MellowDramaLlama
#help-42
potent lotusBOT
frank gull
here I'll help you w/ the first one
pseudo marsh
Yeah right
frank gull
$H = (7, 1), I = (1, 6)\$
$\overline{HI} = \sqrt{(6 - 1)^2 + (1-7)^2} = \sqrt{25 + 36} = \sqrt{61}\$
$\sqrt{61}$ can't be broken down any further so that's our answer in radical form
potent lotusBOT
MellowDramaLlama
desert panther
calm coralBOT
desert panther
would
(2,-1) + t(2,-3) be correct?
since the general equation is the normal to the line
calm coralBOT
@desert panther Has your question been resolved?
calm coralBOT
@desert panther Has your question been resolved?
wanton wave
@desert panther Yep, you got it
calm coralBOT
@desert panther Has your question been resolved?
desert panther
<@482946006267330611> Yep, you got it
thanks
wanton wave
👍 np
calm coralBOT
@desert panther Has your question been resolved?
calm coralBOT
how do i solve this
hollow totem
1 = succ(0)
elfin ermine
wtf is succ(x)
hollow totem
Successor function
hollow totem
Really it's true by definition
2 is defined to be succ(1)
a+succ(b) = succ(a)+b
a+0=0
succ(0)=1
So $$1+1=1+succ(0)\=succ(1)+0\=2$$
potent lotusBOT
monikanicity
slim musk
damn tysm :)
hollow totem
idk if this is actually the canonical way to do this with peano but close enough
No problem
slim musk
:)
calm coralBOT
Available help channel!
tacit acorn
i think im too tired to figure out what happened here
calm coralBOT
i think im too tired to figure out what happened here
leaden thunder
Are Q1 and Q2 positive real numbers?
tacit acorn
yea
ah nvm now i see it
the square root of q just went to the other side
and then you had 50-x
so you could do the -x to the other side as well to make it +x
.close
calm coralBOT
calm coralBOT
Available help channel!
maiden wolf
Help on Q4 pls
warm warren
Can you use trig and calculator
maiden wolf
Yes
warm warren
Try split the trapezium into a rectangle and triangle
steel mason
Main idea of these exercises are finding right angle triangles
steel mason
Yes
maiden wolf
okay so now i label the opp for the traingle 2 cm
as 6-4 =2
and i know the adjcent is equal to 15m
so im guessing i work out the angle?
or do i work out the hypotenuse
hello?u still here?
wait i would work out the angle
then add 90 i presume
as all the corners in a ectangle add upto 90
?
steel mason
Angle BAD is Angle A right?
maiden wolf
yes
would AD = 97 degrees
as i used tan to work out the slit triangles angle
and i got 7
steel mason
This triangle is better
steel mason
Dunno what u would achieve with splitting top
Well u can find angle D
Then 360=A+D+B+C
maiden wolf
what did u work out as angle A?
steel mason
Use tan
steel mason
97 degrees?
maiden wolf
yes
steel mason
Ohhh I just realize now splitting top is better
maiden wolf
no worries
steel mason
,w arctan(15/2)
potent lotusBOT
steel mason
,w 1.438 radians to degrees
potent lotusBOT
steel mason
,w A=360-90-90-82
potent lotusBOT
maiden wolf
wouldnt it be 2/15 as 2 is opposite and 15 is adjacent?
maiden wolf
ohh thanks
its just that i really suck at maths
i cant do maths for the life of me
calm coralBOT
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calm coralBOT
calm coralBOT
Available help channel!
glossy eagle
how do I find Q https://prnt.sc/IpCyJcibdox2
calm coralBOT
how do I find Q https://prnt.sc/IpCyJcibdox2
ember lantern
This triangle is better
What're you trying to find, angles?
glossy eagle
@ember lantern this is my channel now
cosmic robin
you can find the coordinates by creating a triangle, thats how id do it
glossy eagle
There already is a triangle
cosmic robin
?
glossy eagle
Ok nvm but how do I create a triangle
cosmic robin
im not sure if this is the correct way to do it for you
glossy eagle
Yea it's 6 and 8
cosmic robin
then you would rise over run that shit
and relate it from P or from R to get the coordinate
so from 2,3, you would rise by y and run by x
glossy eagle
I never heard of this before
cosmic robin
so what is the hypotenuse of the triangle, how long
and what is the opposite angle
using that, i would go to the right by how long the bottom of the triangle is, and rise by the opposite side
glossy eagle
Is there a formula
cosmic robin
no since idk how your teacher would want you to solve it since this is just my intuition
glossy eagle
Yesterday someone told me to find the slope of PS and PR
this is the answer w the arrows
limber nacelle
@glossy eagle
glossy eagle
Yes
potent lotusBOT
Basudev
glossy eagle
Yes
limber nacelle
Then
potent lotusBOT
Basudev
limber nacelle
Aggred??
glossy eagle
I don't get this part tho
limber nacelle
If two lines are perpendicular the product of their slope would be "-1"
glossy eagle
Ok
limber nacelle
Now you have two eqn
glossy eagle
Yea
potent lotusBOT
Result:
100
I'm trying to put the answer in my head (6,8) and it dosen't wanna equal to -1 in the second eq
limber nacelle
,w (h-4)²+(k-17)²=100, ((k-3)/(h-2))×((17-k)(3-h))=-1
prisma mango
What I would do, it you can create two equations, and solve a system of equations
glossy eagle
Ok but we didn't get the answer tho
prisma mango
,w (h-4)²+(k-17)²=100, ((k-3)/(h-2))×((17-k)\(3-h))=-1
Fyi, don't do this for people. Because it doesn't help people learn if you spit out the answers for them
potent lotusBOT
limber nacelle
Yep
prisma mango
First, find the length of SR and SP
glossy eagle
but the answer is 6 and 8 https://prnt.sc/6mwWQ9LOlcGW
limber nacelle
.
prisma mango
but the answer is 6 and 8 https://prnt.sc/6mwWQ9LOlcGW
No it's not
prisma mango
You actually don't need any of that
prisma mango
The mistake is over here
This is overkill
prisma mango
@glossy eagle I can explain how to properly do it
limber nacelle
Go on
prisma mango
Do you agree that SP and RQ are parallel to each other?
glossy eagle
Yea
prisma mango
So what you need to do is to find the distance from S to P and apply that to R to Q
So what I mean is, from S to P, how many units in the x direction is it?
glossy eagle
the distance is like square root of x2 - x1 etc
prisma mango
You could do that but no need to
glossy eagle
Also I'm sure the answer right cuz it was created by professional
prisma mango
Just look at the two points, what's the coords of point S and P?
glossy eagle
-4,11 and 2,3
prisma mango
So from S to P, how many units in the x direction is that?
glossy eagle
6
prisma mango
How many units in the y direction is it from S to P?
glossy eagle
8
prisma mango
And as stated, SP and RQ are parallel
glossy eagle
That was so simple
prisma mango
Meaning that from R to Q, it has to apply the same units in the x and y as S to P
Make sense?
glossy eagle
Yes
calm coralBOT
@glossy eagle Has your question been resolved?
fierce ingot
How do I get "d" in
5d (mod (96)) = 1
I assume I have to use Extended Euclidean Algorithm or Inverse Modulo? But it's only one step:
1 = 96 - 95
(Answer is 77, but not sure why)
wintry glacier
thats what she said ahhahahahhaa
fierce ingot
calm coralBOT
@fierce ingot Has your question been resolved?
void drum
9/11
fierce ingot
9/11 ?
fierce ingot
<@&286206848099549185> Anyone free to help 😄
calm coralBOT
@fierce ingot Has your question been resolved?
calm coralBOT
@fierce ingot Has your question been resolved?
leaden thunder
,calc 4*96
potent lotusBOT
Result:
384
,calc 385/5
potent lotusBOT
Result:
77
You're supposed to find in integers a and b such that 96a + 5b = 1
leaden thunder
,calc 4*96
Here's a
fierce ingot
Just system of equations ?
leaden thunder
No. It's euclidean algorithm
I just gave you a = 4 because 6*4 is -1 mod 5
Saves you some time.
calm coralBOT
@fierce ingot Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
mighty sage
Need help on the question above the columns, been struggling with this question for a day now. Would appreciate if someone helped! Thank you
mighty sage
On the next 2 pages, you will see a series of exponential functions and logarithmic functions. Create the equation for each of the graphs, explain the transformation that are occurring for each function and identify the appropriate asymptote.
<@&286206848099549185>
calm coralBOT
@mighty sage Has your question been resolved?
mighty sage
No
<@&286206848099549185> Sorry for pinging once again, I just need help with this.
Would be very much appreciated
calm coralBOT
@mighty sage Has your question been resolved?
mighty sage
No
coral osprey
Each curve shares a similar point you can use a reference
Compare those to find translations from@the parent (the dashed)
mighty sage
Compare those to find translations from@the parent (the dashed)
Im honestly still super stuck
calm coralBOT
@mighty sage Has your question been resolved?
calm coralBOT
calm coralBOT
Available help channel!
remote mural
Is anyone able to help me with the full working out of x=cosec(2y) find dy/dx
coral osprey
Find the differential of both sides, then divide by dy, raise everything to the -1 power for convenience's sake
so like
$$dx = -2\csc(2y)\cot(2y)dy$$
potent lotusBOT
Umbraleviathan
remote mural
I’m ending up with a tan in my answer but the answer sheet is giving -1/2xrootx^2-1
remote mural
Got it now thanks
calm coralBOT
Available help channel!
eternal vector
if I am calculating an angle that is related directly to a variable I already know, whilst knowing where the highest value and lowest value of that angle would be, what type of function would I have to use to calculate it?
edgy raven
for example:
in this example the angle can be anything from >0 to <45?
eternal vector
no, the angle can be anywhere from 0 to the max value of the equasion (in the example angle is from 0 ---> 180(the value of y at x = 90))
@edgy raven
edgy raven
no, the angle can be anywhere from 0 to the max value of the equasion (in the ex...
whats the max value here?
both y values approach infinity as x approaches infinity
eternal vector
the max value is the value that I set to be at x = 90
edgy raven
you didnt show that in the example...
eternal vector
ok one sec
edgy raven
this honestly doesn't make much sense, what is the actual task?
potent igloo
That was my question exactly
Linda why can't you just share the problem? Obviously, not sharing it hasn't helped you
eternal vector
heres an example of two equations that accomplish the same task of mapping a vertex at (0,l3) and a point on (90,l2). this then allows me to input a x value to find out the value of the angle, which in this case is the y axis
im trying to figure out which equation I should use
there
and heres the original problem:#help-27 message
@edgy raven
sorry
calm coralBOT
@eternal vector Has your question been resolved?
potent igloo
@eternal vector do you know the length of each arm?
calm coralBOT
@eternal vector Has your question been resolved?
radiant monolith
if D F G are non empty sets.
i need to prove
D x (F intersect G) = (D x F) intersect (D x G)
how would i go about proving this?
solar spruce
how do you show set equality?
radiant monolith
im not sure
what do you mean?
i think i should plug variables that represent the items within each set
thin tendon
$x \in D \times (F \cap G)$ iff .....
potent lotusBOT
Benjamin
thin tendon
you just write the definitions and work your way
radiant monolith
and show how if i take a certian amount as an assumption then i can either show it's true or false
solar spruce
when in doubt, show either set is a subset of the other
thin tendon
to the other statement
radiant monolith
when in doubt, show either set is a subset of the other
oh yah
i would check each one to see if it was a subset or another
so im kind of stuck
should i plug in variables that represent the sets?
solar spruce
let (a,b) be in D x (F n G)
then a in D and b in (F n G)
what does b in (F n G) mean?
radiant monolith
that b is in F and G
solar spruce
yes, so $(a, b) \in D\times (F \cap G) \iff a\in D \land b\in F\land b\in G$
radiant monolith
why is a in F
solar spruce
you basically wanna tweak this into getting to "(a,b) in (D x F) n (D x G)" which is just
"(a, b) in D x F and (a,b) in D x G"
"a in D and b in F, and, a in D and b in G"
...
meant to be a D sorry
potent lotusBOT
maximo
radiant monolith
why do we not say that b and z? are in F
we dont know that that something was not intersected out of F do we?
solar spruce
what are you refering to
radiant monolith
"(a, b) in D x F and (a,b) in D x G"
we know that it would have a,b
but why would it not also have a,z?
solar spruce
you basically wanna tweak this into getting to "(a,b) in (D x F) n (D x G)" whic...
this message is essentially saying "work back from the other side, find a midpoint where the expressions meet"
i don't know where your z came from
we essentially want to do
$$(a,b) \in D\times (F\cap G) \iff\
...\iff \
(a,b) \in (D\times F)\cap (D\times G)$$
potent lotusBOT
maximo
solar spruce
in order to do that we employ the literal definitions of being "in" a set, intersections, cartesian products, etc..
radiant monolith
ahh i just was dumb that is a known element yes
there could be more we didnt say it was the only one
im on the same page
solar spruce
we say (a,b) to mean an arbitrary element in the set
kind of like if we're saying let n be in Z (the integers), we're assuming it's arbitrary
it could be 1, 3, -50, 7
but if we want to show it works for all integers, we take an arbitrary one and show it has some property (so then we can claim every single integer has that property)
in the same vein, we take an arbitrary element (a,b) from our set
and if that arbitrary element is in our set IFF it is in the other set, the sets must be equal
as it is true for any element
radiant monolith
**maximo**
we are here
solar spruce
**maximo**
we are here
we can then say $$a\in D \land b\in F\land b\in G\iff (a\in D \land b\in F)\land(a\in D\land b\in G)$$
potent lotusBOT
maximo
solar spruce
we just tweaked them a little bit. it should be clear why this is still true
but notice that those are the literal definitions of $$ (a,b)\in D\times F \land (a,b) \in D\times G$$
potent lotusBOT
maximo
solar spruce
and this should look familiar as an expression (it is an intersection)
radiant monolith
you are using the triangle as a AND not a intersect right?
potent lotusBOT
maximo
radiant monolith
i think my teacher wants a bit more than that. i feel like
solar spruce
what would they want to see?
radiant monolith
i guess it works because we showed they are equivalent
let me dig up an examp;e
example
solar spruce
that's pretty much what we just did
the only thing is that we can use iff to go both ways at the same time
they had to do => and <= separately
radiant monolith
ohhhhh
solar spruce
we just did <=> all at once
radiant monolith
well is iff short for something?
solar spruce
if and only if
radiant monolith
ok
solar spruce
$P\iff Q \equiv (P\implies Q) \land (Q\implies P)$
potent lotusBOT
maximo
radiant monolith
so let me see if i can create this from mostly memory
D x (F intersect G) = (D x F) intersect (D x G)
assume that a eD and b eFnG
so when we look at Dx(FnG) we get (a,b)
and because b eFnG
we know b eF and b eG
so we can show that (a,b) eDxF
and (a,b) eDxG
so we can show that
(a,b) e(D x F) intersect (D x G)
meaning that (a,b) = (a,b)
solar spruce
meaning that (a,b) = (a,b)
no
meaning that Dx(FnG) = DxF n DxG
but yes, that's the gist
solar spruce
that's just a definition of if and only if
solar spruce
not really
you can just state that since this is for any arbitrary (a,b) in Dx(FnG), and since this reasoning holds both ways, the sets are equal
if you wanted to be thorough you'd say that then the sets are both subsets of each other, and so the sets are indeed equal
radiant monolith
i might do that
considering thats how he showed us the example
im sure he would look for it
do i have to do anything different for the subset thing?
or do i just basically restate the above proof?
i can put that all into a lema
solar spruce
the subset thing is implied in all this
do you remember how to show something is a subset of something else?
if you don't, $A\subseteq B \equiv x\in A \implies x\in B$
potent lotusBOT
maximo
solar spruce
since we showed $x\in A \iff x\in B$, we've showed $x\in A \implies x\in B$, that is, $A\subseteq B$, and we've also shown $x\in B \implies x\in A \implies B\subseteq A$
potent lotusBOT
maximo
solar spruce
since $A\subseteq B$ and $B\subseteq A, A=B$
potent lotusBOT
maximo
solar spruce
this is what most of your set equality proofs will come down to
radiant monolith
if you don't, $A\subseteq B \equiv x\in A \implies x\in B$
we didnt go over that
or i missed it
solar spruce
well it's what your professor used in the images you sent
regardless, this is what basically all set equality and set inclusion proofs come down to
ours here was no different
radiant monolith
awesome!
thanks so much
i think im going to ship it!
i did one but i assumed real values and i got it wrong
i had enough values to represent each possible solution
but it was supposed to be arbitrary and you helped with that
thanks!
lethal shadow
calm coralBOT
lethal shadow
calm coralBOT
@lethal shadow Has your question been resolved?
lethal shadow
lethal shadow
<@&286206848099549185>
calm coralBOT
@lethal shadow Has your question been resolved?
calm coralBOT
@lethal shadow Has your question been resolved?
calm coralBOT
@lethal shadow Has your question been resolved?
steel karma
calm coralBOT
steel karma
$\binom{2n}{n}=\frac{2\cancel{n!}}{n! \cancel{n!}}=\frac{2}{n!}$
potent lotusBOT
hazysleet
steel karma
visual nimbus
wrong
steel karma
Why?
graceful dust
2n choose n is def not a number between 0 and 1 haha
visual nimbus
$\binom{n}{k} = \frac{n!}{(n-k)!k!}$
potent lotusBOT
Ｈｅｒｅｌｓ
visual nimbus
$\binom{2n}{n} = \frac{(2n)!}{(2n-n)! n!} = \frac{(2n)!}{(n!)^2}$
steel karma
Ok
potent lotusBOT
Ｈｅｒｅｌｓ
steel karma
So, $\binom{2n}{n}^{\frac{1}{n}}=\left(\frac{(2n)!}{(n!)^2}\right)^{\frac{1}{n}}$ is a decreasing function?
potent lotusBOT
hazysleet
steel karma
If it is decreasing then I can just plug the least positive integer 1 and get the bound (m)
@visual nimbus
bronze adder
,w graph {\frac{(2n)!}{(n!)^2}}^{\frac{1}{n}}
potent lotusBOT
visual nimbus
,w compare (2n)! and (n!)²
potent lotusBOT
visual nimbus
$\exp(\frac{1}{n} \log(\frac{(2n)!}{(n!)^2}))$
potent lotusBOT
Ｈｅｒｅｌｓ
visual nimbus
(2n)! grows faster than (n!)^2, so log is positive
visual nimbus
because its greater than 1 ?
(2n)! > (n!)^2
now I need to compare the log with 1/n
steel karma
I don't understand anything
limpid skiff
Set
visual nimbus
Im trying to find a way for finding an upper bound
visual nimbus
welp i was tempted to use Stirling formula
steel karma
Bruh
steel karma
Hey snoow
potent lotusBOT
visual nimbus
that double factorial
potent lotusBOT
steel karma
Wait
ancient thistle
now to prove you actually reach the bound 
potent lotusBOT
ancient thistle
its the double factorial
visual nimbus
with stirling i got this :
$\frac{(2n)!}{(n!)^2} \sim \frac{4^n}{(\pi n)^{\frac{1}{2}}}$
potent lotusBOT
Ｈｅｒｅｌｓ
graceful dust
stirling 
potent lotusBOT
steel karma
Same
ancient thistle
no its just notation
like
all im doing is splitting the odd and even terms from (2n)!
theres nothing complicated going on at all
dont be scared of the notation
steel karma
Ok but, How do I do it without stirling and these notations?
visual nimbus
anyway its just true that $\binom{2n}{n}^{\frac{1}{n}} \leq 4^n$
ancient thistle
all im doing is splitting the odd and even terms from (2n)!
do this
you split the odd and even terms apart
steel karma
ancient thistle
thats what you see here
https://cdn.discordapp.com/attachments/948770026914213909/1053269545206419476/118663865264242688.png
even terms
odd terms
and so like
in the first term the n!s cancel
in the second term the factor is <1
ancient thistle
well then the conclusion is
potent lotusBOT
ancient thistle
now you prove that you can actually reach that upper bound
or well
break 3
so i guess you need uh
potent lotusBOT
visual nimbus
yea i know
potent lotusBOT
potent lotusBOT
steel karma
steel karma
I tried plugging in numbers and saw it
ancient thistle
i guess that also works if you're not trying to prove it
if a numerical answer is all thats needed
then 4 is a good guess
steel karma
ancient thistle
steel karma
The answer is given as -1
steel karma
For n=-1, the LHS is, $$\frac{ab}{a+b}$$
potent lotusBOT
hazysleet
ancient thistle
expand and see what happens
,w expand (a^(n+1) + b^(n+1))(a+b) - 2ab(a^n + b^n)
this is easy enough to do by hand
potent lotusBOT
ancient thistle
you find that you have
potent lotusBOT
ancient thistle
or by slight rearrangement
steel karma
I showed this yesterday, yes
potent lotusBOT
ancient thistle
from which you find that
ancient thistle
think harder next time
remote mural
sry
remote mural
theres always something small sticking out
calm coralBOT
@steel karma Has your question been resolved?
ancient thistle
,w 2^4
potent lotusBOT
potent lotusBOT
ripe spade
?
ancient thistle
,w 2^2 + 2^4
potent lotusBOT
ancient thistle
f(2^6) = f(2^3 + 2^3) = f(2^4 + 2^2)
f(9) = f(4+5) = f(20)
f(8) = f(4+4) = f(16)
i think thats it
i mean realistically like
ripe spade
f(64) = f(8 + 8) = f(16 + 4)
ancient thistle
what else could it be
ripe spade
why is that necessary
ancient thistle
the question only gave you one number to work with 
ripe spade
so u cant determine a value?
ancient thistle
f(9) = f(4+5) = f(20)
f(8) = f(4+4) = f(16)
literally said it here
calm coralBOT
@steel karma Has your question been resolved?
calm coralBOT
@steel karma Has your question been resolved?
calm coralBOT
@steel karma Has your question been resolved?
dusky flax
Hmm
f(8) = f(4+4) = f(4 * 4) = f(16)
f(16) = f(8+8) = f(8 * 8) = f(64)
f(64) = f(16 * 4) = f(16+4) = f(20)
f(20) = f(5 * 4) = f(5+4) = f(9)
so, f(8) = f(9) = 9
@steel karma
calm coralBOT
dusky flax
welcome
calm coralBOT
Available help channel!
uneven hull
calm coralBOT
tacit compass
You can find this by finding the price of each one for one ounce
that way you can compare the price
uneven hull
.close
old wraith
I just want for q.69 ,find the volume of the solid
calm coralBOT
I just want for q.69 ,find the volume of the solid
old wraith
https://media.discordapp.net/attachments/1061663479733432452/1061663480521969854/20230108_204027.jpg
old wraith
https://media.discordapp.net/attachments/1061663479733432452/1061663480761041006...
Is this right?
untold breach
Your filled answer is correct . All you need to do is to use unitary method to find /unit price . Lowest is with Option-1 @uneven hull
calm coralBOT
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summer parcel
How do I solve the equation: 2x(x - 1) = y(y - 1)
calm coralBOT
How do I solve the equation: `2x(x - 1) = y(y - 1)`
dull wagon
the instructions are unclear
summer parcel
I am looking for the smallest solutions x and y where x and y are whole numbers
The smallest solutions are supposed to be: x = 4 and y = 3. How can this be calculated, aside from trial-and-error?
dull wagon
um there's a smaller solution
summer parcel
Where x and y are non-zero positive integers?
dull wagon
with x=1, y=1
coral osprey
You get that if you utilize zero product theorem
At least that's how I also got (1,1)
dull wagon
and what you typed isn't even a solution
summer parcel
Alright, is it possible to get the higher solutions as well somehow?
coral osprey
No not really
There's an infinite number of natural numbers
You can def find a low end because N has a "low end" but
It goes on to infinity
,w Solve[2x(x-1) == y(y-1), y]
potent lotusBOT
coral osprey
And then choose any x natural number
The thing is
Like I did
Natural numbers go on to infinity
summer parcel
So my best bet is using trial-and-error moving towards infinity?
coral osprey
Well no, there is no max is what I'm tryna get you to understand
For I care if you could let x = 288383744738383939282838382828282828282828
But you can go higher
summer parcel
I understand that, but assuming that there would be a max range that would be computationally feasible
e.g. max = 100
Or something
coral osprey
I guess
remote mural
calm coralBOT
lament siren
calm coralBOT
calm coralBOT
@hushed knot Has your question been resolved?
pine topaz
hey
pine topaz
anyone know a series that converges to 1 or i?
pine topaz
either one would help me
glass heart
i,i,i,i,...
alpine stone
1 + 1/n?
pine topaz
i meant sequence i think
infinite sum
im not english, sorry, i tend to mix the english words up sadly
robust oar
geometric?
remote mural
anyone know a series that converges to 1 or i?
$\sum_{n =1}^{\infty} = \f{1}{n(n+1)} = 1$ if thats what you mean
alpine stone
So do you want an infinite sum or a sequence?
pine topaz
thank you, i think that helps alot
potent lotusBOT
♡Lex♡
pine topaz
btw, why i need this:
i have to derive a series form of sinh(z)
therefore i use the series form of sin(z)
i was stuck with trying to pull an i into a sum
flat tendon
infinite geometric series where radius is 1/2 that starts from n=1 converges to 1 too
pine topaz
$\sin(z)=\sum_{k=0}^{\infty} (-1)^k \frac{z^{2k+1}}{(2k+1)!}$
potent lotusBOT
~Martin
pine topaz
like that
pine topaz
i think so, yeah
robust oar
maybe the exponential representations also would help
$sinh(x) = \frac{e^{x} - e^{-x}}{2}$
potent lotusBOT
biggboy
pine topaz
btw, is this even legit?
suppose i have the a times the infinite sum of something
if i have a series notation of a, can i then just add the terms of the two series together?
i will write it out and send it here as it is written, maybe that will make it clearer
nvm
robust oar
I mean, infinite sums mostly act like an normal sum when the order of terms doesn't change
(a_1 + b_1 + a_2 + b_2 + ... + a_n + b_n) is equavilent to (a_1 + a_2 + ... + a_n) + (b_1 + b_2 + ... + b_n), I think
pine topaz
the thing is that this is a multiplication of sums
not so nice afterall
the same task for cosh was so nice haha
wait
i think i did a mistake
wouldnt this be true?
that would make the task really easy
yeah i think this looks good
robust oar
yea it distributes over the sum
stiff pivot
Help in linear algebra
calm coralBOT
Help in linear algebra
stiff pivot
Do you see part 2 in exercise 1
Deduce that C is invertible and find it's inverse
How to do this?
<@&286206848099549185>
I have an exam tomorrow 😫
pine topaz
a quadratic matrix is invertible, meaning it has an inverse, exactly then when the determinant is not 0
this is the case if the rank is not 0
also it is the case if you can row reduce to echelon form
pine topaz
if you want to argue, why C is invertible, you can use either:
-the rank of C is not 0
-the determinant of C is not 0
there are probably other ways as well
stiff pivot
I should write the rank of C is not 0 and it's det(C) is not 0?
Or just one is enough
??
pine topaz
either one is enough
stiff pivot
Ok
pine topaz
if we don't row reduce, we could have no 0 columns, however we could have equal rows
stiff pivot
How to deduce it's inverse
pine topaz
I should use this method
to get the inverse, we do exactly what you did
stiff pivot
Ok but I should get this, not this
Since it's edited and I should edit it with I3
But I should deduce it
OMG
stiff pivot
What I should use?
pine topaz
since you want to find the inverse of C, do what you did with A to find it's inverse
stiff pivot
The r.e.f of C or C without r.e.f
pine topaz
you row reduce C to echelon form
and while you do that, you do the same steps to an identity matrix
pine topaz
I should use this method
what you did with A
stiff pivot
I find it's inverse
pine topaz
you found it? great!
stiff pivot
But he say deduce
pine topaz
you cant really argue why something is an inverse matrix
you can argue if a matrix is ivertible
we can do this by row reducing to find the rank or we can find the determinant
or we could just try to find the inverse
if we find an inverse then C is invertible
if we dont find an inverse then C is not invertible
pine topaz
yes
swift magnet
calm coralBOT
calm coralBOT
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strange lichen
Just plug in f and u
calm coralBOT
calm coralBOT
Available help channel!
lost ice
hi. is this right so far? i have [1/cos^2(t) + 5] from pi/3 to 0 but i'm not sure how to treat the 1/cos^2(t) term before plugging in the bounds.
lost ice
would it be ln|cos^3/3| ?
oblique wasp
hi. is this right so far? i have [1/cos^2(t) + 5] from pi/3 to 0 but i'm not sur...
1/cos^2 = sec^2 and you can go from there
lost ice
thank you.
narrow rose
Hi I have a question is the p.m.f the whole thing (table) or just an individual thing likes p(X=4)=1/12 I'm kinda confused
leaden thunder
Hi I have a question is the p.m.f the whole thing (table) or just an individual ...
just ask your question
calm coralBOT
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remote mural
Hey ! I need to factorize this (x² - 8x + 12) but I don't know how to do it there, could someone help me please
remote mural
Maybe there's a fault or something but I can't find it
velvet osprey
twin crypt
Subtracting a sum of two numbers is equivalent to subtracting the first number and then subtracting the second, hence for two real numbers a and b, -(a+b)=-a-b. It's the same the other way around : -a+b=-(a-b) (with -b instead of b).
calm coralBOT
@remote mural Has your question been resolved?
hidden elbow
hey my babies
calm coralBOT
hey my babies
upper sparrow
Have you managed to differentiate what they have so far at least?
leaden thunder
• Show your work, and if possible, explain where you are stuck.
hidden elbow
> • Show your work, and if possible, explain where you are stuck.
the entire question c bro 😭
hidden elbow
Have you managed to differentiate what they have so far at least?
wait which
upper sparrow
The differentiation bit is at least the easiest (laying down rn 
)
hidden elbow
oh that bit
upper sparrow
Sum and product notation makes stuff somewhat easy for that part
hidden elbow
nope not yet
the thing is
I’m 16 and in high school
my teacher made this paper
and he says it’s TECHNICALLY in our syllabus
that technically is soooo cap
wtf is this
upper sparrow
Hahah well seeing that first question
hidden elbow
nah that’s trauma inducing
leaden thunder
nope not yet
do the derivative
upper sparrow
Anyways, are you familiar with the notation $\Pi$ and $\sum$ for products and sums?
potent lotusBOT
chartbit
hidden elbow
nope
hidden elbow
do the derivative
how do I do that?
upper sparrow
Hmmm fair fair, stuff would be a bit harder to typeset then
upper sparrow
how do I do that?
Use $\ln(xy)=\ln(x) + \ln(y)$ on the function they give you
potent lotusBOT
chartbit
upper sparrow
That’ll get you a sum of linear factors like $\ln(x+l)$, each of which are easy to differentiate
potent lotusBOT
chartbit
upper sparrow
(And much better than doing product-chain rule )
hidden elbow
ah soo ln(x+1)(x+2)…(x+k) = x+1+x+2+..x+k?
wait no
I saw wrongly
ln(x+1)(x+2)…(x+k) = lnx + ln1+lnx+ln2…+lnx +lnk?
crap
upper sparrow
More that $\ln[(x+1)(x+2) \ldots (x+k)] = \ln(x+1) + \ln(x+2) + \ldots + \ln(x+k)$
potent lotusBOT
chartbit
upper sparrow
Their notation 💩
hidden elbow
LOL
hidden elbow
More that $\ln[(x+1)(x+2) \ldots (x+k)] = \ln(x+1) + \ln(x+2) + \ldots + \ln(x+k...
ah
AHHH
ok
yea gotchu
now is that a sum
how would I differentiate when there’s ellipses
upper sparrow
Basically differentiate what’s in them like the first few ones
Say I give you a random $\ln(x+m)$, you can differentiate that yea?
potent lotusBOT
chartbit
hidden elbow
yea
upper sparrow
Basically you have stuff that looks like that inside (which is why I wanted sigma and pi notation for the sums and products respectively)
hidden elbow
so I get $\frac{1}{x+1} + \frac{1}{x+2}…\frac{1}{x+k}?$
potent lotusBOT
Springsskateboard
hidden elbow
NICE
upper sparrow
Now try and common denominator that 
upper sparrow
It’s gonna be pain, so I’ll say this
upper sparrow
Try do it for a given k (such as k=2, k=3, etc)
potent lotusBOT
Springsskateboard
hidden elbow
man
hidden elbow
Try do it for a given k (such as k=2, k=3, etc)
oh
hidden elbow
nope my teacher just said try 8c
upper sparrow
,w diff ln[(x+1)(x+2)(x+3)]
potent lotusBOT
leaden thunder
pain
hidden elbow
..
upper sparrow
,calc 1(2)+2(3)+3(1)
potent lotusBOT
Result:
11
Well you’re here now, so you have to finish the question
hidden elbow
let’s do this
upper sparrow
,calc 1(2)+2(3)+3(1)
Explain why I did this?
hidden elbow
yea
hidden elbow
,w diff ln[(x+1)(x+2)(x+3)]
and this
wait what’s the expression after we take common denominator
upper sparrow
Hahah I’m asking you to explain why I did that :kek:
upper sparrow
This one I believe
upper sparrow
,w expand (x+1)(x+2)(x+3)
potent lotusBOT
leaden thunder
A is supposed to grow like k! ?
hidden elbow
wait what does A grow to k! mean
or wait nvm u said grow like k!
oh shit I just realised it’s 5 marks
crap this is gonna be another ass question like the first one
upper sparrow
Mind you the constant term of the numerator will basically be like, you basically multiply the first few then leave the first out, then do the same and leave the second out, and so on so forth
Then you add them together
Too lazy to TeX that up, on mobile 
hidden elbow
wait so we had $\frac{1}{x+1} + \frac{1}{x+2}…\frac{1}{x+k}$
potent lotusBOT
Springsskateboard
hidden elbow
then what happens if we have common denominator?
upper sparrow
Basically do the work for k=3
hidden elbow
oh so just sub in a value
can we do it with just k being there
without subbing in anything
or is that more pain
upper sparrow
,calc 1(2)+2(3)+3(1)
You’ll see what I meant by this
upper sparrow
Yeah so do 1/(x+1) + 1/(x+2) + 1/(x+3)
hidden elbow
so $\frac{3x+6}{(x+1)(x+2)(x+3)}$
potent lotusBOT
Springsskateboard
upper sparrow
Should be quadratic
hidden elbow
wait wtf did I lose algebra knowledge
upper sparrow
Remember you want e.g. (x+2)(x+3) + (x+1)(x+3) + (x+1)(x+2) as our numerator
hidden elbow
wait $\frac{1}{x+1} + \frac{1}{x+2} + \frac{1}{x+3}$
potent lotusBOT
Springsskateboard
hidden elbow
when we take common denominator
upper sparrow
The denom becomes (x+1)(x+2)(x+3)
hidden elbow
ok cool
upper sparrow
It happens 