rare edge
Shit
#help-39
cosmic charm
-1 = -b/2a
cosmic charm
yeah but is that b = 28 or b = -28?
if you put b = -28 then it'll be -(-28) = +28
+28/28 = 1
pearl pondBOT
pearl pondBOT
Available help channel!
wary spear
.help
pearl pondBOT
Commands:
- clopen:
.close,.reopen - consensus:
.poll - factoids:
.tag - help:
.help - version:
.version
Type .help <command name> for more info on a command.
wary spear
?help
wary spear
i dont understand when i plug in -3 into the equation i get 1 why is it giving me 1.5
regal herald
you shouldnt get 1
wary spear
and i can plug -3 since denominator doesnt equal zero
wary spear
you shouldnt get 1
i thought denominator shouldnt equal zero tho
wary spear
it does equal 0
i thought it equalled -18 when i did it on the calculator
wary spear
oh right mb it is zero
wary spear
thats not the same as (-3)^2
can i do this tho?
regal herald
i like the spirit of the idea, but no it doesnt work like that
try factorising the denominator
wary spear
i like the spirit of the idea, but no it doesnt work like that
i js solved it and got 1.5 thank u
.close
pearl pondBOT
regal herald
no worries
pearl pondBOT
Available help channel!
spiral rover
In a triangle ABC, P is a point on AB . PR is drawn parallel to BC such that PR=BC and PR intersects AC at Q. Show that area of triangle AQR = area of triangle BPQ.
found that PRCB was a parallelogram , angle PQC=angle AQR ( vertically opp), and then I'm kinda stuck now
tardy reef
Have you sketched a diagram for this? And/or roughly identified a direction to proceed?
!status
pearl pondBOT
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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
@spiral rover Has your question been resolved?
spiral rover
Have you sketched a diagram for this? And/or roughly identified a direction to p...
I'll send it in a min
spiral rover
```
What step are you on?
1. I don't know where to begin.
2. I have begun but go...
1
I mean i found a few statements but I'm not sure where I'm going with that
spiral rover
Have you sketched a diagram for this? And/or roughly identified a direction to p...
the image is loading sideways , but this is the diagram
wheat flint
- Draw heights $h_1$ from A to PR and height $h_2$ B to PR
tardy reef
one thing when you think of areas is look at best heights and bases you can compare
jolly parrotBOT
timuko
tardy reef
!nosols
pearl pondBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
spiral rover
oh right
wheat flint
In a triangle ABC, P is a point on AB . PR is drawn parallel to BC such that PR=...
In this problem, you need to prove that PQ.h_1 = QR.h_2
spiral rover
so if PR=BC=x and I take PQ = a , I can write QR as x-a?
wheat flint
so if PR=BC=x and I take PQ = a , I can write QR as x-a?
Yes
spiral rover
ar(BPQ) = (1/2) (x) (h2) and ar(AQR) = (1/2)(h1)(x-a)
wheat flint
Given that PR is parallel to BC, what follows after it?
spiral rover
Given that PR is parallel to BC, what follows after it?
PR also equal to BC, so PRBC is a parallelogram ( then BP also parallel to CR), and in terms of something that hepls with the height or relavent angles, I'll think for a moment and tell
wheat flint
The fact that PQ and BC are parallel might be useful
spiral rover
The fact that PQ and BC are parallel might be useful
ifI take trapezium PQCB and join CP, I get area of CPQ =area of BQP ( same base and b/w same parallel lines)
my brain isnt working for this sum , and I missed a lot of my plane geometry classes
wheat flint
The fact that PQ and BC are parallel might be useful
Angles APQ and B are equal, as well as AQP and C
What we can conclude from that?
spiral rover
What we can conclude from that?
BAC similar to PAQ
and sides are in proportion, so
AP/PB = AQ/QC= PQ/BC
and I remember learning something abouts heights also being in proportion
Im gonna check what that was
is PQ/BC = h1/h2 = AQ/QC
spiral rover
The height of triangle BAC is not h_2
oh right sorry
my bad
angle PRC= angle B (the parallelogram) and it was already equal to APQ(corresponding angles)
so CP parallel to AR
wheat flint
so CP parallel to AR
Not always
wheat flint
The height of triangle BAC is not h_2
So PQ/BC = h1/(h1+h2)
spiral rover
So PQ/BC = h1/(h1+h2)
yeah\
1 min
I think I can try to solve here now
@wheat flint thanks
I got it now
I was being very dumb (sorry for that)
wheat flint
.close
spiral rover
.close
warm spruce
The 11th question
pearl pondBOT
The 11th question
buoyant bane
The 11th question
What step are you stuck at?
warm spruce
Basically I tried to take in terms of sin and cos
Then I tried rationalising it
Idk why
Then I got stuck
buoyant bane
Can I see your steps
warm spruce
Ohhh
Uuh
Ok
I can't find the book where I did it first
But I wrote it again
I then squared it
And simplified the denominator
buoyant bane
Instead converting in terms of sin and cos you could write 1 in terms of sec and tan
I had about the same problem when i was in 10th grade
buoyant bane
1 = sec^x - tan^x
warm spruce
So should i rationalise first?
buoyant bane
So should i rationalise first?
No just find away to cancel out terms in the numerator and denominator
warm spruce
No to like square it
warm spruce
1 = sec^x - tan^x
So I can use this
buoyant bane
I don't get what you mean sorry
buoyant bane
You should get this
You can separate the terms secx + tanx in the numerator
And that's basically it
Wtf my screenshots
sterile turtle
ok
sterile turtle
so
i have this
these are the answers
if you think about it, the answer for part c is obviously k>1
I can use the graph to kinda cheese my way into saying it
but is there an algebra method to this or nah
actually
@oak quiver come back man
tame portal
is it just part c ur having trouble w
tame portal
like just drawing it and be like tangent = 1 point, if i decrease gradient then it won't cut the line at all hence k >1
for 2 pts
tame portal
like idk if theres an easy way to do it algebraically
tame portal
yea thats what i was thinking
well you're right :D
tame portal
yipeee
sterile turtle
.close
pearl pondBOT
pearl pondBOT
Available help channel!
sharp pewter
C)
sharp pewter
Is it just like computing B, but instead have n as 12*20?
pearl pondBOT
@sharp pewter Has your question been resolved?
sharp pewter
.close
pearl pondBOT
pearl pondBOT
Available help channel!
worthy hare
im lost how do i continue from here?
pearl pondBOT
im lost how do i continue from here?
next dove
im lost how do i continue from here?
factorize the denominator
then try to separate the whole thing into two fractions
either by observation or partial fraction decomposition
next dove
nice
jolly parrotBOT
pearl pondBOT
pearl pondBOT
Available help channel!
tardy parrot
I don't understand how (1+x²)arctanx-x=2x arctanx?
pearl pondBOT
I don't understand how (1+x²)arctanx-x=2x arctanx?
pearl pondBOT
Available help channel!
agile ridge
btw what does this limit even mean? the derivative at a-h ?
pearl pondBOT
btw what does this limit even mean? the derivative at a-h ?
plucky python
btw what does this limit even mean? the derivative at a-h ?
it'll tend towards 3*f'(a)
heady radish
I don't understand this
pseudo oxide
I don't understand this
!occupied
pearl pondBOT
I don't understand this
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
agile ridge
it'll tend towards 3*f'(a)
I dont understand.. why is it not the derivative at a-h ?
plucky python
I dont understand.. why is it not the derivative at a-h ?
well it can't be the derivative at a-h
since h->0
so basically if it were the derivative at a-h, then since h -> 0, it'll be the derivative at a
agile ridge
btw what does this limit even mean? the derivative at a-h ?
so this limit is exactly equal to lim f(a+h)-f(a)/h?
plucky python
i think it's easiest to see that
$\lim_{h \to 0} \frac{f(x+3h)-f(x)}{h} = 3 \big ( \lim_{h \to 0} \frac{f(x+3h)-f(x)}{3h} \big ) = 3 \big ( \lim_{h \to 0} \frac{f(x+h)-f(x)}{h} \big )$
jolly parrotBOT
LY
agile ridge
I know this but just not sure if they're still exactly the same after the subsitution a=a-h
plucky python
I know this but just not sure if they're still exactly the same after the subsit...
i think for this, break it up into 2 pieces
$\lim_{h \to 0} \frac{f(x+2h)-f(x-h)}{h} = \lim_{h \to 0} \frac{f(x+2h)-f(x)}{h} + \lim_{h \to 0} \frac{f(x)-f(x-h)}{h}$
jolly parrotBOT
LY
agile ridge
but after you split it up, the limit might exist while the components not have a limit
plucky python
but after you split it up, the limit might exist while the components not have ...
i'm not sure what u mean?
the limits exist bcus we know the value of the limits
agile ridge
i'm not sure what u mean?
like if you have a difference f(x)-g(x), then it may have a limit somewhere even if neither f nor g do
plucky python
like if you have a difference f(x)-g(x), then it may have a limit somewhere even...
but f and g do have a limit in our case
agile ridge
maybe I mixed smth up.. Ok so if this limit exist, can we deduce that f is diff at a?
btw does this limit ( in the pic) mean f'(a) also? Does this limit also exactly equal to lim f(a+h)-f(a)/h after the substition a=a-h? @plucky python
plucky python
btw does this limit ( in the pic) mean f'(a) also? Does this limit also exactly ...
well i'd do the substitution h' = -h
but yeah
plucky python
maybe I mixed smth up.. Ok so if this limit exist, can we deduce that f is diff ...
yeah i believe so
plucky python
btw what does this limit even mean? the derivative at a-h ?
what context did u see this in?
plucky python
u'd have to actually substitute it in
and then see that they work out to be the same
agile ridge
yea I know I mean for those valid substitutions? like the substitutions which transform the current form into the lim f(a+h)-f(h)/h form
agile ridge
what context did u see this in?
plucky python
yea I know I mean for those valid substitutions? like the substitutions which tr...
i'm not sure i understand ur question
plucky python
ah k
agile ridge
idk if this statement is true or not
plucky python
i think this statement should be true, but proving it isn't trivial
jolly parrotBOT
yalaw
plucky python
yh, that's just like limit laws
soft surge
How is e^(ln(5)*X) = 5^X?
pearl pondBOT
How is e^(ln(5)*X) = 5^X?
grim fractal
$e^{\ln(5) \cdot x} = (e^{\ln(5)})^x = 5^x$
jolly parrotBOT
Ari
stoic imp
Calculate $\dim , \text{Nu} , f$ and $\dim , \text{Im} , f$.
\begin{itemize}
\item[a)] $f: \mathbb{R}^3 \to \mathbb{R}^5$, \quad monomorphism
\item[b)] $f: \mathbb{R}^4 \to \mathbb{R}^3$, \quad epimorphism
\item[c)] $f: \mathbb{R}^4 \to \mathbb{R}^4$, \quad $f(x) = 2x$
\end{itemize}
jolly parrotBOT
ඞඞඞ
unborn abyss
is Nu nullspace?
stoic imp
yes the kernel
or something
is f a linear transformation?
or is it like a function
woeful stump
a linear transformation is a function
stoic imp
,w monomorphism definition
jolly parrotBOT
jolly parrotBOT
gleaming musk
Part 2
For x>0, n=2,3...., define $F_{n}(x)=f(x)-f(n-1)-\int_{x}^{n}\frac{1}{t^2f(t)}dt$. For each fixed n, prove that there exists a unique real number $a_{n}$ such that $F_{n}(a_{n})=0$. Does the limit for $a_{n}$ exist as n approaches infinite
jolly parrotBOT
Dootud
gleaming musk
Part 1 was to show for x>0, $f(x)=(1+\frac{1}{x})^{x}$ is strictly increasing
jolly parrotBOT
Dootud
pearl pondBOT
pearl pondBOT
Available help channel!
pine vortex
I need help with this
pearl pondBOT
I need help with this
autumn fossil
is it neither?
pine vortex
is it neither?
no, there is a solution
pine vortex
no those are all, I know the soultion but I dont understand why
I do even have a video explaining, bu its still a bit hard to get it
autumn fossil
whats their solution?
compact ridge
is it neither?
it's just n - 5 right
you can count upwards, so n - 11, n - 9 and so on
pine vortex
no its acutallay n-1
compact ridge
nearest to what is the question
pine vortex
pine vortex
nearest to what is the question
nearest to the larger odd integer
mayeb the translation is the problem, I made sure its right tho
autumn fossil
is it possible that they meant n-3 and n-13 is a typo?
compact ridge
oh
pine vortex
is it possible that they meant n-3 and n-13 is a typo?
it is a national test, so it cant be wrong
autumn fossil
I need help with this
this is translated, right?
can you show the non-translated version?
pine vortex
this is translated, right?
yea
pine vortex
ohhhh im sorryyy
autumn fossil
when you translated it, it changed n-3 to n-13 for some reason
pine vortex
yeaaa i see it now
autumn fossil
Anyway, let's arrange numbers around n-3 in a row
n-5, n-4, n-3, n-2, n-1, n, n + 1
those are all consecutive integers btw
now notice that odd and even integers alternate
1 is odd, 2 is even, 3 is odd, 4 is even, 5 is odd...
so since n-3 is odd, n-2 must be even
and then n-1 must be odd
n must be even
n+1 must be odd
....
do you follow till now?
O = odd
E = even
since n-3 is odd, n-2 must be even
because it has to alternate
pine vortex
do you follow till now?
Yeaa, I'm with until this point
autumn fossil
ok, so we're looking for the nearest larger odd integer
the next larger integer is n-2
but n-2 is even
so we have to look further
the next one is n-1
and that is odd
so it must be the nearest larger odd integer
pine vortex
I dont understand how you knew the next larger integer
autumn fossil
I dont understand how you knew the next larger integer
we always get next larger integer by adding 1
the next larger integer to 6 is 6+1 = 7
the next one is 7+1 = 8
the next one is 8+1 = 9
and n-3 + 1 = n-2
so the next larger is n-2
and then n-2 + 1 = n-1
and then n-1 + 1 = n
drowsy leaf
Wouldn't the distance be 10 units?
pearl pondBOT
Wouldn't the distance be 10 units?
wet swallow
Show your work
drowsy leaf
i mean I did it in my head
the slopes are the same
if one intercepts at -5 and one intercepts at 5
that's a distance of 5
wet swallow
Are you sure it's not the perpendicular distance you need
drowsy leaf
(0,5)
idk
one of the points of interception is (0,5)
obviously
But what do I do after that
wet swallow
Find the equation of the perpendicular line
wet swallow
one of the points of interception is (0,5)
Passing through this point
wet swallow
oh its -2x
👍
drowsy leaf
and we know one of the points that it goes through is (0,5) right/?
wet swallow
Now use the one point form
wet swallow
and we know one of the points that it goes through is (0,5) right/?
Yes
drowsy leaf
y-y1=m(x-x1)
wet swallow
Yes
drowsy leaf
so y-5=1/2(x-0)
wet swallow
Right
wet swallow
Yes
drowsy leaf
Now can you substitute 1/2x+5 for one of the points
to find the point it intercents
intercepts
wet swallow
to find the point it intercents
Yes
drowsy leaf
1/2x+5=-2x+5
wet swallow
You've probably got this
drowsy leaf
3/2x=0?
wet swallow
Wait
wet swallow
1/2x+5=-2x+5
We can't use this
drowsy leaf
why
wet swallow
We already know it passes through (0,5)
wet swallow
So we use the other line
drowsy leaf
so 1/2x+5=-2x-5
its still 0
wait
its -10
3/2x=-10
so its
x=6.666666666666666666
wet swallow
yes x=-4
drowsy leaf
(-4,3)
wet swallow
Yes
wet swallow
distance formula?
wet swallow
Yes
wet swallow
answer is sqrt 20
2√5
pearl pondBOT
If you are done with this channel, please mark your problem as solved by typing .close
wet swallow
If you are done with this channel, please mark your problem as solved by typing ...
@drowsy leaf
pearl pondBOT
@drowsy leaf Has your question been resolved?
stoic imp
Let
$S = \left{ \mathbf{x} \in \mathbb{R}^4 \mid x_1 + x_3 - x_4 = x_1 + x_2 + x_3 + x_4 = 0 \right}$
and
$T = \left{ \mathbf{x} \in \mathbb{R}^4 \mid x_1 + x_2 + 2x_3 + x_4 = ax_1 + bx_2 + cx_3 + dx_4 = 0 \right}$
Determine all real values of $a$, $b$, $c$, and $d$ for which the sum $S + T$ is not direct.
\end{document}
jolly parrotBOT
ඞඞඞ
stoic imp
if the sum is direct
aka S (+) T
then
S ∩ T = {0}
so if is saying
that the sum is not direct
then
they have a non trivial intersection
stoic imp
how do I do dat
stoic imp
how do I find the intersection
is like 4 equalities
are the four equations equal to zero
cam u tell me if thats true
no they are not
yes they are
all of them are equal to zero
solving the intersection would be equal to solving the system
lets form a system with the four equations and then translate it to a augmented matrix and solve
@hot stone
are you following?
hot stone
Sorry at work
hot stone
lets form a system with the four equations and then translate it to a augmented ...
Yes this is it
The conditions they told you give a set of linear equations
Stick them in an augmented matrix and solve to find the intersection
(My bad I'm likes popping in here between work stuff)
hot stone
Yea it looks ok i think i cant check carefully rn
As long as it agrees with the equations in the set conditions you should be good
stoic imp
ok
is just that
I really need you to check carefully
is like the only important step before we finish
stoic imp
is not that
I need you to check if the previous steps is fine before I rref into a matrix solver
becaaause
if its alright
then the matrix solver will spit the correct results
.closd
.close
pearl pondBOT
pearl pondBOT
Available help channel!
tawdry raft
how do i do this problem? i have de morgan's law for quantifiers in front of me but i don't know how to apply it
pearl pondBOT
how do i do this problem? i have de morgan's law for quantifiers in front of me ...
@tawdry raft Has your question been resolved?
tawdry raft
how do i do this problem? i have de morgan's law for quantifiers in front of me ...
this is what i got for part a, is it correct?
pearl pondBOT
@tawdry raft Has your question been resolved?
kindred light
how to open a help channel
pearl pondBOT
how to open a help channel
hallow cedar
yes
kindred light
This is the question
I am stuck
need help step by step solution may be written explanantion to atleast get the function drawn out
cant seem to draw it out
pearl pondBOT
need help step by step solution may be written explanantion to atleast get the f...
The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.
kindred light
Apologies
So I am stuck like getting to understand like how to graph it out
I can get the jist of it like plotting out the main points etc.
but not sure where to go from there
Its very easy
sorry apologies ignore the post but I will put a answer and let me know if its correct if anyone is watching!!
hallow cedar
why do you need to plot it?
hallow cedar
nws haha
pearl pondBOT
@kindred light Has your question been resolved?
kindred light
No
need help
<@&286206848099549185> wsp been 30 mins
Need to find insight on the inverse
chatgpt says the inverse is the exact same as d + r but i remember it cant be
.close
pearl pondBOT
pearl pondBOT
Available help channel!
unique oracle
Just wanted to know if I did well or nto
pearl pondBOT
Just wanted to know if I did well or nto
@unique oracle Has your question been resolved?
supple citrus
In part a in the answer scheme we use permutation and b we use combination, but how am I suppose to know if its permutation or combination because the question are so similar "How many different codes?" "Find the number of codes" it seems same to me..
cyan lily
does order matter?
supple citrus
uhh in b i guess not since its just numbers
supple citrus
does order matter?
but i dont know about a
cyan lily
but i dont know about a
is ab1111 the same as ba1111?
pearl pondBOT
pearl pondBOT
Available help channel!
spice nest
What am I doing wrong for this question?
pearl pondBOT
What am I doing wrong for this question?
spice nest
Answer for blank: #1 2/9 is my answer btw
are the vertical and horizontal asymptotes both 2/9?
fossil drum
how did you solve number 1
spice nest
and the point of discountinuity (5,13/43)?
spice nest
how did you solve number 1
asking me?
spice nest
I simplified it to:
((2x + 3)(x-5))/((9x-2)(x-5))
cancelled out x-5
9x - 2 != 0
x != 2/9
fossil drum
seems right to me
spice nest
and for the horizontal asymptote since the degrees are the same it is the ratio of the leading coefficenents
2/9
I am just gonna guess it's some formating issue
I just wanna make sure I am correct in believing that
fossil drum
yeah the horizontal is 2/9
pearl pondBOT
pearl pondBOT
Available help channel!
supple citrus
in 14(b) why dont we divide by the number of repeat?
pearl pondBOT
in 14(b) why dont we divide by the number of repeat?
heady finch
supple citrus
😢 8! / (2! x 3!)
snow sail
in 14(b) why dont we divide by the number of repeat?
the word "different", presumably
meant here to mean "distinct"
snow sail
😢 8! / (2! x 3!)
anyways this is counting incorrectly
youd want to divide by 2! or 3! to remove an overcounting where you are considering actually identical outcomes as distinct
but since youre using 8!, you've already forcibly grouped the R's and the E's together, by only counting RR and EEE as a single letter
there's nothing that needs to be removed
supple citrus
Ohh okay thank u i got it it was explained well 😊
snow sail
supple citrus
.close
pearl pondBOT
supple citrus
@snow sail can you help me with the (a) as well? why isnt it 6! x 3! x 2! ?
snow sail
.reopen
pearl pondBOT
✅
snow sail
You understand that this is identical more or less to asking how many ways we can select 6 people from the 9 to go in the first group?
snow sail
<@331558346333224964> can you help me with the (a) as well? why isnt it 6! x 3! ...
usually if youre using factorials in means you're considering order, i mean its a rough rule of thumb, but you should use choose here
supple citrus
ahh sorry i get confused about when to use factorial or permutation/combination.. i can usually tell whether to use permutation or combination because they depend on order but factorial confuses me
snow sail
factorial is best for dealing with problems where order matters
supple citrus
so if we can put any people in 6 it means order matters and we wont use factorial :-]?
doesnt*
snow sail
theres no reason to use factorial since it doesnt seem like order matters
if you use factorial anyways, and get the answer right, youll have to reconstruct binomial
pearl pondBOT
pearl pondBOT
@mental bluff Has your question been resolved?
remote rivet
raw crater
I used both trig sub and u sub to find the answer to this question but they gave me different answers. When I plugged in the question into an integral calculator, it showed u sub as the method to get the right answer. This question was on my test and I got it wrong because I didn’t use trig substitution. Can someone help me understand which method to use and the correct answer?
pearl pondBOT
I used both trig sub and u sub to find the answer to this question but they gave...
@raw crater Has your question been resolved?
pearl pondBOT
pearl pondBOT
Available help channel!
royal gull
When using lagrange interpolation to write a quadratic equation, and i have one negative x and one positive x, say -3 and 2, is it (x - - 3) (x - 2)?
loud garnet
@raw crater you still need help?
pearl pondBOT
@royal gull Has your question been resolved?
royal gull
<@&286206848099549185>
mossy drift
When using lagrange interpolation to write a quadratic equation, and i have one ...
yeah
u can just write the (x--3) as (x+3)
royal gull
(x—3) is x+3 right
mossy drift
no (x-(-3)) is (x+3)
mossy drift
yes
mossy drift
ye pretty sure the answer is -4
mossy drift
ok gimme a sec
mossy drift
g(x)=2x^2 -6x+4
h(x)=-2x^2 +10x -12
j(x)=3x^2 -12x +9
are you sure u gave me the right equations
the only matching answer i got was of g(x)
royal gull
Ok for h(x) its 8=(x - - 3) ( x - 2)
So x= 1 , ( 1 + 3) (1-2)
(4)(-1)
=-4
then i divided 8 by -4
which makes -2
go back to (x - -3) (x -2) and this time multiply them which is
x^2 -5x + 6
multiplied by the -2
so = -2x^2 +10x -12
did i do something wrong during that
mossy drift
picture of the whole thing
pearl pondBOT
@royal gull Has your question been resolved?
pearl pondBOT
@royal gull Has your question been resolved?
candid steppe
Function problem
pearl pondBOT
Function problem
candid steppe
The value of x is 3x^2 - 4x +1
candid steppe
bracketing is important
Can you check my work?
cosmic charm
you cant do this
3 and (h+3) have different exponents
expand (h+3)² first then distribute
candid steppe
expand (h+3)² first then distribute
cosmic charm
,rccw
jolly parrotBOT
jolly parrotBOT
cosmic charm
candid steppe
+16 i mean
candid steppe
Hmm?
cosmic charm
distribute your signs properly please
candid steppe
Ohh 3h
pearl pondBOT
@candid steppe Has your question been resolved?
pearl pondBOT
pearl pondBOT
Available help channel!
rare niche
Hello! May I ask if this is correct?
pearl pondBOT
Hello! May I ask if this is correct?
midnight haven
should be -x in the numerator instead of x
midnight haven
ur way of doing the rest seems fine
quartz ermine
pearl pondBOT
quartz ermine
i managed to do part a
but how do you do part b?
any tips?
should i sub in z = a + ib and w = c + id
rough forge
should i sub in z = a + ib and w = c + id
looks like a good start
quartz ermine
im just going in circles tbh
i ended up saying that bd = -ac
but not sure how that helps
rough forge
how did you end up there?
quartz ermine
i made it zw* + z*w = 0
quartz ermine
should i sub in z = a + ib and w = c + id
and then subbed this in
rough forge
and then subbed this in
Hmm I think there might be something
If we use the assumption and square both sides
You end up with 4zw = 0
You can also divide by 4w² since it's not 0
z/w = 0
And now when we use z = a+bi and w = c+id
dusky scaffold
quartz ermine
i didnt ask m8
dusky scaffold
take a peek lil bro
z/w equals the negative of its own conjugate
what does that say about z/w ?
quartz ermine
im not answering your questions
quartz ermine
because ur violating
dusky scaffold
quartz ermine
hardstuck
bro its like my first week in maths idc
i didnt sign up for proofs but its compuslory in year 1
rough forge
bro its like my first week in maths idc
if they get you on your nerves you can just ping mods
dusky scaffold
*her
dusky scaffold
what does that say about z/w ?
???
pearl pondBOT
@quartz ermine Has your question been resolved?
pearl pondBOT
pearl pondBOT
Available help channel!
sudden badger
pearl pondBOT
sudden badger
Find the value of n so that the identity is true
silent bramble
how is it true that Arg (z1-z2/(z3-z4))=+-pi/2 iff z1 and z2 (making line l) is perp to z3 and z4 (making line L)
silent bramble
because its arg(z1-z2)-arg(z3-z4), the angle is theta1-theta2
oh
would you use angles 0 to 2pi?
so like pi/2-0, pi-pi/2, 3pi/2-pi, 0-3pi/2
giving pi/2, pi/2, pi/2, and -pi/2 as the answers
or is there any sort of restriction?
I dont think there is a restriction
it doesnt have to be limited to 0-2pi
it could literally be like 3pi-5pi/2 and it would still work
lost flax
it could literally be like 3pi-5pi/2 and it would still work
Usually with arguments of complex numbers you just consider -3pi/2 to be the same as pi/2, et cetera
silent bramble
oh ok
lost flax
And angles are determined up to adding an integer multiple of 2pi
silent bramble
right because theres this rule where its like -pi<argz<=pi right?
lost flax
right because theres this rule where its like -pi<argz<=pi right?
You can choose any version of that rule
There is also 0 <= arg z < 2pi
As long as the length of the interval is 2pi and only one of the limit points is allowed, it works
And that gives the principal argument
But adding a multiple of 2pi gives another argument, which will not be principal
pearl pondBOT
@silent bramble Has your question been resolved?
silent bramble
im just gonna stay for now in case of more q
pearl pondBOT
@silent bramble Has your question been resolved?
silent bramble
how can you find the angles for (1-i)(-sqrt(3)+i)
I did cos theta= (-sqrt(3)+1/(2sqrt(2))
sin theta =(1+sqrt(3)/2sqrt(2))
tried tan theta = (b/a) too, (b being (1+sqrt(3)...)
I tried multiplying denom by (c-d) if the denom is (c+d)
I cant get a good value to solve for theta
I guess its a case for calculator
for some reason I keep getting 5pi/12 but its 7pi/12
oh all good
main oxide
oh all good
oh did you get it or you still need help on this? ping me if you respond
silent bramble
Yess I need help w another q
question says given z, interpret geometrically the vector (cos phi + i sin phi)z
some things I wrote but how do I interpret?
@main oxide
I also have the answers if you want to refer to it
main oxide
some things I wrote but how do I interpret?
I'm guessing they mean, geometrically what does it look like?
silent bramble
yea
main oxide
so for instance if you have the vector z and then multiply it by i, what does iz look like?
main oxide
I'm a little confused by your steps but I think you're close to what it should be with the algebra
main oxide
im not sure
does it stretch or rotate z at all?
silent bramble
idk i dont think I learnt this before
main oxide
for instance if I have the vector z and multiply by 3, then 3z is the same direction as z, but stretched 3 times in length. Similarly, iz changes what z looks like by a stretch or rotation
silent bramble
Its usually plotting but you're given a z and you expand
main oxide
let's pick an example to graph
z=3+4i graph this and then work out what iz should be and then graph that. did it get longer or shorter? Did it rotate if so by what angle?
silent bramble
main oxide
ok good so far, now what's iz and graph it on the same picture
main oxide
yeah perfect
this is a special case of what you were asked to show multiplying z by (cos phi + i sin phi) but picking phi = pi/2
in general geometrically this is what you get, it rotates the vector by the angle phi
main oxide
so it roated counterclockwise by pi/2
to see a bit more from this specific case, if you rotate 90 degrees four times, you end up back where you started right?
similarly i^4 = 1 if you were to multiply i^4 * z = z
hopefully that helps to see the connection between the rotations in the picture and the algebra a bit more
main oxide
yeah you're welcome!
pearl pondBOT
@silent bramble Has your question been resolved?
silent bramble
how is 2^12(e^(i6pi)) simplified to 2^12?
silent bramble
i don’t know how to simplify further, because there’s no standard angle for (2+5pi/2)
@main oxide
main oxide
that's ok, not every angle has to be a perfect rational multiple of pi
silent bramble
how is 2^12(e^(i6pi)) simplified to 2^12?
this one I got!
yea but solution for b) is e^2 i
so theres prob a good way to simplify
ohh
yes
e^2i(e^i5pi/2)
e^(i5pi/2) is e^0 so 1
okok
main oxide
wait that doesn't look quite right
you added an i on the 2
it's just e^2 not e^{2i}
silent bramble
oh
main oxide
so if you're thinking re^{i theta} then r=e^2 and theta = 5pi/2
silent bramble
yup!
main oxide
cool cool
silent bramble
thank you!
main oxide
yeah you're welcome
main oxide
what is this weird squiggly symbol called
ah greek letter zeta $\zeta$
jolly parrotBOT
Merosity
main oxide
why is b false?
hint: think about what happens when you make a full rotation
silent bramble
but e^z means e^x(e^(iy)) and you cant have i to the power of anything
so theres not going to be a rotation?
oh you mean the argument?
main oxide
so theres not going to be a rotation?
ah there is part rotation and part scaling
the e^{iy} part is the rotational part and e^x part is the scaling part
so to break one to one, I'm picturing doing two different rotations that end up landing you in the same place
main oxide
oh you mean the argument?
yeah I think so, I forget the terminology here like "modulus" and "argument" tbh lol
just fancy words for length and angle to me
silent bramble
you mean angle?
silent bramble
so to break one to one, I'm picturing doing two different rotations that end up ...
so just y would be say, 2pi?
main oxide
yeah exactly
silent bramble
ok ill be back in like 2hrs
pearl pondBOT
@silent bramble Has your question been resolved?
pearl pondBOT
@silent bramble Has your question been resolved?
pearl pondBOT
pearl pondBOT
Available help channel!
main void
would this use the washer method to find the volume?
pearl pondBOT
would this use the washer method to find the volume?
main void
im guessing it is integral from 3 to 7 (25/16x^2 - 9) dx
but i got a negative number so i don't think its correct
pearl pondBOT
@main void Has your question been resolved?
faint mica
Idk if you call it the washer method but personally I have like a rule of thumb
Shell method and disc method
I'm guessing disc method is washer method
I tend to use disc method when rotating around horizontal lines and shell method otherwise
Since you're going around the y-axis here it makes more sense to use the shell metbod
pearl pondBOT
@main void Has your question been resolved?
pearl pondBOT
pearl pondBOT
Available help channel!
wicked flicker
So for this problem, my answer was <-y^3/3, x^3/3>
pearl pondBOT
So for this problem, my answer was <-y^3/3, x^3/3>
wicked flicker
I simply sorta reverse curled it, are both these answers correct? Or am I doing smth wrong?
pearl pondBOT
@wicked flicker Has your question been resolved?
pearl pondBOT
@wicked flicker Has your question been resolved?
pearl pondBOT
@wicked flicker Has your question been resolved?
slow plank
I've done 3/4 of the step but I don't understand the last step
midnight haven
I've done 3/4 of the step but I don't understand the last step
find k1, k2 by putting given values in above equations
uncut timber
pearl pondBOT
uncut timber
how to
round patio
I'mma try this
uncut timber
th
round patio
I'll try Feynman
pearl pondBOT
compact ridge
ah okay
pearl pondBOT
Available help channel!
slow plank
I found the value of k but not the value of x^2
pearl pondBOT
I found the value of k but not the value of x^2
placid zealot
so
it says y varies inversely as the cube of x
do you know how to express that as an equation?
slow plank
Yes
slow plank
,
placid zealot
good
slow plank
Now what
placid zealot
yep
slow plank
Uhhh
placid zealot
rearrange to isolate x
north talon
how many ways can a row of n people be arranged?
pearl pondBOT
how many ways can a row of n people be arranged?
north talon
would it be nC2
north talon
yeah
north talon
yes
autumn fossil
would it be nC2
(This would be the number of ways to choose a pair out of n people)
north talon
oh
north talon
so what does a factorial do?
uhhh number of ways to arrange n objects
north talon
oh
placid zealot
got it?
north talon
n! ? 😭
north talon
yeah
placid zealot
great
north talon
I’m so bad at this permutation stuff lmao
placid zealot
lol