hey so to go back on this
#help-0
alpine sable
I have to come up with sizes of the prism
marble saffron
or any negative value?
alpine sable
I dont have an image
dusky rain
i dont think it can then
alpine sable
Leme translate it from dutch
tidal bane
How does one hypothesis test?
alpine sable
Can i dm you the text?
dusky rain
alright
coral wren
i asked the teacher if we could do some system of equations, instead of doing random equations we did last year, and she said, later and then we never did the m 😂
tidal bane
specifically to find the alpha value associated with p1 =/= p2
coral wren
what do you need?
alpine sable
i need help with polynomial functions and real roots
quasi lodge
do u know about OO prime and RR prime?
dusky rain
no
im actually not too sure about that question
are you supposed to answer it in terms of a or in terms of a number
alpine sable
does anybody know? <@&286206848099549185>
coral wren
are you supposed to answer it in terms of a or in terms of a number
i suppose both go
dusky rain
im pretty sure it doesnt work in terms of a number
coral wren
so thats the final answer?
dusky rain
i guess yeah
coral wren
to me it seems fine
ivory gulch
alr u guys done
coral wren
what
dusky rain
its ok lol
coral wren
anyone can ask whenever
alpine sable
@tough tangle
crisp grove
f(x) =x^¼ @ivory gulch , x0=256
ivory gulch
$L\left(x\right)=f\left(a\right)+f'\left(a\right)\left(x-a\right)$
ocean sealBOT
ski
ivory gulch
and when i sub everything in i get L(x) = -12 + 1/16 x
tough tangle
one of the last 2
ivory gulch
f(x) =x^¼ <@650764302512422974> , x0=256
so what then
crisp grove
-12?
crisp grove
$f(x+\delta x) = f(x) + f'(x)\delta x$
ocean sealBOT
Ryuzaki
crisp grove
yr x is 256 and dx=-1
ivory gulch
$L\left(x\right)=4+\frac{1}{16}\left(x-256\right)$
ocean sealBOT
ski
crisp grove
🤨
crisp grove
think it is
ivory gulch
alr so
if i plug everything i get
$L\left(x\right)=4+\frac{1}{16}x-\frac{256}{16}or:16$
ocean sealBOT
ski
ivory gulch
or x/16 - 12
alpine sable
4+1/32
crisp grove
yeah
tough tangle
<@!219008247254876160>
the last ans probably
crisp grove
then sub in 254, what's the issue?
crisp grove
yeah 264
ivory gulch
bc it's wrong
stuck delta
ivory gulch
answer is 129/32 according to the key
crisp grove
,w derivative of x^(1/4) at x=256
ocean sealBOT
coral wren
How do i know where to put the x=
coral wren
yes
crisp grove
ivory gulch
,w derivative of x^1/4
ocean sealBOT
alpine sable
It's correct
karmic rapids
Have you done here?
ivory gulch
<:sully:651816820122189834>
hey
crisp grove
@karmic rapids there are 9 different channels to ask
ivory gulch
i forgot to cube
alpine sable
How do i calculate the area of an cone again?
stuck delta
bold quail
alpine sable
How do i calculate the area of an cone again?
Ï€rl
excluding base
alpine sable
Ï€rl
excluding base
is L the height of the cone from the side of the base?
alpine sable
is L the height of the cone from the side of the base?
no if h is the height
L = sqrt(r^2+h^2)
alpine sable
[0,inf) write in this way maybe
alpine sable
how would it look like with that?
wait how do you know it's always moving in the +ve direction
edgy sand
i found the slope of the function for position
silver current
Take lcm for the LHS
after making both LHS and RHS in one term each, cross multiply
pine cipher
slow swift
For every 5 pizzas increased, the price is increased by roughly 26
The plus c should always be the "initial cost"
Because when you sub in 0 for x you should be left with just c for example like in questions where height of a thrown object is modeled
Not sure if ur meant to take the price for 5 pizzas as initial though
alpine sable
I have to sum every 3 digit number that can be formed with 1, 5, 6, 7, 8 and 9, and those digits can't be repeated
So we have 120 different numbers
And I don't know how to start calculating this sum... I don't find any clue... or just anything
placid zinc
I have to sum every 3 digit number that can be formed with 1, 5, 6, 7, 8 and 9, ...
There's 6 numbers. You're choosing 3 of those numbers to build a three digit number. Order matters in the choice. So, you've got 6P3 possibilities
peak iron
Hi, how can this be done?
placid zinc
I might not be familiar with the notation. Does the x² + x + 1 part mean that x satisfies x² + x + 1 = 0?
peak iron
It is like Z2, Z3, Z4,... with modulos
But instead of modulo a number, it's the 'modulo' of a polynomial
It's a field
placid zinc
Right, I understand what Z2[x][y] would be
But that x² + x + 1 bit in the middle is something I haven't seen before
peak iron
What would Z2[x][y] mean?
sick torrent
How do you do a question like this?
alpine sable
@past sleet @alpine sable So I already proved it for n =1 , n = 2
But im confused at this part
past sleet
Now what we want to do is assume it is true for any n, and then show that that implies it holds for n+1
alpine sable
past sleet
well ur gonna wanna do this one sec
alpine sable
Now what we want to do is assume it is true for any n, and then show that that i...
See im confused where K came in though...
Like if were proving for n + 1 wtf is K
n is just K i dont understand why we switched notation lol
past sleet
ah, these are dummy variables dont pay too much mind to it
basically the idea with induction is
prove that you can get onto a rung on a ladder (prove a base case), and then prove that you can get from one rung to another (inductive step). So you can conclude then you can climb the whole ladder
does that make sense
alpine sable
Yeah that makes sense to me
past sleet
Right so you've shown you can get onto a rung on a ladder
now we just need to do the inductive step
So consider for any natural number k
$\sum_{i=1}^k i = \frac{(k)(k+1)}{2}$
ocean sealBOT
mirzathecutiepie
past sleet
Now we need to show $\sum_{i=1}^{k+1} i= \frac{(k+1)((k+1)+1)}{2} = \frac{(k+1)(k+2)}{2}$
r u with me
alpine sable
umm one sec
ocean sealBOT
mirzathecutiepie
past sleet
we are just setting up the problem rn
like what are we starting with, what do we want to prove
alpine sable
Oh ok so, if I remember corecty you just have to show that this will work for K + 1 and then it will imply it works for any K + infinity. So we only need to prove the K + 1 case? Or do we still have to prove just K also
past sleet
No we assume its true for any K, then we show it's true for K+1. We need to show we can get from one ladder to another
one sec let me give u some intuition for this
suppose we have a proposition P, some property relating to the natural numbers. Now suppose we start with P(1) being true. Suppose we've proven this. And suppose also that P(k) => P(k+1)
Now let's say i want to know if P(4) is true
well I know that P(1) is true, and P(1) => P(2) is true, and P(2) => P(3) is true and P(3) => P(4) is true
So we get this chain of implications
Suppose i want to know if P(10) is true
P(1)=>P(2)=>P(3)=>P(4)=>....=>P(9) =>P(10)
so this can be done for any natural number
So this is what we want to do
does that make sense 
alpine sable
Yeah so instead of => we just want to see if this specific formula holds true for K + 1?
which is represented by P
lmao
past sleet
No when we're doing P(k) => P(k+1) we're setting up this way to climb the ladder per se
alpine sable
ok ok
past sleet
If we show P(1) is true and P(k) implies P(k+1) then P(2), P(3),P(4),P(5),.... all are known to be true
alpine sable
I think I get it were just assuming K is true , and setting up K + 1, we havnt solved anything yet
past sleet
yeah precisely
past sleet
**mirzathecutiepie**
now consider this $\sum_{i=1}^{k+1} i = \sum_{i=1}^k i + (k+1)$
ocean sealBOT
mirzathecutiepie
ripe rock
Hello quick question, how do you do c^d mod n for large numbers on the TI calculator Nspire for RSA method
currently giving me this
but answer is 2021
past sleet
**mirzathecutiepie**
do you follow?
alpine sable
**mirzathecutiepie**
Ok im looking at this rn
past sleet
remember because $\sum_{i=1}^k i = 1 + 2 + 3 + ... + k$
ocean sealBOT
mirzathecutiepie
alpine sable
Right so for i = 1 is just K + 1 + 1
past sleet
$\sum_{i=1}^{k+1} i = 1 + 2 + 3 + ... + k + (k+1)$
ocean sealBOT
mirzathecutiepie
past sleet
Right so for i = 1 is just K + 1 + 1
wdym
alpine sable
ohh
hybrid flower
If i have 10% chance for event to happen, and i roll 4 times, what is the chance for the event to happen twice?
Kind of noob question lol
alpine sable
So you sum untill K + 1 , increasing by K times to K + 1
past sleet
**mirzathecutiepie**
anyways now notice that we can pull a trick here $\sum_{i=1}^{k+1} i = \sum_{i=1}^k i + (k+1) = \frac{k(k+1)}{2} + (k+1)$
ocean sealBOT
mirzathecutiepie
past sleet
So you sum untill K + 1 , increasing by K times to K + 1
you sum until k+1, each time incrementing. So this is basically a for loop, im assuming ur a comp sci student so trying to relate with what u know
alpine sable
Yes that makes sense
past sleet
i = 1 and then you evaluate the expression after the sum sign, then i = 2 and you evaluate the expression after the sum sign, and you add these two together, and so on
past sleet
**mirzathecutiepie**
anyways, can you try seeing what the next steps are?
keep in mind the expression we want to reach
past sleet
**mirzathecutiepie**
we want to show this
alpine sable
anyways, can you try seeing what the next steps are?
Yeah lemme write it down
past sleet
yeah
past sleet
Sure go for it
it's how we learn
plus don't be worried about being cringe and stuff there's always someone out there who'll find you cringe for something, best not to worry about it
alpine sable
Well If I remember my fractions, you cant just add a fraction with a different denominator, so I multiplied (k + 1 ) by 2 so I could add it to K(K+1)/2.
Is that even close to what I should be doing lmao
ocean sealBOT
mirzathecutiepie
past sleet
now just one step left
alpine sable
Right, thanks! Then I cant remember... you could just reduce 2/2 so it would be just k(k + 1) + (k + 1)? I cant remember if thats allowed because 2 is part of the (k+1) term
past sleet
no that's not allowed
alpine sable
dangit i always try doing that lmao
past sleet
$\frac{k(k+1) + 2(k+1)}{2}$
you see what we have here is basically notation just notation for
gloomy wharf
alpine sable
Okay ill do it without randomly canceling the 2
past sleet
$(\frac{1}{2})(k(k+1)+2(k+1)}$ so "cancelling out" is just applying distributive property ukwim
ocean sealBOT
mirzathecutiepie
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
vague coral
slope formula
gloomy wharf
...
past sleet
**mirzathecutiepie**
remember our end goal, you're very close to it. You need to do just one thing
gloomy wharf
y=11x?
vague coral
I don't know, I didn't calculate
alpine sable
remember our end goal, you're very close to it. You need to do just one thing
Ok lemme see if i can get the correct transofmation
past sleet
How do you get from $\frac{k(k+1)+2(k+1)}{2}$ to $\frac{(k+2)(k+1)}{2}$
ocean sealBOT
mirzathecutiepie
alpine sable
So my thinking is that the k from the first term and 2 creates the (k + 2) , and that some how one of the (k + 1) terms is canceled... I know multiplying the numerator out is not the answer cause you'd end up with a quadratic equation of k^2 + 3k + 2. So my next thought was to multiply by 1. I tried multiplying the whole equation by (k + 1 ) and (k -1 ). That did not seem to work either 😅 I feel like that should have been the method though maybe I chose the wrong number to multiply by lol
ocean sealBOT
mirzathecutiepie
past sleet
so basically we can pull out the (k+1),
past sleet
So my thinking is that the k from the first term and 2 creates the (k + 2) , and...
multiplying is the answer actually, since both are well quadratics
in fact both answers work
you can multiply out the numerators in both and show that they are equal
or, you can factor out the k+1 and make it (k+2)(k+1)
to drive this further home
(k+1)(k+2) = (k+1) * k + (k+1) * 2
= k(k+1) + 2(k+1)
alpine sable
Ohh I didn't know if you could just pull it out of the two terms like that, my math fundamentals are so bad
past sleet
ah it's nothing
we were all there
i recommend having a look at khanacademy or paul's online notes. Try to understand why the rules are the way they are and stuff will start to click nicely 
I hope that helped tho
so we've completed the inductive step
and so the proof is complete!
alpine sable
Yesss I'll have to check that out, I use KA for linear algebra rn 😅 . Thank you! You made alot more sense than the book
alpine sable
Thank you! Ill be writing this out now formally and make sure it makes sense to me
past sleet
sure no problem, ping me if u get stuck or need clarification
proud kestrel
How can I show that the magnitude of H is dependent on KA but the angle isn't?
I mean it makes sense if I think about it graphically like a vector, multiplying by a scalar doesn't change direction
alpine sable
ew is that physics looks familar
toxic meadow
can someone please guide me through this
alpine sable
Should I consider each factor as a complex exponential?
I find its better to ask if anyone is knowledgeable in the channels about your specific problem first, otherwise it gets lost in the sauce
pale pond
anyone know what "Log-temporal delay" means?
glass lichen
anyone know what "Log-temporal delay" means?
Have you tried Google?
pale pond
ya don't see anything for that exact wording, main stuff that comes up is on "Logarithmic based optical delay", which might be what its referring to
buoyant kayak
can someone please guide me through this
do you know what the graph of ln(x) looks like?
toxic meadow
do you know what the graph of ln(x) looks like?
yeah
point at (1,0)
buoyant kayak
right, and where does your graph go through the x axis?
toxic meadow
(0,0)
buoyant kayak
so which coordinate changes?
toxic meadow
x
toxic meadow
In(-x) right ?
toxic meadow
f(x+1) ?
buoyant kayak
right, which in the ln function would be ln(x+1)
so now we have our graph translated to the right spot, it now crosses through the origin (0,0)
but it still doesn't look quite like the ln(x) graph
toxic meadow
don’t i need to reflect it over the y-axis
toxic meadow
make x negative
buoyant kayak
sorry bathroom
quartz osprey
buoyant kayak
oh shoot i thought it had an asymptote at 1
toxic meadow
oh shoot i thought it had an asymptote at 1
it’s at 2
buoyant kayak
$xln(a)=ln(a^x)$
ocean sealBOT
a disappointing son
buoyant kayak
it’s at 2
yeah my bad, i read your graph incorrectly
so new strategy same concept lol
toxic meadow
so new strategy same concept lol
i get the (-x+2) part but how do it get it to go through (0,0) and (-2,1)
buoyant kayak
well, when x is 0, y is 0
so, y=ln(-x+2), plug in 0 for x and solve for y
what do you get?
toxic meadow
2
buoyant kayak
not just 2
toxic meadow
In(2)
buoyant kayak
right
so when x is 0, y is ln(2)... so we can fix that by translating our graph down ln(2) units
pallid void
is anyone using this channel
pallid void
(2,0)
faint elbow
x first then y
and since there are 4 squares between 0 and -2 you can find the number inbetween
dusk solstice
-1
faint elbow
yes
dusk solstice
What’s the answer
faint elbow
You got it
faint elbow
Well the dot is not on x = 0, so read the x-axis first, and then the y-axis
faint elbow
yeah buddy
dusk solstice
Ok ty
faint elbow
That's the standard procedure
vernal wind
Hey can someone explain me this Y = c*Ln(X)+b ?
It should be the equation for a logarithmic trend line. But i dont what letter stand for?
<@&286206848099549185>
vagrant falcon
where do i even start with this?
faint elbow
derive 8e^y by taking the log of e
say derivative of y': 2x^y =2x^y * log(x) for the first derivative
and since you need to do it a second time, its a repeat of the log section, since it doesn't have y in it
@edgy sand
edgy sand
derive 8e^y by taking the log of e
where does the log appear from?
forest sage
Search the remainder theordm
frail rivet
can i ask
paper holly
how do we simplify sin(arccos(x)) or cos(arcsin(x))
ivory zinc
Just quick clarification on algebriac word problems. Typically when asked for the variable k when it wasn't already provided in the problem, it's the constant correct? In this case "At a constant t the v varies inversely as P" [Then it asks for K and P]
north needle
Ln(e) is 1
north needle
No? I don’t think you could split the Ln(1+e^x)
north needle
Yeah
north needle
I think it’s cause it’s a function within a function
Ln(1+e^x) ≠Ln(1) +x I think
Yeah Ln(1) is O so the function can’t be split
quartz osprey
ok i see thank yuoui
empty snow
need help
void solar
Do you know remainder theorm
quartz osprey
x^2+
empty snow
i know factor theorem not heard of remainder
void solar
i know factor theorem not heard of remainder
same thing but instead of 0, its a remainder
empty snow
so would i get the answer with long division?
north needle
You could but it would involve simultaneous equations and be kinda hard to do and higher risk of a mistake
north needle
180-
stiff idol
?
stiff idol
so is p = 19
north needle
Yeah
stiff idol
ok
void solar
need help
Basically its saying f(x) diveded by 2x-1 = -5
so you can change 2x-1 into x = 1/2
then sub that into the equation and equal it to -5
then solve
brisk sentinel
I am having trouble on this problem, and idk how to start it
empty snow
Basically its saying f(x) diveded by 2x-1 = -5
so you can change 2x-1 into x = ...
ooh thx
magic root
Write a mixed number and then convert it to an improper fraction. Draw a diagram to confirm your answer is correct.
how would I draw a diagram to confirm this?
<@&286206848099549185>
hushed pasture
I am having trouble on this problem, and idk how to start it
$|x-a| \ge b \ \implies x\ge a+b$ and $x\le a-b \ \implies a+b = -2, a-b = -8$
ocean sealBOT
Salah
brisk sentinel
$|x-a| \ge b \\ \implies x\ge a+b$ and $x\le a-b \\ \implies a+b = -2, a-b = -8$
so what would a=?
ocean sealBOT
Salah
dawn glade
Question: 4 people pay different amounts for a shared item but want to even out after. What's the formula?
brisk sentinel
solve that system
When I enter a or b in the answer sections it says "b,a is not defined in this context" I put a=-2-b, a=-8+b and b=-2-a, b=8+a Am i missing something? thank you for helping me
brisk sentinel
nvm I was being a small brain I figured it out. I was trying to do what you said separately and was getting all messed up. thank you.
hazy knoll
?
soft sun
north needle
C
a, b, c are constants
Constants means their value isn’t dependent on x (they don’t change)
So subbing in the co-ordinate gives:
1 = a + b + c
brisk sentinel
brisk sentinel
thank you!
kindred warren
no
prime fjord
If $\mathbb{P}(Y ≤ y) = \mathbb{P}(X ≤ y)$, then can I conclude that $X = Y$?
ocean sealBOT
egg bird
alpine nacelle
Not necessarily
wild oar
What is the probability that a number between 1 and 119 is a multiple of 2 or 3?
Does anyone know?
alpine nacelle
Can you rephrase your question ?
prime fjord
I believe he means is it true that P(X = a) = P(Y = a)?
However that would imply they are the same random variable I think
alpine nacelle
Two variables can follow the same law without being the same variable
sick torrent
Why is the second part incorrect?
alpine nacelle
Nope
sick torrent
Should be 3x(x - 6)
I also did that and it was wrong
There’s something else I’m doing wrong I just don’t know
prime fjord
Nw
north needle
What part?
north needle
For A do 5! x 5!
It’s looking for combinations
zealous adder
I did apparently that's not the answer
north needle
So for A since you have 5 possible tens you also have 5 units
zealous adder
prime fjord
I still got it wrong ðŸ˜
Fix the f' and f
north needle
Wait no it’s 5 x 5!
prime fjord
Get them both right, then the whole answer will be right
zealous adder
Why
north needle
You can only have the first digit once
So you can do 11,12,13,14,15
21,22,23,24,25
zealous adder
Isn't 5! = 5×4×3×2×1
ashen anchor
north needle
Ah
zealous adder
Ohhhhgggggg
alpine nacelle
Random variables are functions, they're equal in the usual sense of function equality, iff they're equal for all values. They don't even have to be the same variables to follow the same law, and if they have different law they can still be coincidentally equal for some value. One equality of proba on some specific value for two different variables and laws doesn't imply anything.
north needle
Why was I doing combinations?
ashen anchor
no problem, hope my handwriting is understandable
zealous adder
Your handwriting is good
north needle
Why was I doing combinations?
Stats!! 
that’s why I was going combinations 
sick torrent
Fix the f' and f
Oh my gosh it worked thank you so much
simple python
How do i get from the second to the third line?
gaunt mulch
Guys ima try to learn a years worth of calc in one night got any tips for staying up or just in general?
north needle
Guys ima try to learn a years worth of calc in one night got any tips for stayin...
You don’t really want to stay up all night because it’s bad for retention but energy drinks/caffeine and staying focused will help keep you awake
fresh parcel
Guys ima try to learn a years worth of calc in one night got any tips for stayin...
buy brilliant subscription
lol
gaunt mulch
Ok thanks ! 🙂 lol
zealous adder
How do I apply this rule here (23)
north needle
How do i get from the second to the third line?
Is this an integral?
fresh parcel
How do I apply this rule here (23)
for the first one cant u just do combinations
zealous adder
for the first one cant u just do combinations
Elaborate
zealous adder
A's answer is 60 apparently
fresh parcel
oh wait it needs to be even
zealous adder
Yer
fresh parcel
well then the last digit has to be 2 4 or 6
ashen anchor
How do i get from the second to the third line?
fresh parcel
so then there are 5 choices for the first digit in the number
and 4 choices for the second
and since the last digit could be 3 different values then you just multiply by 3
so
5 x 4 x 3
is 60
zealous adder
Ohhh
fresh parcel
the second one is a bit harder
as 0 cant be the starting digit
but you can just do casework
fresh parcel
mhm
so
there are 2 cases
either 0 is at the end
or it isnt
if it is
then we can do the same thing as last time
5 values for the first digit, 4 values for the second
so we get 20 for the first case
ah wait
there are more cases
fresh parcel
if 0 isnt inside the number
then we get 4 choices for the first
and 3 choices for the second
crap
this is kind of hard to explain
zealous adder
..
fresh parcel
mb
ill really dont know how to answer it in a well explained way
maybe ask someone else?
zealous adder
Okokok thanks anyway
ashen anchor
what was the answer supposed to be?
zealous adder
52
north needle
Ending is 0:
5 possible starts and 4 middle so 20
Ending is 2:
4 possible starts, 4 middle so 16
4 is exactly the same as 2
32 + 20 is 52
Stars means first number and middle is second number
zealous adder
So when we see 0 we always have to evaluate it as if there are 2 options?
north needle
Wdym?
zealous adder
Like if I see 0,2,6,8 I have to make two separate circumstances
One for 0 one for not zero
north needle
Yes though technically here I made three except the none 0 give the same val
So I cba to write out
zealous adder
Okokok and if there's no 0 I just use the method fiction showed
north needle
It’s annoying because of the three digit number
Otherwise you could do the same as before
zealous adder
If it's 4 digits I do the same thing, yes?
zealous adder
i did the same thing as <@!804837062163300363>
Thank u
north needle
If it's 4 digits I do the same thing, yes?
Yes doing the same should be fine
zealous adder
Okok thank u
ashen anchor
its just a bunch of case checking which is annoying
there's probably a more elegant solution but im too small brain for that
lol
ocean sealBOT
marc
alpine nacelle
The set of positive integers is itself closed under addition
x, y positive integers, x+y is a positive integer
Wait no
Idk why I imagined finite subsets I'm so dumb
You obviously have ok subsets
Like 2Z
The subsets of all positive even numbers is closed
Under addition
Since the sum of positive even number is a positive even number
obsidian scarab
alpine sable
,w calc
ocean sealBOT
marc
alpine sable
,w calc 90/480 * 100
ocean sealBOT
alpine nacelle
You also have more trivial examples, like the subset of integers greater than 5
Is a subset of positive integers
Closed under addition
wary jungle
can someone help me figure this out
alpine sable
i dont know?
wary jungle
ok i want ppl who do know how to help
warm brook
@wary jungle I’m assuming that you’re using
[\lim_{h\to0} \frac{f(x+h)-f(x)}{(x+h)-x}]
ocean sealBOT
kirby
fresh parcel
isnt the bottom just h
warm brook
the denominator is just h, but I wanted to write it out completely so it’s change in f over change in x
yes
fresh parcel
oh
opal reef
quick question, with linear functions does it matter if the input is negative or positive?
fresh parcel
quick question, with linear functions does it matter if the input is negative or...
for?
warm brook
this channel is taken rn, but no, it shouldn’t matter
opal reef
what are linear functions
Functions describe situations where one quantity determines another
fresh parcel
quick question, with linear functions does it matter if the input is negative or...
yeah
like for 5x + 2
if the input is negative it changes?
alpine sable
Functions describe situations where one quantity determines another
example
fresh parcel
im confused
opal reef
if the input is negative it changes?
lets say (5,8) and (-5,4) are on a graph, does the positive and negative integer change the fact it is not a function>
warm brook
no
alpine sable
hm.
fresh parcel
still confused but i guess it got answered
warm brook
okay this is not a function
opal reef
okay this is not a function
yes
alpine sable
okay this is not a function
thats a graph
fresh parcel
im in 8th grade too, don't you learn it there
opal reef
im in 8th grade too, don't you learn it there
depends if its alg 1 8th grade or pre alg 8th grade
alpine sable
i will google it myself
fresh parcel
its better to learn stuff now than later
warm brook
thats a graph
fresh parcel
if you know calc by gr8 you'll pretty much be fine
warm brook
if you know calc by gr8 you'll pretty much be fine
what
opal reef
if you know calc by gr8 you'll pretty much be fine
calculus?
zealous adder
fresh parcel
who knows calculus in 8th?
idk
warm brook
so how many more bears are there than earlier
zealous adder
What do I do here
warm brook
yes, so what’s the percent gain? So if there are 7 more bears when there used to be 10..
fresh parcel
increase
opal reef
i was bad at math before quarantine but quarantine gave me a chance to learn
math is essential in finance and economics, thats why im into it
warm brook
uh oh
fresh parcel
yes, so what’s the percent gain? So if there are 7 more bears when there used to...
whats 7/10
its 70%
so yeah
warm brook
I-I know
ocean sealBOT
marc
alpine sable
ok so
IF
shelby could run 4 miles now
its 2 times the distance she could run at the beggining of the year
which is 200%
- 100 %
but this is 3.5 miles
so we notice that 2 + 4*(0.5) = 4
warm brook
the integers form a ring, so yes, as long as the subset also forms a ring (which you can prove is always)
placid zinc
Any subset of Z under an associative operation, yes.
alpine sable
we can divide 100 by 4
25%
so 3.5 miles is 2 miles + 3*0.5miles = 3.5miles
then you go for it
+75%
you gain nothing by getting the answer
warm brook
The amount gain is the final - initial, then the percent gain is (final - initial)/initial * 100
alpine sable
The amount gain is the final - initial, then the percent gain is (final - initia...
where did you find that formula, damn
warm brook
so if final = 3.5 and initial = 2.0..
alpine sable
Anyone mind explaining this to me? Why does it being a constant term make it 0?
Dont get how k=-3 either
so 75%
\ ¯_(ツ)_/¯
warm brook
it’s okay they’re trying, they’re in 8th grade, I appreciate their commitment to at least trying to help
alpine sable
k
radiant barn
Hrlp
fresh parcel
Anyone mind explaining this to me? Why does it being a constant term make it 0?
if the constant term isnt 0 then it wont be divisible by x
alpine sable
if you dont know how to do just remember this formula
(final - initial)/ initial)) * 100
alpine sable
if the constant term isnt 0 then it wont be divisible by x
So it has to be 0 in order for it to be divisible by X?
ok here
so
no do the - first
warm brook
yeah so the idea is not to divide by 10, but rather you take the difference (15-12=3) and divide it by 12, which was the first number of laps
fresh parcel
So it has to be 0 in order for it to be divisible by X?
ye
fresh parcel
Dont get how k=-3 either
see when you factor the first part you get a constant of 15
alpine sable
but not always
alpine sable
see when you factor the first part you get a constant of 15
Yeah because if k = 0 then it would just be 15
yeah how much percent he gained
fresh parcel
nono
k isnt 0
the overall constant has to be 0
like after you add everything
the constant doesnt refer to k
alpine sable
the constant doesnt refer to k
So what is the general rule of constants? It seems like im missing something here rule-wise
In this scenario
fresh parcel
So what is the general rule of constants? It seems like im missing something her...
im kind of confused here
so the overall constant must be 0
or else x wont factor out
alpine sable
so the **overall** constant must be 0
I think I know what you're saying, so without a constant there is no problem to solve correct?
So the only thing to assume is that its 0
fresh parcel
I think I know what you're saying, so without a constant there is no problem to ...
first distribute everything
just try that first
alpine sable
Ok I get that part
warm brook
So the only thing to assume is that its 0
[P(x)=a_0x^n+a_1x^{n-1}+\dots+a_{n-1}x+a_n]
notice how if $a_n=0$, then you can pull an x out of $P(x)$ so that
[P(x)=x(a_0x^{n-1}+a_1x^{n-2}+\dots+a_{n-1})]
so then P(x) is divisible by x
fresh parcel
correct?
fresh parcel
but you'll see that theres a 15
ocean sealBOT
kirby
warm brook
So you’re not getting buried I can explain in DMs
fresh parcel
you'll also see that at the end theres a 5k
alpine sable
Mhm
fresh parcel
so the only 2 terms that dont factor out are 5k and 15
alpine sable
Yes Yes go on
fresh parcel
therefore, the best way to make sure the whole term is divisble by x we need 5k and 15 to cancel out
fresh parcel
now think: What does k need to be such that 15+5k = 0?
now you can easily see its -3
:)
slim sun
can i get help
alpine sable
oops
ocean sealBOT
marc
marc
marc
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)
warm brook
yes
Although it’s Q, think about the fractions..
1/2 is in the equivalent class for 2/4,4/8,etc.
so same works here
well, i don’t like the 1/2 neq 4/8, but in some way yes
ocean sealBOT
marc
warm brook
not really i don’t think
maiden saffron
alpine nacelle
Z_n is another notation for Z/nZ, these are modulo
The class of 0 has the elements that are equivalent to 0 mod n
But you'll probably see it further in the book
You can write the class of x as
$\bar x$
ocean sealBOT
Mélo
alpine sable
Hello, how should I use the chain rule for deriving this?
I first tried to split it up into 3 separate functions.
f(x), the outer function: 3x
g(x), the middle function: 3x^2-4
h(x), the inner function: 1/x
but when i tried to apply the chain rule, I couldn't apply g(x) to f'(x), since f'(x) is just 3.
no variable to apply it to.
sour dove
yes you'll need chain rule but only for one thing
I would distribute out the 3 first. What do you get?
alpine sable
9((1/x)^2)-12 ?
alpine sable
9x^2-12
sour dove
not quite
so we're deriving with respect to x
our only x is 1/x
but it's wrapped in a power of 2
now there are 2 options:
- You can distribute the square and turn it into 1/x^2 which is x^-2
- You can do the chain rule of (1/x)^2, which would be 2* (1/x) * (1/x)'
the -12 will go away since d/dx(-12) = 0
can you get it from here? 🙂
sour dove
@alpine sable feel free to ping me when you're at a place or get stuck
alpine sable
sure cosmos
craggy niche
Is this channel busy?
Doing a paper on correlation of two functions. Easy, issue is finding a dependent/independent variable. Independent cannot be time. Example was affect of time (years) on iPhone sales after 2007. Sales went up.
dreamy flint
bruh
alpine sable
placid zinc
@zinc cosmos
In order to prove two sets are equivalent, you prove that each is a subset of eachother. That is:
If x is a member of [k] + [l] then it is also a member of [k + l]
And if x is a member of [k + l] then it is also a member of [k] + [l]
alpine sable
lil help
ocean sealBOT
marc
placid zinc
Good, that's the hard one haha
ocean sealBOT
marc
ocean sealBOT
marc
placid zinc
No no. It shows that, if you choose any element in [k], and any element in [l] and add them together, you have an element in [k + l]
That is, you can add the representatives, rather than the elements themselves
I can make it concrete.
What's 202 + 2002 (mod 4)?
You can actually add those together, then reduce...
But you probably reduced first, then added them
zealous adder
For B I did 6P2 but C idk where to start
placid zinc
We're proving that doing the reduction first is legal
peak kite
I neeed help inaths question
Who can help mr dm me
Pls
Maths
Marc urs tough
If y can help
U
Dm me
placid zinc
Okay! Hopefully it helps. Feel free to ask if you need anything else with it
red mirage
are there any dedicated tutors on this server?
sour dove
@peak kite if you have some specific question post it here and helpers will help you. But it's on a per problem basis
red mirage
Looking for help with Math 169 trades mathematics 😫
sour dove
@red mirage see above. If you have a specific question feel free to post
red mirage
<@!693639304953724979> see above. If you have a specific question feel free to p...
ill have to post my whole text book lmaooo
sour dove
ill have to post my whole text book lmaooo
lol I feel you. But if you're stuck on a homework question or can come up with an example of something you're not understanding than feel free to ask!
but people helping do it on a volunteer basis, so it's a per question basis
red mirage
thank you!
midnight girder
hello!
could someone explain implicit differentiation
we have to self learn this concept b4 class and im a bit confused
how is it different from the basics of differentiation?
sour dove
@midnight girder implicit differentiation is super fun!
so whenever you take a derivative of something, say y = x^2
then you get (dy/dx) = 2x right?
midnight girder
right!
sour dove
but what if you wanted to take the derivative of something, say y^2 = x^2 + sin(x)?
buoyant kayak
it's taking the derivative treating y as a function of x
sour dove
if we're taking something the derivative with something with respect to x, then we need to manipulate something that is not x as well
so typically how that looks is of the form d/dx (y) = (y)'(dy/dx)
and we can see that in action with just a single y value!
alpine sable
can anyone explain derivatives
sour dove
y = x^2 using implicit derivation is (y')(dy/dx) = (x^2)', or 1*dy/dx = 2x
buoyant kayak
slope of a line at a point
alpine sable
im trying to understand
sour dove
so believe it or not, you're already doing implicit derivation without even realizing it!
alpine sable
so believe it or not, you're already doing implicit derivation without even real...
can you explain derivatives? i want to know how it works
midnight girder
y = x^2 using implicit derivation is (y')(dy/dx) = (x^2)', or 1*dy/dx = 2x
I SEE! let me try that on a problem now
sour dove
I SEE! let me try that on a problem now
so in the example earlier of y^2 = x^2 + sin(x), we get:
(y^2)'dy/dx = (x^2 + sin(x))'
2y(dy/dx) = 2x + cos(x)
dy/dx = (2x + cos(x))/2
@sour dove if for a problem where the y is not already isolated, would we have to isolate it first?
small cypress
<@&286206848099549185>
alpine sable
median...
buoyant kayak
the point of implicit differentiation is that you don't need to isolate y
sometimes it's impossible to do so
midnight girder
oh i see
alpine sable
sour dove
can you explain derivatives? i want to know how it works
Do you know what the definition of a derivative with a limit?
sour dove
I would start with that then
but basically you know the equation y = mx + b?
we know the slope is m, right?
alpine sable
no idea
sour dove
oh
buoyant kayak
an 8th grader does not need to know derivatives
sour dove
well I think you probably need to build up math foundations first
alpine sable
well I think you probably need to build up math foundations first
what do you suggest
alpine sable
damn i learned algebra when i was 5
sour dove
what do you suggest
Honestly just keep going through school. Get your algebra down and strong and then when you get to calculus you'll be fine
most mistakes made in calculus (aka where you use derivatives) are algebra mistakes
midnight girder
@alpine sable derivatives is a whole new concept
it has its own set of rules but once you learn it, it gets really easy!
its the same like 4 rules applied over and over
peak kite
Anyone that can help me in maths
buoyant kayak
probably not
peak kite
Oh
buoyant kayak
no it isn't
peak kite
1 by 10 right
wary stream
The ans goin to be negative tho
No it's not
peak kite
I have done
rough salmon
Oh
rough salmon
No it's not
Right
buoyant kayak
1/4 + some other number is 7/20
buoyant echo
how is this channel so populated lma
buoyant kayak
so $\frac14 + x = \frac{7}{20}$
ocean sealBOT
a disappointing son
buoyant kayak
solve for x
peak kite
Done
buoyant echo
am needing help
peak kite
1/10
wary stream
Is 1 by 10
1 over 10?
buoyant echo
how do i use the bot
wary stream
Yes
buoyant echo
yo how do i use that bot
peak kite
In a Rhombus ABCD ,if the measure of <A=50degrees then find the measure of <ADC
What about tis
past sleet
just ask the question spamton
wary stream
In a Rhombus ABCD ,if the measure of <A=50degrees then find the measure of <ADC
Draw a diagram first
rough salmon
I have a question too
Let's say I HV a num 80
a * b * c must be equal to 80
How many combinations r there of the values of a, b and c considering 2, 20, 4 and 4, 2, 20 is the same
peak kite
Okay
Wht us standard form of 1234000 is
Also what is depricet
@wary stream
What is depricet
Or sumthing
Hello
<@&286206848099549185>
buoyant kayak
not a word in the english language
shy thicket
WHAT THE ANSWER NOW 😡
buoyant kayak
use the formula for sum of a series
placid zinc
What are you allowed to use? Do you know sigma notation?
alpine sable
What are you allowed to use? Do you know sigma notation?
I am in alg 1
this is from the 2020 oxford mathmatics admission exam
I have no idea what sigma notation is
buoyant kayak
why are you taking the 2020 oxford mathematics admisison exam
peak kite
Find the depreciated value of a rikshaw after two years whose present cost is RS.144000 and rate of depreciation is 5/2% p.a.
placid zinc
Practice I assume
alpine sable
to get a sneak peak of what I will hopefully take when I go to uni
placid zinc
Never too early to learn sigma notation, as it makes problems like this easy
alpine sable
are you a math teacher
peak kite
Somoje help me
Pls uwh
Uwu
Find the depreciated value of a rikshaw after two years whose present cost is RS.144000 and rate of depreciation is 5/2% p.a.
alpine sable
*UwU
peak kite
UwU
placid zinc
No haha I've never taught professionally
alpine sable
also what is the best way to get advanced in math
peak kite
Find the depreciated value of a rikshaw after two years whose present cost is RS.144000 and rate of depreciation is 5/2% p.a.
placid zinc
Actually, I can think of a good solution you should be able to work with. Every two terms of this sum are of the form:
n² - (n + 1)²
= n² - n² - 2n - 1
= -2n - 1
So you can sum that for all odd n
alpine sable
that's called sigma notation?
placid zinc
No no I haven't included it haha