half saffron
#help-17
vocal sleetBOT
vocal sleetBOT
Available help channel!
vast shale
Quick question
vocal sleetBOT
Quick question
vocal sleetBOT
@vast shale Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
vast shale
This is the shape, and I got 2 trigonometry questions
-
Prove that DB=square root(a*b+d^2)
-
angle alpha is marked there, so they want me to prove that if alpha + beta = 90, sin alpha/sin beta-alpha = square root((a^2-a*b) / (2b^2))
vast shale
so basically I'm kinda stuck, it's math summer work I got, just started it and I'm already stuck
simple mason
This is the shape, and I got 2 trigonometry questions
1. Prove that DB=square r...
The second point isn't much obvious
Do you want to say
$$\frac{\sin(\alpha)}{\sin(\beta)} - \alpha = \frac{a^{2}-a \times b}{2b^{2}}$$
twin meteorBOT
Sherif Player
vast shale
The second point isn't much obvious
Do you want to say
$$\frac{\sin(\alpha)}{\si...
I mean this
simple mason
Oh
vast shale
the fact I just started it and I'm already stuck and demotivated pisses me off
simple mason
So the first thing that comes with my mind is to use either sin law or cos law to solve the first point
Do you know either of them?
vast shale
yeah learned both, cuz of the summer break I'll have to re-memorize both tho
or actually I remember sin law, i'll have to re-memorize cos law tho
simple mason
Ok
So the cos law states that
$$c^{2} = a^{2} + b^{2} - 2ab\cos(C)$$
twin meteorBOT
Sherif Player
simple mason
As C is the angle opposite to the line c
simple mason
But I think we need to use the sin law instead
Or actually I think we need to use both
simple mason
So
$$(DB)^{2} = a^{2} + d^{2} - 2ad\cos(\beta)$$
twin meteorBOT
Sherif Player
simple mason
So did he state that it is an isosceles trapezoid
twin meteorBOT
Sherif Player
vast shale
hmmmm
vast shale
Do you see how?
i'm not sure I can see how
simple mason
So I want from you to draw a perpendicular line from point B on DC as F and do the same with A as G
Do you know how to get the value of FC
@vast shale done?
vocal sleetBOT
@vast shale Has your question been resolved?
vast shale
<@456226577798135808> done?
yeah sorry for late response
I figured it out thanks for the help
radiant harness
let’s say there is a random number generator and there is only a 1/20 chance to get a 2 otherwise you would get a 1, what are the chances of rolling 1 thousand times and only getting a two once in percentage
vocal sleetBOT
let’s say there is a random number generator and there is only a 1/20 chance to ...
winter linden
can someone tell me why the -3 disappeared on the next step?
thin vale
can someone tell me why the -3 disappeared on the next step?
this channel is occupied.
!help
vocal sleetBOT
Please read #❓how-to-get-help
thin vale
open an available channel for your question
thin vale
let’s say there is a random number generator and there is only a 1/20 chance to ...
so what is the chance of rolling a 1?
radiant harness
so what is the chance of rolling a 1?
19/20
thin vale
what is the chance of rolling two 1's and one 2? In any order
tranquil lodge
how do i figure out if its horizontal or vertical
vocal sleetBOT
how do i figure out if its horizontal or vertical
tranquil lodge
worthy citrus
what do the words horizontal and vertical mean to you?
tranquil lodge
i cant tell how the graph would be changed if its horizontal or vertical
@worthy citrus
worthy citrus
you didn't answer my question
what is a vertical asymptote? a horizontal asymptote?
edgy matrix
Hi i'm trying to figure out the perimeter of this ellipse shape for a game and also cause i saw it in class and we didn't go over it.
I started with this formula. (1st attachment)
To find y for this ellipse equation we do. (2nd attachment)
Then i thought that to get the perimeter we just sum up smaller and smaller segments of the curve. (3rd attachment)
Then we multiply by 4 because there are 4 of those corners on a ellipse.
So i came up with this merging all the previous things together. (4th attachment)
Which i simplified to this (attachment 5)
vocal sleetBOT
Hi i'm trying to figure out the perimeter of this ellipse shape for a game and a...
edgy matrix
currently im stuck at the final attachment because i simply don't know if its possible to simplify that
or what to do
or even if its correct
vocal sleetBOT
@edgy matrix Has your question been resolved?
edgy matrix
<@&286206848099549185>
vocal sleetBOT
@edgy matrix Has your question been resolved?
sudden gulch
currently im stuck at the final attachment because i simply don't know if its po...
are you 100% sure it's an ellipse and not an oval or something
sn't there like you know
an easier formula for the perimeter of an ellipse instead of using calculus
vocal sleetBOT
@edgy matrix Has your question been resolved?
vocal sleetBOT
vocal sleetBOT
Available help channel!
signal rover
Can someone tell me what the difference between these 2 equations answers is?
signal rover
Equation 1: 5 + 2 * (3 + 5) x (5-1)
Equation 2: 5 + 2 * 3 + 5 * 5 - 1
I keep getting 189 and I don't know if I'm being dumb or if my teacher's websites answer is wrong
viral gate
if you expand the first equation you get 5+(2*8)(4) whihc is 69
and equation 2 is equal to 35
twin meteorBOT
Free Geoffrey
vast shale
.close
signal rover
.close
reef mica
Q: A car starts travelling at 50mph. Every mile it travels, it speeds up 5mph. How far does it travel in an hour?
vocal sleetBOT
Q: A car starts travelling at 50mph. Every mile it travels, it speeds up 5mph. H...
zinc quail
create a function for the speed depending on the time
the travelled distance thereby is that function's integral
reef mica
I would start with something like...
S = 50 + 5
is it 5D?
I don't know how to tie it back into T
zinc quail
Q: A car starts travelling at 50mph. Every mile it travels, it speeds up 5mph. H...
wait is the change of speed meant to be immediate? Meaning it travels 50mph for the first mile and then instantly switches to 55mph for the next mile?
reef mica
I think so.
zinc quail
ok which means the first mile takes 1/50h
second mile takes 1/55h
etc
which would rather be a sum problem I presume
where you want to figure out how many terms you have to add such that their sum is 1h
reef mica
Apologies, I am also trying to help another guy simultaneously.
Probably not recommended haha
Anyway it sounds like you are right
So do I have to add them all up or is there an equation for that?
zinc quail
So do I have to add them all up or is there an equation for that?
Hm currently I'd consider an iterative test or approximation the easiest way
but it could also be that I misinterpreted the task, may I ask what the context of the task is
e.g. whether you had harmonic series' & limits recently
reef mica
This task is an analog of a different problem I am working on
I thought it was a simpler framing
reef mica
The original context is as such: a character attacks 0.98 times per second, and each attack increases his attack speed by 0.04. How many times will he attack in 20 seconds?
I believe knowing how to solve the car problem gives me the strategy I need, and it's just slightly easier to write it out and explain it.
For even more detailed context, I want to know if a rapidfire cannon gives better or similar DPS to a rageblade in the first 20s of the fight. From Teamfight Tactics.
zinc quail
For even more detailed context, I want to know if a rapidfire cannon gives bette...
Then I'd recommend just using an approximation, will be quicker and doesn't require you to accurately represent the divergence of the harmonic series
reef mica
That's totally fair. I am still not sure how to even go about approximating.
zinc quail
you could also run it through if you rather want exact dps
where you calculate each term as mentioned above for the car
first term being 1/0.98 in seconds
second term 1/1.02
etc
and check the condition if the sum is >=20
reef mica
How would I ask wolfram alpha to do this?
Or a graphing calculator?
Or even chatgpt?
zinc quail
preferably not chatgpt, if then at least gpt-4. but I'm not too familiar with wolframs syntax as I'm a programmer :)
but I'm sure it can solve a harmonic series for a value
reef mica
Maybe I could even do it in Python
I just don't know how to start
Actually that might be a good direction to go, though. I feel like that offers better control than the other three options have been providing.
zinc quail
Actually that might be a good direction to go, though. I feel like that offers b...
yes it'd just require maybe 4-5 lines, the approximation would btw instead be an exponential function
where speed(t) = initial_speed * e^(k*t) where k is some yet unknown factor
however you can retrieve k by solving for a single value
reef mica
Huh. I don't quite understand how that works. Anyway I will give python a try, thanks.
.close
vocal sleetBOT
zinc quail
Huh. I don't quite understand how that works. Anyway I will give python a try, t...
hm k, the approx. would be mathematically more interesting tho :P
vocal sleetBOT
Available help channel!
weak leaf
Hi I need help understanding this problem
vocal sleetBOT
Hi I need help understanding this problem
vocal sleetBOT
@weak leaf Has your question been resolved?
weak leaf
well, do you know what sin means?
O/H?
weak leaf
So 5sqrt3/10
weak leaf
You want the sin(60), so do O/H from the 60 degree angle
Would this be the answer?
spiral inlet
not quite
sin(60) IS 5sqrt(3)/10
get rid of the sin(60) in that expression
Desmos will interpret it as 60 radians, not 60 degrees
and you don't need it anyway
spiral inlet
to four decimal places, yes
weak leaf
Ok thank you
spiral inlet
np 👍
weak leaf
.close
keen stirrup
vocal sleetBOT
keen stirrup
need help w this problem fo rmy multivar class
gaunt sparrow
- Convert angles in that form to angles from the positive x-axis
- Convert polar vector expressions to cartesian expressions using cos/sin
- Choose F3x and F3y such that the total sum in the vertical and horizontal directions are null
- Convert F3 back from cartesian to polar coordinates
What's bugging you?
vocal sleetBOT
@keen stirrup Has your question been resolved?
keen stirrup
What's bugging you?
i was lwk just gonna ask for the answer 😭
gaunt sparrow
That's not the point of this server and this problem shouldn't take you much more than 10 minutes.
keen stirrup
ok ill try it
timid leaf
vocal sleetBOT
timid leaf
can someone please explain how to find combinations using pascals triangle?
i asked chtgpt but i think its giving me bullshit
timid leaf
uh
timid leaf
Sure, here are a couple of examples using Pascal's Triangle for combinations:
Example 1: Choosing Ice Cream Flavors
Imagine you're at an ice cream shop with 5 flavors, and you want to know how many different two-flavor combinations you can create.
- Find the row that corresponds to the total number of flavors, which is 5.
- Count to the position that matches the number of flavors you want to pick, which is 2.
- In the 5th row, the number at the 2nd position is 10.
So, there are 10 different ways to choose two ice cream flavors from 5 options.
Example 2: Picking Books for a Reading List
You have 6 books, and you want to know how many possible combinations of 3 books you can include in your reading list.
- Go to the row that represents the total number of books, which is 6.
- Look at the position that corresponds to the number of books you want to pick, which is 3.
- In the 6th row, the number at the 3rd position is 20.
Thus, you have 20 different ways to select a reading list with 3 books from your collection of 6.
By using Pascal's Triangle, you can quickly find the number of combinations without having to list them all out!
does this make anysense or is it bs
like what are the steps to determining combinations using the triangle
<@&286206848099549185>
timid leaf
i couldnt understand any online explanations
timid leaf
Why use chat gpt for that
i thought it would be nice to have it "explain to me step by step like im 5"
i think it gave me trash though
orchid nacelle
i see
timid leaf
yeah
dull maple
does this make anysense or is it bs
It's not bullshit.
It's actually correct.
What's it failing to mention that you have to count rows starting with 0.
Not 1.
Same goes for columns.
timid leaf
It's not bullshit.
ok good to know
timid leaf
What's it failing to mention that you have to count rows starting with 0.
it keeps on saying rows though
how is everything a row
dull maple
Well, they are rows.
dull maple
how is everything a row
What do you mean?
dull maple
Yes. That's correct.
dull maple
from top row. Which we also call 0th row.
dull maple
starting from where
From left
dull maple
Okay. Yes
timid leaf
then from the left move desired amnt
dull maple
then from the left move desired amnt
Yes
dull maple
thats the max amnt of combinations
That's the exact amount of total combinations.
dull maple
Btw, this only works when you are allowed to choose each object only once.
Also, when objects are distinguishable.
timid leaf
unfortunately 
everytriangle has their flaws 
this is the most sense anything has made all day thank you for constantly putting up with my nonsensical bullshit
sand lodge
triangles
timid leaf
its not even cries for help anymore its squawking
dull maple
Lol. No one minds as long as you are actually trying to learn.
vocal sleetBOT
timid leaf
our love is theoretically infinite
vocal sleetBOT
Available help channel!
scarlet depot
can l get some help mechanic btw <@&286206848099549185>
vocal sleetBOT
can l get some help mechanic btw <@&286206848099549185>
vocal sleetBOT
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
rugged orchid
Secondly, try drawing a diagram
vocal sleetBOT
@scarlet depot Has your question been resolved?
scarlet depot
Secondly, try drawing a diagram
ok
rugged orchid
Answer the bot or this channel may get closed
scarlet depot
i did but only given weight amd a angle
scarlet depot
sorry my friend was trying to explain but he too doesnt know lol @rugged orchid
scarlet depot
i did but only given weight amd a angle
do i send a pic?
scarlet depot
vast shale
20 degrees is annoying
shouldve been 30 or 45 for easier calculation, but whatever
alright now can you picture what is happening without any horizontal force acting on it?
rugged orchid
Well clearly the box can’t go through the floor
So the 60N is redirected somewhere else
scarlet depot
its weight
rugged orchid
Find the components of the 60N parallel and perpendicular to the plane
scarlet depot
so 60 n is showing weight
rugged orchid
so 60 n is showing weight
I know
But the box can’t move through the floor
So it will move along the plane instead
So find those components
scarlet depot
Find the components of the 60N parallel and perpendicular to the plane
sorry how
horizontal and veritcal
using the 20 degrees
rugged orchid
Did you find the magnitude of the new arrows
vocal sleetBOT
@scarlet depot Has your question been resolved?
zenith wren
Determine a so that f(x)<0 for any real x
vocal sleetBOT
Determine a so that f(x)<0 for any real x
zenith wren
this is my work but i didnt get anywhere
lone linden
this is my work but i didnt get anywhere
For the function to be less than zero for all real x, the graph cannot cross the x axis, meaning the discriminant should be negative.
Also, note that ||the graph should open downwards||
zenith wren
if the discriminant is negative then how can i get a real solution
lone linden
A real solution to what?
zenith wren
so if the discriminant is negative then x=(a+/-sqrt( discriminant)*i)/2(a+1)
and the problem is asking me for any real x
lone linden
You’re solving f(x)=0, which is what you don’t want
zenith wren
yes I solve for f(x)=0 and then I find the values for which is negative
how else am I supposed to solve it?
lone linden
yes I solve for f(x)=0 and then I find the values for which is negative
This makes no sense
How can something that equals 0 be negative
lone linden
For the function to be less than zero for all real x, the graph cannot cross the...
Do you understand what I meant here?
zenith wren
yes in order for the function to be positive it would have to cross the x axis
but i dont get the discriminant part
if it is negative then the solutions wouldnt be real
zenith wren
How can something that equals 0 be negative
x1 x2
-inf 0 0 +inf
its not aligned well but I verify for values so that the function is negative
smaller than x1 bigger than x2 and between them
lone linden
if it is negative then the solutions wouldnt be real
That’s the point.
What you’re doing is deciding to make the function negative for certain, but not all, values of x
lone linden
and the problem is asking me for any real x
You said it yourself here
What you’re doing contradicts the question statement itself
vocal sleetBOT
@zenith wren Has your question been resolved?
zenith wren
I got it now.There shouldnt be any real x solutions because the function never crosses the x-axis
thanks
.close
pallid cairn
vocal sleetBOT
small quarry
U can write "9" better (Sorry for that cuz I just looked as a "g" lol)
pallid cairn
Ahahaha
proven garden
same lol
pallid cairn
Yeah i get that alot
small quarry
u solve x right?
pallid cairn
Si
proven garden
I don't see any mistakes
pallid cairn
Except for the G /9 all good then
pallid cairn
these are the solutions i got from using quadratic formula
pallid cairn
How so?
small quarry
BRUH
I type wrong my calculator
I type the constant with 60
lol
nvm u all correct
congrats
torn pecan
vocal sleetBOT
torn pecan
I need help with these two please
river minnow
!status
vocal sleetBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
pi = 22/7 
river minnow
I think they just rounded up 3.1415 lol
torn pecan
yea
torn pecan
```
What step are you on?
1. I don't know where to begin
2. I have begun but got...
Im stuck on calculation
river minnow
Could you show what you've got so far?
river minnow
So $V = \frac{22}7\left(8^2 - 5^2\right)\frac72$, right?
First you just need to simplify what's inside the parenthesis
torn pecan
not quite I think
river minnow
What's 8^2 equal to?
torn pecan
there is h aswell
twin meteorBOT
A Lonely Bean
torn pecan
What's 8^2 equal to?
yea
river minnow
I wrote 3 and 1/2 as 7/2 here
torn pecan
so using ditrabutive i did 7/264 and 7/225 first
instead of doing with 22/7
can I do that or is it wrong
river minnow
**A Lonely Bean**
I think it will be better if we first cancel the 7's and divide 22 by 2
torn pecan
sorry
river minnow
So that now it's 11(8^2 - 5^2)
torn pecan
I think it will be better if we first cancel the 7's and divide 22 by 2
yea
Ohhh
okay
my bad I calculated wrong
Sorry
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
warped dirge
I am quite lost on how to start my proof for the generalised ramsey inequality for $r(s, k) < r(s,k-1) + r(s-1, k)$
vocal sleetBOT
I am quite lost on how to start my proof for the generalised ramsey inequality f...
twin meteorBOT
Curuy
hard atlas
presumably start with one vertex and then consider the sets of neighbors of each color
warped dirge
presumably start with one vertex and then consider the sets of neighbors of each...
Similar to the method used for R(s,t) right?
I'm just a first year at uni, looking into ramsey theory for fun
hard atlas
Similar to the method used for R(s,t) right?
yes
warped dirge
hmm, what if I start by
$$R_1 = R(t_1-1, t_2,...t_k)$$
$$R_2 = R(t_1, t_2-2,...t_k)$$
$$\vdots$$
$$R_k = R(t_1, t_2-2,...t_k-1)$$
and then set $n=R_1+R_2+...+R_k-1$ and then pigeon hole principle tells us that there is at least $(n-1)/ k$ edges in 1 colour, lets say $t_1$. Not too sure if this can be used?
Curuy
warped dirge
building up from that
Like I need to gurantee that I have at least R_1 or R_2 etc edges I think
But like I do not know how you get the "-k + 2" term
I've also thought about using induction, but I do not know how I will prove the k+1 term
I've stumbled upon this question while trying to understand a bit of the proof of fermant's last theorem
I do apologise If my wording is a bit bad (I'm quite new to this)
Is it possible to continue this thread in a few hours (because it's 1 am where I live) I do not mind if you give me more hints (or even better give me a solution XD)
hard atlas
trying to understand the proof of flt is perhaps a bit too ambitious
just go to bed and when you wake up this server and helpful people will still be here
warped dirge
trying to understand the proof of flt is perhaps a bit too ambitious
perhaps you could recommend some readings or a solution? XD
hard atlas
good joke
timid plume
vocal sleetBOT
timid plume
Change quadratic equation into standard form
vast shale
Start by merging these fractions into one
vast shale
Ok and how?
Using the good ol' multiply the top and bottom trick
paper depot
show what you get.
paper depot
i'm gonna preemptively ask for a picture unless you definitely know how to type it properly
timid plume
X²+4x -X² -4x -2²+4x²-8x =x² -2x
paper depot
...
timid plume
I don't think so that you can understand my handwriting actually
paper depot
looks bad
paper depot
I don't think so that you can understand my handwriting actually
in that case, rewrite your entire work in such a way that your handwriting is understandable.
paper depot
maybe you are one of those people who consider this to be an adequate handwritten form for the letter x.
paper depot
Thats my ugly handwriting 💔💔💔
believe me i have seen a thousand times worse.
i can give you some tips for how to improve it, but i will not do so unless you explicitly ask for it.
now show your work for your problem.
timid plume
Aunty seriously you think this is a bad handwriting
paper depot
note i did not say your handwriting was bad...
timid plume
Ok
hasty kernel
note i did not say your handwriting was bad...
lol
paper depot
i actually think it is decent, though it does have room for improvement.
hasty kernel
it's pretty good
paper depot
i would rather see your work first though.
paper depot
ping me when done.
timid plume
ping me when done.
.
paper depot
,rotate 180
twin meteorBOT
timid plume
😁😁
paper depot
alright let's take a look...
bold wasp
time both sides by x^2-2x, quadratic forumula, done
timid plume
Oh ok
paper depot
(x-2)(x)(0) = ? @timid plume
timid plume
0/1 (x-2)(x)
bold wasp
(we still on this question?)
timid plume
It's will be 0
timid plume
Ok
paper depot
left hand side appears ok
paper depot
so you now have x^2 + 4x - (x-2)^2 + 4x(x-2) = 0
timid plume
Mhmm
bold wasp
time both sides by x(x-2), get the denominators off, use the quadratic formula and done
(this is not really giving off the answer right?)
timid plume
I just want to kill math rn
bold wasp
(It's just process)
paper depot
if you have murderous intentions then it is best to step back, shake those off, and come back later
you should probably expand it yes.
"expend" is a different word that means a different thing.
which doesn't make sense in your context.
bold wasp
step by step, time both sides by the denominators and get rid of them
timid plume
For just "A" I got that big lesson
paper depot
3 discord messages
big lesson
timid plume
Ok ok mam I am doing
paper depot
anyway, as before, you'll need to do it slowly and carefully and send all your work.
bold wasp
then simplify, combine the terms with the same variables
timid plume
So (A+B )² = A²+ B² + AB²
paper depot
❌
paper depot
(a+b)^2 = a^2 + 2ab + b^2.
bold wasp
actually I suggest we start from scratch
timid plume
It's same
paper depot
you should be able to see this by expanding (a+b)(a+b) the honest way.
timid plume
Ok
paper depot
no, alone boy, ab^2 is not at all the same as 2ab.
no, "that's what i meant" is not good enough.
bold wasp
no, alone boy, ab^2 is not at all the same as 2ab.
(just start fresh actually)
timid plume
timid plume
Sorry it's X-TWO
paper depot
(x-2)^2 transmogrified into (x+2)(x+2). it should not do that.
and 4(x-2)(x) transmogrified into 4x^2 + 8x.
what you should have had at this point is:
x^2 + 4x - (x^2 - 4x + 4) + 4x^2 - 8x = 0
timid plume
Ok mam
bold wasp
(x-2)^2 transmogrified into (x+2)(x+2). it should not do that.
and 4(x-2)(x) tra...
(ok how we even got here it shouldn't have been so complex)
paper depot
ain't my fault op overcomplicates the simple things.
and makes sign error after sign error.
timid plume
Hell i should take rest and start listening songs and play vid game
timid plume
My mind is laging
timid plume
Alright
vocal sleetBOT
timid plume
I got 33 out of 75
vocal sleetBOT
Available help channel!
sudden compass
Does the property GCD(a,b) = GCD(a+bk,b) hold in some way to three numbers?
sudden compass
Perhaps something like (a,b,c) = (a+ck, b+ck,c)?
hard atlas
shouldn't even just adding it to one of them still work?
(a,b,c)=(a,(b,c))=(a,(b+ck,c))=(a,b+ck,c)
mild flower
nice
humble flame
Any idea how to proceed
humble flame
<@&286206848099549185>
spiral turtle
@humble flame For clarity you're given that
$$\frac{\sin^4 \alpha}{a} + \frac{\cos^4 \alpha}{b} = \frac1{a+b}$$
And you need to evaluate
$$\frac{\sin^8 \alpha}{a^3} + \frac{\cos^8 \alpha}{b^3}$$
in terms of $a, b$ and potentially also $\alpha$?
twin meteorBOT
OmnipotentEntity
vocal sleetBOT
@humble flame Has your question been resolved?
spiral turtle
@humble flame if you come around, I have a solution, I just have to typeset it. Ping me
vocal sleetBOT
vocal sleetBOT
Available help channel!
vast shale
How do I do 8-9?
wary mantle
How do I do 8-9?
What's stopping you from using the same method as in 7.?
,w a*(1 - 13)^2 + c = 4, a*(5 - 13)^2 + c = -1, solve c
It'd deliver the correct answer here aswell
As you can see from the WA result
vast shale
It'd deliver the correct answer here aswell
I see
wary mantle
(I deduced that the vertex is at x = 13, since the values m(x) are equal at an equidistant x from that)
For 9. aswell, the same method
wary mantle
You’re a good person
Thanks
wary mantle
<@332561465405865985> what can I do in return for your help
Nothing, I love mathematics and I like to help, when I'm free and I see a question
vast shale
Nothing, I love mathematics and I like to help, when I'm free and I see a questi...
Thank you
vast shale
Nothing, I love mathematics and I like to help, when I'm free and I see a questi...
i need your help
vocal sleetBOT
@vast shale Has your question been resolved?
vast shale
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
fading island
hey I need help with a linear Equation
vocal sleetBOT
hey I need help with a linear Equation
fading island
vocal sleetBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
chrome raptor
OK
vocal sleetBOT
Available help channel!
vagrant cypress
hello
vagrant cypress
i have a quick question
i have already solved this problem but i was wondering which form is correct
is the answer
h+ 9 or 9 + h?
vast shale
Can’t you simply that problem further
vagrant cypress
i can show work if needed, but im wondering if the number comes before the variable?
yes
gray crescent
They are the same.
gray crescent
Usually by convention, we put the variables first.
vagrant cypress
ah so h+9 and 9+h is the same
vast shale
But overall it doesn’t matter
vast shale
ah so h+9 and 9+h is the same
yea
vagrant cypress
my teacher said 9+h is right
chrome raptor
h+ 9 or 9 + h?
Addition is conmutative
2+3=5=3+2
vast shale
my teacher said 9+h is right
he's wrong
vast shale
my teacher said 9+h is right
Dumb teacher
Unless the problem has specific rules for some reason
gray crescent
Why? By going in order from left to right, you get h + 9 anyways.
vagrant cypress
teacher and i’s work are the exact same
but our answers are flipped
so i was confused
ok thank u all
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
bleak moon
Need help with this problem, I feel like I forgot how to do integrals entirely and partially trig functions too, I want to try and solve it but not sure where to start, maybe if a step by step solution would clear it up for me?
vocal sleetBOT
Need help with this problem, I feel like I forgot how to do integrals entirely a...
bleak moon
also is 1/2 (cos^2x) hard to take integrals of
I got no clue at all right now, I just know that it turns into 1/2(1+cos2x) because of trig identity
bleak moon
I think it's sin2x?
gray crescent
Remember the chain rule?
bleak moon
derivative of the first * the second + the first * derivative of the second
I think
gray crescent
That's product.
bleak moon
ugggh
gray crescent
You should create a list of the formulas, it's good to have around.
Then, by using them often, you will remember them.
bleak moon
I know how chain rule works just don't remember it right now, so the integration of cos2x is...
the inside of it needs to be taken out and take derivative of, I remember that much
gray crescent
By chain rule, I mean the reverse chain rule for integrals. You might want to use u-substitution if you are not familiar.
Great website, crazy stuff. You can check it out whenever you want to solve integrals.
gritty spade
vocal sleetBOT
gritty spade
This is my work
I made a mistake here
I think
Im not getting the same solution as the answer sheet
karmic imp
$x^4 + x^2 \neq x^6$
vast shale
how did u get x^6
twin meteorBOT
dldh06
karmic imp
You don't add exponents like that
gritty spade
ok
vast shale
you did that multiple times
gritty spade
you did that multiple times
adding exponents?
vast shale
yup
novel mountain
it should be 13-1 in the next step
gritty spade
oh
novel mountain
also you cannot divide 14 by 2
gritty spade
ok
karmic imp
it should be 13-1 in the next step
This work is wrong
novel mountain
I already know that
gritty spade
im at x^2 + x^4 -2x^2 = 12
vast shale
you know how to solve quadratic equations?
karmic imp
im at x^2 + x^4 -2x^2 = 12
Combine like terms. set it equal to 0, then a = x^2 and you have a quadratic that you can factor
novel mountain
you can add and subtract the terms with the same power on x, you can do x^2 + x^2 = 2x^2
novel mountain
yes
gritty spade
is this the most i can go or can i simplify further?
karmic imp
is this the most i can go or can i simplify further?
Combine like terms. set it equal to 0, then a = x^2 and you have a quadratic that you can factor
gritty spade
we cant combine x^4 and x^2
novel mountain
now you can factor out x^2 from this
gritty spade
now you can factor out x^2 from this
so x^2( x^2 - 1) = 12
karmic imp
set it equal to 0
novel mountain
oh yeah
gritty spade
> set it equal to 0
x=0 ?
vast shale
and?
vast shale
what does factoring do
gritty spade
Manipulate x^4 -x^2 = 12 so it's = 0
ok
novel mountain
what does factoring do
yeah my bad
gritty spade
ok
gritty spade
Manipulate x^4 -x^2 = 12 so it's = 0
wait how do i manipulate that to make it equal to zero
karmic imp
If you have x^2 = 4, you subtract 4 on both sides to get x^2 - 4 = 0
karmic imp
Yes
karmic imp
You can
karmic imp
Yes
karmic imp
for u = -3
Not quite for this too
karmic imp
Yes
gritty spade
ok
and to find the points
nvm i just have to graph it
@karmic imp thanks for your help i got the correct answer
.close
thorn stump
vocal sleetBOT
thorn stump
So I got 2 of the solutions before considering the domain for each case, but when considering the case for positive and negative, which it says is the answer, the inequalities look as if theres no solution. So my question is how I'm meant to know which of the results is the answer and how I'm meant to know an x value that could be between the two points
vocal sleetBOT
@thorn stump Has your question been resolved?
vocal sleetBOT
@thorn stump Has your question been resolved?
ornate lotus
Can someone help me
thorn stump
Use an available room
ornate lotus
What is the available rooms
thorn stump
Look at the subheadings for each group of channels
vocal sleetBOT
@thorn stump Has your question been resolved?
vocal sleetBOT
@thorn stump Has your question been resolved?
simple mason
i think it would be better solving it this way
[
f(x)=\left{\begin{array}{@{\mathstrut}l@{\quad}l}
10X - 5 + 3X - 3 & X \geq 2 \[1ex]
-10X - 5 + 3X - 3 & 2 > X > 1 \[1ex]
-10X - 5 - 3X + 3 & X \leq 1
\end{array}\right.
]
twin meteorBOT
Sherif Player
simple mason
then checking for each one when is it bigger than 18
simple mason
for the first case
[13X - 8 > 18 ]
[13X > 26 ]
[X > 2]
whcih mean for any value for x in the first case (following the domain)
it will be always greater than or equal 18
for the second case
[-7 X - 8 > 18 ]
[-7X > 26 ]
[X < -\frac{26}{7}]
which is not possible in that case following the domain
for the third case
[-13X - 2 > 18 ]
[-13X > 20 ]
[X < -\frac{20}{13}]
which gives us that the property is possible in the third case when
[ X < -\frac{20}{13} ]
which gives us that the way to get value bigger than 18 in the whole function is when
[X > 2 ]
or when
[ X < -\frac{20}{13} ]
so given that
[a < b]
the best that would suit this question is when
$X < a$ or $X > b$
twin meteorBOT
Sherif Player
simple mason
@thorn stump that would help you i think
thorn stump
@simple mason I’m at work right now, will have a look when I get home. Thanks heaps man 🙂
simple mason
No problem @thorn stump
You can save the picture and close the channel using
.close to make others able to ask there questions here
thorn stump
.close
craggy hamlet
vocal sleetBOT
sage wind
yea first step is to plug in -2
if you get an indeterminate form then you should do some algebraic manipulations before yo plug in -2
craggy hamlet
if you get an indeterminate form then you should do some algebraic manipulations...
what is an indeterminate form ?
sage wind
forms like $\frac{0}{0},\frac{\infty}{\infty},\infty -\infty,0^0,1^{\infty},\infty . 0$
twin meteorBOT
calculus is fun
craggy hamlet
forms like $\frac{0}{0},\frac{\infty}{\infty},\infty -\infty,0^0,1^{\infty},\inf...
ok i got the square root of 19
is that right
sage wind
so basically qny number you get is not an indeterminate form ok
sage wind
ok i got the square root of 19
correct
sage wind
no
so always when you want to evaluate a limit start by plugging the value that x is moving towards
if you get a number or $\infty$ or $-\infty$ then you are done
twin meteorBOT
calculus is fun
sage wind
**calculus is fun**
if you get one the above forms then you need to do some work
are you just starting limits ?
so still in the beginning of learning about limits ?
vocal sleetBOT
@craggy hamlet Has your question been resolved?
elfin moon
LCM of three numbers is 80
vocal sleetBOT
LCM of three numbers is 80
elfin moon
HCF can't be
6,10,20,40
untold surge
What is HCF
You mean GCD?
80=(2^4)(5)
Three numbers x_1,x_2,x_3
x_i=(2^a_i)(5^b_i)
You have max{a_i}=4, max{b_i}=1
You are looking for min{a_i} and min{b_i}
I mean let u=min{a_i}, v=min{b_i}, gcd of those three is (2^u)(5^v)
10=(2)(5)
(u,v)=(1,1)
20=(2^2)(5)
(u,v)=(2,1)
forest stump
What is HCF
Highest Common Factor
untold surge
40=(2^3)(5), (u,v)=(3,1)
forest stump
Not the same as GCD.
untold surge
Not the same as GCD.
Same
untold surge
I leave it to your to verify that those (u,v) are achievable
paper depot
did you mean:
"The LCM of three numbers is 80. Which of these can't be their HCF?"
@elfin moon
untold surge
6 has a prime divisor 3 , so it’s not definitely
I gave the corresponding (u,v) for last three construct yourself to show that they are achievable
Actually any u<=4, v<=1 is achievable
vocal sleetBOT
@elfin moon Has your question been resolved?
untold surge
Okay
elfin moon
.close
vocal sleetBOT
scenic ravine
if you want help, @vast shale , go to #❓how-to-get-help , don't attempt to close someone else's channel
vast shale
if you want help, <@456226577798135808> , go to <#488120190538743810> , don't at...
shuddup ill do what i want because im einstein
vocal sleetBOT
@vast shale Has your question been resolved?
dense stump
sounds right to me
iron thunder
how would one enter this into TeXit?
vocal sleetBOT
how would one enter this into TeXit?
paper depot
with a cases environment
rugged orchid
vast shale
Use dcases* if you want to or simply brute force it using aligned or alignedat
iron thunder
i genuinely don't know how to, can anyone?
vast shale
i genuinely don't know how to, can anyone?
\[
f(x) = \left\{\begin{alignedat}{2}
&0, &\quad &\text{if } x \neq 0\\
&\infty, &\quad &\text{if } x = 0
\end{alignedat}\right.
\]
or even simply \[
f(x) = \begin{dcases*} 0, &if $x \neq 0$ \\ \infty, &if $x = 0$ \end{dcases*}
\]
blissful vector
I need to find a point between n number of 3D points.
In this example I have three 3D points located at [x,y,z] and for each point a % distance from the point needed to be calculated. In this example point C is 10% of the total combined distance between the computed point and every point, while A and B are 45% of the combined distance each.
How would I go about calculating the point marked '?'?
Thanks
blissful vector
just as added info, this could be the data given:
pt A: [x1, y1, z1], 45%
pt B: [x2, y2, z2], 45%
pt C: [x3, y3, z3], 10%
"Calculate point D"
vocal sleetBOT
@blissful vector Has your question been resolved?
blissful vector
I assume this would be some kind of 3D regression method needed to calculate this point, perhaps a bit too much for asking here
sullen sinew
What do the symbols mean
vocal sleetBOT
What do the symbols mean
paper depot
which symbols?
obtuse sierra
(x,y) such that x belongs to X, y belongs to Y
sullen sinew
the e
paper depot
yeah that's "belongs to" or "is in"
hearty thunder
vocal sleetBOT
@sullen sinew Has your question been resolved?
lapis marten
abstract moon
how do i solve this? (x-1)²/36+(y-3)²/9
pls help idk what im doing wrong. this was my answer x²+4y²-2x-24y+1=0
vocal sleetBOT
how do i solve this? (x-1)²/36+(y-3)²/9
pls help idk what im doing wrong. this w...
obtuse sierra
!show
vocal sleetBOT
Show your work, and if possible, explain where you are stuck.
obtuse sierra
same question
lunar lagoon
$\frac{(x-1)^2}{36} + \frac{(y-3)^2}{9} (=0?)$
twin meteorBOT
Poelymole
abstract moon
What's the question?
i have no problems solving the ellipse, but i have problems turning standard equation to general equation
standard equation to general equation
abstract moon
near tartan
4(y²) u wrote it as 16y² for some reason
obtuse sierra
your answer is correct.
lament arch
im confused
vocal sleetBOT
im confused
lament arch
any1 here
these are inverse functions no??
I substituted the q for y btw
Oh
does it become a binomial
and not just take out the square root
im so confused
proven garden
What's the question
rugged orchid
What am I even looking at on the right
lament arch
LOL
simple mason
What is your question bro
rugged orchid
Where did x come from
rugged orchid
No?
lament arch
to find if its inverse
rugged orchid
f(x) is a function of x
rugged orchid
f(x) = q is not a function of x
rugged orchid
No
lunar lagoon
the way we were taught find inverse functions is replace f(x) with y, then rearrange to make x the subject
rugged orchid
In this question
lament arch
the way we were taught find inverse functions is replace f(x) with y, then rearr...
exactly what I did
On the left side there is an x
that's the q
rugged orchid
That is also not how you determine if they are inverses
lament arch
it swapped with the f(q)
simple mason
You don't know what f(x) mean right
Do you know the difference between
f(q) and f(x)
lament arch
and q to x
lament arch
You don't know what f(x) mean right
Do you know the difference between
f(q) and ...
It doesn't matter how it looks like its the same thing
simple mason
Oh my bad
simple mason
No problem
lament arch
Then why does this still have q in it
My mistake
lament arch
I substituted the q for y btw
Tried to explain it w this but my bad
rugged orchid
You can change the letters yes
But you need to change all of them
At the same time
rugged orchid
The way you see if f is an inverse of g (and vice versa) is to compose the functions
lament arch
cuz I don't know how to go from here tbh
lament arch
The way you see if f is an inverse of g (and vice versa) is to compose the funct...
swap x and f(x), then solve for y (f(x)
lament arch
brother
lunar lagoon
y is f(q), x is q
so the first equation would be written y = x^2 -3
then rerrange to x^2 = y+3
plain field
hey can anyone help
rugged orchid
if $(g\circ f)(x) = x$ then $g$ is the left inverse of $f$