I knew the simple ones from practice but it takes a conscious effort to remember them all
#help-27
atomic dome
atomic dome
Its a derivative
atomic dome
^
weary parrot
oh ok
how long did it take you to memorize these all, it seems like a lot
or just do questions by looking at the sheet and eventually it will come?
atomic dome
I memorised all of the identities, inverses, and hyperbolic derivatives and integrals yesterday
I knew the others from before
weary parrot
what degree are you doing?
ok so du = 1 / sinx^2 dx
so du sinx^2 dx
that leaves e^u
so e^(-cotx)
atomic dome
so e^(-cotx)
Did you solve the integral?
atomic dome
+C
atomic dome
What work have you done so far
atomic dome
have any hints
You need to know a half angle identity
weary parrot
do you think Pre Calculus Trigonometry or Calculus 1 re do would help me know all this
atomic dome
Trigonometry would, but you wouldn't do derivatives in that course
weary parrot
ok so while doing Calculus 2 work just always have the trig identities and integrals formulas out to look at?
atomic dome
I would say yes but you need to try and remember them without a sheet
Do some basic problems with a sheet but otherwise try to memorise them
weary parrot
yea we do get a sheet for tests, that's whats tough
I don't remember any of this, there is so much
you don't think Calculus 1 would help me with any of this? other than the derivatives at the end? and you don't think I need to re do Pre Calculus either just the Trigonometry identities?
weary parrot
what half angle identity to use?
weary parrot
@atomic dome what half angle identity should I use?
weary parrot
@atomic dome I only see when it's divided by 2
weary parrot
can someone help me with logic math?
weary parrot
.close
restive river
ok guys, when it comes to graphing y= rise/run or slope (x) + b in which b is the y intercept,
devout snowBOT
ok guys, when it comes to graphing y= rise/run or slope (x) + b in which b is th...
restive river
does that mean x= run/rise(y)-b in which b is x intercept?
i hate how they never use x= in a graph and suddenly show us this shit in a question omg
fossil locust
does that mean x= run/rise(y)-b in which b is x intercept?
yeah, so if you go rearrange $y = mx + b$
woven radishBOT
south
fossil locust
you do get $\frac{y - b}{m} = x$
woven radishBOT
south
fossil locust
so yeah that's x = 1/m * (y - b) or (run/rise) (y - b), your brackets are a bit off
acoustic leaf
we can also write it as x = (run/rise)y + c, where c is the x-intercept
rigid pewter
im confused as fuck
lol do you have a question
but just to reiterate, all 4 of these statements say the same thing
fading ledge
"Knowing the magnitude of a vector one could abstract only the circle in which the vector belongs."
devout snowBOT
"Knowing the magnitude of a vector one could abstract only the circle in which t...
fading ledge
i know this is more a grammar question
but does anyone know if they mean circle as in an actual circle
or
circle as in like radius (not mathmematical)
devout snowBOT
@fading ledge Has your question been resolved?
stiff spindle
but does anyone know if they mean circle as in an actual circle
A vector is a mathematical object with two properties: magnitude and direction. To my understanding, with magnitude only, then the vector could point in any direction starting at an origin point. Hopefully that answers your question.
fading ledge
oh
fading ledge
A vector is a mathematical object with two properties: magnitude and direction. ...
" vector unlike a scalar has direction, and it is broken into two components: magnitude
and angle"
so is angle here
meant to be direction??
stiff spindle
meant to be direction??
yes
devout snowBOT
devout snowBOT
Available help channel!
lament schooner
devout snowBOT
lament schooner
why is A and B not compatible
stone stump
what is B and what do you mean by compatible
lament schooner
what is B and what do you mean by compatible
like if A is invertible
why does Ax=0 only ave one solution
stone stump
you can multiply on both sides by A^-1
devout snowBOT
@lament schooner Has your question been resolved?
lament schooner
you can multiply on both sides by A^-1
huh?
lost crag
does T have to be isomorphism?
upper schooner
does T have to be isomorphism?
(assuming context, holds for any linear map, isomorphism or not)
small harness
How do I do 79
devout snowBOT
How do I do 79
north roost
Chain rule
mystic scarab
By applying it
mystic scarab
like ik how to do chain rule but like how do i set it up
What does chain rule formula say?
small harness
like if x^3 = 3x^2
mystic scarab
This is power rule, not chain rule
Chain rule involves composition of (two) functions
small harness
oh yeah like if (g(x))^3= 3g(x)^2 * g'(x)
north roost
Yes
small harness
ok... how do i apply it to this i dont get it
north roost
oh yeah like if (g(x))^3= 3g(x)^2 * g'(x)
If this is f(g(x)) In this case f(x) is x^3
Let’s think about what u did
devout snowBOT
devout snowBOT
Available help channel!
quasi vortex
Pls
final dune
Do you know how to complete a square?
atomic dome
<@784145995760009247> what half angle identity should I use?
$1 - cosx = \sqrt{2\sin^2\frac{x}{2}}$
final dune
That question is long closed
atomic dome
That question is long closed
Thanks for telling me
woven radishBOT
mari
neat solstice
@quasi vortex you wanna use complete the square.
Say
Y=x^2+ax+b
Then:
Y=(x+a/2)^2-(a/2)^2+b
You can easily verify this by expanding the second equation
quasi vortex
Bro im too high to do all that ima just take the %80 i hot
devout snowBOT
@quasi vortex Has your question been resolved?
reef solstice
here i think opt b&c both are correct can u check it
devout snowBOT
here i think opt b&c both are correct can u check it
faint zinc
@reef solstice there is no way both b and c can be correct
B scales with n^4 and C scales with n^3
faint zinc
Which values?
reef solstice
but in anc c is correct only
reef solstice
Which values?
let n=1 or 2 or any int u get same value
faint zinc
What if you put in n = 10?
woven radishBOT
faint zinc
,w 10*191/2
woven radishBOT
faint zinc
@reef solstice are 2860 and 955 equal?
faint zinc
Here is a hint: $\sum_{k=1}^n k = n(n+1)/2$
woven radishBOT
OmnipotentEntity
faint zinc
And $\sum_{k=1}^n k(k+1)/2 = k(k+1)(k+2)/6$
woven radishBOT
OmnipotentEntity
faint zinc
@reef solstice ^ the above should help you prove this
devout snowBOT
@reef solstice Has your question been resolved?
reef solstice
i know this
devout snowBOT
@reef solstice Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
vivid estuary
Hello I’m having trouble with these two
devout snowBOT
Hello I’m having trouble with these two
vivid estuary
so I know that
I know how to solve it normally
but I assume they want us to like
use some method that makes it simple
using the fact that like 2 columns are linearly independent
hmm if two columns are linearly independet
that means they span the entire space
is [1, 1, 2, 3] are in the space
then I can just use those two columns as the coefficient matrix to find vector T that works
is that right
so I should be able to use A = {c1, c5}
and solve the corresponding system
or do we pick two linearly independent rows
for our coefficient matrix
For e I’d find the solution of the null space and add it to my unique solution?
devout snowBOT
@vivid estuary Has your question been resolved?
devout snowBOT
devout snowBOT
Available help channel!
amber merlin
Is this correct?
devout snowBOT
Is this correct?
amber merlin
import numpy as np
import sympy as sp
from matplotlib import pyplot as plt
def g(x):
return (np.cos(x) - 1) / x
L = np.arange(1, 18, 1)
base_seq = 0.5**L
xLeft=-base_seq
yLeft = g(xLeft)
print("Left Seq = ", xLeft)
print("g(Left Seq) = ", yLeft)
fig = plt.figure()
plt.plot(xLeft, yLeft, marker="o", color='red', label='Approaching from Left')
x = sp.Symbol('x')
g = (sp.cos(x) - 1) / x
limit_value = sp.limit(g, x, 0, dir='-')
print("The limit of g(x) as x approaches 0 from the left is: ", limit_value)
This is funnily enough for my math class🥲
I don’t know why we have this lab
I’m just hoping someone knows python as well🫠
junior chasm
also try asking in python discord server
polar chasm
this looks kinda like math
amber merlin
also try asking in python discord server
I did but they don’t seem to know what’s going on either
amber merlin
this looks kinda like math
It’s calculus, we need to show limits using python
By graphing it
And they didn’t teach us anything they just threw us into it
polar chasm
but wouldnt it just suffice to write
print(np.cos(-0.0001) - 1) / -0.0001)``` or sth like thisWhat did problem 1 say? As in "look at the graph and what it looks like" or something?
amber merlin
Problem 1 is a whole mess we had to write it in sections which is so annoying because for each small change you have to run each block separately to make the next block run properly
Like this
And we had to show what number it’s approaching
I didn’t know how to do any of this btw, I just copy pasted the code from the example sheet
But I don’t know if that’s correct🥲
What am I reading
I don’t know what any of that means
supple knot
<@&268886789983436800> spam
vast helm
how is that spam
junior chasm
how is that spam
this is a help channel, you're not supposed to send random stuff in help channels
winter patrol
@vast helmCan you explain why you're talking about US GDP (unrelated to the ops question) when replying
vast helm
this is a help channel, you're not supposed to send random stuff in help channel...
oh sorry
amber merlin
Anyway🤣
vast helm
ill leave
amber merlin
What can I use to know what I’m supposed to do here🥲
I don’t know how to even approach that
devout snowBOT
@amber merlin Has your question been resolved?
junior chasm
```
import numpy as np
import sympy as sp
from matplotlib import pyplot as plt
...
seems fine
but the range in np.arrange()
1 to 18
your points will be too cluttered
,calc 0.5^15
woven radishBOT
Result:
3.0517578125e-5
,calc 0.5^16
woven radishBOT
Result:
1.52587890625e-5
,calc 0.5^17
woven radishBOT
Result:
7.62939453125e-6
The guy there wrote that I wrote 10 but he changed it to 18 to show the point 0.00
To show that it’s approaching 0
When it was 10 it only showed 0.05
junior chasm
,calc 0.5^10
woven radishBOT
Result:
9.765625e-4
hmm
amber merlin
What is that😅
junior chasm
keep it 18 then
junior chasm
```
import numpy as np
import sympy as sp
from matplotlib import pyplot as plt
...
im not entirely sure if the yLeft thing works out or not
but just change it to g(xLeft)
amber merlin
I really don’t understand why they throw us into that, the professor said it’s so we can see how the graph behaves, but why aren’t we just using desmos
Should the graph below show if it’s correct or not?
It generated that graph when I ran the block
junior chasm
which graph
amber merlin
In this question
import numpy as np
import sympy as sp
from matplotlib import pyplot as plt
def g(x):
if x < 2:
return x**2 - x - 1.5
else:
return np.cos(x) + np.sin(x)
x_left = np.arange(1.5, 2, 0.01)
x_right = np.arange(2, 2.5, 0.01)
y_left = [g(x) for x in x_left]
y_right = [g(x) for x in x_right]
plt.plot(x_left, y_left, label='x < 2')
plt.plot(x_right, y_right, label='x >= 2')
here's the code for convinience haha
that's the assignment itself btw
junior chasm
```
import numpy as np
import sympy as sp
from matplotlib import pyplot as plt
...
seems right
amber merlin
Thank you! Gemini is pretty good at this it seems lol
junior chasm
Thank you! Gemini is pretty good at this it seems lol
u still have to check it tho
amber merlin
What do I look for when checking if it’s correct or not?
amber merlin
But they are all different graphs🥲
junior chasm
i can explain if you want
junior chasm
But they are all different graphs🥲
approach is same
amber merlin
Yes please, although I don’t think I have enough context to understand
amber merlin
Here for example you need to do a part b to problem 3, and you need to guess using code, what does it even mean to guess using code it just shows the answer nothing is guessing here
junior chasm
np.arrange and plt.plot
np.arrange(start, stop, step), the interval is [start, stop), this basically gives u a list with values within the given interval and the step u put
amber merlin
So like what number it starts what number it stops and the gap in between?
junior chasm
for example np.arange(1, 2, 0.1) will return [1. 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9]
u start at 1 (the start is included, stop isnt)
then add the step 0.1
so next value is 1.1
then again +0.1
1.2
and so on
until you hit the stop
amber merlin
I see, that one makes sense thank you😄
junior chasm
and the .plot(), well it just plots what you give
first argument is list of x values
second argument is list of y values
you can also give it label
junior chasm
No dots different colors and thinner
for markers u can add the marker="o" argument
and for color, color="<color you want>"
the lines arent thinner than before but if u want to increase their width then u can add linewidth= argument
u have to use float btw
like 2.3
4.0
amber merlin
I pasted it from the previous problem and it gave me an error
junior chasm
dont add extra .plot() line
modify the one u have above it
these
plt.plot(x_left, y_left, marker="o", color="red", label="approaching from left")
junior chasm
yeah
amber merlin
Wth🤣
amber merlin
Where do I see that?
junior chasm
they are also evenly split
so you will have a bead garland type line
if you want it to be more like the first one, like the closer u get the more points increase
then use the exponential thing u did before
amber merlin
Inside the function or outside?
And why is desmos showing me this
It doesn’t look like the thing I just coded lol
junior chasm
Inside the function or outside?
anywhere works, but do it outside
amber merlin
import numpy as np
import sympy as sp
from matplotlib import pyplot as plt
def g(x):
if x < 2:
return x**2 - x - 1.5
else:
return np.cos(x) + np.sin(x)
L=np.arange(1,10,1)
base_seq=0.7**L
x_left = np.arange(1.5, 2, 0.01)
x_right = np.arange(2, 2.5, 0.01)
y_left = [g(x) for x in x_left]
y_right = [g(x) for x in x_right]
plt.plot(x_left, y_left, marker="o", color='red', label='x < 2')
plt.plot(x_right, y_right, label='x >= 2')
here
It’s the same as you have it but still looks different how🤣
This whole assignment is so frustrating 🫠
Or are you supposed to just zoom in? And focus on the point where it meets?
junior chasm
It’s the same as you have it but still looks different how🤣
its not different
i was just very zoomed
amber merlin
Ohh I see, my bad🤣
junior chasm
amber merlin
I miss my previous professor he actually explained things
The graph that I coded doesn’t really show that they are approaching different values🥲
junior chasm
```
import numpy as np
import sympy as sp
from matplotlib import pyplot as plt
...
import numpy as np
import sympy as sp
from matplotlib import pyplot as plt
def g(x):
if x < 2:
return x**2 - x - 1.5
else:
return np.cos(x) + np.sin(x)
L=np.arange(1,10,1)
base_seq=0.7**L
x_left = 2-(0.7**L)
x_right = 2+(0.7**L)
y_left = [g(x) for x in x_left]
y_right = [g(x) for x in x_right]
plt.plot(x_left, y_left, marker="o", color='red', label='x < 2')
plt.plot(x_right, y_right, label='x >= 2')
try this
amber merlin
This works but the blue is higher than the red
Shouldn’t it be the opposite?
In desmos it also approaches 0.5 but here it’s 0.4
amber merlin
Oh it includes the limit??
junior chasm
wut
junior chasm
btw change the blue line to include markers too
amber merlin
Like x<2 but it includes 2
junior chasm
```py
import numpy as np
import sympy as sp
from matplotlib import pyplot as plt...
replace the last line with plt.plot(x_right, y_right, marker="o", color='blue', label='x >= 2')
amber merlin
Yup this looks good thank you!
Hopefully it’s correct cuz I still don’t understand it fully lol
I understand b. Cuz that’s like me answer in human language I guess
junior chasm
can you temporarily try changing if x < 2: to if x < 2.1: and check how it affects graph
i dont have the packages installed so cant run the code
amber merlin
It did this
amber merlin
i dont have the packages installed so cant run the code
I’m using google collab
junior chasm
Hopefully it’s correct cuz I still don’t understand it fully lol
it is
amber merlin
Thank you🥲
junior chasm
I’m using google collab
ah
i had the all these packages installed (i use python) before but due to recent drive crash all got wiped and i havent managed to installed everything again
amber merlin
Oh damn.. how did it crash?
junior chasm
fr
amber merlin
Use a raid system for important data
I’m gonna build a storage system with UnRAID, it’s really useful
junior chasm
Use a raid system for important data
thankfully i had important things store in a pendrive (not everything but the most important so its fine)
amber merlin
That’s lucky, but I feel your pain having to install everything🥲
junior chasm
fr
it crashed once before too
but only c drive was wiped
had to install everything back but i didnt mind it at that time
should've replaced it at that time
but welp
junior chasm
Ohh, yea once it shows these problems it’s no good😅😅
yeah, learnt the hard way
amber merlin
Do you like vs code btw? I saw you are using it rn, I tried using it for c++ to learn it but when I got to classes it caused problems cuz it can’t run multiple ccp files in one project
So when you try to run a class from the main file it doesn’t run it then shows you an error that the class doesn’t exist
junior chasm
Maybe you can RMA it
you mean like return it?
amber merlin
you mean like return it?
Yes to the manufacturer and they send you a new one
junior chasm
its out of warranty lol
junior chasm
Damn🥲🥲
and im yet to try getting its stuff recovered
so even if it was in warranty i wouldnt return it
amber merlin
Can it be recovered once it fails?
junior chasm
How old is it haha
3-3.5 years i think
junior chasm
Can it be recovered once it fails?
they said they could recover the stuff
amber merlin
Damn yea warranty is usually 2-3 years on new drives
amber merlin
they said they could recover the stuff
Oo hopefully🙏🏻
junior chasm
they said they could recover the stuff
as for the drive itself, idk, i wouldnt risk it anyways
amber merlin
Yea I wouldn’t use it for anything important
junior chasm
Do you like vs code btw? I saw you are using it rn, I tried using it for c++ to ...
vs code ftw
amber merlin
How do you run multiple files🥲
junior chasm
wdym
amber merlin
It doesn’t work for me
Like when you create a class
You open a new file right?
For that class
amber merlin
Then you mention that class in the main file and press run, but that only runs the main file
junior chasm
Then you mention that class in the main file and press run, but that only runs t...
you have to import the class file first
amber merlin
Like import “class name”
?
In cpp it’s include and I did that but it still doesn’t run the class file itself
junior chasm
it wouldnt run the class file, yeah
you use the functions from that class file as needed
amber merlin
And then it’ll give you an error, so what do you do haha
junior chasm
you use the functions from that class file as needed
you dont import a file to run it with another file
amber merlin
Ohh, so you can’t work with multiple files then?🥲
You put your classes with the main code?
junior chasm
Ohh, so you can’t work with multiple files then?🥲
are all files seperate?
junior chasm
like whatever is inside them isnt being used anywhere outside of its own file
amber merlin
Damn
junior chasm
ill give you an example how you use it
amber merlin
That sucks, because for classes I need a .cpp file and a .h file then include it in the main code
This is what I mean haha
junior chasm
ill give you an example how you use it
if you have a file named tools.py with the following code in it:
def sum(a,b):
return a+b
def multiply(a,b):
return a*b
now if you want to use the functions from tools.py in another file, lets say main.py
so what you do is: (in main.py)
import tools
print(sum(1,5))
what error does this give
amber merlin
Tasks.json not found something like that
Like the thing that runs the code
Because it’ll only run Classes.cpp but not Cat.cpp
Since it can’t run multiple ccp files
junior chasm
can you run it rn and send ss of the error
amber merlin
amber merlin
It doesn’t do anything haha
junior chasm
you have a launch.json in your directory?
amber merlin
It just sends me here
junior chasm
you sure you installed compiler, added it to PATH
and also installed c++ extension in vsc
amber merlin
Yes it works fine when it’s one file
The problem happens when it’s multiple files
Hold on it gave me another error
There you go, this should answer it haha
amber merlin
Nope I just press run
junior chasm
try to compile using the terminal
amber merlin
What should I write?😅
junior chasm
g++ -o main Cat.cpp Classes.cpp
amber merlin
It didn’t do anything this time haha
amber merlin
No it just didn’t do anything, I wrote it pressed enter and nothing
junior chasm
no error, nothing?
amber merlin
Now it won’t let me write in the terminal at all wth
junior chasm
open an actual command prompt in the directory
junior chasm
`g++ -o main Cat.cpp Classes.cpp`
then write this there
amber merlin
you are using GNU compiler?
I forgot which one but the windows one
junior chasm
press on the address bar (in the directory) and type cmd
amber merlin
Here?
junior chasm
not vsc
i meant windows explorer
where the Classes.cpp file is
go there and open cmd in that directory
amber merlin
Wait what’s a directory haha
junior chasm
like the place where the files are stored
amber merlin
It’s on a folder on my desktop
junior chasm
junior chasm
It’s on a folder on my desktop
yeah open it
amber merlin
Yes I’m there
junior chasm
and type cmd
junior chasm
yes
amber merlin
Yes but it already had it
amber merlin
When I ran it through yes main
junior chasm
run it
amber merlin
And it doesn’t do anything, it opens and closes something quickly
junior chasm
Same thing just sends me to the next line
type main.exe in this terminal
junior chasm
yeah
amber merlin
Wait so you have to go through all of this to use classes?🥲
junior chasm
the issue was in compiling, it wasnt linking the files together (Classes.cpp and Cats.cpp) thats why it was giving undefined reference error because for it the function isnt defined
amber merlin
Yes that’s the thing that runs it right?
junior chasm
can u send its ss
amber merlin
junior chasm
replace the ${file} with ${fileDirname}/*.cpp
woven radishBOT
Astar777
junior chasm
lmao
amber merlin
🤣🤣
junior chasm
replace the `${file}` with `${fileDirname}/*.cpp`
and delete the main.exe that u built before
then try to build it from vsc
amber merlin
What language is even tasks.json??
Thank you haha I’d have never figured this out
So on every project I just replace file with that and it’ll run all the cpp files?
junior chasm
What language is even tasks.json??
its not actually a "language"
its just a format for storing data
the tasks.json file stores info on how to build the project
by default it only buils 1 file
amber merlin
Oh so it’s like raw code?
junior chasm
so if you want to compile all files in your directory then you repalce the ${file} with what i told
amber merlin
by default it only buils 1 file
Ohh I see, there should be a setting for it haha
junior chasm
Oh so it’s like raw code?
its not "code"
its just a format for data storage
here its storing the settings and info to use while building
things like ${file} and other similar things in it are all processed by compiler, json isnt doing any of it
amber merlin
Ohh it compiles that al together that’s cool
It’s like instructions for the compiler basically
On how to do it
Or what to do
junior chasm
its not "instructions"
its basically just storing the settings
so that the compiler can use them
they could also use a text file for storing settings, but json is better for this use case
amber merlin
I see, that makes sense haha
Thank you for your help🥲 I’ll try to do the next math problems
junior chasm
oh yeah i totally forgot about that
amber merlin
Hahaha
Code is more fun but college won’t allow me to just do code
They shove all this bs just so I can “earn” learning cpp
amber merlin
Thank you!
amber merlin
I guess so haha
junior chasm
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gentle wagon
devout snowBOT
gentle wagon
how did they get (i-1) for the left endpoint and
i for the right endpoint
im trying to figure it out with intuition but i cant 😭
devout snowBOT
@gentle wagon Has your question been resolved?
devout snowBOT
@gentle wagon Has your question been resolved?
inner wharf
So ur using the limit def of an integral?
gentle wagon
no, sum definition
finite stag
devout snowBOT
finite stag
For a I think i kind of get it
Do I just first find t at 0
Then at 5
Theb subtract and divide by 5
And do the same for 10?
But what about b
I’m confused
Wait hold up is an instantaneous rate?
Bc it says at the end
atomic dome
For a I think i kind of get it
Why not f’(5)?
finite stag
Yeah that makes more sense
But how would I find the derivative
Like do I use chain rule or
atomic dome
You don’t need the chain rule
It’s basic differentiation power rule
Average flow rate would be what?
finite stag
Ohhh so it would be 40t-1609
1600
Then I just plug in right
Ya I think I get it
And I’ll just use velocity formula for b right
woven radishBOT
mari
devout snowBOT
@finite stag Has your question been resolved?
unreal linden
Why doesn’t the nested interval property hold for rationals?
devout snowBOT
Why doesn’t the nested interval property hold for rationals?
@unreal linden Has your question been resolved?
devout snowBOT
@unreal linden Has your question been resolved?
dense lynx
amphx 
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Available help channel!
restive olive
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restive olive
I have been trying this question for a while but I still dont know what to do
I could just tryout the numbers from the choises but I want to know the actual solution
vague frigate
let it be x, then (x/52)+33, (x/78)+59 should be equal right?
restive olive
let it be x, then (x/52)+33, (x/78)+59 should be equal right?
lets say x = 52*78
78+33 = 52+59
it is
it is equal.
but I dont understand where it come from tho
hmm
how is it equal
visual hazel
i would say chinese remainder theorem but you probably dont know what that is
dense lynx
do not crt this
dense lynx
some notable things here
52, 78, 117 all divisible by 13
and 52 - 33 = 78 - 59 = 117 - 98
restive olive
some notable things here
52, 78, 117 all divisible by 13
and 52 - 33 = 78 - 59...
oh
52 - 33 = 19
78 - 59 = 19
117 - 98 = 19
it's a coincident?
or it's a property
dense lynx
it is neither
this is a deliberate way this problem was set up so it would have an easy solution
restive olive
ah
if I know that they are all divisible by 13
and divisor - remainder = 19
(x/52)+33 means that..
i'm not sure
52a+33 =x
divisor = remainder + 19
33(a+19) = x
no
restive olive
let it be x, then (x/52)+33, (x/78)+59 should be equal right?
the equation should look like this
can you explain how this equation is formed?
vague frigate
just make those two equal and solve for x
restive olive
(x/52)+33 = (x/78)+59
(78x-52x)/7852 = 26
26X = 26 78 * 52
X = 26 * 78 * 52 / 26
4056
i did something wrong
vague frigate
how you do that?
vague frigate
thats not how ya solve
restive olive
wait why?
restive olive
4056
?
I couldn't understand their solution either
they did include what you said
I see now
ok ok I understand
thank you
.close
stiff oyster
For the love of God, how does this work, i understand this upto the derivation of a = x² - y² and b = 2xy but after that it falls apart for me.
Why are we computing x² + y² anyways? Like it's so random, like sure it probably helps later but how exactly, the textbook does not specify a reason as far as I know, second, what identity are they even using to reexpress x² + y²? This is probably a stupid question but I am sorry i just woke up and can't think straight
devout snowBOT
For the love of God, how does this work, i understand this upto the derivation o...
stiff oyster
While we are there, also explain the later steps to me once someone is able to get this thing through my thick skull
supple knot
For the love of God, how does this work, i understand this upto the derivation o...
sqrt(x^2 + y^2) is the modulus of sqrt(a+ib)
stiff oyster
if root(x² + y²) = root( root( a² + b² ))
Then by squaring both sides
x ² + y ² = root(a² + b²)
Do i follow?
The a = x ² - y ² and b = 2xy so
x ² + y ² = root( (x² - y²)² + (2xy)² )
Oh yeah i think i get it
But why is root(x² + y²) equal to the mod of root(a+bi) again?
@supple knot
supple knot
What's the modulus of a complex number z = c + id?
stiff oyster
|z| = root(c² + d²) i think
devout snowBOT
@stiff oyster Has your question been resolved?
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Available help channel!
vast violet
devout snowBOT
supple knot
Yes
vast violet
so
like am i responsible to memorize these conversions
becuz they are not telling me how many inch in yard
);
fathom flint
becuz they are not telling me how many inch in yard
they literally wrote in a bracket
vast violet
w0t\
fathom flint
like am i responsible to memorize these conversions
we can't tell thats on your school
fathom flint
they just do cm to inch
is it that hard to memorise
vast violet
i want to memorize
but dont know what to search
like if there is a paper that has them all i want to find it
fathom flint
like if there is a paper that has them all i want to find it
try chatgpt or google
devout snowBOT
@vast violet Has your question been resolved?
shadow ruin
i dont know how to do the third and fourth question. Even chatgpt cant help me
wicked pulsar
i dont know how to do the third and fourth question. Even chatgpt cant help me
try finding x such that the value for some expression of x is -12, and p(-12)
proud palm
I need to calculate solar panel energy generation, i have these parameters:
- sunlight 3d Vector
- sunlight intensity
- solar panel tilt angle
- solar panel azimuth angle
- solar panel size
chatgpt told me this:
Calculate solar panel normal vector based on tilt and azimuth angles
panel_normal = np.array([
np.sin(tilt_angle) * np.cos(azimuth_angle),
np.sin(tilt_angle) * np.sin(azimuth_angle),
np.cos(tilt_angle)
])
# Calculate the dot product between sunlight and panel normal
dot_product = np.dot(sunlight_vector, panel_normal)
angle_cosine = max(0, dot_product / (np.linalg.norm(sunlight_vector) * np.linalg.norm(panel_normal)))
# Effective sunlight intensity
effective_intensity = sunlight_intensity * angle_cosine
# Panel area
panel_area = panel_size[0] * panel_size[1]
# Energy generation
energy = effective_intensity * panel_area * panel_efficiency # in watts
Is this correct?
devout snowBOT
I need to calculate solar panel energy generation, i have these parameters:
- su...
@proud palm Has your question been resolved?
proud palm
<@&286206848099549185>
wind prism
yo
proud palm
hi
proud palm
is it correct to calculate solar panel vector like this:
X = Math.sin(tilt) * Math.cos(azimuth)
Y = Math.cos(tilt)
Z = Math.sin(tilt) * Math.sin(azimuth)
wind prism
yips👍
proud palm
great thx
wind prism
np
proud palm
.close
hardy parrot
devout snowBOT
spiral geyser
((F \circ G)(x)) means (F(G(x)))
woven radishBOT
Invariance
hardy parrot
yes I already know that,
wait i will show my wrok
i don't even know if this is correct
dapper fable
why would g(x) = 3(x-1)^3?
hardy parrot
bc i simplified the original g(x)
spiral geyser
it's 3 (x - 1)^(-3)
dapper fable
oh there wasnt a minus sign sorry
dapper fable
bc i simplified the original g(x)
you wrote ^3
hardy parrot
oh i forgot to write the minus there
dapper fable
the domain of (FoG)(x) would be a subset of the domain of F
hardy parrot
so how do I find the domain?
dapper fable
have you found the domain of F and the range of G?
dapper fable
oh wait i mixed up some things mb
devout snowBOT
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Available help channel!
blazing wren
devout snowBOT
blazing wren
Is the equation right?
olive jasper
fervent hornet
from second step its wrong
fervent hornet
no
blazing wren
Why
fervent hornet
$x^2 -2x+4 \neq (x-2)^2$
woven radishBOT
convergence
restive river
also that yea
blazing wren
Wut
fervent hornet
you can do this equation like this instead $2x^2-4x+4=2(x^2-2x+1)+2$
woven radishBOT
convergence
blazing wren
Why is there a 1 in the end tho?
fervent hornet
2(1) =2
fervent hornet
$2x^2-4x+4=2x^2-4x+2 +2\
2x^2-4x+4=2(x^2-2x+1) +2$
woven radishBOT
convergence
blazing wren
So you divided the 4 into +2+2?
fervent hornet
yes
fringe timber
$(a + b)^2 = a^2 + 2ab + b^2$
woven radishBOT
decaf
blazing wren
.close
devout snowBOT
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Available help channel!
fervent hinge
hi um let me get this straight i hate maths AA and this is about the binomial thorem
this is where i am so far
5N2 = 10
10 . (3x^2)^3 . -(2/x)^2
(please tag when you see this)
devout snowBOT
hi um let me get this straight i hate maths AA and this is about the binomial th...
fervent hinge
i am most confused about the -(2/x)^2, how do i write it? (- 2/x)^2 or like how
anyhow, 10 . 9 . -4 . x^6 ÷ x^2
-364 x^4?
mystic scarab
hi um let me get this straight i hate maths AA and this is about the binomial th...
$(A + B)^5 = {5 \choose 0} A^5 + {5 \choose 1} A^4B + {5 \choose 2} A^3B^2 + {5 \choose 3} A^2B^3 + {5 \choose 4} AB^4 + {5 \choose 5} B^5}$
woven radishBOT
Alberto Z.
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
fervent hinge
oh my God what the hell is that
mystic scarab
The formula you should use 😅
mystic scarab
I've expanded it for you, if you want I can write it with the summation symbol
fervent hinge
you will make me end my life samarth
fervent hinge
I've expanded it for you, if you want I can write it with the summation symbol
i just want to know where do i place the negative 😭
fervent hinge
year 11 IBDP
restive river
Im in 11th btw :) [16yr old]
fervent hinge
same here
fervent hinge
alberto sounds like a very intelligent human being
fervent hinge
tf they're teaching in IBDP
foundation college year
fervent hinge
where r u from?
Originally german, living in bahrain
restive river
waht
(never heard of that thingy)
fervent hinge
IBDP?
radiant anvil
what is happening
mystic scarab
$$(A + B)^5 = \sum_{k = 0}^{5} {5 \choose k}A^{5-k}B^k$$
fervent hinge
is K = R?
restive river
but not sooo much
woven radishBOT
Alberto Z.
fervent hinge
i am getting scared
mystic scarab
i am getting scared
How do you expect to solve that exercise without this? 🤔
fervent hinge
idk im doing sequences and series and log and yeah that's all
i am doing 40 pages assignment for the binomial theorem
fervent hinge
How do you expect to solve that exercise without this? 🤔
i solve it very easily
like
fervent hinge
restive river
(yeah i never learnt it)
restive river
and like i missed classes of binomial yk
mystic scarab
Ahnn you have to use the Pascal triangle?
restive river
rah
fervent hinge
TEACH ME THAT SHIT
I NEED TO BE TAUGHT TO TEACH FIRST, MY TABLE IS FILLED WITH TEARS FROM THIS ASSIGNMENT
restive river
so you're in 11th and you're a mum?
restive river
im curious but ok
fervent hinge
.close
devout snowBOT
mystic scarab
.reopen
devout snowBOT
✅
mystic scarab
I wrote the steps, if you want
The most important thing is knowing the Newton's binomial formula
$${\left(A + B\right)}^n= \sum_{k = 0}^{n} {n \choose k}A^{n-k}B^k$$
atomic nacelle
It is the binomial theroem
woven radishBOT
Alberto Z.
mystic scarab
**Alberto Z.**
This one @fervent hinge
solid osprey
**Alberto Z.**
if you want something more visual, its like this, but this is only assuming its like (x+1)^n
fervent hinge
**Alberto Z.**
ive never seen this in my life
fervent hinge
if you want something more visual, its like this, but this is only assuming its ...
i've never seen this either
1
11
121
1331
this is the one that i know
goes more
depending on the n
solid osprey
yeah thats pascals
you can see they are technichally the same just in a diffrent form
fervent hinge
i am crying what the hell is this
ill just not solve it all around
i dont care if i lose marks
mystic scarab
If you want I can paste my process anyway
So that you can see how it could be solved
mystic scarab
**Alberto Z.**
In your exercise, the formula here becomes the following: $${\left(3x^2 + \frac{-2}{x}\right)}^5 = \sum_{k = 0}^{5} {5 \choose k}{\left(3x^2\right)}^{5-k}{\left(\frac{-2}{x}\right)}^k =$$
woven radishBOT
Alberto Z.
fervent hinge
i found another answer
mystic scarab
$$= \sum_{k = 0}^{5} {5 \choose k} \cdot 3^{5-k} \cdot {\left(-2\right)}^k \cdot {\left(x^2\right)}^{5-k} \cdot {\left(x^{-1}\right)}^k =$$
fervent hinge
-1080x^4
woven radishBOT
Alberto Z.
fervent hinge
wait
the negative
is it inside or outside the ()
believe me i dont understand what i am looking at
just hear me out
alberto
woven radishBOT
Alberto Z.
mystic scarab
**Alberto Z.**
$$= \sum_{k = 0}^{5} {5 \choose k} \cdot 3^{5-k} \cdot {\left(-2\right)}^k \cdot x^{10-3k}$$
woven radishBOT
Alberto Z.
mystic scarab
$10 - 3k = 4 \iff k = 2$
woven radishBOT
Alberto Z.
mystic scarab
**Alberto Z.**
So the coefficient of x⁴ will be the number in the sum when k = 2
Hence, it's $$\text{coeff} = {5 \choose 2} \cdot 3^{5-2} \cdot {\left(-2\right)}^2 = 10 \cdot 27 \cdot 4 = \textbf{1080}$$
woven radishBOT
Alberto Z.
fervent hinge
mystic scarab
Yeah that's it
mystic scarab
$${\left(-\text{stuff}\right)}^2 \neq -{\left(\text{stuff}\right)}^2$$
woven radishBOT
Alberto Z.
fervent hinge
what
mystic scarab
That's (very) basic algebra
fervent hinge
i know
thats
why i am asking
because they're not the same
and the answer might be -1080x^4 or 1080x^4
mystic scarab
**Alberto Z.**
This is the general formula, therefore in your case A = 3x² and B = **-**2/x
swift valve
fervent hinge
its only 6 marks
swift valve
Please explain parts d and e to me
mystic scarab
By the way the square of these two is the same
mystic scarab
Please explain parts d and e to me
!occupied
devout snowBOT
Please explain parts d and e to me
Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).
fervent hinge
By the way the square of these two is the same
how are they the same?
one gives me -4x^2 and the other 4x^2 (after ^2)
mystic scarab
one gives me -4x^2 and the other 4x^2 (after ^2)
Nope
mystic scarab
how are they the same?
$${\left(-\text{stuff}\right)}^2 = {\left(-{\left(\text{stuff}\right)}\right)}^2$$
woven radishBOT
Alberto Z.
fervent hinge
how the hell did you () the ()
junior chasm
wdym
fervent hinge
wdym
we're discussing
how
-(2/x)^2 is NOT the same as (- 2/x)^2
because one will give me a positive and the other a negative
junior chasm
-(2/x)^2 is NOT the same as (- 2/x)^2
yeah its not, what is there to discuss about
fervent hinge
EXACTLY
fervent hinge
.
ill resend it
my question is
for this one
main question showing its -(2/x) and not (- 2/x)
junior chasm
im missing the context to answer that
fervent hinge
im missing the context to answer that
sent it
fervent hinge
i am questioning my sanity
junior chasm
that doesnt make any sense
2/x is one term
and the minus is in front of this term
$-\frac{1}{2} = \frac{-1}{2} = \frac{1}{-2}$
woven radishBOT
Astar777
fervent hinge
i am okay with losing 6 marks.
i will jsut
close this chat
i wont do this question
.close
devout snowBOT
junior chasm
💀
mystic scarab
i wont do this question
I think you won't be able to do other exercises as well, unless you understand the minus sign thing...
fervent hinge
i am willing to lost all marks, my sanity is more important
devout snowBOT
Available help channel!
swift valve
devout snowBOT
swift valve
Parts d and e please
devout snowBOT
@swift valve Has your question been resolved?
swift valve
<@&286206848099549185>
real osprey
welp... im not sure if this is how you're meant to do it, but for (d), notice how 1/(4^2) is smaller than 1/(3^2) and in general 1/[(n+1)^2] is smaller than 1/n^2
so the avg btw 1/(3^2) and 1/(4^2) is smaller than 1/(3^2)
do this for the rest of the integers and (d) should be fine
for (e), you can manipulate the other inequalities to show it, what have you tried?
swift valve
so the avg btw 1/(3^2) and 1/(4^2) is smaller than 1/(3^2)
God I love you
This entire question has been driving me nuts
part a and part d have made me question my existence
real osprey
np, it do be like that some times, i take it that (e) is ok?
swift valve
np, it do be like that some times, i take it that (e) is ok?
Yes as long as I have d and c
Thank you kind woman
real osprey
np have a nice day
real osprey
haha... well i would try prove 3/2 < sum and sum > 7/4 cases separately
hint: use the red one for 3/2 < sum and the blue ones for sum > 7/4
swift valve
hint: use the red one for 3/2 < sum and the blue ones for sum > 7/4
Do I need both for blue one?
real osprey
uhhhhh, the way i did it, yeah, there might be other ways