@quasi kraken Has your question been resolved?
#help-0
lone heartBOT
lime tartan
lone heartBOT
lime tartan
y=-x²+6x-16
lone heartBOT
@lime tartan Has your question been resolved?
lone heartBOT
@lime tartan Has your question been resolved?
lime tartan
<@&286206848099549185>
lunar girder
What's your question?
lone heartBOT
@lime tartan Has your question been resolved?
lime tartan
What's your question?
Written up how do I make it into vertex form
And get the max/min function on graph
lunar girder
How do you make what into vertex form?
It would help if we could see the top of the table
alpine sable
hello
lone heartBOT
@lime tartan Has your question been resolved?
lone heartBOT
@lime tartan Has your question been resolved?
cobalt ridge
Why is (-2)^6 diff than -2^6
lone heartBOT
Why is (-2)^6 diff than -2^6
snow spire
alpine sable
-2^6 = -(2^6)
cobalt ridge
Pls explain I still no understand
low gust
Hello
cobalt ridge
Oh wait
alpine sable
if you see 3-4², then you read it as 3-(4²)
cobalt ridge
Ohhh
alpine sable
they are one unit
alpine sable
yeah
mystic parrot
so here are 5 questions i didn’t get in my review for a test i have tomorrow based on the material (complex numbers, operations w/ complex numbers, matrix operations: add, sub, mult by a scalar, and vectors operations)
for #7, I’ve been taught that matrixes must have the same dimensions, or else they’re undefined if they cannot be added/ subtracted; i chose undefined as my answer but didn’t get it right and would like an explanation to the correct answer and why
for #11, i didn’t understand how to find the value of b and at first went by finding the vector of the given line (<a, b>) and then using the pythagorean theorem (square root a^2 + b^2) but that didn’t work as my final answer was none of the choices given
for #17, i tried finding the magnitude of l, m, and n and substitute the answers with the equation given but my answer again, was none of the ones given
for #22, i have a feeling it’s solved by distributing but don’t know how to approach it or where to start
and for #24, don’t understand where i was incorrect on half of my work
(pictures provided below in order if dc doesn’t mess up)
gusty gorge
so here are 5 questions i didn’t get in my review for a test i have tomorrow bas...
in question 7, the matrices are being multiplied
for question 11, not sure what you mean by using the pythagorean theorem
it was asking for a vector, not the magnitude
for 17, it is not true in general that | l + n - m | = |l| + |n| - |m|
not sure what question 22 is asking, haven't seen an actual question there
as for question 24, I don't see any work you've shown
,w (-3 - 4i)^2
ocean sealBOT
mystic parrot
as for question 24, I don't see any work you've shown
for 24, i think the partial credit came from answer 2 (+) but here’s the work i did for it using the foil method (still confused as how the answer is -7 + 24i)
mystic parrot
it was asking for a vector, not the magnitude
for the vector, our teacher taught us to use rise/run to find the vector (so what i got was <-7, 6>) but the answer wasn’t there
mystic parrot
for 17, it is not true in general that \| l + n - m \| = \|l\| + \|n\| - \|m\|
in this case, how should i approach the equation then?? i originally got these answers, subbed them in but didn’t get any of the answers shown
mystic parrot
not sure what question 22 is asking, haven't seen an actual question there
22 is based on this section of my notes
and i need an elaboration on 7 (don’t understand how they are multiplied)
gusty gorge
for 24, i think the partial credit came from answer 2 (+) but here’s the work i ...
it is 9 + 12i + 12i - 16, not sure how you got whatever you wrote there
gusty gorge
for the vector, our teacher taught us to use rise/run to find the vector (so wha...
-2b is the vector drawn, and it is [-7, 6], but you were asked for b
gusty gorge
in this case, how should i approach the equation then?? i originally got these a...
l, m, and n are not equal to that
there is a difference between m and |m|
gusty gorge
22 is based on this section of my notes
so it's asking you to combine terms and stuff?
gusty gorge
and i need an elaboration on 7 (don’t understand how they are multiplied)
the notation AB means that A and B are multiplied
lone heartBOT
@mystic parrot Has your question been resolved?
mystic parrot
so it's asking you to combine terms and stuff?
basically but idk how to or where to start—and i have to make sure it’s something along x - y since my teacher included the minus sign already, indication it’s supposed to be a subtraction answer
figured out what i did wrong on 24—forgot the i in the second 12 and forgot to make it i^2 on the 16
and figured out 17
anyways i’ll close this now—ty for the help
.close
alpine sable
Is there any integer such that x + x = 1?
lone heartBOT
Is there any integer such that x + x = 1?
alpine sable
In this problem, the domain is the set of all integers. Which statements are true? If an existential statement is true, give an example. If a universal statement is false, give a counterexample.
(a) ∃x (x + x = 1) ```confused because I can't think of a single integer where this would be true
but the question is worded in a way that implies it is true and my task is to prove it
gusty gorge
Is there any integer such that x + x = 1?
nope
lone heartBOT
@alpine sable Has your question been resolved?
fickle nacelle
Yo this is an arrow diagram. I wanted to ask if it’s a function or not. The book says it’s a function but I believe otherwise
lone heartBOT
Yo this is an arrow diagram. I wanted to ask if it’s a function or not. The book...
@fickle nacelle Has your question been resolved?
lone heartBOT
@fickle nacelle Has your question been resolved?
pseudo moon
Let h(x) = f(x)g(x).
if f(x) = -4x^2 + 5x -2, g(2)= 3, g'(2) = -2
What is h'(2)?
rose sigil
you can use the product rule to write h'(2) in terms of f(2), f'(2), g(2), and g'(2)
pseudo moon
I apologize I am not that familiar with the product rule. Could you explain that for me? If not I'll try to watch a video. First time here, sorry!
rose sigil
oh, have you ever seen it before?
pseudo moon
I'm trying to learn up on calculus in order to get better at it. I've sorta seen it but never really understood the idea of it.
rose sigil
it gives you a recipe to compute the derivative of a product of functions
it might be better to watch a video or something
pseudo moon
Okay no worries I'll do that. Thank you. One second
rose sigil
sure thing
lunar girder
Hello
lone heartBOT
@lunar girder Has your question been resolved?
lone heartBOT
@lunar girder Has your question been resolved?
carmine pagoda
wheres the question start
oops at the top
ye looks good to me
easy problem since you the L[y] cancels
lunar girder
ye looks good to me
All the way to the end looks correct to you?
carmine pagoda
yes
vestal crag
<@&286206848099549185> can someone help me with something please
lone heartBOT
<@&286206848099549185> can someone help me with something please
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
@vestal crag Has your question been resolved?
rose ivy
how would I isolate n where n > the rest of the terms
lone heartBOT
how would I isolate n where n > the rest of the terms
rose ivy
yeah
does it make a difference if I know that n > 1? which means the denominator would always be negative
vale wigeon
is there more context to this
rose ivy
I'm trying to do a proof for limit of a sequence
and I need to isolate n, where n > M which would be the rest of the terms
alpine sable
does it make a difference if I know that n > 1? which means the denominator wou...
if the denominator is negative then the thing inside | is also negative
so u can translate this to -24/(5(3-5n^2))<H
rose ivy
do the absolute value signs need to be there
alpine sable
yes without the absolute u could get a different answer
rose ivy
wait so |-24/ 5(3-5n^2) | < H?
rose ivy
yeah
alpine sable
5n^2>5
so 3-5n^2 this bit is negative
5 times that bit is negative
24 by that bit is negative
alpine sable
so in the absolute u are just taking away the negative which is the same thing as multplying the -1
rose ivy
oh
alpine sable
like |-1|=-(-1)=1
rose ivy
so it would end up as just 24/5(3-5n^2)
rose ivy
so in the absolute u are just taking away the negative which is the same thing a...
aren't i taking away the negative because of the absolute value
alpine sable
do you know $|x|=-x$ if $x<=0$
ocean sealBOT
does calc even end(cat gang)
alpine sable
in this case $\frac{24}{5(3-5n^2)}<0$
ocean sealBOT
does calc even end(cat gang)
rose ivy
**does calc even end(cat gang)**
yeah
alpine sable
so $|\frac{24}{5(3-5n^2)}|=-\frac{24}{5(3-5n^2)}$
ocean sealBOT
does calc even end(cat gang)
alpine sable
thats what i am saying
rose ivy
**does calc even end(cat gang)**
yeah because when n>1 the denominator has to be negative
alpine sable
yeah because when n>1 the denominator has to be negative
yes
rose ivy
oh
alpine sable
now u are left with $\frac{24}{5(5n^2-3)}<H$[bring the - to the denominator and multply it out]
ocean sealBOT
does calc even end(cat gang)
rose ivy
what
rose ivy
ok
alpine sable
**does calc even end(cat gang)**
this implies $5(5n^2-3)>\frac{24}{H}$
ocean sealBOT
does calc even end(cat gang)
rose ivy
omg
alpine sable
**does calc even end(cat gang)**
this one
rose ivy
yeah
alpine sable
ok now if i distribute the 5 then $25n^2-15>\frac{24}{H}$
ocean sealBOT
does calc even end(cat gang)
alpine sable
i hope u can do it from here
rose ivy
yeah
got it
thanks @alpine sable
i need to work on my absolute value skills 💀
.close
dark patrol
lone heartBOT
alpine sable
what did u try
dark patrol
i think there is only one square root of 225 and 15
alpine sable
i think there is only one square root of 225 and 15
no
what do you by understand by square root lemme ask first
dark patrol
the opposite of square is square root
alpine sable
correct
it tells u what number/numbers when u square it gives the desired value
and what do you understand by $\sqrt{x}$
ocean sealBOT
does calc even end(cat gang)
alpine sable
for x>=0
dark patrol
ok
dark patrol
**does calc even end(cat gang)**
that x is being square rooted
dark patrol
ok
alpine sable
$\sqrt{225}=15$
ocean sealBOT
does calc even end(cat gang)
alpine sable
but isnt $(-15)^2=225$
ocean sealBOT
does calc even end(cat gang)
alpine sable
but the principal square root only gives the non negative solution
alpine sable
but the principal square root only gives the non negative solution
however the square root gives both
dark patrol
ye
slender gull
No square root of a non negative number only means the non negative value lol.
Sqrt(4) is 2 always.
Bruh
ocean sealBOT
alpine sable
coz $\sqrt{x}$ is not the square root
ocean sealBOT
does calc even end(cat gang)
alpine sable
its the principle square root
slender gull
sqrt(x^2) = |x|
dark patrol
.close
lone heartBOT
slender gull
Good call.
slender gull
Nope.
dark patrol
lol
slender gull
sqrt is square root, the square root is always meant for the positive value.
alpine sable
we cannot argue whats defined as what if we dont use another source except telling each other as this is defined as that
so here i have for u
a source
ornate condor
this is your source, it says sqrt(x) is positive, we use a negative in front to denote the negative version of it
alpine sable
this is your source, it says sqrt(x) is positive, we use a negative in front to ...
correct
and also its written
lone heartBOT
Available help channel!
idle apex
hi which formula should i use to determine the n for blue and red balls? (separately)
lone heartBOT
hi which formula should i use to determine the n for blue and red balls? (separa...
@idle apex Has your question been resolved?
idle apex
<@&286206848099549185>
lone heartBOT
@idle apex Has your question been resolved?
idle apex
<@&286206848099549185>
idle apex
.close
lone heartBOT
lone heartBOT
Available help channel!
heady imp
heady imp
Let 𝑡 be a parameter. For which values of 𝑡 does the system of equations have a) exactly one solution, b) no solution or c) infinitely many solutions?
thats what i have done so far, but i have no clue how to start with b) (no solution) or c) (infinitely many). Can anyone explain how I can start/complete this or know a good video that explain similar problem?
<@&286206848099549185>
gusty gorge
basically all values of t such that t / 1 = 10/(t+3) fall into either (b) or (c), because you can imagine that both of the x and y cancel out
so you just get some number = some other number
and if it's true, then you get infinitely many solutions (the values of x and y don't matter)
and if it's false, then no value of x and y is going to satisfy that
so if t/1 = 10/(t+3) = 8/2t, then you have infinitely many solutions
otherwise if just t/1 = 10/(t+3), you have no solution
if you want to see it in matrix form, reduce to rref and look for what makes the left matrix have a row with all zeroes
rough ice
So i want to ask a simple question
lone heartBOT
So i want to ask a simple question
vale wigeon
rough ice
So (sinx)^2+(cosx)^2 = 1 right?
vale wigeon
indeed
rough ice
Does that mean 1/(secx)^2+1/(cscx)^2 = 1?
vale wigeon
yes
sand depot
why is this true?
lone heartBOT
why is this true?
alpine sable
hint : cos(x)=-cos(π-x)
vale wigeon
who circled that?
one would think it's C...
"which of the following must be false"
there exist functions with a VA at x=1 for which C is true
1 + 1/(x-1) for example
dawn quail
Is (2.5/5) considered a rational number?
lone heartBOT
Is (2.5/5) considered a rational number?
ornate condor
yes
dawn quail
My professor told me it’s not rational and it’s not irrational
Because of the decimal
gray isle
your professor is wrong
gray isle
are you sure those were his exact words?
dawn quail
I have to double check with him but I’m certain he said the decimal makes it different
gray isle
if your number can be expressed in the form p/q where p and q are integers,
then it's rational
dawn quail
2.5 is an integer
gray isle
is he implying that 2.5 is an irrational number?
dawn quail
I think so
gray isle
2.5 is not an integer
dawn quail
What is 2.5?
sudden hinge
its a rational, too because it can be written as 5/2
dawn quail
2.5 is the same as 5/2?
Hmmm I will have to think about that
Interesting
Is that the case for all decimal numbers?
dawn quail
its a rational, too because it can be written as 5/2
I didn’t realize that before
So what do we call (2.5/5)?
Rational?
gray isle
if your number can be expressed in the form p/q where p and q are integers,
then it's rational
sudden hinge
a rational divided by a rational is always a rational
gray isle
also ^
dawn quail
What is it called when decimal is divided by integer?
gray isle
depends on the decimal
gray isle
if your number can be expressed in the form p/q where p and q are integers,
then it's rational
dawn quail
So it’s not rational?
gray isle
i said can be
dawn quail
But it’s also not irrational either?
sudden hinge
integers are a subset of the rationals, so you still could interpret "decimal divided by integer" as "rational divided by rational"
any integer is also a rational, but not all rationals are integers
gray isle
just because you don't originally have an integer divided by an integer doesn't make what you have irrational
dawn quail
OK but on it’s own (2.5/5) without any conversion what would you call it?
Not rational
But also not irrational?
gray isle
if your number can be expressed in the form
it doesn't matter what you're starting with
dawn quail
Oh so to say (2.5/5) is not rational is incorrect
gray isle
yes. that can be expressed as 1/2 which is rational (and would satisfy the definition of a rational number)
dawn quail
At the end of the day it can be converted in 5/10 and 1/2 so therefor it is rational. It just isn’t obvious from the very beginning with decimal but it can be expressed in this form so therefor it is rational
OK I think I understand now.. I think what the instructor was trying to demonstrate is that 2.5/5 is not it’s final form to be rational but he didn’t explain it very well
Thank you for the clarification
gray isle
and also
a rational divided by a rational is always a rational
(if you aren't dividing by 0)
dawn quail
Right the denom can never be 0
gray isle
also note that repeating decimals are also rational
dawn quail
Oh sorry
dawn quail
also note that repeating decimals are also rational
They are rational.. I misread this
Why would repeating decimals be rational?
Because there is an end to it?
The pattern
With pi there is no known end
And infinity too
gray isle
Why would repeating decimals be rational?
look up converting repeating decimals to fractions
lone heartBOT
@dawn quail Has your question been resolved?
serene heart
how to know the orientation of a parabola with the points of a parabola without graphing?
serene heart
like if we have 3 points in a parabola how do i know its y or x ?
from the points alone?
vale wigeon
you don't
trim wagon
Do you have a question to work
vale wigeon
unless two of them just happen to align horizontally or vertically, i guess...
trim wagon
Right as Ann said
serene heart
so you graph it ?
trim wagon
Look at (1,2) and (3,2)
They align vertically right?
Meaning for same value of y there are 2 different values of x
mellow tusk
ohnvm
trim wagon
h and c being?
serene heart
Ah we are finding for the equation here
so i just need the c and the h
(x-h)^2=4c(y-k)
gilded kiln
so for I've done (4/52) * 12 + (12/52) * 1
lone heartBOT
lone heartBOT
Available help channel!
marsh sonnet
lone heartBOT
mortal trellis
is that the vieta jumping question?
mortal trellis
well you could just google "imo 1988 q6 without vieta"
google immediately gives you a stackexchange post
in general it's a famous enough question that you can probably find lots of solutions on the net
raven rivet
in my textbook (about limits) they went through this step:
tan(pix + pi/2) = -1 / tan(pix)
what formula did they use?
raven rivet
thanks
vale wigeon
tan(t+pi/2) = sin(t + pi/2)/cos(t + pi/2) = cos(t)/(-sin(t))
raven rivet
how can we find that
lim(x->0-) t / tan(pi×t) = 1/pi
knowing that
lim(x->0) tan(x) / x = 1
?
agile condor
The dots of the plane have been colored in 2015 different colours. We say that triangle ABC is colored if its three vertices, A, B, and C are the same colour. Prove that there are an infinite number of triangles, all of the same color and the same area.
agile condor
@oak perch
carmine reef
Old competition problem I see
alpine sable
it seems easy tho
carmine reef
I think I got it
alpine sable
pretty sure this is not a easy problem
ornate condor
yea same, idt its easy
carmine reef
Choose 2016 parallel lines in the plane
alpine sable
never seen a problem from this guy thats easy tho takes me atleast a hour to solve
carmine reef
Then two of them must contain an infinite number of points of a common color C
alpine sable
im tripping my solution is simple enough but is very poorly constructed i thinki its wrong
ornate condor
idt i even understand the problem lol
alpine sable
id t?
carmine reef
Choose two points of color C from one of the lines, and construct an infinite number of triangles by choosing points of color C from the 3rd line
oak perch
Then two of them must contain an infinite number of points of a common color C
Brilliant
alpine sable
Then two of them must contain an infinite number of points of a common color C
why tho
if one line has the first half of colors
carmine reef
every line must contain an infinite number of points of at least one color
carmine reef
Well that's why I started with 2016 parallel lines
oak perch
Pigeon hole
carmine reef
So even if every line has infinitely many points from only 1 color you can still find 2 where it's the same
alpine sable
Well that's why I started with 2016 parallel lines
oh clever
carmine reef
Cool problem
carmine reef
The dots of the plane have been colored in 2015 different colours. We say that ...
This
alpine sable
mine is just using that the plane is infinite
ya thats what i thought too lol
prime badge
this is kinda easy
ornate condor
like assuming cart coordinates, there are color on each point?
alpine sable
can anyone check if mine is correct?
oak perch
Sure
oak perch
He is answering this question
carmine reef
probably
alpine sable
He is answering this question
oh yeah
prime badge
if i draw a reg 4031-gon, i will get at least one triangle of a certain area and color, if i keep doing this, it will have to repeat
alpine sable
every line must contain an infinite number of points of at least one color
wait
cuz idk the exact amount i need
carmine reef
if i draw a reg 4031-gon, i will get at least one triangle of a certain area and...
Ooh sick
alpine sable
how do u prove same area?
carmine reef
There's only so many distinct possible areas
ornate condor
bro same area T.T
alpine sable
hol on the question says same color and area
carmine reef
dots on plane is saying like for x,y in reals, x,y have a dot
Yeah
alpine sable
the aree will also have to repeat
carmine reef
Every point (x,y) gets a color
alpine sable
i dont think the monikanicity solution told about the area part
"it"
will have to repeat
carmine reef
all the triangles have the same base and height in mine
carmine reef
base is on the line with 2 points, height is the distance between the lines
alpine sable
oh yeah the base
wait i dont think i get why height is same either
u put 3 points
one on each line
i think
height is same
carmine reef
nah
alpine sable
base idk
carmine reef
I chose 2 constant points from one line
alpine sable
ohhhh
carmine reef
They form the base of the triangle
alpine sable
yeah
oh i dont think then its obvious that such a combination will exist always
where one line has 2 same colors
carmine reef
That's what the first part of the argument was for
Every line must have an infinite number of points of at least 1 color
So I choose 2016 parallel lines
alpine sable
oh nvm i am just dumb lol ur right
carmine reef
That way, 2 are guaranteed to have infinite amounts of the same color
ornate condor
based
carmine reef
I chose 2 constant points from one line
and then made an infinite number of triangles by choices of the third point on the other line
alpine sable
and then made an infinite number of triangles by choices of the third point on t...
yes
with same color
but i am asking about the same area part
carmine reef
Yeah
ornate condor
i didnt even understand that
carmine reef
Choose an infinite number of disjoint regular 4031-gons
carmine reef
Smallest number that guarantees 3 points of at least 1 color
oak perch
Finitely many colors. Finitely many areas, have to repeat infinitely many times, for one color one area
carmine reef
If there were 4030 vertices, you could have 2 points of every color
carmine reef
Regular 4031-gon yeah
oak perch
Regular 4031-gon
oak perch
Or doesn’t have ti be regular, just infinitely many copies of 4031-gons of the same shape
ornate condor
ye how do u say its existence
carmine reef
any 4031 point structure without 3 collinear points really
oak perch
Yeah, better
carmine reef
ye how do u say its existence
mainly just imagining putting a bunch side by side
carmine reef
infinitely many
carmine reef
take circles with radius 1 centered at (3n,0) for every integer n
and inscribe the polygons in the circles
ornate condor
no i mean
if u find 4031 gons of same shape
n inf of it
it doesnt work as the color might be of the same shape
as u arent finding regular 4031 gons
carmine reef
well there's only a finite number of ways to choose 3 points for a triangle
ornate condor
and showing if u can fond regular 4031 gons on a grid is also hard
carmine reef
so eventually it'll have to repeat if you have infinitely many
ornate condor
i mean
that isnt rly an explaination
o well
the same area 1 is gd enough for me
ty
carmine reef
np
lone heartBOT
@agile condor Has your question been resolved?
agile condor
thnx guys
humble scroll
Hi
ornate condor
context
carmine reef
Why 21?
weary wyvern
I think because 9+10=21
carmine reef
smh dumb teacher must've thought it was 19 or something
carmine reef
Are the answers wrong or am I wrong
but really the correct answer is on there
flat saddle
Wouldn’t the answer be 21 for that?
you can write out all the different combinations and count how many there are
abstract badge
you can write out all the different combinations and count how many there are
nvm
humble scroll
Ok so 11
humble scroll
you can write out all the different combinations and count how many there are
I can order it 5 different ways
prime badge
then why 11 if it's 5
prime sluice
Are you solving this with combinations or a tree
prime badge
how would i solve this if the order is relevant but you can also say nothing about an ingredient🤔
prime sluice
Order doesn't matter so you use combinations
You have 4 possible toppings
You can use all 4, 4C4
You can use 3 out of the 4, 4C3
You can use 2 out of the 4, 4C2
You can use 1 out of the 4, 4C1
And finally you can just add no toppings if you have a boring personality, 4C0
(correct me if I am wrong I suck at the perm. and comb.)
prime sluice
No clue what jacks and clubs are
humble scroll
Me neither
ornate condor
lol
abstract badge
Me neither
a deck has 52 cards
there are 4 jacks and 4 clubs in it
this is the explanation of why we find the possible toppings using
2x2x2x2
following each path gives you 1 possible combination of topings
in total there are 16 paths you can take
and the tree doesnt count with different orders
k: ketchup
y: mayo
r: redish
m: mustard
with and without indicated by the red dash
prime sluice
a deck has 52 cards
Being in a test and not explaining this would be messed up
abstract badge
very true i had to look it up online
humble scroll
very true i had to look it up online
So 1/52
abstract badge
what are all the desired draws?
prime badge
there are 13 clubs, but one of them is a jack
lone heartBOT
Available help channel!
shadow nacelle
hello
shadow nacelle
i have a question about a certain problem
what formula would you use for this problem?
i'm not quite sure how to approach this
carmine reef
you know arc length, radius
er
you know arc length, and the angle of the arc
you want to find radius
do you know the formula that relates those 3 values
shadow nacelle
isn't it like s=rO
carmine reef
O is angle?
shadow nacelle
ye the theta symbol
carmine reef
Yeah
prime sluice
do you know the formula that relates those 3 values
Btw does this work or am I dumb
$\frac{207}{360}2πr=50$
ocean sealBOT
ahmed349
carmine reef
it would work yeah
prime sluice
Yes
dawn quail
lone heartBOT
dawn quail
Did I do this correctly or is it (√6)⁶
mellow tusk
Did I do this correctly or is it (√6)⁶
this
dawn quail
OK
alpine sable
So when do you add or subtract exponents?
$x^{n + m} = x^n * x^m$
$x^{nm}= (x^n)^m$
dawn quail
dawn quail
Sorry?
alpine sable
Sorry?
i meant about this message
(the one the bot sent)
does it make sense now @dawn quail
dawn quail
I think so, but what about negative exponents?
ocean sealBOT
trololol !
alpine sable
this is when you multiply and when you add exponents
dawn quail
alpine sable
yes
dawn quail
This is correct too?
alpine sable
yes
alpine sable
yes
alpine sable
yes
dawn quail
Thank you
Just to drive it home
You go in order inside to outside? Or doesn’t matter
alpine sable
it doesn't matter, because multiplication is commutative
dawn quail
Division too
alpine sable
division isnt commutative
dawn quail
Oh
Right, there is no division here
I mistook the fraction as division
½
Addition and multiplication are the only commutatives in math?
alpine sable
yes
dawn quail
Good to know.. in theory can every equation be forced to use commutatives?
What I mean is fraction is division, but 2 ÷ 3 can also be written as ⅔ almost like it’s a single term.
2 - 3 is subtraction but it can also be written as 2 + (-3)
alpine sable
i mean, you can write $a - b$ as $a + (-b)$, making it commutative
same for multiplication : $a \div \frac{x}{y} = a \times \frac{y}{x}$
ocean sealBOT
trololol !
alpine sable
for exponentiation it is a bit harder, though
in fact, i dont think it is possible to write it in a commutative way
dawn quail
**trololol !**
And in theory you can move those values anywhere if they belong on LHS or RHS of the equation? It won’t affect the outcome if they are written as commutative?
alpine sable
And in theory you can move those values anywhere if they belong on LHS or RHS of...
what does lhs and rhs mean
left-hand-side and right-hand-side ?
if yes, then yes, it won't affect the outcome - this is the very definition of being commutative - the order of the operations doesnt matter
but remember to not mix addition with multiplication - you can only move the terms within the same "addition chain", and the same "multiplication chain"
u cant say that $a + b \times x = a \times x + b$
ocean sealBOT
trololol !
dawn quail
This is because BEDMAS only works for multiplication/division and addition/subtraction in order from left to right, correct?
alpine sable
what is BEDMAS ?
dawn quail
Brackets Exponents Division Multiplication Addition Subtraction
Order of operations
For DM/MD it should be treated left to right whatever order they come in
Same for AS/SA left to right whatever order they come in
But with the commutative property that makes me think I can rearrange DM or AS if I really want to
dawn quail
**trololol !**
But not when they are combined.. I think that’s what you are saying here
So commutative only works if LHS or RHS is DM/MD exclusively or AS/SA exclusively. It can not be both DM/MD+AS/SA on LHS or RHS for commutative to work
I hope someone can confirm this for me? I don’t know if I explained that correctly?
alpine sable
But not when they are combined.. I think that’s what you are saying here
exactly
dawn quail
And this doesn’t account for brackets or exponents either. I think those could change things too
alpine sable
And this doesn’t account for brackets or exponents either. I think those could c...
brackets can be changed, added/removed however you like, too
this is called associativity
and multiplication and addition are also associative
exponentiation is neither
dawn quail
Are exponents considered included as part of MD/DA?
wind yoke
and multiplication and addition are also associative
then what is distributive?
alpine sable
Are exponents considered included as part of MD/DA?
no
alpine sable
then what is distributive?
$x(a+b) = xa + xb$
ocean sealBOT
trololol !
alpine sable
this is distributive
dawn quail
OK, so exponents are kept on their own.. √ and ² are like saying a new family such as DM and SA
alpine sable
OK, so exponents are kept on their own.. √ and ² are like saying a new family su...
yes, to a certain degree
wind yoke
$x(a+b) = xa + xb$
mhh we profesional englesh speakerre call ita foil
alpine sable
yes, to a certain degree
root is not the only opposite of exponentiation - there are also logarithms
but this is another topic
dawn quail
mhh we profesional englesh speakerre call ita foil
Foil would be two binomials no? This is distributive
alpine sable
so for now, you can say that root and exponentiation are of the same family
wind yoke
Foil would be two binomials no? This is distributive
FOIL!
dawn quail
**trololol !**
This is FOIL or Distributive?
wind yoke
This is FOIL or Distributive?
Idk all i heard is engleshmen never use distributive
they say
FOIIIIIIIIIIIIIIIIIIIIIIIIIL
dawn quail
Engleshmen?
wind yoke
yes
lets not talk about engleshh men please
I need real mathematical help
I am dealing with one trignometric qn
dawn quail
dawn quail
trignometry
*Trollonometry
wind yoke
*Trollonometry
You think im trolling?
dawn quail
Yes
wind yoke
Is this related to my question or do you want to start a new thread?
i just want answer
dawn quail
To what?
alpine sable
trignometry
dawn quail
trignometry
Start a new thread
It’s easy and free to do so, you are just confusing people by stating something is FOIL when it’s distributive
Which has nothing to do with trigonometry
wind yoke
Which has nothing to do with trigonometry
when it comes to cross multiplying it does
dawn quail
when it comes to cross multiplying it does
Can someone confirm?
Is FOIL algebra, trigonometry, or both?
First Outside Inside Last
I am curious now
AFAIK it’s a convention for remembering to do all the operations when multiplying binomials
wind yoke
Can someone confirm?
help pramad please in pramad help channel
alpine sable
anyways, if your question has been answered, remember to close the thread, @dawn quail
lone heartBOT
@dawn quail Has your question been resolved?
dawn quail
anyways, if your question has been answered, remember to close the thread, <@313...
Not yet I’m looking for clarification on @wind yoke’s point
Is FOIL algebra, trigonometry, or both?
lone heartBOT
@dawn quail Has your question been resolved?
mortal trellis
multiplying out brackets is algebra
and FOIL is a common trick to remember how to do that
was that your question?
lone heartBOT
@dawn quail Has your question been resolved?
dawn quail
No the question is whether FOIL is a common trick for algebra only
Or if it can also be used for trigonometric questions too
But perhaps this is where algebra and trig blend together so FOIL perhaps can be used for both? It’s not so black and white one or the other?
If someone can give me an example where FOIL is used for a trigonometric question that would be greatly appreciated
This will also finally answer @wind yoke ‘s question here too…
mortal trellis
well FOIL is used whenever we multiply out brackets
if you wanna multiply out (sin(x)+cos(x))(tan(x)+sec(x)) or something and call that trig, sure FOIL is used for that
multiplying out brackets is something that happens often in a lot of contexts in math
dawn quail
.close
lone heartBOT
serene flame
i know this is a lot to digest here so i'll dissect it
i'm evaluating the integral of sqrt cos x
which is a non elementary
so i did it with taylor series
i just got the taylor series for sqrt x and plugged in the cosine
since the cosine has a power i just used the beta function right away to calculate the integral, shown in upper right corner
i then developed the calculation a little and then changed the gamma's to their product definition
and got that product below
and just plugged it into the taylor series
that's it
the small sum in the center, ignore it, i was tryna simplify the thing more but didnt know how to so called it
so i plug both the integral and the sum in desmos
i get a result around 2.39 for the integral, and one of the order of 1e-169, for the sum
pretty darn close to 0
so what went wrong
if there's any clarification to do, ping me
thanks in advance
lone heartBOT
@serene flame Has your question been resolved?
serene flame
<@&286206848099549185> i'm sorry for pinging, is anyone down to help here
lone heartBOT
@serene flame Has your question been resolved?
lone heartBOT
@serene flame Has your question been resolved?
chrome plank
@serene flame 👋 You may want to check the early university and advanced sections of the server since this is quite advanced, there you don't have to also confirm to the bot that you are actually there and it may be nicer if you want to do other things in the meanwhile
humble scroll
Hi
humble scroll
Can someone help me with this
lone heartBOT
@humble scroll Has your question been resolved?
humble scroll
humble scroll
<@&286206848099549185>
stray radish
So I think i can help you with number 22
Have you seen something like this before?
stray radish
Basically what this is
is it shows all the possible outcomes of rolling 2 dice
Can you see how the dice outcomes correlate to the numbers on the inside?
basically you just add together the numbers in the right row and column
so if you rolled a 4 on Dice B and a 4 on Dice A, you would see what box is in Column 4 Row 4
and there is your answer
Basically the reason I am showing you this is because if you count all of the middle boxes, there are 36
which means there are 36 possible solutions to rolling 2 dice
Or just rolling a dice twice
How this can be used is
since it is asking you the probability of rolling a 10, you would count how many boxes have a "10" in them
so how many is that?
A hint to help you is that the same numbers are diagonal to each other
humble scroll
.close
rain scaffold
limit as x approaches 0 of (1-cos^2(x))/x^2
lone heartBOT
limit as x approaches 0 of (1-cos^2(x))/x^2
rain scaffold
plz help i am begging and will fail my life if i dont get this
tough jasper
L hop it
If you dont know what that is then lim as x approaches a of g(x)/h(x)=lim as x approaches a of g'(x)/h'(x)
lone heartBOT
@rain scaffold Has your question been resolved?
old sinew
@rain scaffold
find the derivative of numerator and denominator separately and post here
rain scaffold
what is a derivative
we were never taught that
@old sinew i have a question
how can i simplify 1 - cos^2 x?
rain scaffold
can it be (1+cos x)(1- cos x)
old sinew
$\lim_{x \to 0} \frac{1-\cos^2 x}{x^2}$
ocean sealBOT
CapitalW
old sinew
try dividing both numerator and denominator with x^2
so essentially we will not change anything, as we are multiplying by 1
old sinew
infy will pop up
rain scaffold
**CapitalW**
i dont understand how i can simplify the top part
would difference of squares work
old sinew
essentially we need to get rid off x^2 in the denominator
else applying limit will go to infy
rain scaffold
okay
old sinew
do you know lim x to 0 sin x/x = 1?
rain scaffold
yes
old sinew
great
rain scaffold
i also know lim x to 0 (1-cos x)/x = 0
whats tripping me up in the problem is the square on the cos
i dont understand how to rid of that
old sinew
let's try this way
$\lim_{x \to 0} \frac{1-\cos^2 x}{x^2}= \lim_{x \to 0} \frac{\sin^2 x}{x^2}$
ocean sealBOT
CapitalW
old sinew
$\lim{x \to 0} \left(\frac{\sin x}{x}\right)^2$
rain scaffold
wait
you can do that????
i understand that 1-cos squared equuals sin squared
but how are you removing the squared
ocean sealBOT
CapitalW
rain scaffold
OHHHHHH
old sinew
$\sin^2 x = (\sin x )^2 = \sin x * \sin x$
rain scaffold
OK THAT MAKES SO MUCH MORE SENSE NOW
ocean sealBOT
CapitalW
old sinew
keep this in mind
old sinew
that does make sense, but there shouldn't be an equals
rain scaffold
in the end?
old sinew
not after lim x to 0
rain scaffold
okay i took it off
old sinew
@rain scaffold btw, your answer to 16 is wrong
you are asked to find the limit not f(0)
last ether
16's limit exists
rain scaffold
i wrote IND next to it
that's how our teacher taught us
when u plug in 0 (first step)
u have to see whether it is indeterminate
look ill send my full work
0/0 is not my answer
2 is
old sinew
okay, then you shouldn't put =0 in first
old sinew
just hear me
rain scaffold
he wants us to write it the way he wants it
last ether
Have you learned L'Hopitals?
rain scaffold
no
last ether
If not, you can use difference of squares then
rain scaffold
ya i used difference of squares
last ether
Which is what you did
old sinew
you found lim x to 0 is 2 not 0/0
old sinew
so you should only write f(0)=0/0
last ether
Nah their work is fine
old sinew
not lim x to 0 f(x)=0
last ether
ALTHOUGH
rain scaffold
dw thats just how the teacher wants it
last ether
You DO NOT put an = 0/0
old sinew
Nah their work is fine
not precise to what the definition of limits are
last ether
It would be $\rightarrow \frac{0}{0} (\text{IND})$
ocean sealBOT
Umbraleviathan
old sinew
that will work
rain scaffold
he wants us to write f(0) is 0/0 (IND) but lets us skip the f(0) part
old sinew
he wants us to write f(0) is 0/0 (IND) but lets us skip the f(0) part
f(0)=0/0 but lim x to 0 is not 0/0
which is what whole question is about
that's the key distinction you need to understand
gusty gorge
any ideas on how to approach it?
lone heartBOT
@rain scaffold Has your question been resolved?
rain scaffold
i got it