y = (x+3)∣x-3∣ I need to find monotonicity property
#help-0
slender gull
Basically you're asking how you'd graph this?
ancient pine
yeah
ancient pine
yeah
ancient pine
we learned like x-3 >= 0 -x+3 <0
slender gull
Sure. It doesn't matter where you include zero.
So y = x^2 - 9, x >= 3
y = 9 - x^2, x < 3
Yes?
lone heartBOT
@ancient pine Has your question been resolved?
rigid wedge
I’m not quite sure where to start on this problem. (I am not in the class so you will have to be patient with me it was a problem that a friend challenged me to solve
lone heartBOT
I’m not quite sure where to start on this problem. (I am not in the class so you...
@rigid wedge Has your question been resolved?
lone heartBOT
what do i do
vapid steppe
BRUH what
inner path
maybe with that guess a possible value for z ?
like take x = 2 and y = 1
you have 4 and the rest is true also
vapid steppe
you have 4 and the rest is true also
what does it mean by solve tho
like does what i wrote it in the first step do it
inner path
if x = 2 and y = 1 you can put in the first equation to have z = 2 and verify the second to see if the value of z can be 2
it says "generate a possible solution" don't know what it means
wind cloak
what does it mean by solve tho
I think you need to solve for the set (x, y)
vapid steppe
so (x,y)=(2,1)
wind cloak
That's not what I meant
wind cloak
$$z = 2x + 3y - 5$$
$$z = \frac{x}{4} + \frac{y}{2} + 2$$
ocean sealBOT
NEONPerseus
wind cloak
vapid steppe
so like what do i do with that
wind cloak
i got (x,y,z)=(2,1,2) but idk what it means by solve for z
How did you get a definite value with only three equations
inner path
if you have 2 equation with 3 unknown variable you can't solve that
vapid steppe
How did you get a definite value with only three equations
i guessed x=2,y=1
wind cloak
That's one possible solution
vapid steppe
yea i think that’s what it means by generate a possible solution
inner path
I think that too
pseudo ice
,rccw
ocean sealBOT
wind cloak
Just use the same coefficients but a different constant
Yeah what you did
Also works
Technically the same thing
pseudo ice
do i just write 2x+4y+4z=-3
That does work, but there are many other choices
vapid steppe
yea ik
pseudo ice
Just use the same coefficients but a different constant
[turns into this]
wind cloak
Just use the same coefficients but a different constant
This means the lines are parallel
Yup
vapid steppe
How do I use that
vapid steppe
i’m setting it up hold on
wind cloak
Do that
vapid steppe
look
i did it in the order (x,y,z,w)
Wait should I just put it in my calculater
i got x=1,y=-2,z=3,w=-4
let’s go
dim matrix
lone heartBOT
What step 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
Can I write (-infinity, -2/3] U [5/2, infinity) as the solution set?
fallen verge
dim matrix
what happened to your other question
Is is the answer
velvet cliff
ic
alpine sable
Help
alpine sable
lone heartBOT
What step 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
wary stream
Since both plots are identical, find the area of one plot, multiply by 2 to get the total
alpine sable
How?
wary stream
Do you know how to find the area of a rectangle?
alpine sable
Not in this situation
wary stream
The formula for area of a rectangle doesn't change, it's still a rectangle
So do you know the formula?
wary stream
What did you do
alpine sable
What Width and height do I multiply?
wary stream
What did you get as the length and width?
alpine sable
Hold up
wary stream
Can you find how long the yellow and pink line is?
alpine sable
I think the yellow is is 80 and pink is 120
wary stream
How many units is each grid mark?
alpine sable
What’s a grind mark?
wary stream
Each dash on the grid
alpine sable
I think 20
wary stream
Yes
wary stream
Can you find how long the yellow and pink line is?
So the yellow line is 2 dashes, correct?
And if it's 20 per dash, how many units is that?
alpine sable
Pink is 100
alpine sable
80
alpine sable
Lemme see
wary stream
So do we length times width?
Recall this
wary stream
What is the area for one of the rectangles?
You found the length and width
Multiply the two values, you get the area for one rectangle
And as mentioned, the two rectangles are identical so you multiply that answer by 2 to get the total area
wary stream
You found the length and width
Multiply the two values, you get the area for one rectangle
alpine sable
Ok
wary stream
What is that area?
alpine sable
> Multiply the two values, you get the area for one rectangle
Is it 1,600?
I mean 1,200?
I mean 1,600
wary stream
The length is 80 and the width is 40, correct?
wary stream
That's the area for one of the rectangles
You now need to multiply by 2, to get the total area of both
slim bramble
what is x) worth
lone heartBOT
what is x) worth
slim bramble
what is( x) worth
slim bramble
Any textual information?
what is the route length (x)
vague mirage
That's it?
You can use Thales theorem
Or similarity Theorem
If I make a symmetrical assumption that the base and the line intercepting the triangle are parallel
slim bramble
If I make a symmetrical assumption that the base and the line intercepting the t...
ok thanks
vague mirage
🫂
errant grail
lone heartBOT
@slim bramble Has your question been resolved?
flint belfry
do u know if x,y and z are integers
grim garden
Where can I get some help on set theory proof writing?
lone heartBOT
Where can I get some help on set theory proof writing?
keen pasture
Just ask 🙂
grim garden
I am not doing well in this subject for some reason, I feel like he is hyper critical but who knows
lone heartBOT
@grim garden Has your question been resolved?
lone heartBOT
@grim garden Has your question been resolved?
lone heartBOT
@grim garden Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
icy marten
hi
alpine sable
what
first off, not a good idea to leak your school
second of all
what are you confused about
surreal meadow
do you know what a sum is?
icy marten
yes of course
surreal meadow
then you're not confused about everything
you could be a bit more specific
so we can help you
icy marten
like i dont understand what the instructions are
surreal meadow
they want you to write two rational algebraic expressions whose sum is (x-2)/(x+3)
icy marten
ohhhhh ok that makes more sense
surreal meadow
note that i wrote word for word what is written on your sheet
icy marten
oh shet im bloody dumb
i cant even read the instructions right💀💀💀
So I just found two expressions when divided, added , etc led up to (x-2)/(x+3)
surreal meadow
yes
icy marten
im i right?
surreal meadow
make sure they are rational
obsidian tide
Helppppo
kindred vale
yessooo
obsidian tide
I need help with my algebra 2 project
last ether
Read the first bullet point.
last ether
<@&268886789983436800>
last ether
_ _ (if deleted check logs)
obsidian tide
@last ether you here to help me?
obsidian tide
Both
solemn oyster
lone heartBOT
solemn oyster
Quick Question
Why is are both Crows and Doves, and their relationships with their grams of twigs represented by division?
surreal meadow
consider the case where there's 10 crows nests.
what would be the value of C?
fringe mist
Hey I have a question with ruffini's rule, I dont know at what point im supposed to stop, like here, where I can continue but if I do, the answer is wrong.
surreal meadow
Hey I have a question with ruffini's rule, I dont know at what point im supposed...
!help
lone heartBOT
Hey I have a question with ruffini's rule, I dont know at what point im supposed...
Please read #❓how-to-get-help
solemn oyster
consider the case where there's 10 crows nests.
what would be the value of C?
I don't understand what it's representing
surreal meadow
then read the question over again
solemn oyster
10/8?
solemn oyster
How is their use of twigs correlated to division?
is it the distribution among said amount of birds?
solemn oyster
Yes, numerous times, but it's not clicking. What to you want me to understand?
surreal meadow
what C and D represent
surreal meadow
solemn oyster
Yes, but why is this theoretical amount divided on a simple level?
surreal meadow
do you understand what C and D represent?
solemn oyster
MY BRAINS NOT BRAINING
surreal meadow
C is the total amount of twigs in grams for all the crows nest
jovial chasm
you’re trying to figure out how much they used so if crows use 8g and doves use 6g, you’re going to divide them to figure out what c and d is that will add up to 1500
surreal meadow
so if there's 10 corws nests, you'd have C = 10 * 8
jovial chasm
if that makes sense
surreal meadow
so then C/8 = total number of crows nests
similarly, D/6 represents the total number of dove nests
as D = total number of nests * 6
solemn oyster
Why times 8?
surreal meadow
mb 
solemn oyster
you chillin
surreal meadow
but that shows you understand what's happening
then D / 8 = total number of dove nests
solemn oyster
Could you hop on call for a brief moment so I can go through my though process and see where I am flawed?
surreal meadow
so total number of nests = total number of dove nests + total number of crow nests
so total number of nests = C/8 + D/6
no sorry
solemn oyster
that's okay.
WHY CAN'T FATHOM THE DIVISIVE RELATIONSHIP
My girlfriend explained it to be as such: The divisive relationship is due to "C" or "D" representing the respective total amount in grams for each bird, when you divide each total, you can deduce the amount of that respective bird that contributed to the 1,500 mass of crow and dove nests. Sorry for being a pain, that's very similar to what you said it just wasn't clicking, because although I read total, I did not understand the implications of the division of that total. Thank you to anyone who helped! Thanks @surreal meadow and @jovial chasm I appreciate your time and compassion. Case closed.
solemn oyster
thank you though
lone heartBOT
@solemn oyster Has your question been resolved?
ivory gull
Hey, I got this answer and I am sure I did it right,
lone heartBOT
Hey, I got this answer and I am sure I did it right,
ivory gull
But it does not look like the textbook answer and I am not sure what to do
This is the textbook answer
grand fable
what does the : mean here
lone heartBOT
what does the : mean here
grand fable
and the epsilon?
grand fable
thats confusing
last ether
And then $\in$ means, well, an "element of"
ocean sealBOT
Umbraleviathan
grand fable
my lecturer asked if anyone knew what it meant and then didnt explain
last ether
I can translate it
grand fable
wait so for range
vapid steppe
**Umbraleviathan**
belongs in
grand fable
f(x) such as x is an element of the domain of f?
last ether
dom(f) is the set of x values such that f(x) is defined,
range(f) is the set of corresponding outputs
vapid steppe
f(x) such as x is an element of the domain of f?
such that is better in this context
last ether
Well it is math
It's logic
That's what it's called
If you google "Logic symbols" you'll find a whole bunch
grand fable
im not working anything out tho
last ether
im not working anything out tho
Logic doesn't have to deal with working anything out. Logic is kinda like "math language"
Delete your post
This is not your channel.
cosmic token
my fault
chilly dove
lone heartBOT
chilly dove
How do I find f in this case? I got 36 hours but that seems to be wrong
jagged cobalt
1/3% of f=12 is not the same as 1/3 f=12
chilly dove
what do i do in this case then?
jagged cobalt
say it was 10% of f=12 what would you do
chilly dove
10/100 * f = 12
chilly dove
1/3% of f=12 is not the same as 1/3 f=12
would that be 33/100 * f = 12?
jagged cobalt
not quite, that would be 33% of f=12
chilly dove
im not sure what you mean then
chilly dove
1/3/100??
jagged cobalt
seems good
chilly dove
i better get this right cuz my parents are gonna get mad if i do it wrong 🥲
yea nvm its correct
ty guys
jagged cobalt
np
chilly dove
wait
i have another problem
i just need to know if its correct
@jagged cobalt do you mind helping?
jagged cobalt
sure
jagged cobalt
why did you do it over 34?
chilly dove
someone just told me
the answer i put before that was 29.2%
and my calculation was 14/48*100%
jagged cobalt
your previous answer was right
jagged cobalt
i got 41.2% because 14/34*100%
this is the percentage increase from 34 to 48
jagged cobalt
the answer i put before that was 29.2%
this is the percentage decrease from 48 to 34
chilly dove
your previous answer was right
apparently its not tho, as my parents stated
limpid turret
parents getting mad at mistakes is wild
chilly dove
the thing is
my class teacher sent them the answers
and then my parents checked it
limpid turret
Still pretty crazy that they get mad at you rather than offer help
chilly dove
Still pretty crazy that they get mad at you rather than offer help
yea 🥹
jagged cobalt
,w calc [1-(14/48)]*48
ocean sealBOT
limpid turret
@chilly dove Talk to your school counselor
You may be being abused
I don't know your situation, but it's worth knowing
limpid turret
Abuse is still abuse
ah ok
Just put them in a elder home when they get older then
And when they ask for help, get mad and don't offer to help them
chilly dove
alright
that sounds great 😂
but what do i do
do i just tell my parents they are wrong?
limpid turret
hold on let me look at the actual problem
chilly dove
i think this has to do with the total score 50
wait i gtg rn sorry
i will look back at this channel tmr
jagged cobalt
take care
its possible it might be 48/50 - 34/50, thats the only alternative thing i think it may be asking for
limpid turret
its possible it might be 48/50 - 34/50, thats the only alternative thing i think...
This is what I got
So a 28% decrease
jagged cobalt
yeah
limpid turret
The problem is vaguely worded so it's hard to say
Also, @chilly dove, there are more kinds of abuse than physical abuse. There are also emotional and verbal abuse.
No one ever thinks they're in an abusive relationship, because they do not have an outside perspective.
And it's so easy to write off as a "cultural thing" or "my parents are just like that lol"
But that does not make it excusable
Anyway, I know nothing about your situation, and I may be completely off base, so keep that in consideration with my words.
But the fact that the teacher gave your parents the answer, and are just breathing down your neck waiting for you to get it right rather than offer help or guidance.. That's a huge red flag to me.
median oar
It’s still important to realise they very likely want the best for you
Not saying abuse is okay but they likely have good intentions, actioned poorly
lone heartBOT
@chilly dove Has your question been resolved?
rotund crater
someone can explain me this
lone heartBOT
someone can explain me this
gusty gorge
do you know what implicit differentiation is
rotund crater
not quite clear
derivate implicit resolves to y ?
but in this case is x?
@gusty gorge
rotund crater
yes
gusty gorge
what have you done
gentle owl
grim delta
i see but new question why is -3/x/x
this is the same as $-3x^{-1}\cdot -x^{-1}$
which using properties of exponents simplifies to $3x^{-2}$ or $\frac{3}{x^2}$
rotund crater
Where does the 3 come from if the derivative is 0?
rotund crater
someone can explain me this
.
real basin
lone heartBOT
real basin
Is this correct?
carmine reef
you should probably everything into the standard a+bi form
real basin
Those are the options I cant choose the form
carmine reef
just on paper or something
real basin
the answer for additions is 4 + i, the answer for * is 5+5i
carmine reef
The problem is as much about translating the answers as it is about the question
real basin
but i dont know what the double bar means
carmine reef
Double bar means applying the conjugate operation twice
tardy nest
I seem to have forgotten how to find the coordinates given an equation in slope intercept form.
How would I go about solving y=-3/2x+12?
I think I'm supposed to do something with the slope and y-intercept but I forgot what.
alpine sable
real basin
Double bar means applying the conjugate operation twice
so it would only be a?
carmine reef
what does conjugate do?
real basin
double conjugate you mean right?
carmine reef
kinda yeah
real basin
carmine reef
in that when you do it twice you get the original back
real basin
Could you explain this a bit to me?
tardy nest
Is this the right channel to send my question? It says help-0 but it has someone's user next to it
real basin
I think its true
surreal meadow
Is this the right channel to send my question? It says help-0 but it has someone...
!help
lone heartBOT
Is this the right channel to send my question? It says help-0 but it has someone...
Please read #❓how-to-get-help
carmine reef
Is this the right channel to send my question? It says help-0 but it has someone...
nah you have to find an available one
real basin
if z = 5 + 0i, then z bar would be 5 - 0i, which is 5
surreal meadow
I followed the instructions and I can't find the help-0 channel
it's not the help 0 channel
carmine reef
if z = 5 + 0i, then z bar would be 5 - 0i, which is 5
Yeah so we see 5+0i = 5-0i = 5
real basin
So in that case the statement is true
carmine reef
Yeah
tardy nest
it's not the help 0 channel
Ohhh I got it now sorry for the interruption
carmine reef
So if you have like 3+7i
The conjugate is 3-7i
and those two arent equal
so when a+bi = a-bi
bi = -bi
b = -b
2b = 0
b = 0
carmine reef
Also for this would it just be a and d?
There's another equivalent answer
real basin
Has to be C then
carmine reef
how so?
carmine reef
yeah
carmine reef
you're welcome
lone heartBOT
@real basin Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
gritty wing
I need help with trying to find this
lone heartBOT
I need help with trying to find this
gritty wing
so far I have:
buoyant kayak
seems you're making this a bit too difficult for yourself
for a function f(x)=a/x^n, what values of n make the improper integral convergent?
slate jolt
its ok just if 1-2a is equal to 0.5 for example
b^1-2a is still not convergent
so 1 is not the right threshold
lone heartBOT
@gritty wing Has your question been resolved?
gritty wing
wait so would it be 0 < a < 0.5?
buoyant kayak
no
gritty wing
o wait
buoyant kayak
for a function f(x)=a/x^n, what values of n make the improper integral convergen...
.
buoyant kayak
guessing is not the best strategy
buoyant kayak
is $\int_1^{\infty}\frac{1}{x}\dd x$ a convergent or divergent integral
ocean sealBOT
a disappointing son
gritty wing
that's convergent right?
slate jolt
b^x for which values of x does the lim of this when b goes to infinity converges?
buoyant kayak
have you not learned the p series test?
slate jolt
just your last step is wwrong
gritty wing
cause as x approaches inf, it's 0?
slate jolt
cause as x approaches inf, it's 0?
remember when you do an integral you are doing a summation, its not just the function
buoyant kayak
just because the limit as x approaches infinity is 0 doesn't mean the area under the curve converges
slate jolt
so you can add smaller and smaller things
and the result can still go to infinity
if the bits dont go small fast enough
@gritty wing just take
this
for which values of x b^x converges?
when b goes to infinity?
slate jolt
its not a trick question
gritty wing
the line
slate jolt
which line?
gritty wing
b^1?
slate jolt
we want to know when this limit is <+infinity
so i'm dumbing it down
by just considering b^x
and when we answer lim(b^x)
we can go back
to the main track
so yeah lim(b^1) =+inf
gritty wing
ok
slate jolt
what about lim(b^x) for x>1?
gritty wing
wouldn't it also approach inf?
slate jolt
yeah
also no need to formulate as if you are unsure
if you know you know
i'm not trying to trick you
w/e
what about x<=0
lone heartBOT
slate jolt
.reopen
gritty wing
.reopen
lone heartBOT
✅
gritty wing
x<0 would approach 0?
gritty wing
0? too
slate jolt
b^0=?
twin bolt
hello can i get help on this math problem
slate jolt
#❓how-to-get-help @twin bolt
gritty wing
thus x should be less than or equal to 0?
slate jolt
x > 1 -> inf
1?
gritty wing
what
slate jolt
well either this is a 0 or you didnt do all the cases for x
gritty wing
mhm
gritty wing
if x is between 0 & 1 it's inf?
slate jolt
x > 1 -> inf
thats why i asked if this was a 1?
slate jolt
ok
gritty wing
so now we have 3 cases
slate jolt
so now lets go back to the main track
either 1-2a<0 or 1-2a>0
it cant be 0
because of the denominators
gritty wing
mhm
slate jolt
ok
gritty wing
we want to know when this limit is <+infinity
so when 1-2a < 0, the first part of this 1 approaches 0
slate jolt
yeah
gritty wing
and the 2nd part is just some constant?
so that means when 1-2a < 0, the thing is convergent
slate jolt
yeah right
slate jolt
you have to do the case a=0.5 then
since we just dont know for now
like the antiderivative you found just doesnt exist
for a=0.5
even before talking about limit when b goes to infinity
gritty wing
even before talking about limit when b goes to infinity
thanks sm btw
lone heartBOT
thanks sm btw
gritty wing
.close
covert sonnet
lone heartBOT
north hemlock
!status
lone heartBOT
What step 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
@covert sonnet Has your question been resolved?
wet quest
C plz
rocky grove
Well you can just write out $4\frac{1}{2}$ on top of a line and write $\frac 23$ below the line.
ocean sealBOT
VulcanOne
rocky grove
I can't view the image.
wet quest
oh I think I get it
rocky grove
wet quest
tank you
rocky grove
You're welcome! :)
acoustic sorrel
Is my method for 2 i correct
and how can I do 2 ii, iii
lone heartBOT
Is my method for 2 i correct
and how can I do 2 ii, iii
acoustic sorrel
16(cos(2pi/3) + i sin(2pi/3))
cos 2pi/3 = 0.5
sin 2pi/3 = root 3/2
therefore
minor needle
16(cos(2pi/3) + i sin(2pi/3))
that's true
minor needle
cos(2pi/3) = -1/2
minor needle
yeah
acoustic sorrel
and b = 8i root(3)
acoustic sorrel
also
is my thinking right for part 2 ii
where roots would just be conjugate of that
so
roots are -8 + 8i root(3)
and -8 - 8i root (3)
or is that wrong
minor needle
that's wrong
acoustic sorrel
what would I do instead
acoustic sorrel
but they wont give square roots?
minor needle
it comes from de Moivre's formula
k varies from 0 to n-1
in this case n = 2, hence k = 0, 1
and x is 2pi/3
in this case
acoustic sorrel
is there another way to do it
lone heartBOT
@acoustic sorrel Has your question been resolved?
acoustic sorrel
that doesnt give us two values when I do it
do we have do
^1/2 and ^-1/2
to get both
.close
lone heartBOT
lone heartBOT
Available help channel!
proven zephyr
Hi, any tips to start solving this kind of questions?
lone heartBOT
Hi, any tips to start solving this kind of questions?
rotund jolt
are you Malaysian ?
proven zephyr
yup
proven zephyr
ehh, good luck for ur tmr's math test 😛
rotund jolt
thanks
proven zephyr
i also from Malaysia.Form 5 student
same btw
rotund jolt
KL ?
proven zephyr
Sabah
rotund jolt
Hi, any tips to start solving this kind of questions?
you want me teach you ?
rotund jolt
1452/12 - (66/12)^2 = 90.75
correct
neon scarab
It is decreasing, and is definitely bounded below by 0. Shd be easy to see it converges(?)
neon scarab
If you want a bound, maybe try $\frac{n!}{(2n)!} < \frac{1}{n}$.
vague coral
but harder to deal with
ocean sealBOT
jimmy1234
vague coral
If you want a bound, maybe try $\frac{n!}{(2n)!} < \frac{1}{n}$.
prove it 🤔
neon scarab
I mean such bound has to be true, its just the details u need to fill it, by induction or whatsoever…
vague coral
I mean such bound has to be true, its just the details u need to fill it, by ind...
why it has to be true ? xd
neon scarab
why it has to be true ? xd
Asmtoptic behavior, anything with factorial will decay faster than 1/n. 🙂
neon scarab
Or this.
$(n + 1)! < (2n)!$
$(n + 1) \times (n!) < (2n)!$
Hence $\frac{n!}{(2n)!} < \frac{1}{n + 1}$.
Then you don’t even need induction.
ocean sealBOT
jimmy1234
vague coral
👌
cinder sundial
lone heartBOT
cinder sundial
Can someone put it on alpha please
I keep getting the y_0=3/8
While the answer on the book is 1/8 instead
I’m frustrated
kindred vale
Can you show your work
magic thistle
Guys do u know the answer to this>
cinder sundial
Can you show your work
They are too complicated, the original is a question from vectors and the system is derived from it
lone heartBOT
@cinder sundial Has your question been resolved?
gusty gorge
,w solve 3x-y-z+2=0, -2x-2y-2z+2=0, -y+z+1=0
ocean sealBOT
lone heartBOT
@cinder sundial Has your question been resolved?
alpine sable
lone heartBOT
alpine sable
what's another way to say the cube can be solved in two moves?
orbit size??
srry the resolution is too low for me to read that. how do u define orbit size
Grp size divide by Stabilizer size
I did it but can't get through it wether how should I calculate probability afterwards
Got the answer for it???
lone heartBOT
@alpine sable Has your question been resolved?
vocal rain
bye😔
lone heartBOT
@upbeat hazel Has your question been resolved?
kindred anchor
0️⃣
kindred anchor
Let M and N be two 3 × 3 matrices such that MN = NM.
$M^2 − N^4 = (M − N^2)(M + N^2)$
ocean sealBOT
kindred anchor
Is this true, because the matrices commute?
lone heartBOT
@kindred anchor Has your question been resolved?
lone heartBOT
@kindred anchor Has your question been resolved?
rough monolith
Is this true, because the matrices commute?
What do you mean? Only matrix addition is commutative
kindred anchor
I have mentioned MN=NM.
modest zinc
lone heartBOT
wind cloak
x^2 _ 4= u
modest zinc
I don’t know if there is anything else that I am missing and then I just need help finishing it
wind cloak
There's no trig sub needed
modest zinc
That’s what our assignment is over, trig substitution
wind cloak
Are you sure
Because this is pretty easy to solve without that 
If you say so though
modest zinc
Mhm! Does doing trig substitution make it harder in this case?
wind cloak
So you have $\int \tan^3 \theta \dd{\theta}$
ocean sealBOT
NEONPerseus
wind cloak
Mhm! Does doing trig substitution make it harder in this case?
Very much so
wind cloak
**NEONPerseus**
Is is where you ended up?
modest zinc
No, I was attempting to do trig substitution lol
modest zinc
Yeah, if you look at the very first picture I sent, it shows what substitution I was doing
But that’s as far as I got to
wind cloak
Looks good, carry on
modest zinc
So substitute x^3 next?
wind cloak
did you not do the actual substitution lol
wind cloak
So substitute x^3 next?
yeah x = tan theta so do that
modest zinc
Like the u sub?
modest zinc
Yeah I do😅
wind cloak
so trig or u?
modest zinc
Trig substitution!😅
modest zinc
Okay. For 2tan theta, would it be 8tan^3 theta since I cubbing the two in the front as well?
wind cloak
yes
wind cloak
yes
wind cloak
yeah sub it all in the integral
modest zinc
Okay, so I’m done labeling all my subs and I can start plugging into the integral?
(Apologies, I’m learning the best I can)
wind cloak
(Apologies, I’m learning the best I can)
Don't apologize for learning
wind cloak
Okay, so I’m done labeling all my subs and I can start plugging into the integra...
and yes
modest zinc
Would the x^3 would the three to the front of the integral?
Oh would I do that if there is a constant for example like 2
wind cloak
Nah
modest zinc
Worth a shot lol
wind cloak
yes
modest zinc
now…I’m lost😅. I can’t integrate yet right?
ocean sealBOT
NEONPerseus
wind cloak
This is what you have right?
modest zinc
This is what I have rn
So you took the 8 out, I got that
But does the 2 cancel out???
And the sec theta??
wind cloak
yes
modest zinc
I’m so smart😄! Alright I got this. Okay, so that I did that, can I integrate tan^3 theta?
Or am I missing a step?
wind cloak
on its own it would need quite some work
but tan^3 x sec x can be done pretty easily
$8\int (\sec^2 \theta - 1)\sec \theta \tan \theta \dd{\theta}$
modest zinc
Isn’t there an absolute value when integrating tan?
ocean sealBOT
NEONPerseus
wind cloak
Isn’t there an absolute value when integrating tan?
We won't be :)
wind cloak
Do you know how to move on forward?
modest zinc
You took one of the tan theta’s out so you can make it tan^2 theta and then integrate it to sec^2 theta - 1
wind cloak
I didn't "integrate" it but I get your point
You need to make use of u sub here
Think you can figure it out?
modest zinc
U sub would be sec theta and then du would be sectheta tantheta?
wind cloak
bingo
modest zinc
Now…ummm…this was where I didn’t pay attention🥲
wind cloak
$u = \sec \theta$
ocean sealBOT
NEONPerseus
wind cloak
Can you find du now?
modest zinc
Yeah I know what du is
wind cloak
What would it be?
