pagoda
What you are trying to do is unclear to me
spring harbor
Hmm, are you familiar with geometric rows?
When you take the limit of tn, the limit doesn't exist. (for q=<-1)
It doesn't exist because your values keep jumping from positive to negative to positive for different n values (with n element of natural numbers)
I just wanted to graph something similar to use it in my project
coral pagoda
Are you talking about a geometric series @spring harbor ?
spring harbor
Are you talking about a geometric series <@316900912398467073> ?
Oh yeah I am
Sorry I thought it was rows
English is not my native language
spring harbor
try to fill in different values and see what happens
coral pagoda
So like [\sum_{k=0}^\infty r^k ; where; |r|<1]
ocean sealBOT
dackid
spring harbor
Isn't that an arithmetic series
coral pagoda
No, that is a geometric series
spring harbor
**dackid**
and that's the sum of the series
Wait
I think it's sequence
not series
Geometric sequence
spring harbor
I thought t2/t1 = q
coral pagoda
Moreover [\frac{T_{n}}{T_{n-1}}=q] for all $n>1$
ocean sealBOT
dackid
coral pagoda
I am not sure how to do this in desmos
Like I said earlied, I do not know the program well enough
coral pagoda
Ask in #computing-software . I do not know
fleet steeple
@alpine sable add -2t both sides, subtract 9 both sides
7 = 7t
7/7 = t
t = 1
yeh
glass estuary
What's the equation for this graph?
glass lichen
What's the equation for this graph?
x=y^2
glass estuary
Thanks
glass lichen
assuming it's a parabola and assuming there's actually a scale
glass lichen
Or y = Sqrt x
nope
tranquil parcel
Wait what
glass lichen
cause that'd only be the upper half
glass lichen
$x=y^2\implies y=\pm\sqrt{x}$
ocean sealBOT
moshill1
tranquil parcel
$x=y^2\implies y=\pm\sqrt{x}$
Can you maybe answer my question in #calculus plz
limpid mist
Can someone explain whats wrong with my argument for the real numbers being countable?
So, the most common way to construct the real numbers, is by associating them when equivalence classes of cauchy sequences.
You start with Q, and then you say that two cauchy sequences are the same if the differences of their respective terms tend towards zero.
And then you complete Q by "appending" all the equivalence classes of cauchy sequences that do not converge in Q.
Then you can define multiplication and addition of reals, by term-wise multiplication/addition of the terms in the cauchy sequences of a given equivalence class which you can easily prove is well-defined.
Now
It seems to me it is very easy to create a bijection between N and all such equivalence classes.
A cauchy-sequence is a function on integer values that fufills a certain criteris (terms grow closer and closer over time)
And for such a function to be a meaningful mathematical statement, it has to be describeable in some formal language we use (first order logic, second order logic, set theory, plain english, it doesnt really matter=
What is stopping me from creating a 1-1 bijection between N and R, by:
- Pick some language
- Enumerate all the strings in such a language.
- When a (first) string appears that corresponds to a cauchy sequence appears I send it to 1
- Continue enumerating strings in our formal language until a second cauchy sequence appears (that is not in an equivalence class we've already encountere) and send it 2, and do this for all strings.
Clearly this will hit all cauchy sequences (there cant be cauchy sequences that arent describable in any formal languge, that wouldnt make any sense), and will thus hit all of R
and
It is clearly countable, as the set of all strings is clearly countable.
<@&286206848099549185>
gray gorge
I've never heard of such a construction of real numbers before
limpid mist
gray gorge
Yep, just looked it up
limpid mist
I don't know of any others, but presumably it would work for stuff like dedekind cuts as well
gray gorge
Can you give an explicit example of how this bijection works
limpid mist
yeah we pick a language thats strong enough to write any cauchy sequence, lets say set theory and second order logic or something like that.
and then we order all the symbols we're allowed to use, lets say {, }, a, b, c, d, e...., 1,2,3,4,5, ∃, ∀....
then we enumerate ALL the strings
{ } a b c d...........
{{, {}, {a, {b.............
some of these will correspond to meaningul mathematical statements
some of them won't of course
and some of them will correspond to descriptions of a cauchy sequence, right?
presumably you can describe all such cauchy sequences using set-theoretic notation
and that means that eventually, this enumeration of strings will form an expression that corresponds to a cauchy sequence
so what we do is that we assign 1 to the first cauchy sequence that appears, it might be the 10^100th string in our enumeration
gray gorge
Ok let's call your bijection f and it acts from N to R, then f(1) = ?
limpid mist
It would be the cauchy sequence that can be described by the fewest symbols in set theory and second order logic (this would correspond to some number in R).
Maybe its not practical to do it, but in principle this is an enumeration that could be done.
@gray gorge are you still here?
limpid mist
candid sluice
why can you describe all cauchy sequences using some sentence in second order logic
this is not a rhetorical question, i honestly dont know
limpid mist
Cauchy sequences are just functions on N, no? If you couldn't write those in set-theory and second order logic, what could you write them in?
gray gorge
I think you'll only get these guys if you're looking at finite descriptions like you're saying
limpid mist
yeah I read this mathoverflow text which is referenced in the wiki-article, but I didn't understand it
gray gorge
Then idk
I trust Cantor's proof on the uncountablility of the reals
You're free to believe otherwise
limpid mist
Do you understand the argument in the mathoverflow thing?
Maybe you could translate it into smol-brain language so I can understand it as well...
gray gorge
I think the gist that they're putting down is: defining things is difficult
noble sinew
What is stopping me from creating a 1-1 bijection between N and R, by:
The problem is the bijection you are trying to create actually isn't possible
timid heath
It's an interesting question. I think @gray gorge has the right idea. Most real numbers, if you think of them as decimal expansions, have no particular nice understandable function giving the nth place
limpid mist
The problem is the bijection you are trying to create actually isn't possible
Can you explain why it is not possible?
limpid mist
I think the gist that they're putting down is: defining things is difficult
Thanks. I will read the mathoverflow link more closely and try to understand it
timid heath
yeah we pick a language thats strong enough to write any cauchy sequence, lets s...
It's not clear that a countable such language exists
noble sinew
It can be proven that (0,1) is not countable which is a way
Kinda long but an example is here: (seems like a fine proof by skimming through it)
timid heath
I don't think the uncountability of (0,1) is in question
but rather why does this idea to prove it's countable not actually work
noble sinew
If you read the proof they show a bijection from R to N isn't possible
hence breaking what he was trying to do
timid heath
it looks like the standard diagonal argument. I know it proves what he's trying to do is impossible
but it's not exactly clear where the necessary problem in his argument is
noble sinew
Well isn't it the fact that he wants his set of strings to cover all Cauchy sequences? Since the set of all Cauchy sequences are uncountable his set of strings will also be uncountable?
timid heath
well, ultimately yes, it has to be that
the question is just which step contains the error
limpid mist
the strings are clearly countable though
from reading more, it seems like the issue is that you cannot create a formal system that can describe all the cauchy sequences
timid heath
can you be more explicit about how you expect any random real number to be "covered" by your idea?
maybe trying to formalize that will help make it clear it can't be done
timid heath
I understand you have this countable set of strings
limpid mist
f(1) would just be the cauchy sequence that can be desribed with the lowest amount of symbols in first order logic
f(2) the second shortest
limpid mist
you just enumerate all strings and see if they correspond to a cauchy sequence
clearly this enumeration is possible
timid heath
Enumeration of strings isn't the problem
limpid mist
you just agree on a list of allowable symbols like a b c ( ), + -, {, } etc etc
timid heath
How do you decide if some string represents a cauchy sequence or not?
Furthermore, how do you make sure every real number is covered by some string?
limpid mist
A cauchy sequence is just a function where the difference between consecutive terms converges to zero. A function is just a subset of of the cartesian product between a domain and a codomain, such that every element in the domain is the first element of exactly one element in this relation.
timid heath
Yes, but that set of functions is uncountable
limpid mist
If you wanted to be super rigorous you could probably use something like CoQ or some automated software to check if a string corresponds to a cauchy sequence.
I mean, I don't think this is super relevant, such a procedure is clearly possible.
fleet steeple
HElp
timid heath
not only is it not clearly possible, there's strong evidence that it's impossible
fleet steeple
Uhm I don't understand the answer provided
Is anyone willing to decipher it in simpler terms?
timid heath
is there a particular line in that solution that doesn't make sense?
fleet steeple
yes
the first one
is says we observe the greatest common denominator (n,100) = 1
timid heath
Let d(k) denote the number of divisors of k?
fleet steeple
Second one*
timid heath
(n,100) = 1 because n ends in 99
so n cannot have 2 or 5 as a divisor, but all divisors of 100 contain 2 or 5
fleet steeple
where do they get the 100 from
it says 100 n
oh wait
so would it be ....9900
for 100n
timid heath
that's true
timid heath
ok, now it's a fact that if (a,b) = 1 then
d(ab) = d(a) d(b)
this property is called being multiplicative
it's something proved elsewhere
timid heath
it's not true if (a,b) =/= 1
fleet steeple
but why
timid heath
well, you should see the proof of why d is multiplicative :]
but it's easy to convince yourself it fails
take 6 and 10
wait, dont
Too big it's annoying to count d(60)
Take 2 and 4
d(2) = 2
fleet steeple
what would be a cause where d(a,b) =/= 1
timid heath
d(4) = 3
fleet steeple
wouldnt d(4) = 4
timid heath
d(2*4) = d(8) = 4
fleet steeple
nvm
timid heath
No I was working out d(2*4) to show it doesn't equal d(2) * d(4)
fleet steeple
ok
timid heath
d(2) * d(4) = 2 * 3 = 6
timid heath
but d(4) = 4
fleet steeple
doesnt d(4)=3
alpine sable
how to find the area of a kite?
fleet steeple
or involving this?
timid heath
yes, it shows up all the time
fleet steeple
bet
do the next part that says d(100n) = d(100)*d(n)
d(n) = 6 right?
so it would be 6d(100)?
fleet steeple
ok
alculate how many divisors there are in 100?
1,100,2,50,4,25,5,20,10,10,
there are 10 divisors
is that wrong?
timid heath
Looks like you counted 10 twice
fleet steeple
oh so 9
timid heath
yup
fleet steeple
s0 6*9=54
w0ah
ty
how did they do it tho?
oh ncm
they did the same thing
tyyy
timid heath
sure
there's a very useful fact you'll want to know about
to quickly count d(n)
given the prime factorization of n
say $n=p_1^{m_1}\cdots p_k^{m_k}$
ocean sealBOT
ManifoldCuriosity
timid heath
where that is the unique prime factorization of n
then there's a simple formula for d(n)
ocean sealBOT
ManifoldCuriosity
fleet steeple
so m1 is the same as mk
timid heath
both powers are 2
fleet steeple
ok
timid heath
I add 1 to each of them, and multiply
timid heath
and that gives the number of divisors, which as we saw is indeed 9
sure
how many divisors does 45 have?
without brute force counting
fleet steeple
alright lets see
45 can be bput as 5 and 9
so sqrt 5^2 +3^2
so it would be 9?
(2+1)'*(2+1)
fleet steeple
i put sqrt 5^2
timid heath
oh, don't use square roots for this
fleet steeple
ok
timid heath
45 = 3^2 * 5^1
alpine sable
,w primes from 1 to 10
ocean sealBOT
ionic jewel
now make it more efficient
this isnt optimal but its a fun one to implement
this is the best approach i know
O(n)
civic harbor
Is the basis for a matrix's image and nullspace the same set?
tired creek
how did u get 0 for f'(5)
alpine sable
how did u get 0 for f'(5)
Well I thought for any constant 0 was the answer
F(5) is just 3
alpine sable
Ok so x=3 at f(5), wouldn’t that also be 0?
alpine sable
Oh so I fine the slope for f’(x) and g’(x)?
jagged imp
are you looking for v'(5)
?
if so, it seems you have g'(5) wrong
@alpine sable
if you correct that it should be right
alpine sable
if so, it seems you have g'(5) wrong
If g’(5) is the slope of g at x=5 doesn’t that mean it’s 3/2
jagged imp
nope, 2/3
rise/run, or however you learnt it
between x=2 and x=5, y goes from 0 to 2 so thats (2-0)/(5-2)=2/3
jagged imp
the final answer should be ||-2/3|| when you correct it
alpine sable
Alright thanks for your help guys
jagged imp
nw
ionic jewel
tangent is opposite over adjacent
so 4/10 seems right to me
= 2/5
looks like you have it right?
@hardy geyser
did someone gives you a different answer?
oh where did the sqrt(29) come from
uhh bad calculations i guess its supposed to be sqrt(116)
warm girder
google always helps me
tidal sapphire
hello I desperately need help for this quadratics word problem
A grappling iron is thrown vertically to catch on a ledge 7.5m above the thrower. if its height h meters t seconds after being thrown is given by h = -4.9t^2 + 11t + 1.5, will it reach the ledge?
thanks!! <@&286206848099549185>
hardy geyser
@ionic jewel I’m getting a decimal
ionic jewel
<@!153882568322711553> I’m getting a decimal
for what?
hardy geyser
tan-1(4/10)
ionic jewel
why are you doing tan-1(4/10)?
hardy geyser
im finding tan 0 or the angle inside right?
ionic jewel
it doesn't ask you to find the angle
it wants you to find the tan of the angle
the angle is tan-1(4/10)
tan of the angle is
tan(tan-1(4/10)) = 4/10
hardy geyser
wait what can we vc
ionic jewel
no
bleak verge
Can someone help me
gray isle
firstly the square root of 29 isn't 29 squared
also the sqrt(29) written there is wrong
hardy geyser
@gray isle square root of 29 isn’t the right answer?
gray isle
no
hardy geyser
wait he confused me it was act math problem he said it might be
the right answer it’s 2/5 though right
gray isle
tan(theta) is simply the ratio of the y and x coordinate of your point
yes. it'd be 4/10 = 2/5
hardy geyser
cause to find tan 0 tan-1(4/10)
gray isle
no need to even go through that
gray isle
simply just apply the definition of tan
tan(theta) is simply the ratio of the y and x coordinate of your point
no need to go through unnecessary stuff like inverses
hardy geyser
theta?
gray isle
its that greek symbol they're using to denote the angle
hardy geyser
oh ok
gray isle
theta: $\theta$
ocean sealBOT
ℝamonov
hardy geyser
ohh whrrre is that on the calculator
gray isle
nowhere
hardy geyser
darn
gray isle
no
tan(whatever symbol you want to denote you angle, in this case they used theta) = 4/10
hardy geyser
tan(🍌4/10)
gray isle
no
hardy geyser
how do I make it show up
gray isle
tan(🍌) = 4/10 = 2/5
if you wanted to use 🍌
hardy geyser
oh ok
gray isle
but since they used theta,
tan(theta) = 4/10 = 2/5
you could calculate the distance from the origin to (10,4)
which would be sqrt(116) = 2sqrt(29)
but that's unecessary
gray isle
yes
hardy geyser
I thought you cross multiplied but idk how to do this it’s my first time seeing this problem
@gray isle
gray isle
standard process for adding fractions
common denominator
is that your work or someone else?
hardy geyser
video
gray isle
start with simpler stuff like:
$\frac12 + \frac13$ \
this isn't that much different
ocean sealBOT
ℝamonov
hardy geyser
oh
this would be 1/2 times 3/3 and 1/3 times 2/2?
like what they did in the video?
gray isle
if by and you mean +
then yes
gray isle
yes
hardy geyser
ok when you multiple a whole number like 4 with a the square root of 3 it would be. 4(sqred3)?
nvm I got it
torpid wing
Can someone explain what does it mean that it must have real roots for y to be range of g
????
sly mantle
@torpid wing g has real number inputs, so if y is in the range of g then y=g(x) for some real number x, thus yx^2+x+2-y has a real root
ionic jewel
you solved for y, now just put (1/6) instead of y in your original equation and solve for x
cinder sundial
is this a simultaneous equation
cinder sundial
whats the value of 1/6
ocean sealBOT
bunny
cinder sundial
well , it is correct?
it is correct or does it correct btw
or its correct
it is correct without "?", sounds like i said "yes that was correct"
tired axle
do u want (xy) or do u want x and y?
ionic jewel
can you type the original problem, I cant read it?
cinder sundial
x and y
tired axle
ok so solve via substituidn
substitution
lol
isolate x and y
one side x and one side y
and use substitution
easy
?
cinder sundial
tired axle
LOL
cinder sundial
let me try
tired axle
math thats easy to you isnt easy to other people
i wasnt implying that it was easy
ionic jewel
you literally said "easy"
tired axle
i weas saying that the method ui can do is simple
any ways i dont need this ^
once u rewrite it
post it
so i can help u
tired axle
ok cool
cinder sundial
its tidy as i can
tired axle
so osilalte x one left side
and y on other side
and use it via substitution
and u ssohuld be good
cinder sundial
u means isolate
cinder sundial
i have no idea, what is subtitution
tired axle
ok
so for this
you can bring the x's to the left side
and the y's to thje right side
telll me what u get once u do that
cinder sundial
what you means bring x to left side
tired axle
so like
tired axle
8x+5y+4x-y
k
so whqat we do
is isolate
and we have
"subtract 4x"
from the rifght side
bring it to the left
so u get 8x-4x +5y = -y
so far
understand?
cinder sundial
i see
tired axle
now using that logic
do that with the y term on the left side
and bring it to the right
so the x's are all on one side and the y's are on the other
right>
?
cinder sundial
i think i got the answer now using my method, its 5/4=x and 1/6=y
could you check the answer for me
cinder sundial
thank you
ionic jewel
,w 8x+5y=4x-y
ocean sealBOT
ionic jewel
you cant solve an equation with 2 variable with only one equation
you need two equations
cinder sundial
what should i do
ionic jewel
there is a solution where y = 1/6 but its not the only one
do you have another equation?
ionic jewel
thats the only things?
ionic jewel
what is the other question?
ionic jewel
oh
cinder sundial
and (5x+3y):(2x+9y)
also ratio
do you have any idea to get the x y of 8x+5y=4x-y
ionic jewel
4x+6y = 0
x = -6y/4 = -3y/2
y = -4x/6 = -2y/3
with the information given thats the best you can do for x and y
ionic jewel
Here is your starting equation:
$$8x+5y=4x-y$$
now subtract 4x from each side
$$4x + 5y = -y$$
now add y to each side
$$4x+6y = 0$$
ocean sealBOT
bunny
cinder sundial
let me write it down on paper, one sec
ok
done
then what should i do
@tired axle thats what you means right
i think +5y should be -5y since you drag it into the' right side
am i correct
+5y being drag into the right side will become -5y, thats the rule i mean
tired axle
im almost done!
cinder sundial
well i revised it
tired axle
hang in there
dim cedar
tired axle
LOL
upbeat gorge
cinder sundial
can someone tell me if im right or wrong
tired axle
anyways
cinder sundial
tired axle
yes
tired axle
on so now u have 8x-4x=-y+(-5y)'
how u have to solve for x
so now add like terms on both sides
and tell me what u get from there
cinder sundial
what u means add terms, you means add 4x on both sides
tired axle
yes so "all x's on one side are like terms"
or "anything with an x on the same side are like terms"
so combine them!
and tell me what u get as ur new equation
cinder sundial
wait i cant add 4x on both sides
cinder sundial
4x
uncut osprey
epic drawing
tired axle
now that is ur left side
cinder sundial
ohhh i get it
tired axle
now do that same thing to the right side
with ur y's
good!@
now tell me ur new equation
tired axle
perfect!!!!
donty forget ur "='s" sign
now from there we have to solve for x
so what do we have to do to the left side to make x be all by its self?
cinder sundial
*4
cinder sundial
divide 4
cinder sundial
lets gooo
cinder sundial
emmm
cinder sundial
ohh -3y/2
tired axle
bingo!
and bam youre done with x!
sooooo x=-(3/2)y
now do the same exact process we jsut did
but for y
start all over but do it for y
and you are done!@
cinder sundial
ok im tryin
tired axle
its all good!
jsut do the same exact steps
from b4
-hint ur answer is kinda similar but NOT the same
cinder sundial
so i guess divided both sides by 6
cinder sundial
so x is -3y/2 and y is -2x/3
cinder sundial
now i have to put them into 5x:3y
tired axle
cinder sundial
the another question
craggy steeple
help pls
craggy steeple
oh sorry