absolutely clear
#help-10
royal basin
mighty ether
yeah im pretty sure i calculated the inverse of the wrong matrix anyway
royal basin
i didn't say you were SUPPOSED TO do this or NOT SUPPOSED TO do that
all i said was
you claimed S^-1 = [1/2, -3/2; -3/2, 1/2]
i decided to see if that was the case
mighty ether
yep got it
royal basin
and i multiplied S by what you claimed S^-1 to be
IF you were correct THEN this product would be the identity matrix.
however it is NOT the identity matrix but instead -1 times the identity.
okay, so
let's just establish some basic things about where we're at in this problem.
i'm going to ask you a bunch of yes/no questions and i want you to ONLY answer them with "yes" or "no" and ONLY give more detailed answers when i ask you.
mighty ether
okay
royal basin
okay?
royal basin
the problem gives you this matrix it calls S, and it has you find D and M such that S = MDM^-1.
do you need me to explain how to find D and M?
@mighty ether
mighty ether
yes just a minute, i'm trying to work out whether I need help with that
because I thought D and M were just the matrix with the eigenvectors, and the matrix with the eigenvalues but i'm just double checking
royal basin
is that a yes or a no
mighty ether
I think no? Can I double check with you that my understading of what those matrices are is correct?
royal basin
you got them mixed up. M holds the eigenvectors and D the eigenvalues, not the other way around.
the intuitive reasoning behind this is that, given a list of eigenvalues, the most straightforward matrix you could write down that has these eigenvalues is a diagonal matrix.
mighty ether
the intuitive reasoning behind this is that, given a list of eigenvalues, the mo...
i think that makes sense. sorry i was trying to send you something from my notes but its taking forever
royal basin
can we continue now?
i am still kind of trying to establish where we're at in terms of what you require assistance with
mighty ether
yeah we can continue. So M is just the matrix with the eigenvectors and D is just the one with the eigenvalues, and m^-1 is just the inverse of the eigenvector matrix
I'm pretty sure I know how to get those
royal basin
okay then let's set the computations aside
mighty ether
but maybe I could get the right value for M right now?
just to make sure I have it? because it looks like mine was wrong
I mean for m^-1
royal basin
what do you have for M right now?
mighty ether
the same as this
royal basin
right
well this is a-ok
ok
sorry, my internet decided to shit itself for no reason hence the delay in communication from me
mighty ether
mhm
royal basin
do you need help understanding why S^n = MD^n M^-1?
royal basin
ok
so we are not going to do any number crunching here
instead we will work symbolically with S = MDM^-1
royal basin
...yes?
mighty ether
so just clarifying, S is our matrix
the original
M is the eigenvectors matrix, D is the eigenavlues
royal basin
S is our original matrix, yes.
royal basin
ok
so let's consider S^2
remember matrix multiplication isn't commutative
so $S^2 = SS = MDM^{-1}MDM^{-1}$
warm shaleBOT
Ann
royal basin
do you understand why this equals $MD^2M^{-1}$?
warm shaleBOT
Ann
mighty ether
I think it is because we add the powers on m^-1 and M
so it just turns into 1 and then D.D gives d^2
but i'm not sure
royal basin
$M^{-1}M = I$ (definition of inverse), so $$MDM^{-1}MDM^{-1} = MDDM^{-1} = MD^2M^{-1}.$$
warm shaleBOT
Ann
royal basin
likewise you can get that $S^3 = MD^3M^{-1}$ with more cancellation
warm shaleBOT
Ann
royal basin
and if you want you can also write out an induction proof that $S^n = MD^nM^{-1}$
warm shaleBOT
Ann
mighty ether
likewise you can get that $S^3 = MD^3M^{-1}$ with more cancellation
Yep got it
mighty ether
**Ann**
that is good to know although I don't think i need to know that for this class
So I think it is better to leave it
royal basin
would be a shame not to know such basic things as induction ngl
mighty ether
there are specific things I need to know for the exam so I need to focus on those
okay so, I still am not sure how we get to the point they do in IV
mighty ether
mhm
royal basin
and raising a diagonal matrix to the n'th power is very easy
to raise a diagonal matrix to the n'th power all that needs to be done is to raise each diagonal entry to the n'th power
mighty ether
to raise a diagonal matrix to the n'th power all that needs to be done is to rai...
yeah that makes sense but it looks like they've subtracted values in IV
they have 1+ and 1- and so on
royal basin
$D^n = \bmqty{1 & 0 \ 0 & (-1/2)^n}$
warm shaleBOT
Ann
royal basin
and now you need to conjugate that by M
so $\bmqty{1 & 1 \ 1 & -1} \bmqty{1 & 0 \ 0 & (-1/2)^n} \bmqty{1/2 & 1/2 \ 1/2 & -1/2}$
warm shaleBOT
Ann
royal basin
this is just arithmetic
mighty ether
and now you need to conjugate that by M
what do you mean when you say conjute it?
conjugate*
and what you have there is also what I have
royal basin
i mean the multiplication by M from one side and M^-1 from the other....
god
it is REALLY frustrating when like
apparently i have to remind you of the same things over and over again like
we are calculating MD^n M^-1
we never should've forgotten that
YOU never should've forgotten that
like for real
plus i even SHOWED what i meant immediately after
mighty ether
So i have to actually multiply the matrix M
with the matrix d^n
and then with m^-1?
royal basin
yes, imagine! M * D^n * M^-1 means M multiplied by D^n multiplied by M^-1!
idk if youre having a brainfart or what but like
basic reading comprehension 💀
royal basin
im going to disappear now
slim grove
I am having a circle whose coordinates (cx,cy) and radius r are known. There is point px, py that it lies outside circle. The question is to find the point of intersection of line joing point P to the center of circle and perimeter of circle
obtuse pebbleBOT
I am having a circle whose coordinates (cx,cy) and radius r are known. There is ...
slim grove
Please of someone can help me to drive the expressions 🙏
ancient compass
I have no idea what this is, but turning the picture around could help others.
Took me a while to realize its upside down
ancient compass
Better... But still can't help. Have no idea what this is.
I remember it from somewhere I think.. but.. puh.. can't help.
Plus.. how do you know co ordinates but not use a coordinate system? Im confused myself
slim grove
I think the context might help to change the viewpoint,
Im making colour wheel in python so when user points out from that wheel and moves around it the colour must point to that x,y so that it shows the colour of that intersection point
obtuse pebbleBOT
@slim grove Has your question been resolved?
slim grove
So what values are already given?
Circle centre coord, radius, point location
Given that point always lies outside circle
ancient compass
Maybe I can actually help. Write down like this
r= xxx
cx= xxx
cy= xxx
Px=xxx
and so on
With what you don't know e.g. y= ?
slim grove
cx = cy = 167
r = 150
px and py are variables ie event dependent
If u can solve everything by considering variables then pls go by that
obtuse pebbleBOT
slim grove
.reopen
obtuse pebbleBOT
✅
high tiger
general eqn for a line is $$y=mx+c$$ where $m$ is the gradient and $c$ is the $y$-intercept
warm shaleBOT
Toru
high tiger
you have two points already, both should be found immediately
m = (y2-y1)/(x2-x1)
to solve c, sub in one of the points into the eqn
slim grove
Aah after solving i got two equation one is f(xx, yy) and other is f(x,y)
Then i was blank
😅used two point eqn of line
slim grove
(y-y1)/(x-x1) = (y-y2)/(x-x2)
high tiger
ok
that formula is wrong
the RHS is suppose to be all constants
not variables
so it's $$\frac{y-y_1}{x-x_1} = \frac{y_1-y_2}{x_1-x_2}$$
warm shaleBOT
Toru
high tiger
the RHS is m
slim grove
Then also this will be f{x, y) and eqn of circle will give f(x2, y2, x, y)
high tiger
not quite
the line is f(x, y) but the circle is also f(x, y) as it can only have a maximum of 2 inputs but to avoid confusion, i'm going to call it g(x, y).
Line: f(x, y)
Circle: g(x, y)
slim grove
Can u explain how it will be function of x and y
high tiger
If you need to find the intersection between the line and circle, you would have to sub the eqn of the line into the circle
high tiger
Can u explain how it will be function of x and y
Mathematically speaking, eqn of circle is (x - cx)^2 + (y - cy)^2 = r^2
slim grove
Yes
high tiger
but what you suggest, f(x2, y2, x, y) suggests 4 inputs where there can be only be a maximum of 2 inputs which are the x & y variables
slim grove
but what you suggest, f(x2, y2, x, y) suggests 4 inputs where there can be only ...
That was after expanding the square
high tiger
doesn't matter, they are equivalent forms
high tiger
Let's clear the misunderstanding here
is x2 y2 suppose to be the centre of the circle?
slim grove
Thays x squared and y squared
high tiger
ok that clears the misunderstanding
There is no need to input x squared and y squared
as long as u input x and y, the squared will be calculated
slim grove
But then how will i gwt the expressions for the coordinates of intersection point
high tiger
for example,
return i ** 2 + i
but if u do
i = 2
j = i ** 2
return j + i
the 2nd method wastes calculation that is not necessary
high tiger
But then how will i gwt the expressions for the coordinates of intersection poin...
- Find the equation of the line
- find gradient and y-intercept
- make either
xorythe subject of the eqn - sub the value u chose in step 2 into the eqn of the circle
- you will get the 1st coordinate
- sub that coordinate into the eqn of the line then you will have the point of intersection.
step 2 & 3 are tricky.
IF you chose y from the line to be the variable you want to sub into the eqn of the circle,
make ** x the subject of the eqn of the circle**
For example,
eqn of line: $$ y = \frac{p_y - c_y }{p_x - c_x}(x - p_x) + p_y $$
then eqn of circle: $$x = c_x \pm\sqrt{r^2 - (y-c_y)^2}$$
warm shaleBOT
Toru
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
slim grove
Thanks, it seems that i was just doing wrong equation. I hope this solution works
high tiger
Thanks, it seems that i was just doing wrong equation. I hope this solution work...
if your colour wheel is 360 degrees, since the line will cut the circle at two points, i suggest adding conditions for the x-coordinate. If px is positive, take the positive square root but if px is negative, take the negative square root. Then for the cases where the gradient will be undefined, check if px - cx == 0 so that you will not get a divide by zero error.
timid silo
obtuse pebbleBOT
<:KEK:586240877358350341>
timid silo
.close
placid escarp
Hello! I know you can calculate the Gini-coefficient by taking the area between the two graphs times 2, but what is the difference between that and if you were to find the r^2 between those two graphs (in terms of linear regression)?
obtuse pebbleBOT
Hello! I know you can calculate the Gini-coefficient by taking the area between ...
placid escarp
Huh?
obtuse pebbleBOT
@placid escarp Has your question been resolved?
fallen hollow
obtuse pebbleBOT
somber mural
for percentages just divide by 100 and simplify
fallen hollow
Alright so
somber mural
you can convert decimals to percentages then do what you do for percentages
fallen hollow
Random guess
somber mural
use ur brain
fallen hollow
Alright alright
sharp hare
@fallen hollow The word "per cent" directly translates to per 100. So you can convert percents to fractions pretty simply with that information. For example, 67% is 67/100. You can do the same for any other percent value, just like the 35% you have there
now im not sure if you know how to simplify fractions but if you do, sometimes the fractions you get from converting % to fraction can be simplified
sharp hare
good
fallen hollow
To percentage
sharp hare
thats the answer
fallen hollow
Let's gooo brahhh
sharp hare
can you do 0.19 to percentage?
sharp hare
😆 yessir
fallen hollow
How do I convert a percentage to fraction and a decimal aswell
proven zephyr
percentage to fraction is divide by 100
^^^
sharp hare
so
percentage to fraction
lets say you have 30%
remember, %, or per cent means per 100
so 30% means 30 per 100
your fraction would be 30/100
fallen hollow
I got 7/20
sharp hare
for which one
fallen hollow
While converting 35% to fraction
fallen hollow
Yee
I just dropped the %
35/100 simplify
@sharp hare just completed all of them
And got 6/6
fallen hollow
.close
warm canopy
union
kind hawk
it is the union of Ai and not the intersection
timid silo
Some magic shit
warm canopy
you take everything in A1, and everything in A2, and etc etc
but as you can see the sets get smaller each time
so its all been covered by A1 already
tardy epoch
It's still true even if Q were the integers
obtuse pebbleBOT
@slow timber Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
raw meadow
How Can I find the oblique asymptote with f(x)=mx+q ?
obtuse pebbleBOT
How Can I find the oblique asymptote with f(x)=mx+q ?
grizzled eagle
To calculate the oblique asymptote y = mx + q of a function f(x):
\newline
$m = \lim_{x \to \infty} \frac{f(x)}{x}$
\newline
$q = \lim_{x \to \infty} [f(x) - mx]$
warm shaleBOT
JaimermXD
raw meadow
So I just follow those formulas for them?
grizzled eagle
Pretty much.
grizzled eagle
Doesn't matter, it can be either. The result will remain the same.
grizzled eagle
The asymptote won't change because it's a straight line, no matter if it's at positive or negative infinity.
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
autumn tinsel
obtuse pebbleBOT
restive ridge
• Show your work, and if possible, explain where you are stuck.
autumn tinsel
i don't know how to start
how to find radius?
with E and bases
AD+CB=33
i know this
proven zephyr
try to find this
proven zephyr
do you know how to find it?
autumn tinsel
(AB+DC)/2?
proven zephyr
i think so
autumn tinsel
answer is 4√3
proven zephyr
wait what
autumn tinsel
but i can't got that with this idea
proven zephyr
the answer is 4sqrt3?
autumn tinsel
yes
proven zephyr
oh
autumn tinsel
trigonometry in geometry
obtuse pebbleBOT
@autumn tinsel Has your question been resolved?
autumn tinsel
.close
steep notch
1-2x>x-2
steep notch
what is this type of question called?
rocky lynx
inequation
sour gate
I've always wondered—can I use this to solve the four 4's problem without using square roots:
log(⁴/₄%)(⁴/₄%)=1
log(⁴/₄%)(⁴/₄%%)=2
log_(⁴/₄%)(⁴/₄%%%%)=3
obtuse pebbleBOT
I've always wondered—can I use this to solve the four 4's problem without using ...
@sour gate Has your question been resolved?
sour gate
<@&286206848099549185> , pwease help!
obtuse pebbleBOT
@sour gate Has your question been resolved?
sour gate
Pwease, I'm begging!
kind hawk
I don't know what you mean with the percent signs
but there is a way to solve the four 4s problem using logarithms
see wikipedia
obtuse pebbleBOT
@sour gate Has your question been resolved?
tardy epoch
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
obtuse pebbleBOT
ruby skiff
how would the answer be e?
if its asking for the y value of v(x,y)
would it not be -13/8?
be the parabola is
y=1/4(x+2)^2-(13/8)
hoary coral
v(y) = (4ac - b^2) / 4a
obtuse pebbleBOT
@ruby skiff Has your question been resolved?
ripe basin
hey
ripe basin
The iron pipe has an outer diameter of 10 mm and an inner diameter of 8 mm. What is the thickness of the edge of the pipe? how can i solve that
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
plush epoch
Just confused on how they got the highlighted section
obtuse pebbleBOT
Just confused on how they got the highlighted section
timid silo
Hey, tomorrow I have a math test and im trying to study to I literally dont understand some things like
obtuse pebbleBOT
Hey, tomorrow I have a math test and im trying to study to I literally dont unde...
nocturne minnow
Hey, tomorrow I have a math test and im trying to study to I literally dont unde...
Translate the objective, please
nocturne minnow
You mean simplify?
nocturne minnow
So for that question, you want to factor the numerator, so to do so, you need to determine the GCF of all the terms in the numerator
nocturne minnow
Exactly that
lunar laurel
If the volume of a sphere is increasing at the rate of 8 feet^3/min. What would be the rate at which the radius increases when its diameter is 4 feet?
obtuse pebbleBOT
If the volume of a sphere is increasing at the rate of 8 feet^3/min. What would ...
lunar laurel
So I think I did that and it turns up to be dr/dt = 2/pi r^2
lunar laurel
try writing the formula of volume and differentiating
I don't know if that's correct
If it is I don't know what to do next
lunar laurel
I don't know I don't get this subject all that well so I'm not sure
lusty cedar
no dude your solution is correct so far
lunar laurel
Awesome, that's where I'm stuck now though
lusty cedar
what is the issue?
lunar laurel
Because I have to find the rate at which the radius is increasing when the diameter is 4 feet
lusty cedar
hmm
lusty cedar
ahh no need for that
we need to find the rate of increase of radius
so just put the radius in 2/(pi*r^2)
that is 4/2=2
that's it
lunar laurel
why 2/(pi*r^2) ?
lusty cedar
lunar laurel
Ohh
lusty cedar
so just put in the value of r
lunar laurel
ah yes because the radius is 2 since the diameter is 4
lusty cedar
exactly
lunar laurel
Bruh this subject is so confusing jesus christ
lunar laurel
XD
lusty cedar
it is like you're making a pizza and have all stuff but forgot that you don't have an oven to bake it
anyways
lunar laurel
hahaha
lusty cedar
i hope you got the answer
lunar laurel
Hell yes, thanks a lot for the help!
lusty cedar
no worries
lunar laurel
.close
severe mulch
obtuse pebbleBOT
severe mulch
how do u evaluate into a whole number here?
cedar lichen
What have you tried
cedar lichen
Why -15?
severe mulch
bc positive divided by negative is negative
severe mulch
if h is -15
i already know this information
cedar lichen
h is -15, so what's -h
scarlet locust
yes now just do 15/3
severe mulch
obtuse pebbleBOT
severe mulch
back for more knowledge
obtuse pebbleBOT
@severe mulch Has your question been resolved?
tender yew
7.2^2+ z^2= 12.6^2
timid silo
obtuse pebbleBOT
timid silo
can someone reword the bottom text to help me understand
zenith raft
I'll try if you send the page it was from
zenith raft
sorry, I'm not sure what he means 😭
zenith raft
looks like it to me
timid silo
hm i guess he means this is just a special case
the answer doesnt have to be either -pi/2 or pi/2
zenith raft
that could be
obtuse pebbleBOT
@timid silo Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
spiral pebble
Is there a way to factorize x^2-23x+1 without quadratic formula
obtuse pebbleBOT
Is there a way to factorize x^2-23x+1 without quadratic formula
spiral pebble
Help
kind hawk
,w x^2-23x+1
warm shaleBOT
kind hawk
well if you are good at guessing
wooden cipher
No there isnt basically
spiral pebble
ok
wooden cipher
Just look at the roots section
kind hawk
,w factor x^2-23x+1
spiral pebble
ok so I have to use quadratic formula
wooden cipher
Yes unfortunately
spiral pebble
ok
kind hawk
so here at the top is the factorization
essentially impossible to get without quadratic formula
wooden cipher
Dont think so either
wooden cipher
Since (m-n)^2 produces only a -2mn
spiral pebble
.close
sudden citrus
It takes 1 minute to gain 3000 $ how many hours would it take to get 100,000,000$?
obtuse pebbleBOT
It takes 1 minute to gain 3000 $ how many hours would it take to get 100,000,000...
somber mural
how many 3000s fit into 100,000,000
somber mural
yup
obtuse pebbleBOT
@sudden citrus Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
timid silo
obtuse pebbleBOT
robust sleet
Posting a question without providing context or on what u need help won't attract many helpers.
robust sleet
Read this.
timid silo
honestly not sure where to begin on question one. 2 whole lessons went by. Other than that the rest of the question are old units i would appreciate help with.
I cant solve for volume with the formula l x w x h without the length, and stuck on how to solve for h
Well we know what c is. And the base is a square, so what is a? Then use the fact that h,c,a is a right angle triangle to find h
isnt a 4
obtuse pebbleBOT
Available help channel!
timid silo
f(x)=x⁴+ax³+bx²+cx+d
g(x)=f(x) (x>=0)
f(-x) (x<0)
f(2)=f'(2)=0
|g(x)-4| is not differentiable in x=k,-k
when x1,x2 is in (0,2), f'(x1)f'(x2)>0
so i need to find the maximum value of f(4) and i got 84
is this right
obtuse pebbleBOT
f(x)=x⁴+ax³+bx²+cx+d
g(x)=f(x) (x>=0)
f(-x) (x<0)
f(2)=f'(2)=0
|g(x)-4...
@timid silo Has your question been resolved?
timid silo
i started off by setting f(x) as (x-2)²(x²+ax+b)
and since f'(0)=0 and f(0) has to be 4
2(x-2)(x²+ax+b)+(x-2)²(2x+a)
-4b+4a=0
4b=4
so b=1 and a=1
and (x-2)²(x²+x+1)
so its 4(16+4+1)=84
<@&286206848099549185>
obtuse pebbleBOT
@timid silo Has your question been resolved?
west gale
What?
white basin
In some orthonormal reference, the coordinates of points A, B, D and E are respectively.
A(0, 0, 2);
B(3, 0, 2);
D(0, 4, 2);
E(0, 0, 1);
Calculate the coordinates of point C in this same reference.
obtuse pebbleBOT
In some orthonormal reference, the coordinates of points A, B, D and E are respe...
white basin
what exactly do you mean to work out C
@somber mural we are looking for a result like this? (0,0,1)
obtuse pebbleBOT
@white basin Has your question been resolved?
white basin
no
feral sedge
@white basin Do you know how to find $\vec{DC}$?
warm shaleBOT
kelvinchan9786
white basin
its cus I dont understand the coordinates of each one
what they mean
I am trying to make sense out of it
feral sedge
$\vec{DC}$ means this vector
warm shaleBOT
kelvinchan9786
feral sedge
i.e. vector from D to C
feral sedge
Oh...
white basin
i dont understand
feral sedge
Would it better if I change from $B = (3, 0, 2)$ to $\vec{OB} = 3 \hat{i} + 2\hat{k}$, where $O$ is the origin?
warm shaleBOT
kelvinchan9786
feral sedge
(next time pls tag me)
You are aimed to find $\vec{OC}$.
You can use the addition law of vector, i.e. $\vec{OC} = \vec{OD} + \vec{DC}$
You have already known $\vec{OD}$, i.e. $(0, 4, 2)$.
Try to find $\vec{DC}$
warm shaleBOT
kelvinchan9786
feral sedge
So how to find $\vec{DC}$?
$\vec{DC} = \vec{AB}$
so find $\vec{AB}$.
You can use subtraction law, $\vec{AB} = \vec{OB} - \vec{OA}$
Note that you have already known $\vec{OB} = (3, 0, 2)$ and $\vec{OA} = (0, 0, 2)$
warm shaleBOT
kelvinchan9786
feral sedge
@white basin
obtuse pebbleBOT
@white basin Has your question been resolved?
obtuse pebbleBOT
white basin
.reopen
obtuse pebbleBOT
✅
white basin
@feral sedge you say DC = AB
i mean looking at the image it make sense
but how can. you prove it?
Because technically its parallel but parallel doesnt mean having the same lenght
so idk how to prove it. :I
feral sedge
Could you show the whole question to me?
feral sedge
Is there some terms about "parallelepiped"?
feral sedge
then it is by def. ^_^.
(Same magnitude + Same direction -> Same vector)
warm shaleBOT
BotheringMeAgain
feral sedge
$\vec{AB} = \vec{OB} - \vec{OA}$
warm shaleBOT
kelvinchan9786
feral sedge
Yes
feral sedge
**kelvinchan9786**
Then try to finish the question with this tip.
white basin
aight tyyy
feral sedge
great
warm shaleBOT
BotheringMeAgain
white basin
$\vec{AB} = \vec{DC}$
warm shaleBOT
BotheringMeAgain
warm shaleBOT
BotheringMeAgain
white basin
@feral sedge
warm shaleBOT
BotheringMeAgain
white basin
@feral sedge
feral sedge
Yes, it is correct
white basin
thanks!
feral sedge
My pleasure
white basin
how do I close the channel?
feral sedge
use the command ".close", I guess
white basin
.close
obtuse pebbleBOT
feral sedge
.reopen
white basin
.reopen
obtuse pebbleBOT
✅
white basin
?
obtuse pebbleBOT
@ruby skiff Has your question been resolved?
nocturne sun
$\frac{4000 \cdot 8 \cdot 18}{100}$
are you using this formula or something different?
warm shaleBOT
Doggo
nocturne sun
the answer is (b) if you're using that formula
$\frac{\text{initial money} \cdot \text{annual interest rate} \cdot \text{years waited}}{100}$
warm shaleBOT
Doggo
ruby skiff
the answer is (b) if you're using that formula
wait so the correct answer is b r?
nocturne sun
no using the tn = t1 + (n-1)d
what are the variables here?
ruby skiff
t1 = 4000
nocturne sun
n is years passed?
nocturne sun
hm I feel something's off with that formula
the interest earned isn't related to initial money
nocturne sun
yeah but you earn more money / year if you have more in the bank no?
nocturne sun
yeah
nocturne sun
I think the -1 shouldn't be there
nocturne sun
the formula is probably for t_1 = 4000
ruby skiff
oh
nocturne sun
**Doggo**
interesting that this formula was also in the answers but is the wrong answer
I assume it's to trick people like me
ruby skiff
na this got me too
wait but when the formula is used
t19 = 4000(1.08)^19-1
t19=15984.078
nocturne sun
yeah it depends on whether you take t_0 = 4000 or t_1 = 4000
I prefer t_0 personally
ruby skiff
wait wut does the _ mean?
nocturne sun
$t_0$
warm shaleBOT
Doggo
nocturne sun
like this
ruby skiff
k
obtuse pebbleBOT
Available help channel!
willow ravine
I am needing someone else’s eyes on this. I believe I am supposed to use Liouville’s Theorem on the first one and the second one I believe is 0. This is a complex variables course.
obtuse pebbleBOT
I am needing someone else’s eyes on this. I believe I am supposed to use Liouvil...
willow ravine
I am not sure if this is the correct place to use Liouville’s and the second one I am not sure if my logic is correct in assuming it is 0.
<@&286206848099549185>
obtuse pebbleBOT
@willow ravine Has your question been resolved?
hallow turtle
you can use Cauchy's residue theorem to evaluate the first, there's a single pole z=0 of order 5
the second should be 0 with those conditions by Cauchy's as well
I am not sure what you would need Liouville's theorem for
willow ravine
So is the first one correct or do I need to remove the derivative part and just evaluate f(z)=e^4z at z=0?
hallow turtle
no, the first one looks correct
well
your answer is correct at least, but if you are using Cauchy's then 4th derivative of e^4z is 4^4 e^4z
and you are taking limit as z->0
willow ravine
Should I drop the /4!
?
I was using this, but you think that Liouville’s does not apply here and that I should use Cauchy’s and drop the 4!
?
obtuse pebbleBOT
@willow ravine Has your question been resolved?
hallow turtle
Liouville's theorem is the "if f is entire and |f| <= M implies f is constant"
the bottom of the slide looks like the beginning of some proof or motivating example
idk without having attended the lecture
but regardless, you have everything you need to apply the residue theorem in both cases
proven condor
how do I solve for these?
obtuse pebbleBOT
how do I solve for these?
warm shaleBOT
Pluton
drowsy girder
Second one is just chain rule
knotty crow
or take log both sides, then differentiate (implicit)
obtuse pebbleBOT
@proven condor Has your question been resolved?
proven condor
I got this as an answer
I think it's right?
I hope I did the steps correctly too
@drowsy girder ?
proven condor
<@&286206848099549185> ?
tardy epoch
,rotate
warm shaleBOT
tardy epoch
,w differentiate x^(tan(x)-sin(x))
warm shaleBOT
drowsy girder
,w differantiate (tanx - sinx)lnx
warm shaleBOT
drowsy girder
Seems fine to me
drowsy girder
This is basically same thing just that he factored out x^-1
proven condor
how do I start on the 2nd one?
tardy epoch
Chain rule
obtuse pebbleBOT
@proven condor Has your question been resolved?
proven condor
sorry I procrastinated
is this right?
@tardy epoch
,w differentiate e^((x^4)- cos(x))
warm shaleBOT
proven condor
.close
indigo oriole
obtuse pebbleBOT
tall escarp
Sorry, I have no clue how this question even works 💀
obtuse pebbleBOT
Sorry, I have no clue how this question even works 💀
tranquil arch
$$a^{2/3} = (a^2)^{1/3}$$
warm shaleBOT
秋水
tall escarp
uh well i know that already
tranquil arch
so
$$(\sqrt{2q}+\sqrt{r})^{2/3}=\sqrt[3]{(\sqrt{2q}+\sqrt{r})^2}$$
warm shaleBOT
秋水
tranquil arch
oh, there is no correct choice
timid silo
is q>0 and r<0 relevant?
royal basin
weirded out by the fact they explicitly mention r is negative
one would think they wouldn't want to involve complex numbers at the level this problem seems to be at
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
mellow halo
obtuse pebbleBOT
mellow halo
I need assistance
I used up channel 0 for this Q yesterday
But was left unanswered
Ping me if you think you could help me understand
Part a only
I did part b
lusty cedar
i can help
lets do it here
in fact you don't even need help
you have done everything
just solve for x and put that value for x in any equation
you will get the ordinate of a
and hence the point
obtuse pebbleBOT
@mellow halo Has your question been resolved?
lusty cedar
no worries
sinful mortar
Hello!
sinful mortar
I have a problem calculating the line-point distance with one of the axis
I was trying to get the bisector of the purple line and the X axis
obtuse pebbleBOT
@sinful mortar Has your question been resolved?
obtuse pebbleBOT
timid silo
Hello, again
2i isn't a thing
what you care about is the number of operations
that's what O(n) means
I think it will be n(n/2) in that case
that's a completely different case from i+1 to n
you have to see it as an amount of operations
no, that's not how it works
you have to visualise the amount of times the iterations have
again, observe those lists:
i = [1, 2, 3, 4, 5]
j = [2, 3, 4, 5]
how many elements are in i?
five. There are five elements in i
let's say that n = number of elements in i
so, how would you represent the number of elements in j using n?
that's the number of elements in i which is n
the number of elements in j is 4
which is n-1
the number of the inner iterations is 2n - i - 1
suppose 2n = 4
i = [1, 2, 3, 4]
j = [1, 2, 3]
that's the first iteration
the second iteration
j = [1, 2], so 2n - 2
are you with me so far?
it would help you to go through the iterations manually first
and then generalising the pattern
good
we skip the first iteration of the outer loop
because it's out of range in the inner loop
when i = 2, we get 1 iteration of j
we count the total amount of times the inner loop has been iterated over
$$n_{j} = (2n-1) + (2n-1) -1 + (2n-1) - 2 + ... + (2n-1) - (2n-1)$$
warm shaleBOT
Emran & Knuckles
timid silo
$$n_{j} = \sum_{i=1}^{2n-1}(2n - i)$$
warm shaleBOT
Emran & Knuckles
timid silo
we don't care about constants when calculating big-O
you need to read up more on sequences and sums of sequences
trust me, it will help
sorry, but I have to go now. You'll get there, you just need to get yourself used to noting down patterns and generalising them
that and
$$ \sum_{i=0}^{n} r = \frac{n(n+1)}{2} $$
warm shaleBOT
Emran & Knuckles
timid silo
That's also pretty useful for O(n)
oh, and one more thing, you might get more replies if you ask this in a Computer Science server
since this topic is more related to CS
any time
timid silo
https://discord.gg/eF3Wjsd
Sorry for not being of much help, you'll probably find it here though! :D
Make sure to close if you're done
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
stable apex
obtuse pebbleBOT
stable apex
can I solve this with adjuncy matrix if its so then how do I calculate I know how to create the adjuncy matrix
so lets say I want to find the shortest for 1-->4
do I just have to calculate the cost ?
but in the question seattle to pullman there is no weights are given
or do I have to calculate the length (number of edges)
obtuse pebbleBOT
@stable apex Has your question been resolved?
stable apex
<@&286206848099549185>
balmy raptor
I'm not a CS guy, so you're listening to a kid response
You could split all triangles in square ones
Then you could create a cost factor based on how many times you have to walk on the longest ledge, and assign a value increasing depending on how long is that ledge compared to the other
I would say that shortest implies 0 stop value, which means the overall shortest path
stable apex
sounds kinda hard ?
charred plume
If the question is just about finding the shortest path Seattle -> Pullman in the picture at the top, and there's no extra info given, I think you've got to just eyeball it. To my eyes, there's a pretty clear shortest-path.
(Where I'm assuming it's a normal map, and the length of each green line is the actual length.)
stable apex
seattle ->wentche->spokane->pullman what if the actual road length is higher than the others?
ok so here they are asking for find the adjuceny I just have to draw the table right
something like this ?
charred plume
Haha, I guess it's not so clear! I was thinking Seattle -> Cle Elum -> Moses Lake -> Richland -> Pullman looked shorter. :/
charred plume
something like this ?
Something like that, yes, but if the rows/columns are in the order A,B,C,D,E,F, then that matrix doesn't match the graph above... for example, the matrix says there's an edge between A and C.
stable apex
Something like that, yes, but if the rows/columns are in the order A,B,C,D,E,F, ...
oh yeah I know ,in general if they asked to find the adjuncy matrix I just have to draw that table?
charred plume
Yeah, I'd say so. Probably a good habit to give the order of the rows/columns though.
If the vertices are already labelled 1,2,3,etc, then it's probably obvious, but even still...
stable apex
Yeah, I'd say so. Probably a good habit to give the order of the rows/columns t...
oh ok thank you so much
charred plume
👍
stable apex
before leaving
do you have any idea on this qustion?
is tht how do I have to answer?
charred plume
Well, in general there are algorithms for solving such problems, but... I'd just eyeball it again.
Yeah, that looks correct for the first part.
Look at 4th and Seneca though. Can you get there, and if so how?
stable apex
this is what 4th and senca right how can I go there without taking any steps by flying? the person who made this pdf is not a cool guy
he intentionally puts the wrong answers
timid silo
can anyone help pls
obtuse pebbleBOT
can anyone help pls
scarlet locust
can anyone help pls
do you know the sum of an ap formula?
timid silo
yeah
scarlet locust
or the formula for sum of first n natural numbers
timid silo
or the formula for sum of first n natural numbers
no i dont know this
scarlet locust
do you know the sum of an ap formula?
if you know this then just use this
first find the number of terms
an = a + (n-1)d
plug in an=99, a=3, d=3
and find n
timid silo
Gauss sum can work as well
timid silo
plug in an=99, a=3, d=3
btw when it says the "first" n natural number do we assume a to be 1 or 0?
timid silo
ahhh alright
also it says inclusive in the question
i was thinking S99-S2
why doesn't this work?
@scarlet locust ?
scarlet locust
and find n
what did you get
hexed agate
Do Sn after you find the n
timid silo
what did you get
31
timid silo
there aren't 99 terms
oh yh
hexed agate
Yes
hexed agate
Ok
timid silo
but i get what you're saying, thanks
obtuse pebbleBOT
Available help channel!
spring horizon
obtuse pebbleBOT
spring horizon
anyone want to help make sense of this
warm canopy
What exactly? This is integration by parts
spring horizon
yes, I think they are generally pulling out the values from the second line and integration I am just unclear on this because there are inconsistancies where they are taking the values needed to be integrated
obtuse pebbleBOT
@spring horizon Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
sinful mortar
hello!
lusty cedar
ask
sinful mortar
I have a problem calculating the line-point distance with one of the axis