@teal turret i kinda forgot this lesson
#help-10
proven zephyr
proven zephyr
was i correct?
timid silo
I dont know
timid silo
Yess
teal turret
<@307914411648090113> i kinda forgot this lesson
Haha honestly I wasn’t too sure either
teal turret
Lol he is
robust sleet
write solution
teal turret
Dude be patient
robust sleet
timid silo
My time is running
robust sleet
Skill isue
proven zephyr
Find the area of the smaller trapezoid
We know that:
If two figures are similar, then the ratio of its areas is equal to the scale factor squared
Let:
a = base of smaller trapezoid
b = base of larger trapezoid
A = area of smaller trapezoid
B = area of larger trapezoid
We have:
$$(\frac{a}{b})^2 = \frac{A}{B}$$
Substitute the value in:
\begin{align}
& (\frac{8}{12})^2 = \frac{A}{27}
& \frac{64}{144} = \frac{A}{27}
& \frac{64}{144} \cdot 27 = A
& \frac{1728}{144} = A
& 12 = A
\end{align}
probably like this
wait how do i make new line
timid silo
@proven zephyr
proven zephyr
ok idk how to make new line
proven zephyr
ok wait
timid silo
Thanks brooo
timid silo
I understood
proven zephyr
texit
timid silo
Thank you so much
proven zephyr
you're welcome
timid silo
No bro done
proven zephyr
timid silo
@proven zephyr
proven zephyr
yes?
proven zephyr
ok
proven zephyr
just do the same no?
timid silo
On the second rectangle box
proven zephyr
the (a/b)^2 = A/B
timid silo
just do the same no?
But last time the number we had to find was inside the box , but this time it is outside the box
Formula is different??
proven zephyr
no no no
timid silo
Okay lemme do the same formula
timid silo
@proven zephyr
@proven zephyr
My last and final homework
Pythagoras theorem
Please help
hexed agate
Yeah apply the theorem
warm shaleBOT
proven zephyr
why?
timid silo
I cant understand the (x-2)
nocturne minnow
Do you know Pythagorean theorem?
timid silo
I did the maths with 5cm 7cm and 9cm
But I am confused with the x-2 thing
timid silo
Do you know Pythagorean theorem?
Yes I know a lot
nocturne minnow
But please do it for me
And no, no one here is going to do your work for you
timid silo
And no, no one here is going to do your work for you
Who r u
nocturne minnow
Yes I know a lot
What is it?
slim basalt
ayo
timid silo
What is it?
a²+b²=c²
slim basalt
gg
timid silo
Your father
And me your grandfather
nocturne minnow
You know the sides, of that triangle, plug them into the formula
What do you get when you plug them in?
timid silo
You know the sides, of that triangle, plug them into the formula
But how can I do the x-2 ? If I plug it in, i cant get the answer
slim basalt
you dont know (x-2)^2 ?
nocturne minnow
It's the same process as a triangle with numbers, this time you have variables
timid silo
No
hexed agate
kids these days crave instant gratification
proven zephyr
~~kids these days crave instant gratification~~
i'm offended, because it's true
timid silo
It's the same process as a triangle with numbers, this time you have variables
So now what can I do
slim basalt
you know binomial theorem?
nocturne minnow
First identify the sides
timid silo
Will I subtract x-2² from 8²?
nocturne minnow
No
timid silo
Then?
nocturne minnow
You need to expand (x - 2)^2 first
nocturne minnow
Recall that (x - 2)^2 = (x - 2)(x - 2)
nocturne minnow
Did you expand that?
timid silo
Umm I am doing
nocturne minnow
After you expand it, what is the equation that you have?
nocturne minnow
,rotate
warm shaleBOT
warm shaleBOT
dldh06
nocturne minnow
You need parentheses around the x - 2
proven zephyr
You haven't even expanded that expression yet
Does he know how to?
nocturne minnow
I would assume that the OP has learned it already if they are given a problem like this
timid silo
Plzz bro do it fast I have only 2 mins to submit it
nocturne minnow
Yeah... No
timid silo
Please @proven zephyr
proven zephyr
bro
slim basalt
xd
timid silo
Oky
slim basalt
x^2 = 8^2 + (x-2) (x-2)
timid silo
Then?
nocturne minnow
Expand
slim basalt
expand the second part
timid silo
How
nocturne minnow
Distribute
timid silo
Ok
nocturne minnow
Also it's been 4 minutes now.... L
slim basalt
how is it going
nocturne minnow
It's probably too late now, it's apparently past their due date
slim basalt
obtuse pebbleBOT
@timid silo Has your question been resolved?
tawny compass
obtuse pebbleBOT
royal basin
what stage are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
• Show your work, and if possible, explain where you are stuck.
tawny compass
I can show my working if you want
I don't know what to do after this
Sorry for bad handwriting, i took the left side and simplified it, that's all I've done
elfin belfry
You can try doing componendo and dividendo
royal basin
think some half angle shenanigans might be applicable here.
tawny compass
You can try doing componendo and dividendo
Whats that
tawny compass
think some half angle shenanigans might be applicable here.
Sorry i don't get "half angle shenanigans"
final hornet
replace 1 by cosx^2 + sinx^2 then see if something factorizes
royal basin
cos(t)+1 = 2cos^2(t/2) and sin(t) = 2sin(t/2)cos(t/2)
elfin belfry
cos(t)+1 = 2cos^2(t/2) and sin(t) = 2sin(t/2)cos(t/2)
I am pretty sure they only know the Pythagorean identities
royal basin
and cos(t)-1 = -2sin^2(t/2)
royal basin
I am pretty sure they only know the Pythagorean identities
let's ask OP.
@tawny compass do you know the half angle identities i mentioned just now?
royal basin
what about double angle identities
tawny compass
Oh wait i can derive the second one
tawny compass
what about double angle identities
What's that
elfin belfry
You can try using 1 + cot^2 x = cosec^2 x => cosec^2 x - cot^2 x = 1 and then replacing 1 with that
royal basin
What's that
identities expressing cos(2x) and sin(2x) in terms of sines and cosines of 1x
tawny compass
I haven't learnt this yet
royal basin
sin(2x) = 2sin(x)cos(x)?
tawny compass
I'm pretty sure you don't need that to solve it since it's not covereed
elfin belfry
I'm pretty sure you don't need that to solve it since it's not covereed
Yeah you don't
It just makes it simpler
tawny compass
sin(2x) = 2sin(x)cos(x)?
This is just from the angle sum thing right
elfin belfry
Do you know 1 + cot^2 x = cosec^2 x
tawny compass
Sin(a+b)= yknow
tawny compass
Do you know 1 + cot^2 x = cosec^2 x
Yep
And the one with cosec
Oops i mean sec and cot
tawny compass
Lol
tawny compass
Try replacing 1 with cosec^2 x - cot^2 x
Both of the ones?
royal basin
This is just from the angle sum thing right
sure, as is the one for cosine.
tawny compass
Actually, just do one
I'm not sure what to do after that...
elfin belfry
cosec^2 x - cot^2 x
Do you see some identity (not trigonometric) that can be used here?
tawny compass
Ah yeah I'm blind
tawny compass
You can factorize some stuff from there
Sorry again but err i get this
I dotn think you can simplify it nothing cancels
elfin belfry
Send what you got
elfin belfry
No no
tawny compass
Huh
elfin belfry
You are missing brackets and the signs you have are wrong
(cot + cosec) - (cosec + cot)(cosec - cot)
(cot + cosec)[1 - (cosec - cot)] = (cot - cosec)[1 - cosec + cot]
I omitted the theta so that it's easier for me to type
elfin belfry
I think you copied the question wrong initially
You start out by $\frac{\cot\theta+\csc\theta-1}{\cot\theta-\csc\theta+1}$
tawny compass
Got it
Thanks
You have any tips for doing these questions? The steps feel intuition less
warm shaleBOT
King Dedede
tawny compass
No no i got it yeah it simplifies
tawny compass
You have any tips for doing these questions? The steps feel intuition less
Like i would've expanded it all into sin and cos and stuff
elfin belfry
You have any tips for doing these questions? The steps feel intuition less
I have no tips, but you'll develop the intuition as you keep doing these kinds of problems
tawny compass
Okay 👍 thanks
elfin belfry
Sometimes you replace 1s and sometimes you convert all the ratios in terms of sines and cosines
tawny compass
.close
waxen turret
hybrid gull
See this
waxen turret
See this
Sometimes people have no relevant work to show because they don't know how to solve the problem. The work done is useless because its done by someone who doesn't know what their doing
If I just wanted the answers I would copy and paste into Brainly
hybrid gull
That’s why it’s helpful to explain “Hey I have no idea how to do this”, instead of assuming someone will figure out what you need for you
waxen turret
Ok. I dont know what Im doing
Sorry I just thought that me not knowing what Im doing was assumed with just a post of the problem
I don't mean any disrespect I know you guys are doing this as a free service
.close
simple kernel
Hi could someone help me solve this:
obtuse pebbleBOT
Hi could someone help me solve this:
fierce lagoon
What have you tried
fierce lagoon
fi?
simple kernel
idk what that greek letter is called lol
but basically
i reach
cosx* sqt3 / 2 - sinx*1/2
fierce lagoon
$$R\cos(a+b) = R\cos(a)\cos(b) - R\sin(a)\sin(b)$$
simple kernel
by using the cos(a+b) theorem and the value of fi or whatever that letter is called
warm shaleBOT
Umbraleviathan
fierce lagoon
I think you forgot to distribute the 2sqrt(3)
simple kernel
no
wait let me write it
its painfully slow on keyboard
basically
i am nowhere
lol
could you say how you approach it?
fierce lagoon
**Umbraleviathan**
I just used this
Like directly and you can get A and B
$$\begin{align*}
2\sqrt{3}\cos\left(x+\frac{\pi}{6}\right) &= 2\sqrt{3}\cos\left(x\right)\cos\left(\frac{\pi}{6}\right)-2\sqrt{3}\sin\left(x\right)\sin\left(\frac{\pi}{6}\right) \
&= 3\cos\left(x\right)-\sqrt{3}\sin\left(x\right) \
&= -\sqrt{3}\sin\left(x\right) + 3\cos\left(x\right)\
&\implies A = -sqrt{3}, B = 3
\end{align*}$$
simple kernel
righht my solution is similar
but isn't there a more universal solution so to speak
u do that assuming the final version
of the formula you reach is the same as A*sinx + B*cosx
but what if the equation is crazy complicated
simple kernel
yeah i guess
but what if
how else can you approach it
what if there were 15 As and Bs
.close
simple kernel
i dont even know lmao
fierce lagoon
like youre gonna have to elaborate
warm shaleBOT
Umbraleviathan
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
simple kernel
yeah i understand the solution
simple kernel
no,no ,no
i guess what i meant was
that i feel like the solution assumes something
idk what that something is
but i feel like
its only applicable for this type of problem
simple kernel
yeah
like look at whatever is before
sinx and put that as A
i am wondering
if theres a equation-based solution at the end of which
i would get A=
sqrt(3) in that case
fierce lagoon
compare terms:
$$A\sin(x) = -\sqrt{3}\sin(x)$$
Divide both sides by sin(x)
warm shaleBOT
Umbraleviathan
simple kernel
wait
divide what both sides by sinx
like which equation
are we dividing by sinx
fierce lagoon
**Umbraleviathan**
compare like/similar terms. And then you wanna isolate A
i mean its just algebra
you wanna find A; we dont care what x is
simple kernel
can you draw it?
(i know im looking like a meth head who dont know what 1+1 is but i really really want to understand this)
fierce lagoon
$$\begin{align}
2\sqrt{3}\cos\left(x+\frac{\pi}{6}\right) &= A\sin(x) + B\cos(x)\
&= 2\sqrt{3}\cos\left(x\right)\cos\left(\frac{\pi}{6}\right)-2\sqrt{3}\sin\left(x\right)\sin\left(\frac{\pi}{6}\right) \
&= 3\cos\left(x\right)-\sqrt{3}\sin\left(x\right) \
&= -\sqrt{3}\sin\left(x\right) + 3\cos\left(x\right)
\end{align}$$
This implies:
$$\begin{cases*}
A\sin(x) &= -\sqrt{3}\sin\left(x\right)\
B\sin(x) &= 3\cos\left(x\right)\
\end{cases*}$$
warm shaleBOT
Umbraleviathan
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
quiet hare
obtuse pebbleBOT
obtuse pebbleBOT
Commands:
clopen: .close, .reopen, .solved, .unsolved
consensus: .poll
factoids: .tag
help: .help
Type .help <command name> for more info on a command.
No command called "<command" found.
nocturne minnow
It's literally been 5 minutes since you posted, just wait patiently
quiet hare
I literally just asked for help
And I said please
And I didn’t ping anyone
And I didn’t ask you
nocturne minnow
It seems like you were being impatient
sour jasper
I imagine the idea is that you want to pick any length axis that can contain all of the data values in the table without having too much “empty space,” so to speak
You also should have equally spaced tick marks on the length axis
You’re making a scatter plot, not a bar chart, after all
obtuse pebbleBOT
@quiet hare Has your question been resolved?
spiral knot
A : steps is too big (20)
B : steps change
C : doesn't cover all the values
D : too big
obtuse pebbleBOT
A : steps is too big (20)
B : steps change
C : doesn't cover all the values
D : ...
spiral knot
.close
obtuse pebbleBOT
quiet hare
A : steps is too big (20)
B : steps change
C : doesn't cover all the values
D : ...
It was wrong
spiral knot
A : steps is too big (20)
B : steps change
C : doesn't cover all the values
D : ...
those are the wrong length axis
obtuse pebbleBOT
Available help channel!
sacred root
Helo
timid silo
$frac{1}{(1+nx)^2}
obtuse pebbleBOT
$frac{1}{(1+nx)^2}
timid silo
$frac{1}{(1+nx)^2}$
warm shaleBOT
Idunno
timid silo
What
nocturne minnow
$\frac{1}{(1+nx)^2}$
warm shaleBOT
dldh06
warm shaleBOT
Idunno
timid silo
That much is clear but how do I formulate that it does not converge uniformly
It would converge uniformly if
$x = 0$
warm shaleBOT
Idunno
timid silo
**Idunno**
X could become 0
zenith raft
“It would converge uniformly if x = 0”
zenith raft
sounds like a possible misconception there
timid silo
If it could become zero
Because when I take derivative it needs zero to equate to zero because there is X in the top and not bottom.
Or am I insane because 5 am
zenith raft
what’s the original question, in full?
timid silo
**dldh06**
Does this sum converge uniformly if 0<x<inf
zenith raft
sum?
timid silo
I forgot how to make Tex post series
zenith raft
\sum_{}^{}
zenith raft
\infty lol
timid silo
$\sum_{n=1}^{∞}\frac{1}{(1+nx)^2}$
warm shaleBOT
Idunno
timid silo
Epic
zenith raft
LOL or that
timid silo
**Idunno**
Not converge uniformly if $ 0 < x < +∞ $
zenith raft
how do you know?
zenith raft
whattt
warm shaleBOT
Idunno
timid silo
Yes
zenith raft
are you saying it converges uniformly on [0,\infty)?
zenith raft
doesn't that mean it converges uniformly on (0,\infty)...?
timid silo
Does it work like that?
Ok I will just write what you said
And call it a day
I need to get at least 3 hours of sleep
zenith raft
are you saying it converges uniformly on [0,\infty)?
but now how do you know this?
timid silo
Thanks
zenith raft
okok nvm you should sleep if you need to
timid silo
but now how do you know this?
I found
The function
Which is
Major
Idk what it called in English
And it converges
The
$ /leq $
Function
$ \leq $
zenith raft
wild guess but weierstass m-test?
timid silo
Yes
timid silo
wild guess but weierstass m-test?
Basically
a_n function
Not function
Series
Which are convergent
And greater or equal
zenith raft
yass that's the one
zenith raft
it's ok, go sleep if you need to 🙂
timid silo
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
Choose an integer uniformly from the set {1, 2, . . . , 30}. Let A be the event that it is divisible
by 2; let B be the event that it is divisible by 3; let C be the event that it is divisible by 7.
Determine the probabilities of A, B, and C. Which of the pairs (A; B), (B; C), and (A; C) are
independent?
obtuse pebbleBOT
Choose an integer uniformly from the set {1, 2, . . . , 30}. Let A be the event ...
timid silo
I have no clue how to go about this, any ideas? haha
zenith raft
count how many are divisible by 2, 3, and 7?
timid silo
For A, half of those integers are divisible by 2 so if you were to pick one at random there would be a 50% chance for it to be divisible by 2
You can extend this method to B and C
timid silo
count how many are divisible by 2, 3, and 7?
Yeah but I'm unsure about the second half
What does it mean by which are independent?
Wouldn't they all be?
timid silo
For A, half of those integers are divisible by 2 so if you were to pick one at r...
Yes I have figured thank you
zenith raft
Wouldn't they all be?
why?
timid silo
It means if one depends on the outcome of another, i.e. by knowing the outcome of one it would change the outcome of another
Oh why not?
Probability of the outcome*
OHHH it just clicked omg
I hate counting
But yeah thank you laylaa and 42
.close
lone birch
can someone pls help me w this...?
obtuse pebbleBOT
can someone pls help me w this...?
cloud berry
year have 365 days but leap year have 366 days
2012 was leap year
divide the days between both dates by 7
round off to nearest integer and you'll get answer
1 week = 7 days
lone birch
it wd be cool if u said the answer ..
timid silo
round off to nearest integer and you'll get answer
dont you mean take the remainder and add that many days to monday?
cloud berry
dont you mean take the remainder and add that many days to monday?
maybe i said that indirectly
1461 days between dates --> 365+366+365+365
1461/7 = 208.7
lone birch
round off to nearest integer and you'll get answer
heyy...i think i got it...thnxx ur brilliant
cloud berry
0.7*7 = 4.9 ~ 5
lone birch
1461/7 = 208.7
thnxx pal
cloud berry
5 days after that day = monday
elfin burrow
isn't it saturday?
cloud berry
isn't it saturday?
my bad i calculated wrong i.e, days not calculation
elfin burrow
day of the week increases by one every year, increases by two every leap year (for dates after february 29, otherwise only add one)
actually learned that from a mental math book i read as a child lol
lone birch
so i just found an other sum like the previous one...but notsure why exactly they are involving 2005...help mee
elfin burrow
so i just found an other sum like the previous one...but notsure why exactly the...
seems like the solution is to a different question
narrow vault
no they just went back a day to be able to count full years before adding a day back for..reasons, i guess
completely unnecessary but the answer is still right so eh 
elfin burrow
oh, lol
elfin burrow
day of the week increases by one every year, increases by two every leap year (f...
to avoid confusion, you can always use this rule
lone birch
thnx guyss
shut tulip
2A1+A2=9
5A1+2A2-B1=22
2A1-2B1=11
Can someone help me, how to find the value of A1, A2, and B1?
I've tried and got A1 = 5/2, A2 = 4, B1 = -3/2
but i still confused with 2A1-2B1 = 11
obtuse pebbleBOT
2A1+A2=9
5A1+2A2-B1=22
2A1-2B1=11
Can someone help me, how to find the value of ...
runic void
What you have is a system of linear equation of 3 variables, in addition to solve it we must have at-least 3 different equations
Clearly we have them
Plug in eq 1 into equation 3,
tardy epoch
2A1+A2=9
5A1+2A2-B1=22
2A1-2B1=11
Can someone help me, how to find the value of ...
I told you that you had a sign error. Did you fix that
stable rain
shut tulip
I told you that you had a sign error. Did you fix that
yea, i've fixed it but still cant figure it out
shut tulip
Plug in eq 1 into equation 3,
ok, got A2+2B1=-2...then?
runic void
isolate the variable and plug it one of the equations
tardy epoch
Show all your work
Showing just the one equation doesn't tell us where you made the mistake
tardy epoch
ok, got A2+2B1=-2...then?
How'd you get this
shut tulip
2A1+A2=9
5A1+2A2-B1=22
2A1-2B1=11
Can someone help me, how to find the value of ...
eq1 - eq 3
2A1-2A1+A2-2B1=9-11
elfin burrow
,w 2a_1+a_2=9, 5a_1+2a_2-b_1=22, 2a_1-2b_1=11
warm shaleBOT
tardy epoch
eq1 - eq 3
2A1-2A1+A2-2B1=9-11
Use another subtraction to eliminate another variable
shut tulip
still cant find it
tardy epoch
Show all your work
.
obtuse pebbleBOT
@shut tulip Has your question been resolved?
shut tulip
.close
nocturne mica
obtuse pebbleBOT
nocturne mica
my equastion souloutin was x=10 but photomath says else
Can someone tell me why was i wrong if i did?
I did the same till step 5
copper spade
Send your work
slim basalt
you cant just do that
slim basalt
if you look carefully on the top, you should see that there is also + and - as operators
you can only do that if there was only multiplication
nocturne mica
the +2 is count as+?
slim basalt
$\frac{x+y}{x}$
warm shaleBOT
DieterBowlin
slim basalt
if you have a fraction like this
tranquil quiver
the +2 is count as+?
you have a fundamental flaw in your understanding
nocturne mica
i know i cant
tranquil quiver
keep in mind this:
slim basalt
**DieterBowlin**
in a fraction like this you cant just cross the x
tranquil quiver
$\frac{a+b}{c} = \frac{a}{c} + \frac{b}{c}$
warm shaleBOT
dog.
tranquil quiver
to cancel all the terms from the bottom and the top need to share the term
tranquil quiver
it doesnt seem like it from your working out
tranquil quiver
but if i kick the-8 to the other side
still no luck
nocturne mica
but if i kick the-8 to the other side
can i?
tranquil quiver
the (2x+3) and (2x-3) are part of seperate terms
you cant cancel like that
both terms need to share it
im not even sure why you are trying to cancel anything
the simplification step is very easy
nocturne mica
.close
obtuse pebbleBOT
tranquil quiver
$\frac{a}{b} = 0 \implies a = 0, b \neq 0$
warm shaleBOT
dog.
obtuse pebbleBOT
Available help channel!
jagged terrace
obtuse pebbleBOT
drifting loom
lemme
send
first tell me answer so i
can see
if my solution works
my answer is 4
main rose
The answer is no x= 4, just plug it in and you will see
jagged terrace
I don’t know how to solve big problems with now
proven zephyr
The answer is no x= 4, just plug it in and you will see
it is an answer tho
proven zephyr
but there is another one
drifting loom
i have solution
proven zephyr
try to help him solve it and not give answers directly
drifting loom
@proven zephyr ok
i just send
the -sqrt(x) to right side
and then both side square it
real prawn
$$ 2x + 1 = (1 + \sqrt{x})^2 \iff 2x+1 = 1+2\sqrt{x} + x \iff x=2\sqrt{x} \\ \iff \sqrt{x} = 2 $$
main rose
it is an answer tho
Ah I see, I messed up in my head
warm shaleBOT
agilepotato
proven zephyr
there is another answer btw 🙂
drifting loom
ohh
real prawn
x=0 perhaps
proven zephyr
x=0 perhaps
yes
real prawn
the classic answer
drifting loom
x/sqrt(x) = 2
jagged terrace
@warm shale why did you Square the x?
jagged terrace
How i do 37 for example 
elfin burrow
you can see that x = 0 satisfies x = 2sqrt(x)
whic you must consider before dividing by sqrt(x)
real prawn
,w simplify ((a^2 -6ab +9b^2)/(4a^2-36b^2)) / ((a-3b)/(15a^2+45ab))
warm shaleBOT
high lily
consider factorisation
real prawn
wow, WA is bad at simplifications..
elfin burrow
surprised wolfram didn't do that
real prawn
me too
hexed agate
Wolfram is not human.
real prawn
Wolfram is not human.
it's not human, it's 400 human employees. which is why it's surprising..
jagged terrace
I didn’t understand what happened
real prawn
How i do 37 for example <:tinktonk:481461685501296672>
for 37 you need to recognize various perfect squares, difference of squares, factorize and do as many simplifications as you can between numerator/denominator
real prawn
oh it did work, first answer 15a/4 is the correct one.
those are two different expressions that WA proposes:
- 15a/4
-
- 135a^2...
idk why WA proposes the 2nd expression when it was told to simplify the original one..
seems odd..
hexed agate
Sidenote: agilepotato do you use Scrum?
real prawn
Sidenote: agilepotato do you use Scrum?
always, i'll have my retrospective with myself today
real prawn
Impressive. We are being taught that in school.
yeah.. it's basically an organization structure in which the software developers are at the bottom of the foodchain
(like it's always been)
jagged terrace
How about matrix big problem for me!
real prawn
How about matrix big problem for me!
Sarrus rule or Cramer, learn them, use them
hexed agate
Wow! Simple algebra to matrix is a huge jump.
elfin burrow
where are the cofactor expansion enjoyers?
real prawn
where are the cofactor expansion enjoyers?
oh yeah, it's called cofactor expansion, i forgot.. https://en.wikipedia.org/wiki/Minor_(linear_algebra)#Cofactor_expansion_of_the_determinant
this is much better actually ^^
elfin burrow
long division
real prawn
yeah, do long division, or group terms and attempt to factor the numerator
elfin burrow
you can eliminate two of the answers by checking whether 4 is a root of the numerator
due to the uniqueness of division with remainder
obtuse pebbleBOT
@jagged terrace Has your question been resolved?
nimble harbor
x is supposed to be zero but i dont know how to do that
obtuse pebbleBOT
x is supposed to be zero but i dont know how to do that
raw sedge
How did you get x=1??
obtuse pebbleBOT
trail cloak
i may be stupid
No you aren't 
narrow vault
simple algebraic errors will never go away 
narrow vault
they effectively went from x(4x-5)= 0 to x=1 or x=5/4
obtuse pebbleBOT
Available help channel!
golden stone
obtuse pebbleBOT
golden stone
could someone explain the circled part of the proof to me?
obtuse pebbleBOT
@golden stone Has your question been resolved?
inland mulch
that's not part of the proof
rose dagger
oh there we go, okay so my question:
I'm a developer and in my game i need to find the percentage between a min and max - Let's say for example the maximum hit power is 5 and the minimum hit power is 2, if your item was 3 hit power what would the percentage be on a range of (0 to 1)?
by range i mean: 0.5 = 50% 1 = 100%
lost tree
assuming a linear variation
find the diff between the hit power of interest and the min hit power
divide by the like range of values that the hit powers may take
rose dagger
can you please write an example equation
sharp pecan
so $\frac{3-2}{5-2}$
warm shaleBOT
Jigglyproff
sharp pecan
alas, $\frac{hit power - min}{max-min}$
warm shaleBOT
Jigglyproff
rose dagger
yeah that's right
sharp pecan
alright, there you go
rose dagger
thanks let me try it rlq and then i'll close
it's a really simple question but i don't know why i've been stuck on it lol
sharp pecan
remember that if power=min its 0%, idk if that is intuitive for the user
rose dagger
yeah min and max'll be out of range from any tool possible
sharp pecan
alright
what exactly is 'power' supposed to represent for the user? the luck you had rolling that 'stat' or what?
aka, 100% being the perfect roll
rose dagger
power was sort of an example, in-game there's multiple tools so for example different axes have different hit powers
there's also swing time and all that
sharp pecan
ah, so its a hit
you axe can hit for 5-10 and you want to show how 'good' a roll was I assume
rose dagger
okay i think it worked?
actually no
swing distance for this is 50 which means the percentage being shown is wrong
wait let me check
sharp pecan
the formula is correct...
rose dagger
it might not be
this is strange what
probably a me issue
okay well thank you @sharp pecan
.close
patent jetty
Integral(sin2x/[2-(sin (2x) )^2])
obtuse pebbleBOT
Integral(sin2x/[2-(sin (2x) )^2])
haughty schooner
patent jetty
Lol I used the identities to simplify till here and now again reverse process
,rotate
warm shaleBOT
patent jetty
This was the actual qn
patent jetty
It's mister kutur putur with an integral of his own
Hehehehe lolzlolzz!
distant moth
Well if bounds from 0 to pi/4 certain things do cancel
c^4+s^4 also has that 1-2s^2c^2 identity
haughty schooner
I was able to solve it using a double sub
on hold ser
ruby path
Go forward :/
haughty schooner
u can rewrite the top as 2sinxcosx
u can rewrite the denominator as 1 + (1 - (sinx)^2)
make u = cosx, after rewriting the denominator 
I'll let you work it from there, but its just less tricky integral solving at that point
if u need more help/clarification
obtuse pebbleBOT
@patent jetty Has your question been resolved?
silver plover
could someone lmk if my answer for c is correct?
obtuse pebbleBOT
could someone lmk if my answer for c is correct?
slender tangle
You left a tangent where it shouldn't be. Namely, in the line with the 1/y, you only cancelled out one of the tangents in the numerator.
slender tangle
This fraction doesn't cancel in the way you cancelled--
Yeah.
The x has the same problem.
So what do you want to do here? Fix your steps?
silver plover
So what do you want to do here? Fix your steps?
lemme fix it
slender tangle
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
delicate lion
Hello, this part is going to decompose a linear transformation to its basis eigenvector.
line 1:
Because it is linear, the T could directly link to e1, e2, e3.
line 2:
But why T would become lambda1, 2, 3?
(Source: https://www.youtube.com/watch?v=RW-Seu-yenQ)
Thank you
obtuse pebbleBOT
Hello, this part is going to decompose a linear transformation to its basis eige...
main rose
@delicate lion Notice how he said that in line 2 we choose e to be eigenvectors, does that clarify that step? https://youtu.be/RW-Seu-yenQ?t=587
delicate lion
<@202387743504990208> Notice how he said that in line 2 we choose e to be eigenv...
I don't understand why he choose lambda to replace T?
main rose
Okay so what is the defining property of an eigenvector?
delicate lion
eigenvector is a unit pointer that points to the directions that if we multiply any eigenvector to the underlying vector, it wouldn't change the direction of the underlying vector, in the transformation process.
@main rose
main rose
That's a very unwieldy way of putting it, whats the simplest that you can explain it?
tardy epoch
eigenvector is a unit pointer that points to the directions that if we multiply ...
Eigenvectors don't have to be length 1
delicate lion
That's a very unwieldy way of putting it, whats the simplest that you can explai...
okay. So eigenvectors of T (we name it u) for vector v won't change direction of vector v under the effect from T.
main rose
Precisely, so T(v1) = lambda * v1, for a eigenvector v1
delicate lion
Eigenvectors don't have to be length 1
if it is a unit vector, then the scaling effect would pass to the eigen value?
tardy epoch
The eigenvalue is unchanged
delicate lion
Precisely, so T(v1) = lambda * v1, for a eigenvector v1
T(v1) ? I thought we eigen vector and the underlying vector was two different thing.
I thought R is the eigen vector lol
so what is R?
a vector?
tardy epoch
R is the matrix
main rose
The notation looks a bit peculiar, but R should be the linear transformation here, I am not quite sure why it is written as a vector
main rose
Or as riemann put it more clearly, the matrix that belongs to the linear transformation
main rose
Along what line are we reflecting?
Because any vector on the line of reflection is an eignevector
And any vector perpendicular on this line is an eigenvector with lambda = -1
delicate lion
that's bit confusing, if v_1 is the eigenvector, why we need to solve for P?
that's why I thought P is related to eigenvector before @main rose @tardy epoch
tardy epoch
P is the linear transformation in this problem
Not all problems ask for eigenvectors and eigenvalues
delicate lion
Ok, so P is a matrix, and P could be replaced by lambda1 1,2,3,..... (because lambdas are the root of the Pv = lv problem). These lambdas are all the candidates that when we plug in lambdas to P, to Pv = lv, it could gives us a parallel vector if we multiple them to the eigen vector
@tardy epoch @main rose
In this problem, because we knows the behavior of e1, e2, e3 under transformation T, from the definition of Pv = lv, we infers that Te1 = lambda1e1
isn't it?
main rose
Yes, that is indeed why he replaced T bij lambda in the original question
I struggle to understand some of the things you said in between
delicate lion
I don't understand why a scalar could replace a matrix
but that should be explained by Pv = lv
main rose
Yes, in this case because v is an eigenvector, P can be replaced by lambda
delicate lion
Yes, in this case because v is an eigenvector, P can be replaced by lambda
why we need to break v into e1, e2, e3 in the original problem?
for computation, okay
main rose
Remeber that e are just vectors
and v might not be a eigenvector
but the e's might very well be
delicate lion
so to make this equation works, we need to solve polynomial equation that consist of T, to find lambda 1,2,3 first
v should be any vector, not necessarily eigenvector
and e1,2,3 are eigenvectors
so we have 6 unknowns here? @main rose
@tardy epoch
I guess these 3 eigen vectors are just the basis vectors for vector v? so if we have v, e1, e2, e3 should be known. and also we have alpha 1,2,3 as well
obtuse pebbleBOT
@delicate lion Has your question been resolved?
tawdry meteor
how does this step happen? what i think happens here is that everything is divided by the cosine in the demoninator and the numerator
obtuse pebbleBOT
how does this step happen? what i think happens here is that everything is divid...
tawdry meteor
then you're left with a facotr that's cosine theta / cosine theta
but can this factor be divided away into 1?
afaik that's not allowed because in the case the cosine is 0 you get a divided by 0 error and then you're deleting a possible point that's undefined
but then on the other hand there's the tangents left, which themselves are the sine divided by the cosine, so it's like the cosine is still in there?
i just don't understand how to get to this step
spiral knot
how does this step happen? what i think happens here is that everything is divid...
divide the num and denom by cos(theta)
tawdry meteor
and why is that equal?
spiral knot
like you said
tawdry meteor
it just looks wrong
minor pilot
Want a visual aide?
tawdry meteor
it feels like just dividing, not simplifying
tawdry meteor
Want a visual aide?
yes please
spiral knot
$\frac{\frac{1}{cos(\theta)}}{\frac{1}{cos(\theta)}} = 1$
minor pilot
Kk
warm shaleBOT
Mehdi_Moulati
robust sleet
how does this step happen? what i think happens here is that everything is divid...
Giancoli
tawdry meteor
Giancoli
indeed
i also think i found a potential error in the solutions
i'll just ask here if it's ok
as i was so confused by it
spiral knot
minor pilot
tawdry meteor
it says F radial
minor pilot
Oops looks like you already got it
tawdry meteor
but doesn't include gravity
tawdry meteor
Oops looks like you already got it
i still appreciate the help
minor pilot
It's like g*cos(90˚)
spiral knot
$\vector{P}* \vector{i} = 0$
warm shaleBOT
Mehdi_Moulati
robust sleet
?
tawdry meteor
but the textbook says that expression is the radial component
so i'm confused
is it the radial or horizontal force components in there
because yeah it makes sense to scale the normal force with the sine of the angle
but you wouldn't do that with a radial component, since the angle would be 0 and the sine would be redundant as it would be 1
spiral knot
in Cartesian coordination :
$\begin{cases}
\vector{F_N} = F_n*\sin(\theta) \vector{i} + F_n*\cos(\theta) \vector{j} \\
\vector{P} = - mg \vector{j}
\end{cases}$
tawdry meteor
i think i got it omg
the whole thing is spinning along a vertical axis
so the centripetal force is horizontal
omg
warm shaleBOT
Mehdi_Moulati
tawdry meteor
in Cartesian coordination :
$\begin{cases}
\vector{F_N} = F_n\*\sin(\theta) \ve...
are you moroccan btw?
spiral knot
are you moroccan btw?
yes
spiral knot
coincidence haha
tawdry meteor
what are you studying btw?
spiral knot
what are you studying btw?
now ,self learning
spiral knot
im in belgium studying chemistry in uni
i was studying programing , this year i got my bachelor degree
spiral knot
are you planning on studying any further?
of course
i'm trying to improve my skills
in math and programming
since i will need them
spiral knot
well thanks for the help man
anytime bro
tawdry meteor
how do i close the thread?
tawdry meteor
.close
obtuse pebbleBOT
spiral knot
see ya soon
tawdry meteor
most probably lol
obtuse pebbleBOT
Available help channel!
dawn vigil
obtuse pebbleBOT
dawn vigil
I don't understand the second part of this proof.
How does 0 <= j2^p <= 2^m shows P_m is finer than P_n?
royal basin
do you have on hand a definition for "finer than"?
dawn vigil
.close
obtuse pebbleBOT
obtuse pebbleBOT
✅
dawn vigil
@royal basin Back, very sorry. Had something to do. Here is the definition:
Hello?
<@&286206848099549185>
royal basin
okay
dawn vigil
Hey, really sorry.
royal basin
so you wish to show every point of P_n is also a point of P_m, do you not?
dawn vigil
Yep.
royal basin
i.e. that every point of the form j/2^n can also be written as a fraction with denominator 2^m instead
and that is what is being done. they multiply the top and bottom by 2^(m-n) (or, as is written there, 2^p)
dawn vigil
And that's it?
That makes sense. Quick question, how would you know to set p = m - n?
Actually, you just have to ask yourself what could you multiply by 2^n to make it into 2^m and 2^p does just that like you said. Okay, thank you. 🙂
.close
brisk osprey
obtuse pebbleBOT
<:thonk:406575732563902485>
brisk osprey
robust sleet
Are you stuck?
obtuse pebbleBOT
Available help channel!
distant moth
obtuse pebbleBOT
distant moth
,w (5 choose 3)3!
warm shaleBOT
distant moth
from 5 vacant seats i choose 3 vacant seats, and then i have 3 distinct seats and 3 distinct objects so 3!, would this thought process be correct?
copper spade
from 5 vacant seats i choose 3 vacant seats, and then i have 3 distinct seats an...
You mean you're first selecting the seats
That is by using combination
5c3
Then arranging em
3 factorial?
Ryt?
obtuse pebbleBOT
@distant moth Has your question been resolved?
timid silo
from 5 vacant seats i choose 3 vacant seats, and then i have 3 distinct seats an...
Another way to get the same answer: person one has 5 options, person two has 4 options after that, person three has 3 options thus 5 * 4 * 3 = 60 total possible combinations
distant moth
Another way to get the same answer: person one has 5 options, person two has 4 o...
This was 5c1.4c1.3c1?
As in we are choosing the seat for person A, then B, then C?
timid silo
Im assuming two people cant occupy the same seat, thus knowing the location of one person would change the amount of possible locations of another
the actual ordering is arbitrary
timid silo
This was 5c1.4c1.3c1?
also im not familiar with this notation
distant moth
Im assuming two people cant occupy the same seat, thus knowing the location of o...
Yes two people cannot occupy the same seat
distant moth
This was 5c1.4c1.3c1?
Oh wait this actually doesnt make sense to me anymore
distant moth
also im not familiar with this notation
nCr means n choose r, =n!/(r!(n-r)!)
distant moth
The whole process would be 5c3.3c3.3!
This made the most sense to me 3 seats chosen out of 5 to be sat on, 3 people chosen out of the 3 people who would sit on them, then 3! Ways of shuffling the 3 people on the 3 seats
At least one digit repeated while making 4 digit number = Total ways of making 4 digit number - No digit repeated while making 4 digit number
Total ways of making 4 digit number = 7^4
And no digit repeated while making 4 digit number = 7c1.6c1.5c1.4c1?
My answer matches the solution but is my thought process correct
distant moth
Total ways of making 4 digit number = 7^4
The reason this is 7^4 is because there are 4 places and each place can take one out of 7 numbers so 7c1.7c1.7c1.7c1=7^4
distant moth
And no digit repeated while making 4 digit number = 7c1.6c1.5c1.4c1?
And while making 4 digit number, there are 4 places, the number of numbers i can use are 7 for a single place, so if i want no digit to repeat, for the first place i would do 7c1, for the 2nd place i do 6c1 and so on
obtuse pebbleBOT
@distant moth Has your question been resolved?
