That is another way you can also picturize it.
#help-19
oblique echo
d represents a differential an infinitesimally small change.
if we think abt it for dy/dx we are saying there is an infinitesimally small change in y and x which is the instantneous rate of change (Our derivatve).
but d/dx (x)
d/dx by itself doesn't mean anything we have to actually differentiate something.
Okay Jessica well I'm gonna leave now, but hope this was of some help. GL, and if u r confused I suggest hopping on Khan Academy, they're great.
dire spoke
.close
odd edgeBOT
odd edgeBOT
Available help channel!
fading stump
Hello! I have a question regarding differentiation. Could someone please help me with some tips on how to approach this question. I never know where to start. Currently stuck on 4.1.1
random stirrup
Raise both sides to e maybe
Or just use chain rule
Or how about a trigonometric substitution
The first two proly
fading stump
How would I raise both sides to e?
I understand the chain rule, maybe I should rather go for that..
civic vale
Hello! I have a question regarding differentiation. Could someone please help me...
this is one heck of a chain rule
random stirrup
e^y=that stuff
Then different both sides wrt x
fading stump
so e would be better then?
random stirrup
Note: e^(lnP)=p
random stirrup
so e would be better then?
Try it well see
civic vale
it's bit messy
random stirrup
Note: e^(lnP)=p
Also: if a=b
e^a=e^b
fading stump
Note: e^(lnP)=p
what do you mean by this?
civic vale
but it can be done
civic vale
what do you mean by this?
its a property of log
random stirrup
what do you mean by this?
You're raising e to the answer to this question: what power of e gives me p
That's basically finally p
fading stump
ohhhh okay okay
I understand that
thank you for helping <3 before I go venture the next questions, what are some helpful math websites you guys could recommed?
that would explain the steps quite well
random stirrup
Wolfram ig
This server is also good ...maybe you'll get better solutions if u wait
civic vale
thank you for helping <3 before I go venture the next questions, what are some h...
mathway is good too
civic vale
yes, I use mathway too sometimes.
its p good
fading stump
is that a math pun I'm not getting? T-T
civic vale
oh btw to make differentiation easy , you may cancel out those common factor 'x' inside the log
fading stump
so top and bottom of the fraction then?
civic vale
yup
hidden crown
odd edgeBOT
hidden crown
I think im supposed to get them to a form similar to a quadratic but dont really know how to get there
mystic saffron
Did you take log on both sides?
Remember that log isn't a linear function
So
$log_a(x+y) ≠ log_a(x) + log_a(y)$
clever fjordBOT
𝓘 .
mystic saffron
Will try with that
I'm saying that what you did is wrong
You do have to turn the given equation into a quadratic (by using laws of exponents here)
mystic saffron
No
You won't conclude anything using that, and no algebraic manipulations then would seem possible
hidden crown
Alr
Would this be a better place to be or is that still a bit off what im looking for
mystic saffron
Just start from the beginning and do not use log
It's not required here, and you are using it incorrectly too
hidden crown
Ok
toxic turret
Hey. I'm just looking for a hint for this exercise.
Let $P,Q$ be polynomials in $F[x]$ where $\deg Q \leq \deg P$. Let $R_i$ be the $i$-th remainder in the steps of the Euclidean algorithm (given that $R_{i-1} = P$ and $R_0 = Q$ right), and $R_k$ the last remainder that is not zero.
\\
Exercise: Given polynomials $A,B$ so that $R_k = AR_i + BR_{i+1}$ then there exists polynomials $C,D$ so that $R_k = CR_{i-1} + DR_i$.
clever fjordBOT
fue!
low locust
express R_(i+1) using R_i and R_(i-1)
toxic turret
So like, Ri-1 = SRi + Ri+1?
low locust
yes
toxic turret
Okay so you'd obtain something like
Rk = ARi + B(Ri-1 - SRi)
I am there btw I'm just confused how to obtain the right form from this
toxic turret
(A-BS)Ri + BRi-1
Okay well that was very little algebra
I can't remember why I didn't accept a solution like this
odd edgeBOT
@toxic turret Has your question been resolved?
warm plover
odd edgeBOT
warm plover
How do I do this
odd edgeBOT
@warm plover Has your question been resolved?
odd edgeBOT
@warm plover Has your question been resolved?
odd edgeBOT
@warm plover Has your question been resolved?
sudden shadow
The slope of the line is tanθ
θ is the angle between the line and the positive direction of x-axis (0≤θ<π and θ≠π/2)
In this problem θ=arccos(4/5) so cosθ=4/5>0
By the constraint of θ we know 0≤θ<π/2
So tanθ=3/4
Use the point slope form to write the equation of the line
Then solve the equations simultaneously.
warm plover
.close
midnight jasper
I have to graph f(x) = sin(2x)-5
odd edgeBOT
I have to graph f(x) = sin(2x)-5
midnight jasper
I don’t know how the 2x would effect the graph
cold sage
what do you know of transformations?
midnight jasper
I know basic ones like going up, down, multiplying stuff like that
glass wedge
I don’t know how the 2x would effect the graph
It would reach any point twice as fast
midnight jasper
Wdym?
glass wedge
Well for example
sinx has a zero in x=π
But sin2x has a zero in π/2
Which means the graph is "squished"
cold sage
glass wedge
It reaches points twice as fast
midnight jasper
So the graph would be squished?
glass wedge
Yep
midnight jasper
Should I multiply each x value by 2 or no
glass wedge
sin(2x) ≠ 2sinx
glass wedge
Should I multiply each x value by 2 or no
Wouldn't that be stretching it
sick sigil
I mean you want to think What is sin(20)?
Then What is sin(21) = sin(2)
So when you have sin(pi) you have sin(2pi) right?
Ah i cant do *
cold sage
put a \ before it
sick sigil
On phone cba😆 But I’ll keep that in mind for pc
But if you have say x = pi/4, with sin(2x) it Will be sin(pi/2)
So it’s going to go twice as fast to the same values that sin(x) goes between
We’re not changing the amplitude(the highs and lows of the Y value), just the period
odd edgeBOT
@midnight jasper Has your question been resolved?
strange drum
odd edgeBOT
Available help channel!
high sandal
Why is does it work like that. Do the negative numbers just use / instead of *
trim matrix
Why is does it work like that. Do the negative numbers just use / instead of *
In general, $a^{-b} = \frac{1}{a^b}$
clever fjordBOT
waris
haughty bramble
if you can't read the text,
ABC and DEF are two arcs of circles, centre O. OFA and ODC are straight lines. a Show that the perimeter of the shaded region is given by frac 6 π r+3 π r+10r5 cm
viral frost
,rccw
clever fjordBOT
haughty bramble
cheers
viral frost
Tried anything yet?
ionic heart
Perimeter of the shaded region?
ionic heart
If you have an angle ¢ subtended at the centre
Then the perimeter of the arc is 2πr * ¢/360
viral frost
i know i have to do something with 108/360 x pi x (r+t)
yeah that's arc ABC
viral frost
i know i have to do something with 108/360 x pi x (r+t)
Similarly find the length of arc def.
Then also add 2t
Because that's also included.
You see that?
haughty bramble
yeah
viral frost
Yeah that should be what they're asking.
ionic heart
That's your perimeter
Simplify it
Compare it with the thing asked
Also what you wrote is incomplete. You forgot to add 2t
haughty bramble
oh shit true
so now i have
6/10 + 2pi + 2r + 3t
now i have to compare it with 6 π r+3 π t+10t cm / 5?
ionic heart
Actually, you don't have to compare, you just had to prove it
haughty bramble
so...
haughty bramble
so now i have
6/10 + 2pi + 2r + 3t
this equals
haughty bramble
now i have to compare it with 6 π r+3 π t+10t cm / 5?
this?
viral frost
Yes?
haughty bramble
im still stuck
viral frost
i know i have to do something with 108/360 x pi x (r+t)
You were here.
What did you do then?
haughty bramble
i did that + 108/360 * pi * r
then added 2t at the end overall
and then simplified
so
3/10 * pi * (r + t) + 3/10 * pi * r + 2t
simplified i got 6/10 + 2pi + 2r + 3t
clever fjordBOT
The following error occured while calculating:
Error: Value expected (char 1)
haughty bramble
because thats the formula?
clever fjordBOT
! What the hell am I doing here?
viral frost
If your Angle's in degrees.
viral frost
3/10 is 108/360
haughty bramble
yes
viral frost
Times 2pir
viral frost
Times 2pir
Is what you were meant to do.
haughty bramble
ohhhh
so wait
first time it was supposed to be
108/360 * 2pi * (r+t)
and the second was
108/360 * 2pi * r
and then add them together
and + 2t
so now i have
6/10 + 4pi + 2r + 3t
haughty bramble
oh shi
viral frost
How'd you get straight up 6/10?
haughty bramble
3/10 + 3/10 = 6/10 no?
viral frost
Remember all that other stuff was MULTIPLIED with 3/10
Not casually added.
3/10 * 2pi r = 6pir/10
haughty bramble
oh so 9/100?
viral frost
...
haughty bramble
bro listen
viral frost
What's 2 * pi?
viral frost
What's 3/10 * pi?
haughty bramble
0.3pi or 3/10 pi
viral frost
What's 3/10 * 2pi?
haughty bramble
3/10 2pi
viral frost
Or you can further write that down as...?
haughty bramble
0.06pi?
haughty bramble
fuck me
viral frost
0.6pi
haughty bramble
... i think im a visual learner yk, this typing ting is too hard
viral frost
Anyways, yeah.
You seem to get it.
Now when you wrote:
0.3 * 2pi * r + 0.3 * 2pi * (r+t) + 2t
What do you get, finally?
Take your time but try not to mess it up this time
haughty bramble
just give me a minute 😭
viral frost
Take your time.
viral frost
Anyways, yeah.
You seem to get it.
Now when you wrote:
```0.3 * 2pi * r + 0.3...
As you can very clearly see I hope, the second term has 0.6pi * (r+t)
Which means it'll be 0.6pir + 0.6pi * t
You're missing the fact there's multiplication involved.
Similarly for 1.2pi
haughty bramble
so then 1.2pirt?
haughty bramble
oh shit
viral frost
You're randomly multiplying terms.
Multiply the ones that are meant to be.
* means multiplication.
haughty bramble
thanks
haughty bramble
im still standing
viral frost
After you've done all that, add the like terms.
For instance, 0.6 pi r from here and 0.6 pi r from 0.3 * 2pi * r
What'll that make?
haughty bramble
hold up real quick i need to like pull the thing we just did because now im lost
so
0.3 * 2pi * r + 0.3 * 2pi * (r+t) + 2t
thats 0.6pi (r + t)
viral frost
thats 0.6pi (r + t)
That's only the second term.
Now even the second term can be expanded to be written as:
0.6pi * r + 0.6pi * t
Then there's the first and third terms.
(0.3 * 2pi * r and 2t)
Also add these to the second term.
What do you get, finally
haughty bramble
okay wait
wait am i adding or multiplying
if multiplying, i dont know how to do that
would i just 0.3 x 0.6?
viral frost
You're also adding and multiplying. But they're different.
What you're adding is different from what you're multiplying.
haughty bramble
yeah no bro i am at a brick wall, is there any chance u can like write it and send it and then like guide through what you did?
i genuinely am lost
haughty bramble
thanks
viral frost
You don't really have to watch it fully, but until you get the hang of it.
haughty bramble
yeah i know, i have 2 other questions i gotta do but im trying to understand this one first
haughty bramble
thanks
viral frost
Where were we?
haughty bramble
you want the question?
viral frost
0.3 * 2pi * r + 0.3 * 2pi(r+t) + 2t
0.3 * 2pi * r + 0.3 * 2pi * r + 0.3 * 2pi * t + 2t
(distributed the parenthesis)
0.3 * 2pi * r + 0.3 * 2pi * r = 0.6 * 2pi * r
So you'd have
0.6 * 2pi * r + 0.3 * 2pi * t + 2t
Now you can simplify further.
Like
0.6 * 2pi is 1.2pi
So you'd eventually have
1.2 * pi * r + 0.6 * pi * t + 2t
And that's that.
@haughty bramble
viral frost
Certainly.
You can write 1.2 as 12/10 and so on.
And simplify yourself.
$\frac{12}{10} \cdot \pi r + \f{6}{10} \pi r + 2t \cdot \f{10}{10}$
clever fjordBOT
! What the hell am I doing here?
viral frost
You can also factor out 2, because that's a common factor everywhere.
viral frost
You can check something similar on basic algebra if that's not what you were hoping.
You'll find tons of videos.
haughty bramble
thanks
you want to help with some other questions?
they're easier but idk if uwant to
viral frost
You could post, there'll always be helpers available.
May or may not be me exclusively though.
haughty bramble
okay so i should i close this and make a new one?
viral frost
Ideally, I'd suggest doing so.
Of course you can still post it right here. But that'd be wiser.
viral frost
Cheers.
haughty bramble
.close
winged violet
odd edgeBOT
winged violet
can someone explain this to me
the basic idea
all the symbols and stuff
I know that (x,y) takes values from Di, w takes values from a set of d numbers
<@&286206848099549185>
quasi sparrow
<@&286206848099549185>
!15m
odd edgeBOT
<@&286206848099549185>
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.
odd edgeBOT
@winged violet Has your question been resolved?
odd edgeBOT
@winged violet Has your question been resolved?
cunning pasture
So I wanted to simplify this but I kinda forgot
odd edgeBOT
So I wanted to simplify this but I kinda forgot
south plume
So I wanted to simplify this but I kinda forgot
your denominators are the same
cold urchin
You already have the same denominator so you’d just add the numerator normally
south plume
you can just add the numerators
cunning pasture
you can just add the numerators
Like this?
south plume
yes
odd edgeBOT
@west lance Has your question been resolved?
remote lagoon
i have 9 black counters and 3 white counters.
i select 9 of them at random and place them into three groups. what is the probability that a group has all 3 white counters?
remote lagoon
Have you tried anything for the problem yet
yeah but somewhat confused
remote lagoon
i got that there's a 1/220 chance that our selection contains 3 counters in total
remote lagoon
then from there we could split it into the different cases of the groups they're placed in?
with
cold urchin
<@&268886789983436800>
remote lagoon
then from there we could split it into the different cases of the groups they're...
{3,0,0},{0,3,0},{0,0,3},{2,1,0}... we can imagine that each time we randomly place a counter in a group so there's 3^3 of these or 27 ways they could be distributed across the distinct groups
so then of these, only 3 of them have all 3 counters in 1 group, so 1/9?
then 1/(9*220) would be the final answer?
?
odd edgeBOT
@remote lagoon Has your question been resolved?
remote lagoon
@gilded crater
queen talon
i have 9 black counters and 3 white counters.
i select 9 of them at random and p...
Hi
So basically the question equivalent to what is the probability you select the 3 whute counters when you select 3 from 12
odd edgeBOT
@remote lagoon Has your question been resolved?
bold glen
sly badger
dawg
cold sage
close this one, or close the older one
cold urchin
What’s the confusion here
bold glen
yes
cold sage
show me
bold glen
Ok
wwait
i think i did it
let me see
nvm
5.1 x 10 to the power of 5
thats what i got
bold glen
OK#
ill show u how i got it
so i did this
then i rounded to 2 significant figure
bold glen
where do i put the brackets
cold sage
around the numerator
cold sage
around the numerator
$(5.1\times 10^5 + 1.4 \times 10^4)\div (3.5\times 10^{-4})$
clever fjordBOT
AℤØ
cold sage
well, just around everything i guess
odd edgeBOT
@bold glen Has your question been resolved?
stark coyote
odd edgeBOT
stark coyote
so i was thinking that the third eigenvalue could possibly be 0 and then A wouldn't be diagonalizable, but the answer key says that A must be diagonalizable.
echo ginkgo
why would it matter that the 3rd eigenvalue is 0 ?
the zero matrix is diagonalizable you know
it's already diagonal
stark coyote
means the diagonal would contain a 0 for A = PDP^-1 wouldnt it
stark coyote
a m x n matrix being diagonalizable must have either n distinct eigenvectors or n distinct eigenvalues right?
stark coyote
A wouldn't be full rank and that would mean A isn't even invertible let alone diagonalizable?
det A would be 0 at that point wouldn't it?
or am i getting definitions mixed up
echo ginkgo
you're getting it mixed up yes
echo ginkgo
the zero matrix is diagonalizable you know
^
you can be diagonalizable and not invertible
and there's prolly examples for non diag and invertible
stark coyote
there was a later problem that had me construct a 2x2 matrix that was invertible but not diagonalizable and that was easy, just had to give it only one eigenvalue.
echo ginkgo
you can have one eigenvalue and be diagonalizable
the identity is diagonalizable
has only one eigenvalue
what matters is the dimension of the eigenspaces
which is what that question is getting at
stark coyote
right in this case the matrix is 4x4, meaning the eigenspace is a subspace of R^4
it tells us 3 eigenvectors that exist. and the third eigenvalue must also have a vector then, meaning the eigenspace spans the vector space
so it must be diagonalizable. even when that third eigenvalue might be 0 right?
stark coyote
so what exactly does it mean when an eigenvalue is 0
it means the matrix isnt full rank
echo ginkgo
yea
stark coyote
and full rank means invertable right? also full rank means the determinant isnt 0?
echo ginkgo
yeah
stark coyote
eigenspace of 0 = nullity/kernel right?
echo ginkgo
yeah that's literally what I said above lol
stark coyote
so Ax = 0 is the same solution set of the eigenbasis of 0
sorry im just kinda doing this to try and retain it better
echo ginkgo
aight
odd edgeBOT
real crown
The 2 will still remain on the outside
It's multpied
2(5x - 3y) ( 5x + 3y)
You can't just remove it
Well if you want to you can multiply one bracket by 2 but that wouldn't make it any more simpler
(10x - 6y) (5x + 3y)
Or (10x + 6y)(5x - 3y)
This is not the fully factorised form
You would need to take out the 2 for it to be fully factorised
Capiche?
You mean for the initial equation?
Gcf is greatest common factor right?
Yes
A number which can divide both terms
Yes
If that's the case then you should take out the largest factor
Well there's no short and sweet way of doing it
Trial and error
Although some calculators do have a function for this
I doubt the numbers will be large if it was a technology free exam
It depends on the calculator
My one says gcd
Greatest common denominator
Does it say Gcd or gcf anywhere?
It is a scientific calculator right?
odd edgeBOT
@charred barn Has your question been resolved?
odd edgeBOT
@charred barn Has your question been resolved?
inland hamlet
odd edgeBOT
clever fjordBOT
eclipseryu
inland hamlet
and i need to find the angular speed in rad/min, and rpm
the bicycle is in inches, and the linear speed is in miles and hours, and the answer needs to be in minutes
unit conversion is absolutely a pain in my ass and i dont know how to solve this problem to be completely honest
slow light
ω = v/r yes?
inland hamlet
yeah
slow light
so we want to write r and v in the same units
r is 12 inches
we can rewrite that as 1 ft
v is 15 miles / hr
we can rewrite that is 15/60 miles/minute, yes?
or 0.25 miles / minute
5280 feet in a mile...
so how many feet per minute is 15 mph?
inland hamlet
give me a hot min to read that please
that doesnt make sense to me
way too fast lol
inland hamlet
ik
slow light
[\frac{15}{1}\frac{mi}{hr}•\frac{1 hr}{60 min} • \frac{5280 ft}{1 mi}]
clever fjordBOT
Astral
slow light
5280 ft/1 mile is 1
they're the same thing
we can multiply by 1 as much as we want
the mi on top and bottom cancel out
the hr on top and bottom cancel out
we get
[\frac{15}{1}\frac{1}{60}\frac{5280}{1}\frac{ft\times{mi}\times{hr}}{min\times{mi}\times{hr}}]
clever fjordBOT
Astral
slow light
the miles on top and bottom cancel out, 1 mile / 1 mile = 1
inland hamlet
i want to make it clear that i dont know shit abt unit conversion or dimensional analysis or whatever voodoo we're doing here
slow light
technically dimensional analysis
hmmm
lemme put it this way
we'll do something simpler
your radius is just 12 inches yes?
inland hamlet
yeah
slow light
how would you convert that to feet?
slow light
ok, how would you convert 24 inches to feet? (not directly related to problem)
inland hamlet
uh
okay
well since 1 foot is 12 inches we can just do 24/1 foot = 24/12 in = 2 feet??
idk
hybrid carbon
The math here is just treating units as variables. We have equations that define unit conversions. 12in=1ft
slow light
well since 1 foot is 12 inches we can just do 24/1 foot = 24/12 in = 2 feet??
yes exactly
hybrid carbon
You can do all the normal math stuff with that equation
slow light
# of feet = 24 inches / 1 foot = 24 inches / 12 inches (since 1 foot = 12 inches) = 2 feet total
inland hamlet
okay
slow light
yeah, treating units as variables often helps a lot
it's how dimensional analysis works
fancy words for treating units as variables and making ratios
inland hamlet
right
well when theres a row of like 4 different fractions it's pretty visually confusing
slow light
oh yeah
I'll do it one step at a time
so we know the radius is 1 ft yes?
that's all clear?
inland hamlet
5280ft/60min right?
slow light
= 1 mi/hr yes
inland hamlet
since the miles are cancelling out but the 15 remains do we multiply 15 by 5280?
slow light
[\frac{15}{1}(\frac{mi}{hr})=\frac{15}{1}(\frac{5280\times{ft}}{60\times{min}})]
clever fjordBOT
Astral
inland hamlet
to get the amount of feet we're moving per minute?
yeah
so our linear speed is 79200 mi/min it looks like
slow light
so our linear speed is 79200 mi/min it looks like
ahem
slow light
you said it yourself
1 mile / hr = 5280 ft / min
we simply swap out the parts in parentheses
inland hamlet
uh
clever fjordBOT
Astral
slow light
it's equivalent to what we started with (we subbed in something equivalent)
it's just not simplified
slow light
1320ft/min?
yes!
slow light
so, we know $v=1320\frac{ft}{min}$
clever fjordBOT
Astral
slow light
and if linear speed (v) is rω then ω= r/v??
yup!
wait no]
if v = rω
divide by r on both sides
v/r = rω/r
ω = v/r
not r/v
inland hamlet
oh okay
okay
so now we have 1320ft/min / 12in
because we didnt do enough dimensional analysis
inland hamlet
wtf im actually slow
slow light
$(12in)=(1ft)$
clever fjordBOT
Astral
slow light
wtf im actually slow
no no your bike is going very fast dw
inland hamlet
see something's gotta be wrong today i actually forgot how many inches were in a foot 😭
slow light
any day you have to sound out "five to-mate-ohs" to get a number is a bad day
inland hamlet
my brain is lagging dw
lol
okay
well
1320ft/min / 1 ft is just 1320/min right?
slow light
yup
inland hamlet
and 1320 is the angular speed per minute in radians right?
inland hamlet
it wanted us to find the angular speed of the wheels in rad/min and then the revolutions per minute
inland hamlet
what
slow light
ok so we know we're traveling 1320 feet per minute yes?
inland hamlet
yeah
slow light
however, think about it
that means our wheel has spun and spun and spun
until it has effectively touched the ground over 1320 feet per minute
inland hamlet
right
slow light
1320ft/ its circumference is how many times the wheel spun a whole circle touching the ground to cover that distance in that minute
we can't use v = rω because bicycles aren't pure rotational motion
it looks like this
over one minute, it covers 1320 feet
so the circle (the wheel) had to unwind itself 1320/circumference times to cover that distance
inland hamlet
fuck i gotta finish this tomorrow my chromebook is boutta die
slow light
noooo
anyways you were really struggling with the unit conversions
you should be able to figure out the rest
good luck!
inland hamlet
.close
odd edgeBOT
fair prism
Start by finding side lengths of the squares. There is a relationship between the base and height of the shaded triangle to the length of the big square and also to the small square
How about the big square
Yeah
Lets label some parts of the shaded triangle. Call the longer leg “a” and the smaller leg “b”. We know the hypotenuse is sqrt2. Can you think of a formula relating a and b to sqrt 2?
yeah
try writing it as an equation
close, a and b are the smaller legs and sqrt 2 is the hypotenuse
Yeah
So now we have one equation
To get a unique solution we will need 2 equations
What can you say about these red lines
yeah
and they are also a
so a=sqrt3-b
So now we have two equations.
a^2+b^2=2 and a=sqrt3-b. Do you know what do from here?
Yeah
I get .268
so probably
if you rounded down
np
odd edgeBOT
odd edgeBOT
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hidden igloo
I don’t understand why it’s c
odd edgeBOT
I don’t understand why it’s c
mystic saffron
that is a -i before the (a+bi) ?
hidden igloo
yeah
mystic saffron
are you sure its C it would be c if it was i(a+bi)
mystic saffron
odd, it woulld seem that b is the right answer since multiplying a complex number by i rotates it 90 degrees in the counterclockwise direction and multiplying it by -i rotates it by 90 clockwise
hidden igloo
yeah that makes sense, I did B although its saying C
thanks for clarifying though
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odd edgeBOT
odd edgeBOT
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vague linden
simplify (sqrt of 48 + sqrt of 12 - sqrt of 75)^3
odd edgeBOT
simplify (sqrt of 48 + sqrt of 12 - sqrt of 75)^3
vague linden
complex numbers btw
odd edgeBOT
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rancid basin
odd edgeBOT
rancid basin
idk how to phrase my answer
but isnt it just the factoring of the roots into brackets
because z /= 1 because it must be purely complex
whatever
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naive night
Is there an established way to graph the transformations of an sin inverse, cos inverse, tan inverse graph, without using a calculator?
remote lagoon
is this from the ritangle
odd edgeBOT
@naive night Has your question been resolved?
odd edgeBOT
@naive night Has your question been resolved?
rustic geyser
Is there an established way to graph the transformations of an sin inverse, cos ...
Reflect in x=y and bound x between -1 and 1
naive night
Thanks man!
odd edgeBOT
Available help channel!
old parrot
Can I say that f(x) is the image of the codomain and y is the codomain, and when f(x) = y the function f is surjective?
odd edgeBOT
Can I say that f(x) is the image of the codomain and y is the codomain, and when...
@old parrot Has your question been resolved?
tall veldt
If for all y in the codomain there is some x in the domain such that f(x) = y then f is surjective
old parrot
Sure, but what about "Can I say that f(x) is the image of the codomain and y is the codomain"
Is that always accurate?
odd edgeBOT
odd edgeBOT
@lavish wraith Has your question been resolved?
lavish wraith
<@&286206848099549185>
lavish wraith
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tidal idol
I need help finding the Taylor Series for the function, √x, centered at 1
tidal idol
Let me try this math code for the first time... $\sum_{n=0}^N (((3/2) - n)/n!) * (x-1)^n$
clever fjordBOT
hamzah
tidal idol
Oh, it works
clever fjordBOT
hamzah
tidal idol
(N = degree polynomial being used, I tried it with 15)
If anyone can help me get a Taylor series for this function in summation notation, I'd greatly appreciate it
odd edgeBOT
@tidal idol Has your question been resolved?
tidal idol
<@&286206848099549185> any help would be appreciated, I'll need to head offline in 20 minutes btw
I'll hafta go soon, I guess there's no answer for this one I'll just close it now then
.close
odd edgeBOT
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dim thorn
odd edgeBOT
dim thorn
Im confused here
I drew out the fbd
Sum of the forces in the x direction is T_1(cos(theta))-T_1(cos(theta)) = 0
sum of the forces in the y direction is T_1(sin(theta))-T_1(sin(theta))+T_2-Fg
I dont understand how we can solve for T_1 in any way
dim thorn
1) do they tell u what the mass is?
Fg is 100N
void yew
oh bet
dim thorn
2) y expr isn't right
sum of forces in y?
void yew
Why would it have T1sin(theta) twice 
void yew
The other rope is T2
void yew
Oh wait hm
void yew
OK ic u rite
Hmmm
Well wouldn't it then be T2 - Fg = 0 and 2T1sin(theta) - T2 = 0 ?
Cus there's 2 points of tension
The one connecting the Weight to rope with T2 tension
And then the point connecting rope T2 to ropes T1
Idk maybe I'm bsing actually
Wait
In the first problem how did you solve it if there were 3 unknowns and 2 directions
dim thorn
t1=t3
dim thorn
ya
void yew
OK I got u
It is indeed how I figured
In this vid T3 = Fg
And then another y component equation for the other point of connection
void yew
Ye
dim thorn
Ye
im still confused about wjat us aid earlier
what would be the sum of the forces in the y direction
nvm
void yew
dim thorn
<:catKing:812386361297862747>
gonna keep going on, theres 2 more tension problems i'll lyk if i need help
void yew
okie
dim thorn
dim thorn
okie
here is my work for a new proble
T2 is supposed to be 51.76 but I got 57.73
where did I make a mistake
it should be t2= above the bottom one
in my work
nvm
i put it in calculator wrong
void yew
Woops I forgot about this tbh 
dim thorn
Woops I forgot about this tbh <:bleakkekw:913344117981999125>
dw I got the right answer
i just put it in the calculator wrong
void yew
noice
dim thorn
noice
this one is very confusing
no matter what I try I always end up dividing something by 0
void yew
These should be the 3 points
First two lower points only y component really matters
then third point x and y
So these r the equations I got
dim thorn
is this 3 equations 3 unknowns?
void yew
P much I guess since T4 = Fg is immediate
dim thorn
im not solving this
this is like
15 minutes of work
not doing it
i'll take the -10
i have too many more problems to do to spend that much time on it
ty
.close
tacit narwhal
It's just a quick question because I see this word being used alternatively all the time, and I'm confused. When I grew up I learnt if I say 1 by 1 we mean 1 x 1, but when I'm watching videos or listening to my teachers explain a math topic when they say 1 by 2 they mean 1/2
south plume
It's just a quick question because I see this word being used alternatively all ...
in english it's more common to say 1 times 1
tall veldt
I think this is unfortunate shortening of language, simultaneous shortening of "multiplied by" and "divided by"
south plume
yeah
tacit narwhal
I think this is unfortunate shortening of language, simultaneous shortening of "...
for dividing can't we just say over
1 over 2
tall veldt
You can and probably should
tacit narwhal
why do people like to confuse others
tall veldt
I would interpret by as multiplication personally, like a 2 by 4 piece of wood
tacit narwhal
I would interpret by as multiplication personally, like a 2 by 4 piece of wood
Yeah that's why I'm saying
my classmates do it too
thorn fractal
It's just a quick question because I see this word being used alternatively all ...
1 by 2 is
1 x 2
Teacher is wrong
tacit narwhal
If I hear them say it again, I'll correct them in a respectful way
thorn fractal
Math counsel approves
tacit narwhal
because it always affects the explanation when they don't write what they're saying on the board
tall veldt
Specifically bring up the fact that by usually refers to multiplication
5 by 5 grid etc
torn quarry
How would i find P(CuD)?
torn quarry
<@&286206848099549185>
static totem
from what information
odd edgeBOT
@torn quarry Has your question been resolved?
odd edgeBOT
@torn quarry Has your question been resolved?
odd edgeBOT
@torn quarry Has your question been resolved?
strong elbow
Help me
strong elbow
I’m a bit stuck and how to construct the proof in either direction
Although the proof makes complete sense
I just don’t get the if and only if terminology
cold urchin
The statement is $$s = supA \iff \forall \epsilon > 0, \exists a \in A, s - \epsilon < a$$ You need to prove forward implication ie. $$s = supA \implies \forall \epsilon > 0, \exists a \in A, s - \epsilon < a$$ in other words assume s = supA then prove blah. The backward implication is similar you assume for every epsilon there’s an a such that $s - ε < a$ then you shall prove that s is supA.
clever fjordBOT
$Pure$
odd edgeBOT
@strong elbow Has your question been resolved?
light zodiac
odd edgeBOT
light zodiac
Idk what to do
Ik like an x intercept is -6
But uhhh
Idk wat after
Do I turn it into other forms
cold sage
well, its a repeated root
light zodiac
Fr
cold sage
so its vertex is at the-6
light zodiac
Oh
cold sage
and does it open out, downwards or up
light zodiac
Down
cold sage
yeah
light zodiac
Do I make x 0 to find the y int
cold sage
so you know what itll generally look like
if it wants it to be pretty accurate, maybe get a few points on each side of x=-6
cold sage
Do I make x 0 to find the y int
you can but its not on the graph space you have
you wont be able to show it
light zodiac
Fr
light zodiac
so you know what itll generally look like
if it wants it to be pretty accurate, ...
okkk
light zodiac
you can but its not on the graph space you have
Is this right fr
cold sage
np
light zodiac
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twin urchin
why is the gradient normal to a level surface
odd edgeBOT
why is the gradient normal to a level surface
@twin urchin Has your question been resolved?
odd edgeBOT
@twin urchin Has your question been resolved?
desert marlin
which tells you what?
when the dot product of two vectors is 0
the vectors are perpendicular
so the gradient is perpendicular to the tangent of your level curve
and the tangent of a level curve is the level curve
does that help @twin urchin
twin urchin
Yeah so basically
You’re telling me
I have a level surface of some 3 variable function
And then
A vector valued function exists such that
It is a path on that curve
So basically every value of t
Will lead to a value of xyz
So I get my value
F(r(t))
And if I wanted to derive that
desert marlin
it works for not just R3 also btw, but it is most easy to explain here