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#help-10
obtuse pebbleBOT
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molten bay
obtuse pebbleBOT
molten bay
help please?
hybrid gull
PQ is the length of a line segment on the number line.
Both P and Q are at numbers on the number line.
Try drawing a picture of a number line and label the information you’re given
obtuse pebbleBOT
@molten bay Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
pearl rover
assuming r is an scalar and A a matrix, why doesn't det(rA) = rdet(A)?
obtuse pebbleBOT
assuming r is an scalar and A a matrix, why doesn't det(rA) = rdet(A)?
mental solstice
how does determinant act under a row operation?
pearl rover
if a row is multiplied to get A its det(B) = kdet(A)?
obtuse pebbleBOT
@pearl rover Has your question been resolved?
lusty cedar
and what happens if you multiply a matrix with a scalar?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
granite prairie
obtuse pebbleBOT
rugged kite
what is the question here
granite prairie
Simplify
rugged kite
Get rid of that ugly fraction of fractions and see where it gets you
Recall what the reciprocal of a reciprocal is
granite prairie
is the LCM x(x + 1)
astral ivy
Yeah
granite prairie
yea im completely lost
proven sleet
granite prairie
can you expain to me how 1/x - 1 goes to 1-x/x
hexed plank
= 1/x - 1
= 1/x - x/x
as the denominator is common here ('x')
= 1-x/x
@granite prairie
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
jaunty lance
Hey I have a physics related question. I hope that it is okay, since it is pretty simple.
For torque of an object, it is described as Torque = r * F. For the r vector, if you imagine a book exceeding maximum overhang at the edge of the table, how would you measure the r vector?
The book is uniform. I hope it makes sense
obtuse pebbleBOT
Hey I have a physics related question. I hope that it is okay, since it is prett...
@jaunty lance Has your question been resolved?
glossy ibex
Hey I have a physics related question. I hope that it is okay, since it is prett...
r is where the force is applied relative to the axis of rotation, that would be the edge of the table
the book will rotate around its center of mass, so i think r should start there
jaunty lance
the book will rotate around its center of mass, so i think r should start there
Okay perfect. One question;
would R be the distance from the pivot point, in height and in length, or would it only be the horizontal distance from the pivot point?
Aka which r value is the correct one here?
glossy ibex
r1, from the centroid to the edge of the table
jaunty lance
okay super. but then to calculate torque, you need torque = r * F * sin(theta)
but if R isnt horizontal, then the angle theta between Fg and r1 isnt 90 degrees?
jaunty lance
ah yes correct
glossy ibex
reaction force
jaunty lance
I am just very confused because of this problem that my teacher sent out...
2 seconds
Figure 8: Should a block balance, then the center of mass must be supported Which
is the case in a) and b) but not in c). In situation a) the moments of force are from gravity
and the normal force equal and opposite. In situation b) the arm is equal to zero, then
the torque is equal to zero and in situation c) the arm is at the torque of normal force
equal to zero and for the moment of gravity the arm is equal to r sin (90◦
) The total
torque causes the block to tip clockwise (τ will point into the paper).
this is directly translated, sorry if it doesen't make complete sense
glossy ibex
ok thats different to what i pictured
jaunty lance
but in situation b, he says the arm is equal to zero?
but clearly there is a vertical distance between CoM and the pivot point
for Fg
but not for Fn
glossy ibex
idk why your teacher assumes that the book will pivot around the edge of the table
without friction it will slide
jaunty lance
what situation are you talking about right now?
jaunty lance
But I don't understand situation b, and with his argumentation, why it wont pivot?
wait
nvm
glossy ibex
it wont because sin(0)=0
jaunty lance
yes exactly haha sorry
one last thing
the r vector, does it go from CoM to pivot point when calculating for torque aswell?
for the normal force
glossy ibex
use the vectors as shown in the diagram
torque = r×F_t, with r going from table edge to CoM
jaunty lance
okay woah i really need to learn this stuff
but the material available is so horrible
glossy ibex
really the question is asking you: how much torque does this force contribute assuming the contact point is fixed in place?
jaunty lance
I don't really understand the question, I'm sorry my english isn't really all that great
are you saying if the contact point is like stuck, so the object cannot move?
like as if it was glued to the edge of the table?
glossy ibex
yes, that makes it the pivot point akin to a lever
i know a good video on this, hold on
obtuse pebbleBOT
glossy ibex
ill send you the vid soon @jaunty lance
jaunty lance
oh okay okay I'm sorry haha
obtuse pebbleBOT
Available help channel!
distant cave
If sin(a) = p, 3π/2 < a < 2π
obtuse pebbleBOT
If sin(a) = p, 3π/2 < a < 2π
distant cave
Oh!
That's true
What about the denominator?
Negative square = positive
So I think it'll be positive
spiral maple
???
distant cave
If p = negative, then p^2 = positive
distant cave
.close
hasty folio
Need help with number 1
obtuse pebbleBOT
Need help with number 1
hasty folio
so i got the 2 other angles for the triangle with 55 degrees
the angles are 35 and 90, but I don't know how that can bring me to alpha
.close
pine sail
Consider p(x)= $(c-5)x^2-2cx+(c-4), c≠5$ \newline
Let S be the set of all integral values of c for which one root of p(x)=0 lies in the interval (0,2) and it's other root lies in the interval (2,3). Then the number of elements in S is
obtuse pebbleBOT
Consider p(x)= $(c-5)x^2-2cx+(c-4), c≠5$ \newline
Let S be the set of all integr...
warm shaleBOT
Sakata Yaksha
pine sail
So like I did $(c-5)(p(2))<0$
warm shaleBOT
Sakata Yaksha
pine sail
Then I did, $0< \frac{2c}{c-5}<3$
warm shaleBOT
Sakata Yaksha
pine sail
And took intersection, my answer however does not match to the correct one, did I miss something perhaps?
My final answer is $5<c<15$
warm shaleBOT
Sakata Yaksha
obtuse pebbleBOT
@pine sail Has your question been resolved?
pine sail
pine sail
Oh lol.
You're helping me
I forgot
I thought you were asking something of your own.
So integral value means a value which is integer.
pine sail
Yeah
true rain
Have you tried solving quadratic equation and restraining there
pine sail
Solving the quadratic equation, you mean using quadratic formula?
true rain
Yeah that’s what I mean
pine sail
That makes no sense does it?
true rain
Your constraint is on the two roots, no?
true rain
I mean like there’s only one way to find out
I personally would then break it into two restraints for the /pm
Try to bound them
Get a range for c for each one
gloomy valve
No it's not that hard
pine sail
Well if the roots are between 0,2 and 2,3 the roots are basically in interval (0,3) therefore p(2) is negative.
Then sum of the roots also lies in the interval (0,3)
I used stuff like This
gloomy valve
the roots in terms of c will be an increasing function for the smaller root and a decreasing function for the bigger root
pine sail
How would that be?
gloomy valve
If you use the quadratic formula it simplifies quite nicely at the end, imo
pine sail
I see, I'll try that then.
But then I'll have two roots. Which one do I put in first interval lol.
If that's how we're doing it.
gloomy valve
the terms for the roots just differ by a minus sign
so the bigger root corresponds to the term with the positive sign
gloomy valve
write it out
pine sail
p+q>p-q are you implying?
pine sail
write it out
Okay yeah my bad XD.
gloomy valve
p+q>p-q are you implying?
No, if you apply the quadratic formula you'll get x_1 and x_2, the two roots in terms of c, only. x_1 = u(c) + v(c) and x_2 = u(c) - v(c). Something like that should come out
v(c) is a square root so that can only be positive
unless you deal with complex numbers
pine sail
$\frac{2c±\sqrt{4c^2-4(c-5)(c-4)}}{2(c-5)}$
warm shaleBOT
Sakata Yaksha
gloomy valve
I got $x_{1,2} = \frac{c}{c-5} \pm \sqrt{\qty(\frac{c}{c-5})^2 - \frac{c-4}{c-5}}$
warm shaleBOT
Navix
warm shaleBOT
Navix
pine sail
Alright, I'm back.
So, this is correct.
Even then
There's no way to say the one with plus sign is larger root.
Obviously.
gloomy valve
why not?
pine sail
Bruh.
gloomy valve
well split into two cases: c > 5 and c < 5
pine sail
well split into two cases: c > 5 and c < 5
Now you're talking.
But truly mate, this is too much work I'd say.
I'll try it this way too definitely, could you find an error in my calculation and stuff too for reference? I'd appreciate it.
gloomy valve
Yea, I'll work it out this way and show you if you want, as well
pine sail
Yes, so first we'll finish it this way.
For c>5 the denominator is always positive, and so is numerator.
C≥20/9
This we have to always keep in mind as well.
So case the two cases would be c>5
second 29/5≤c<5
But cases for what?
It's not like we have any RHS.
gloomy valve
What I did was notice that the term is an increasing function on c > 5.
So we should be able to simply set it equal to the endpoints?
of the root boundaries
pine sail
Basically the minimum value for the function should lie in interval (2,3)?
gloomy valve
That's what I thought
basically for c > 5 the smaller root in (0,2) will be the term with the minus sign. so to find the bounds for c we can simply set this term equal to 2 and 0 and solve for c.
because it's increasing, that should also correspond to the interval for our feasible values for c
sterile wyvern
A quick solution comes from just setting $$p(0)p(3)>0 \land p(0)p(2)<0,$$ which gives $13 \leq c \leq 23$
warm shaleBOT
Mat
pine sail
A quick solution comes from just setting $$p(0)p(3)>0 \land p(0)p(2)<0,$$ which ...
That's what I was talking about.
I did p(2) part, but not p(0)p(3) thingy.
gloomy valve
Agree, that's pretty neat
pine sail
Yes, this is the only way I do these, unfortunately my sol was lacking as you can see.
That was nice, thanks mate.
.close
obtuse pebbleBOT
pine sail
.reopen
obtuse pebbleBOT
✅
sterile wyvern
Np! Yeah we were basically on the same idea
timid silo
obtuse pebbleBOT
timid silo
Find if convergent or divergent
jaunty lance
use the integral test. Take the integral of that series and see if the value of the integral is fixed or if it goes towards infinity.
last leaf
Find if convergent or divergent
What is the behaviour of $n\mapsto \sqrt{n+100} - \sqrt{n}$?
warm shaleBOT
Guilhem
last leaf
Oupsie, I didn't mean to interrupt 🌼
timid silo
Whats mapsto?
jaunty lance
Oupsie, I didn't mean to interrupt 🌼
nonono just continue onwards, you didn't interrupt
last leaf
Don't you see the LaTeX?
jaunty lance
I am the one who answered without being allowed to😈
last leaf
**Guilhem**
This
I don't think integrals are appropriate here... What is $(-1)^t$ where $t\in \mathbb{R}$?
warm shaleBOT
Guilhem
timid silo
Don't you see the LaTeX?
Uh i dont know that notation sorry
last leaf
Well I have a bot that makes things look nice
jaunty lance
Uh i dont know that notation sorry
do you not see the bot message from TeXit BOT
timid silo
do you not see the bot message from TeXit BOT
I dont know that symbol from the bot bro
warm shaleBOT
Guilhem
timid silo
It decreases i think
sterile wyvern
,align \func{f}{&\mathbb{N}}{\mathbb{R}} \ & n \mapsto f(n) = \sqrt{n+100} - \sqrt{n}
warm shaleBOT
Mat
last leaf
Nice !
sterile wyvern
It's a symbol used for functions!
timid silo
It's a symbol used for functions!
Ok
last leaf
It decreases i think
No.
It is often simpler to use functions. What is the behaviour of $f(t) = \sqrt{t+100} - \sqrt{t}$ ?
warm shaleBOT
Guilhem
timid silo
It is often simpler to use functions. What is the behaviour of $f(t) = \sqrt{t+...
Its coming decreasing for me
timid silo
Ok
timid silo
What is its limit?
Zero
last leaf
Yes. So what is the behaviour of your series?
last leaf
Allas, there is an oscillation due to $(-1)^n$ !
warm shaleBOT
Guilhem
timid silo
Allas, there is an oscillation due to $(-1)^n$ !
Yes
last leaf
So the behaviour isn't obvious
Maybe the oscillation is not enough prevent the series from going to infinity, maybe it is just perfect to make it converge...
timid silo
Yes
sterile wyvern
$\sum a_n $ converges $\implies \lim_{n \rightarrow \infty} a_n = 0$
warm shaleBOT
Mat
last leaf
Exactly!
timid silo
Yea
last leaf
So in fact the jump at each step if too big to have a convergent series !
timid silo
How do we know that?
last leaf
Because the terms go to infinity, so each step, the series makes a big 'jump'
So it cannot converge to a finite value, because otherwise it would oscillate around
But far around
sterile wyvern
The implication above is equivalent to \
(It is not true that $\lim_{n \rightarrow \infty} a_n = 0$ ) $\implies \sum a_n $ does not converge
warm shaleBOT
Mat
timid silo
So it cannot converge to a finite value, because otherwise it would oscillate ar...
How?
Why would it oscillate far around?
last leaf
Because, for example, the terms will be greater than $1$ after a certain $n$. Each step, you add or subtract a certain quantity depending of the sign of $(-1)^n$. So, after some time, you begin to jump more than one unit left and right in turns
warm shaleBOT
Guilhem
last leaf
This violent change of direction makes it impossible to converge!
idk if this is clear 🥳
If the series was convergent to a certain limit $l$, it would not leave the segment $[l-1/2 ; l+1/2]$ after some time. But we've shown that it does!
warm shaleBOT
Guilhem
last leaf
Why would it oscillate far around?
.
timid silo
If the series was convergent to a certain limit $l$, it would not leave the segm...
Oooh
Ok
Got it
Thank you
last leaf
Derien, c'est toujours un grand plaisir !
timid silo
?
last leaf
You are welcome!
sterile wyvern
Ahah even more obscure than LaTex
sterile wyvern
Derien, c'est toujours un grand plaisir !
.
timid silo
Derien, c'est toujours un grand plaisir !
Haha it was french
I got it now
sterile wyvern
Lol
hasty linden
why is it - when doing the derivitive?
obtuse pebbleBOT
why is it - when doing the derivitive?
hasty linden
line yprime =
cedar lichen
Chain rule
main cargo
A question reads:
obtuse pebbleBOT
A question reads:
main cargo
what does that mean?
the first quadrant bounded by curve
(its a volumetric revolution around y axis curve)
is the '1st quadrant' just top right quadrant or something?
hybrid gull
The curve will be a border to the region in question
hybrid gull
is the '1st quadrant' just top right quadrant or something?
Correct
spiral maple
yes
main cargo
ah alright, didnt know that.
spiral maple
(+,+)
(-,+)
(-,-)
(+,-)
hybrid gull
(+,+)
(-,+)
(-,-)
(+,-)
This
(1 at the top, 4 at the bottom)
obtuse pebbleBOT
civic heron
++
obtuse pebbleBOT
Available help channel!
kindred mango
obtuse pebbleBOT
kindred mango
can someone explain how he reindexed the sum
alpine raven
kindred mango
why is it that the n + 2 goes to just n
obtuse pebbleBOT
@kindred mango Has your question been resolved?
restive swift
Technically, the upper bound of the first sum says „k=n+2“ just like in the lower bound with „k=2“, meaning your sum goes from „k=2“ to „k=n+2“, but people just write „n“ for convenience. So, in your first sum it says „k=n+2“ in the upper bound, but because of the substitution, your sum uses l=k+2. The lowest k is 2, meaning the new lower bound is l=k-2=2-2=0. Since the old „highest“ k was k=n+2, we now have l=k+2=(n+2)-2=n, so we have the new sum going from l=0 to l=n
kindred mango
that makes sense. thank you
warm shaleBOT
spiral maple
Post your working for the question you're asking about
So attempt it first
then ask for help
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
ello
true rain
what's the issue here
true rain
where is the function negative
tranquil crag
just confused on what its asking for
Derivative of a function can be interpreted as when the function increases or decreases
So if the question is if a derivative is positive or negative, you need to ask where the function increases or decreases
timid silo
ok so
wait
i think i got it
it decreases
from
-inf to -2
then increases from
-2 to inf
so if i were to write that in interval notation itd beeee
-\infty
tranquil crag
Yes, but 2 important notes
timid silo
not letting me put the inf sign
tranquil crag
Firstly you measure x values, second when there is sharp point there is no derivative on that point
tranquil crag
I would say so, with -1 not belonging to any interval
tranquil crag
Yes
timid silo
so for the first question itd be none?
or neg infinity ?
im personally feeling neg inf
and for positive values itd be just pos inf
because it contineus on
continues*
tranquil crag
Probably neg inf but I dont know if your program does not let you or if they actually ask for something else
timid silo
it wants me to answer in interval notation
wouldnt it just be like
isnt interval
[-1,inf)
or is that
tranquil crag
Well, I said that it cannot involve [-1 as -1 is not part of it
timid silo
oh right
so 0 then
[0,inf)
andddd
[0,-inf)
i hate math why is this so confusingggg
timid silo
ohhh
tranquil crag
( indicates that the number following it does not belong. [ indicates it does
tranquil crag
Very close, numbers are meant to be in growing order, so (-inf,-1)
tranquil crag
Okay, so we have (-inf,-1) and (-1,+inf)
Which one you think has positive derivative and which one has negative?
timid silo
negative derivative is (-inf, -1) and positive is (-1,+inf)?
if thats wrong
i swear..
tranquil crag
I would say so as well
timid silo
lets gooooo
i have 2 more problems on this practice exam :DDDD so close
wait @tranquil crag you think you can help on these last two
or are you busy
tranquil crag
wait <@!761596368610656287> you think you can help on these last two
Avaliable, sure, send away while you have a channel avaliable 🙂
tranquil crag
Okay, and it is a practise exam, not a real deal, right?
timid silo
oh yeah its practice
theres a total of 30 question on it
questions*
and youve guys helped me out so far withhh 3
the real exam is wednesday
plus the actual exam is proctored and in person
tranquil crag
You need to use derivative theorem
And find a and b for which limits from -inf to 4 and from 4 to inf are the same
I can't help much more on that topic, maybe someone else can
timid silo
well thats a lot of options
well we can skip that one i have another one
actually the last one
here we go
i know for this one youre supposed to substitute
f(a+h) and f(a)
tranquil crag
I think this is reverse of the previous one
timid silo
of the one i just sent or the one we did
tranquil crag
The one you just sent
timid silo
fack
so no help D:
should i close
and reopen another one
or just hope someone comes in here
.close
warm siren
obtuse pebbleBOT
warm siren
hello im checking for lhopitals rule here and found to have inf/inf
so now i know im supposed to take the derivative of the original, how do i do that with ln?
warm siren
so the whole thing wil be 1/inf?
wary vigil
yes
you can actually see that in the original thing
because x goes up much much faster than ln x
it will become bigger and bigger compared to ln x
warm siren
okay so will I put 0 as my answer since the number can be very small?
wary vigil
meaning it will go to 0
wary vigil
i feel like you should be able to find that 1/x is the derivative of ln x from that
but i'm not entirely sure
chrome mesa
what would i plug in for x and h?
Why would you plug in x
warm siren
oh right, so i would get (f(x+inf) - f(x))/inf
right? im kind of confused where the ln x went
chrome mesa
Which problem are we talking about rn
warm siren
its pinned
frosty spoke
okay do you actually need to prove that d / dx ln x = 1/x
or can you just state it
I feel like you can just state it
warm siren
yea but im unsure of how i get it in case its on a test or something
should i just have to remember it?
chrome mesa
You should know that logb'(x) = 1/(ln(b) x)
frosty spoke
should i just have to remember it?
well, remember that the derivative of ln x is 1/x is actually really helpful
like logarithmic differentiation and all that stuff
not a tough one to remember
the proof is considerably worse
warm siren
okay so i'll just remember that ln x is 1/x
chrome mesa
You should remember the derivative of any log
frosty spoke
eh the rest are easy to figure out
warm siren
what are the rest?
frosty spoke
log_b x = ln x / ln b
chrome mesa
It's easier just to remember the general derivative for logs and recognizing ln e is 1
imo
obtuse pebbleBOT
wary vigil
@warm siren
chrome mesa
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
somber inlet
Hi, I'm stuck on this question (namely C and D), I don't really know what to do
somber inlet
For C I've already gotten the sum of 11/500 and 19/500 which is 3/50 in simplified form, but I don't know what to do next
wary vigil
to get the amount of times the mass of the steel is compared to the other mass?
somber inlet
Yeah, idk how exactly to get to that
wary vigil
well we know that the mass of the steel is 47/50 times the mass of the coin
and you've calculated that the combined mass of the others is 3/50 times the mass of the coin
which means that the amount of times the mass of the steel is in terms of the mass of the combined others is
one divided by the other
at least that's how i read the question
i hate text questions 😄
somber inlet
Me too, lemme just read what you said again
So is it the mass of the steel decided by the combined mass of the others?
wary vigil
that's what i read the question as
somber inlet
Idk if this counts as asking for the answer but that would look like
47/50 divided by 3/50
=47/50 x 50/3 right? If this is kinda asking for the answer dw about answering it
wary vigil
yes that's how you could write it
somber inlet
Okay I think I know how to do C
And then D is just 4.4 x 40 divided by the mass of the nickel?
wary vigil
i read d as
the difference in mass of the copper in the 40 4.4g coins compared to the nickel in the coins
somber inlet
Ohh okay
Thank you!
I'm gonna close the channel now, tysm and have a nice day
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
brisk arrow
obtuse pebbleBOT
brisk arrow
Okay just look at the statistics, it’s a question about calculation
The purple underlined get me fked up, cuz it’s different from what I had
Here’s my attempt
Oh I see the problem
.close
obtuse pebbleBOT
@mossy plume Has your question been resolved?
mossy plume
I'm solving this sphere filling with water problem. It asks for d(A)/dt, rate of expansion of the waters surface area. I'm confused, why is it when I derive area first, plug in r, and solve for the rest of the variables I get the wrong answer, but when I initially plug in r into the area equation then derive, solve for variables, I get the right answer
obtuse pebbleBOT
I'm solving this sphere filling with water problem. It asks for d(A)/dt, rate of...
obtuse pebbleBOT
@mossy plume Has your question been resolved?
obtuse pebbleBOT
@mossy plume Has your question been resolved?
modest ruin
those r some gooood notes
also i’d recommend asking that on multi variable calc
cus people there actually know how to do partials
mossy plume
those r some gooood notes
Thank you. Part of the reason I enjoy math is the way the notes look afterwards.
.close
spice chasm
can someone explain what my teacher did
obtuse pebbleBOT
can someone explain what my teacher did
spice chasm
i’m so confused
lusty cedar
which part?
spice chasm
like his diagram
lusty cedar
well see
the blue part is a rectangle
and common tangent is a part of the rectangle
and properties that has been used is opposite sides are equal and angles are 90 degrees
and finally pythagoras theorem has been applied
spice chasm
.close
obtuse pebbleBOT
lusty cedar
bruh
obtuse pebbleBOT
Available help channel!
ornate mantle
hi, i was hoping for someone to double check my answers to linear algebra questions. i just have to say true or false to a question, but if true, prove it, and if false, provide a counter example.
obtuse pebbleBOT
hi, i was hoping for someone to double check my answers to linear algebra questi...
@ornate mantle Has your question been resolved?
ornate mantle
<@&286206848099549185>
tardy epoch
- And 3 look good
I think you can come up with a counterexample for your proof of 1. Try the 2x2 matrix with only one nonzero entry
The statement of 1 is still true, just fix your proof. It only relies on the linearity of matrix multiplication
ornate mantle
I think you can come up with a counterexample for your proof of 1. Try the 2x2 m...
i'm confused by this
[ 1 0 ]
[ 0 0 ]
```?but that has a free variable
tardy epoch
This matrix isn't invertible
ornate mantle
it's also linearly dependent
oh fuck you mean 1?
shit hold on
my bad
i was looking at the wrong thing for a moment
wait wait
wait wait wait
riemann
would i fix the whole thing by just removing the whole 'if there was a free variable in a (making it non-invertible)' thing?
tardy epoch
Maybe? I'll have to see an updated version
ornate mantle
idk if it matters at this point i ended up submitting it cause it was due at 11:30 :/ its okay i have other question
idk how this works whatsoever
i understand matrix multiplication
idk what this singularity thing is
tardy epoch
Singular means it doesn't have an inverse. A theorem which you should have proven says that only happens when the determinant is zero
prisma raft
@tardy epoch
obtuse pebbleBOT
<@!261933205387477002>
prisma raft
tulip kestrel
Dont ping people like that
prisma raft
what the answer?
short spruce
is this a quiz/test
prisma raft
reviewer
short spruce
can you take a picture of the title
nocturne minnow
reviewer
If it's a reviewer, shouldn't you be reviewing instead of asking for answers?
short spruce
can you take a picture of the title
.
obtuse pebbleBOT
@prisma raft Has your question been resolved?
hasty flume
hi
hasty flume
I am utterly confused on how to approach these problems
forest sinew
which problems
hasty flume
Thank you
forest sinew
(f o g)(x)
warm shaleBOT
jan Niku
forest sinew
idk the latex maybe not necessary
how do you feel about evaluating this
what happens first?
hasty flume
thats where my brain stumbles, when I look at that I look at the graph to find 1 for (x) and then I match the f and the x to it
so for this, I got (3)(0)(1)
which leads me to believe it's 0 for a even though that is not correct
forest sinew
so you gotta go inside out
lets say that like
we start with f(g(1)) right
g(1) should evaluate to something
lets call it a
so g(1)=a
whats a?
if we plug 1 into g, what comes out?
hasty flume
1?
forest sinew
not quite
use the table
look for 1 on the x column
then go down to g(x)
we just want g(1), dont worry about f right now
hasty flume
g(x) is 0 right
forest sinew
no
hasty flume
huh
forest sinew
g(x) takes on a bunch of different values
not to be like
too picky
g(x) takes on a bunch of different values
but g(1) is 0
idk that may be too picky 
but also you never know
so g(1) is 0
we take 1, put it into g, it spits out 0
everywhere we see g(1)
we can put a 0
theyre the same thing
then f(g(1)) is f(0)
we see the g(1), we know its 0, we replace
forest sinew
yup
forest sinew
use the table
hasty flume
it would be -1
forest sinew
so heres a horrible drawing
hasty flume
so (f x g)(1) = f(g(1)) = f(0) = -1
forest sinew
yup
hasty flume
ohhhh that's so easy
hasty flume
Alright ty
obtuse pebbleBOT
@hasty flume Has your question been resolved?
slow tundra
guys do u help here
obtuse pebbleBOT
guys do u help here
halcyon tulip
Yes ig
brittle swan
$a^3 - b^3 = (a - b) (a^2 + ab + b^2)$
warm shaleBOT
Chromium
brittle swan
identity
obtuse pebbleBOT
@slow tundra Has your question been resolved?
obtuse pebbleBOT
slow tundra
but its confusing we need to use different formulas in each questions
and idk all of them
brittle swan
but its confusing we need to use different formulas in each questions
.it's just experience
.don't reopen the channel
.put a dot
slow tundra
.
obtuse pebbleBOT
Available help channel!
ionic summit
It's a physics problem
obtuse pebbleBOT
It's a physics problem
ionic summit
@everyone pls help me.... I am under the woater
obtuse pebbleBOT
Available help channel!
buoyant pumice
Pls help lol
brittle swan
close this channel
spiral maple
You don't need 2 channels
timid silo
hi i need to create "progress bar" using emotes ⬜⬛ i have % value what would be the best amount of emojis so its easy to calculate how many emojis must be filled (white) max amount is 17
obtuse pebbleBOT
hi i need to create "progress bar" using emotes ⬜⬛ i have % value what would be ...
timid silo
but i dont think 17 is good here
brittle swan
hi i need to create "progress bar" using emotes ⬜⬛ i have % value what would be ...
???
is this a programming problem?
timid silo
so i can use 17
fierce siren
yeah, there'd just be a tiny little error:
take each to be 6% with 17 boxes, that gives 102, not 100
but it's very close anyway
timid silo
okay thats fine
fierce siren
you might want to use a number that's a factor of 100
timid silo
thanks
fierce siren
np
fierce siren
that is lower than 17 but higher than 10 doesnt exists i think
you're right - you could try 20 though. it's only 3 more
timid silo
.close
vital kindle
obtuse pebbleBOT
vital kindle
I need help with this, please.
pine sail
Have you done similar questions before?
vital kindle
Have you done similar questions before?
yes, but this is the first one I encountered with that restriction
brittle swan
ways you can stick I, E together in a string of length 6
vital kindle
I tried this, however I'm not sure if its correct
pine sail
yes, but this is the first one I encountered with that restriction
So like you take I and E together, then you get total 4 letters and one IE unit. Then calculate for this this, the same is possible for EI as well, hence you multiply your answer with certain something which I want you to figure.
brittle swan
it's the way to do it
vital kindle
pine sail
oh I see
You just calculated IE cases.
It could be EI too.
Therefore what would you multiply your answer with?
pine sail
Yes if there were three letters you'd not multiply by 3 but 3!
pine sail
Yeah
I think.
But, if some letter were repeated then you'd divide the answer with x! (Where x is the number of times a certain letter is repeated) alright?
vital kindle
yes. I have read about that
pine sail
FOOL for example, it would be
(3!×2!)÷2! As there are two O.
vital kindle
I see. that makes a lot of sense. thank you :))
pine sail
Yw.
vital kindle
.close
proper snow
@brittle swan
obtuse pebbleBOT
<@!701895792763600896>
proper snow
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
rocky wigeon
if x~ is the median why is the sum minimal?
obtuse pebbleBOT
if x~ is the median why is the sum minimal?
compact shadow
if x~ is the median why is the sum minimal?
First you show that sum of absolute values being minimal implies sum of squares being minimal:
If positive real numbers r_1,…,r_n s_1,…,s_n such that Σr_j<Σs_j
Then Σs_j^2-Σr_j^2=
Σ(s_j+r_j)(s_j-r_j)>=M(Σs_j-Σr_j)>0
Where M is min{s_j+r_j :j}>0
Now sum of square you can calculate its derivative
The rest is clear
Wait a second some error
rocky wigeon
ok thx
compact shadow
Wait huge error, fixing
Oh you let x_1<=x_2<=…<=x_n
|x-x_k|+|x-x_(n-k)| is minimal when x is contained in [x_k, x_(n-k)]
So such x must be contained in the intersection of all [x_k , x_ (n-k)]
Median value satisfies that right? I think
Oh yes Any point x such that that sum is smallest must be contained in the intersection of all [x_k, x_ (n-k)] and median value is one of them you can check the details
rocky wigeon
ah ok
woven marsh
abstract void
can anyone help me understand how to solve this? im so confused
obtuse pebbleBOT
obtuse pebbleBOT
woven marsh
.reopen
obtuse pebbleBOT
✅
woven marsh
Topic: Applied Read Analysis
Does this look accurate for the Fourier coefficient a0? My professor has the denominator as 2pi instead of just pi.
By the way, the screenshot is from a website: https://mathworld.wolfram.com/FourierSeries.html
.close
lilac valve
obtuse pebbleBOT
lilac valve
So if velocity is displacement over change in time, shouldn’t all racers have an average velocity of 0?
obsidian isle
No
lilac valve
Since their displacement is all 0
hybrid gull
@lilac valve You're right - you should argue against whoever made it to get points back
(If applicable)
wispy shadow
what does it mean to expand around $z=\pi i$ within a taylor/laurent expansion for $e^z +1$? We've got
\begin{align}
e^z +1 = 1 + \sum_{n=0}^\infty \frac{z^n}{n!}
\end{align}
Does this mean replacing $z$ with the variable $w$ where $w=z-\pi i$?
obtuse pebbleBOT
what does it mean to expand around $z=\pi i$ within a taylor/laurent expansion f...
warm shaleBOT
madlor
compact shadow
It means you write e^z+1 in the form Σa_k(z-πi)^k
wispy shadow
so
\begin{align}
\sum_{n=0}^\infty a_k (z-\pi i)^n
\end{align}
warm shaleBOT
madlor
compact shadow
Yes
Or from negative infinity to positive infinity
Depends on what kind of expansion
wispy shadow
right
i am looking to do a Laurent expansion specifically yeah
quite honestly not sure how to start, but i will try some things
but i solve the bottom expression?
\begin{align}
e^{z} + 1 =\sum_{n=-\infty}^\infty c_n (z-\pi i)^n
\end{align}
warm shaleBOT
madlor
wispy shadow
oh. i do feel a little bit silly now, ive already done the taylor expansion, but i did it for z_0 = 0.
obtuse pebbleBOT
@wispy shadow Has your question been resolved?
wispy shadow
Not resolved but moving on
hollow badger
Hi! I'm working on some arithmetic sequences and noticing factorizing isn't my strong side. In the problem, T2 can be expressed as
T2 = T1 * 0.95 + 600
or upon inserting T1
T2 = (8200 * 0.95 + 600)0.95 + 600
Could someone walk me through how that is factorized into
8200 * 0.95^2 + 600(0.95 + 1)?
obtuse pebbleBOT
Hi! I'm working on some arithmetic sequences and noticing factorizing isn't my s...
@hollow badger Has your question been resolved?
halcyon tulip
If you open brackets, then first you will multiply $82000.950.095$ then you multiplied 0.95 with 600.
We ddint do anything apart from opening brackets.
And last two terms, 600*0.95 + 600 have 600 as common factor so we took it out.
warm shaleBOT
hoi
hollow badger
I understand I multiply the two 0.95 and that I can factor out the 600, but what happens to multiplying 8200(0.95)?
halcyon tulip
Hi! I'm working on some arithmetic sequences and noticing factorizing isn't my s...
Nothing happened here afaik
One more 0.95 is multiplied and hence it's square there
hollow badger
Maybe I'm being really stupid and not seeing something but what I can't wrap my head around is why there's no effect on the 8200 if 0.95 is supposed to multiply with every term. because I see 0.95 is multipled and hence squared as you said and 600 just factored
halcyon tulip
What effect are you talking about, the only thing that will happen is multiplication of 0.95.
Are you asking why isn't it in calculated form?
hollow badger
Why isn't it
8200(0.95) * 0.95(0.95) + 600(0.95) + 600
8200(0.95) * 0.95^2 + 600(0.95+1)
What mistake am I doing in the above factorization?
halcyon tulip
Why isn't it
8200(0.95) * 0.95(0.95) + 600(0.95) + 600
8200(0.95) * 0.95^2 + 600...
Okay you know that we use distributive property while multiplying?
Which is multiplying number outside of brackets, to each term individually and putting ± signs in between
If you know, then you must be knowing there won't be extra 0.95 with 8200×0.95 there
hollow badger
So I percieve 8200 x 0.95 as a unique term basically?
How the fuck did I get so far without being aware of this.
halcyon tulip
Okay, lemme state again, multiplication is distributive over addition not multiplication itself.
$\implies (a+b)c= ac+ab$ and if you have (ab)c you won't do ac*ab.
warm shaleBOT
hoi
halcyon tulip
It will be $abc$ only
warm shaleBOT
hoi
hollow badger
Alright. I understand now and once again, I'm confused how I did not know this by heart.
Thanks a lot.
.close
candid wharf
How can I get a non-e number when trying to reduce an imaginary number like i^21 on a ti-84
obtuse pebbleBOT
How can I get a non-e number when trying to reduce an imaginary number like i^21...
candid wharf
for example our teacher said i can be i, -1, -i, or 1
but calculator spits back an E number
foggy marsh
What's the exact number it spits back?
(idk if I can help you, I'm just curious about this calculator lol)
wispy shadow
$i^{21}$?
warm shaleBOT
madlor
candid wharf
What's the exact number it spits back?
-1E-13+i
wispy shadow
is it required to do this on the calculator?
wispy shadow
so this is a numerical error
-1E-13 is a tiiiiny number
its basically 0
your calculator cant compute things perfectly, i think this one is unavoidable
does this seem logical?
$-1E-13 = -1\cdot 10^{-13}$
warm shaleBOT
madlor
candid wharf
our teacher told us to break it in fours so wouldn't it be like i^20 and then whatever i^1 is or something, I forget
wispy shadow
i agree that sounds like a good idea
if you're comfortable with power rules, it shouldnt be too bad
feel free to ping me if unsure how to go about that
candid wharf
which way do you think is the easiest idea to solve
obviously after like i^4 the numbers repeat
but if you get a number like i^800 you can't just write it 800 times
you can but you'll be there all day
wispy shadow
i think it would be handy to do utilize $a^{bc} =(a^{b})^c$ for instance
warm shaleBOT
madlor
wispy shadow
but 21 is an akward number
so id advise making it so that the power is 20 instead of 21 by utilizing $a^{b+c}=a^b a^c$
warm shaleBOT
madlor
foggy marsh
but if you get a number like i^800 you can't just write it 800 times
You can group it into groups of 4. Like writing i 800 times is like writing iiii 200 times, right? But iiii is just 1
candid wharf
ok so I just skimmed thru a video from another professor
her method was if you have say i^302, get the remainder of 302/4
the remainder of that is 2
so: i^302 = i^2
i^2 = -1
to me that seems like the easiest way, no?
foggy marsh
That is indeed TheBest way
candid wharf
so that means to solve
i^21 sqrt -8
remainder of 21/4 = 1, i^1 = I
i sqrt -8
I get a decimal of -2.828 for i sqrt -8
is the final answer suppose to be a decimal?
candid wharf
yeah that's what the internet shows me -2root2
how did you get that
like how's you convert that decimal to that
obtuse pebbleBOT
@candid wharf Has your question been resolved?
candid wharf
ok thanks yeah I figured out how to do that now
good for now I guess until harder problems come up
static patio
how to get inverse element for this operation ?
obtuse pebbleBOT
how to get inverse element for this operation ?
static patio
i ended up with these equations: suppose (c,d) is inverse
ac + 5bd = 1
ad + bc = 0
how to get inverse element for this operation ?
raven spire
.
I suppose Ann helped you with this one?
it's literally solving the simultaneous equations in
e_1, e_2
static patio
I suppose Ann helped you with this one?
with identity
static patio
it's literally solving the simultaneous equations in
e_1, e_2
i have tried but unsuccessfully