#help-0
ocean sealBOT
knotty trail
velvet pelican
mb, I looked at the wrong domain
Why have you taken the absolute value for the second integral
knotty trail
Huh?
rich basin
$\int_0^{\pi/4} \cos\left(x + \frac{\pi}{4}\right) - \int_{\pi/4}^\pi \cos\left(x + \frac{\pi}{4}\right)$
ocean sealBOT
Roenbaeck
velvet pelican
If you take the absolute value then you don't need to subtract them
knotty trail
$\int_0^{\pi/4} \cos\left(x + \frac{\pi}{4}\right) - \int_{\pi/4}^\pi \cos\left(...
Wait why subtract
That's what I don't get
rich basin
To reverse the sign.
knotty trail
Shouldnt you add the two areas?
rich basin
The integral for the area below the x-axis will be negative.
velvet pelican
yw
runic horizon
Handwriting too good
ripe bough
Latex question. How can i get this aligned correctly?
\begin{align*}
F_{\triangle MAB}&\leq F_{\text{Sektor}MAB}&\leq F_{\triangle MAC}\\
\iff\frac{\sin{x}}{2}&\leq\frac{x}{2}&\leq\frac{\tan{x}}{2}
\end{align*}
ocean sealBOT
ＬＹＮＩＸ
glass lichen
Idk how to solve
what are domain and range by definition?
elfin relic
what are domain and range by definition?
Doman are the x values range are the y values
rich basin
,,
\begin{alignat*}{3}
F_{\triangle MAB}&\leq F_{\text{Sektor}MAB}&&\leq F_{\triangle MAC}\\
\iff\frac{\sin{x}}{2}&\leq\frac{x}{2}&&\leq\frac{\tan{x}}{2}
\end{alignat*}
@ripe bough ^
glass lichen
yes, so what x values (horizontal axis values) can the graph take on?
ripe bough
@rich basin thanks. What exactly is alignat and what does the 3 mean?
ocean sealBOT
Roenbaeck
rich basin
The extra 3 shouldn't have been there 🙂
alignat tells latex how many "columns" you have, and makes the output more "compact"
elfin relic
yes, so what x values (horizontal axis values) can the graph take on?
I don't understand that
glass lichen
where does the function start and end horizontally?
ripe bough
alignat tells latex how many "columns" you have, and makes the output more "comp...
nice thanks
elfin relic
Starts at 1950 and ends at 2000
glass lichen
so what's the domain?
ripe bough
@rich basin Is there a way to write the calculation | * 2/sinx a bit nicer? i just used a lot of spaces and |
rich basin
Hmm... you could have an additional column and let it be empty on the other rows?
You need the extra & at the end of every row though, to indicate that empty column.
ripe bough
\begin{alignat*}{4}
F_{\triangle MAB}&\leq F_{\text{Sektor}MAB}&&\leq F_{\triangle MAC}&&&\\
\iff\frac{\sin{x}}{2}&\leq\frac{x}{2}&&\leq\frac{\tan{x}}{2} &&&|\cdot\frac{2}{\sin{x}}\\
\iff 1&\leq\frac{x}{\sin{x}}&&\leq\frac{1}{\cos{x}} &&&\\
\iff 1&\geq\frac{\sin{x}}{x}&&\geq\cos{x}&&&
\end{alignat*}
ＬＹＮＩＸ
elfin relic
@glass lichen -0.5 and 0.4 I think
glass lichen
no
the allowed horizontal values are from 1950 to 2000. Domain is the set of allowed horizontal values
so what's the domain?
elfin relic
-0.5 and -0.1 I think or idk
glass lichen
what are the x values allowed?
no clue why you keep saying decimals when you already told me the horizontal values are 1950 to 2000
pale cargo
Hello
I'm trying to evaluate this integral
Using the definition of the integral
I got it wrong tho
Its supposed to be a/3
And I got a/6
Why?
shell widget
,w sum i^2 from i = 1 to i = n
ocean sealBOT
tiny lodge
Ok so I’m learning trig rn or something and I get how to put it in the calculator but what I don’t get is if I use sin cos or tan
Like when I use it
Can someone plz explain to me
alpine sable
Is there any way to find arc length (ds) in any given co-ordinate system using Jacobian?
($ds=\sqrt{{dx^2}+{dy^2}}$)
I can find in Cartesian, polar,cylindrical and spherical but how to find it in any given coordinate system?
ocean sealBOT
Riyango
mellow oriole
anyone knows add maths its geometry btw 😪 been stuck on the question
i only could find the gradient 🥲
glass lichen
,rotate
ocean sealBOT
glass lichen
which question...?
mellow oriole
8a 💀
mellow oriole
<@&286206848099549185>
sorry for the ping but ^
uncut briar
ok so can someone teach me the entire 11th syllabus of indian mathematics?
💀
i have an exam in a few days
trim hull
rich basin
@trim hull We do not help with test questions.
trim hull
its not a test
uncut briar
its not a test
all u had to do was not take a full screen shot man
tired creek
lol
green quartz
torpid estuary
sand lion
Can anybody help right now.
tall wing
balmy light
do you know logarithm rules?
balmy light
uhm, are you allowed calculators?
slow scaffold
Yeah
slow scaffold
Bruhhhhhh
slow scaffold
But it does say use special properties
balmy light
But it does say use special properties
ohhh well then now lemme think
ayt
@slow scaffold i got it
balmy light
How would I do it?
sending
ocean sealBOT
A*
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
balmy light
**A\***
Compile Error! Click the <:errors:504266556054962196> reaction for more ...
@slow scaffold there
slow scaffold
Okay
balmy light
you know that rule?
slow scaffold
I think so
balmy light
well if you see i took ln on both sides which is the same as log 10
slow scaffold
Okay
balmy light
so i made no difference to the equation
then just applied the power property and took the x down
from where you probably know it
slow scaffold
Yeah it is
celest gorge
coral pagoda
Are you familiar enough with trigonometry? Like do you know what sine is?
If so, we don't need to consider 3 cases. We can do this pretty nicely
Let me know when you're here
lucid quiver
Bob Ross pfp good
west tiger
alpine sable
$V_{\triangle\text{Prism}}=\frac{1}{4}h\sqrt{-a^4+2\left(ab\right)^2+2\left(ac\right)^2-b^4+2\left(bc\right)^2-c^4}$
Tasmav
rapid nova
The base area is 1/2 * 12.8 * 4.8, then multiply it by the height. The volume then is 344.064.
jovial talon
Is this channel open
alpine sable
I believe so
glass lichen
I mean.. my guess is no since C isnt a midpoint?
west tiger
ok
jovial talon
How are we supposed to find c
rapid nova
Can we solve for C using the midpoint of a line segment formula
You can find the center of parallelogram (as a midpoint of DB). Note that it is the point where diagonals intersect so it is also a midpoint of AC.
glass lichen
How are we supposed to find c
slope of AB is the same as slope of DC
jovial talon
Ohhhh you are saying that the midpoint of db is also for ac?
rapid nova
Exactly
jovial talon
Ohhhhh thank you so much
alpine sable
hi any channels not in use?
manic quail
We could go #prealg-and-algebra , if it fits, @alpine sable
manic quail
Sure, let's go prealg
jovial talon
Is it same for rectangle btw
rapid nova
Is it same for rectangle btw
because rectangle is a special case of parallelogram
vagrant zenith
Does find the sum mean simplify or factor
jovial talon
I have another issue
glass lichen
Does find the sum mean simplify or factor
need more context
jovial talon
Can i quickly ask
vagrant zenith
What would I do
glass lichen
collect like terms
glass lichen
yes
glass lichen
yes
vagrant zenith
Ok ty
jovial talon
glass lichen
k and y are obvious, then the slope for OA is the same as the slope for CB
nocturne gazelle
anyone know bigO notation for computer science
knotty mason
Example 1
Use the given triangle to fill in each blank.
sin B= __
tan B= __
__ B=ac
__ A=bc
alpine sable
Example 1
Use the given triangle to fill in each blank.
sin B= __
tan B= __
__...
ok
what's this for
Where the questions
glass lichen
Example 1
Use the given triangle to fill in each blank.
sin B= __
tan B= __
__...
what's the definition of sin(B)?
what ratio?
glass lichen
do you know the ratios?
knotty mason
ahh its fine i dont even know what im asking but ty anywayyy
surreal sinew
@alpine sable here
alpine sable
Here
surreal sinew
so first we have to do $\log_{25}9$ right
ocean sealBOT
αρη
alpine sable
Um, yes but am I supposed to react to an emote?
surreal sinew
no
alpine sable
Oh okay. Yes.
surreal sinew
and we know $\log_{25} 9 = \frac{\log_{10} 9}{\log_{10} 25}.$ right
alpine sable
Yes
ocean sealBOT
αρη
ocean sealBOT
αρη
alpine sable
Ok
surreal sinew
so do that with a calcualtro
alpine sable
On it
alpine sable
3.4130309724?
snow roost
alpine sable
Er, it's wrong?
ocean sealBOT
surreal sinew
@alpine sable
alpine sable
I'll try with a dif calculator if you would wait a sec
surreal sinew
sure
send a picture of your calculator
i tried it on my calculator, wolfrom alpha, and google calculator
i got 3 everywhere
alpine sable
Maybe I'm entering the equation incorrectly
surreal sinew
send me a picture of what you have on your calculator
alpine sable
surreal sinew
its 5 raised to the power of log9/log25
alpine sable
Ah
surreal sinew
you did 5 multiplied by log9/log25
alpine sable
Got it!
alpine sable
Yes
An 8 meter long ladder is erected up a wall. The distance along the ground to the wall is 3 meters.
How high up on the wall does the ladder reach?
At the same time, the same ladder reaches 6.5 meters up the wall.
Calculate the angle that the ladder forms with the ground.
alpine sable
oh thought u guys were done, sorry
surreal sinew
now we have to do $3^(log_3 2)$
ocean sealBOT
αρη
alpine sable
On it
surreal sinew
so $log_3 2 = \frac{log_2}{log_3}.$
ocean sealBOT
αρη
alpine sable
Yes
surreal sinew
so $3^(log_3 2) = 3^( \frac{log_2}{log_3})$
ocean sealBOT
αρη
surreal sinew
understand?
alpine sable
Yes
alpine sable
Yes!
surreal sinew
Yes!
Great! Do you have any more questions?
Or do you need help with anything else
alpine sable
Not right now, I'll do similar questions then move up to next type of questions
surreal sinew
Not right now, I'll do similar questions then move up to next type of questions
Sure, feel free to ask me any questions if you have any difficulty with the other types of questions.
alpine sable
Thank you! You helped me a lot!
surreal sinew
No problem !
ocean sealBOT
Thunder7
ocean sealBOT
Thunder7
alpine sable
can someone explain how u can easily get the two numbers that will add and multipy?
cuz i honestly cant just guess the numbers im slow
stoic hound
can someone explain how u can easily get the two numbers that will add and multi...
Let b=-2-a, substitute in the a*b=-35 to get a quadratic in a, solve for a
alpine sable
Let b=-2-a, substitute in the a*b=-35 to get a quadratic in a, solve for a
so it would be b=-2-a*b=-35 ?
stoic hound
so it would be b=-2-a*b=-35 ?
Sorry, could you clarify?
alpine sable
Sorry, could you clarify?
you said plug a*b=-35 in b=-2-a in a
stoic hound
so it would be b=-2-a*b=-35 ?
You can do a*(-2-a)=-35, or -35/a=-2-a,
M, N, P being aligned means vector MN+ vector NP=vector MP. And keep in mind that AB + BC=AC. Hope this helps
frigid hatch
it also means that they are a 180 angle
ye
I mean if I do won't it become
,,a(ax - a - 4) -3(ax - 7)
ocean sealBOT
Thunder7
frigid hatch
I just can't do anything with it
junior osprey
how do i calculate spearman’s coefficient on demos
dry plover
frigid hatch
**Thunder7**
I got it, the second, third and last terms can be written as -(a+7)(a-3) then you group the first and fourth terms by ax and you get
-(a+7)(a-3)+ax(a-3) so (a-3)(-a-7+ax)
alpine sable
Number 3. I really can't grasp consecutive numbers when it evolves problems like these...anyone can help or guide me to some videos or explain to me this and another related question? I really tried looking this up but other than the general method of consecutive numbers and what they are I couldn't find anything related to this. All the best, luo
stoic hound
Let the first number be x. Then the next number is x+1. Now the sum of their squares is x²+(x+1)²=221. This leads to the quadratic equation, 2x²+2x-220=0. Now just solve for x
alpine sable
Let the first number be x. Then the next number is x+1. Now the sum of their squ...
omggggggggggggggg
🤦♂️
Is there an algebraic structure like Monoid, but instead of (or in addition to) a neutral element, an element e where e*x = e for all x
like 0 for number multiplication or false for boolean and
I literally dunno where to begin
If it's a hole, there can't be any dirt in it. That's probably the trick question.
Yeah I just don't know what to do with the pizza problem
combinations without repetition:
cumulate with k 0 through 10
What do those letters mean for this problem
What goes where
n being the number of toppings available, and k being the number of different toppings used for a given pizza
if you use n = 10 and k = 3 for example, you will get the different pizzas you can make when using 3 toppings, with 10 available
So can I just throw that into like mathway with 10 and 3 put in
i suppose. you have to add up the results with k 0-10 because you want all numbers of toppings.
I don't understand I'm so sorry
you put in that formula with n=10 and k=1. thats how many different pizzas with 1 topping there are. then put in n=10 and k=2, thats how many different pizzas with 2 toppings there are. add the two results. then do k=3 and add that too. and so forth until k= 10
and k=0 too
thats when you take no toppings, aka a cheese pizza.
and the exclamation mark is a factorial. i dont know how you would punch that into mathway
I can't do the math in my head or written down so I'm trying to figure out how I can do it
it's not meant to be done in your head, so no worries
Yeah I don't know how I'm supposed to do it if I don't like
Use a calculator or something
you can punch this into wolframalpha: "with k = 0 to 10, sum 10!/(k! * (10-k)!)" without the quotes
hold on a second, there is an easier way. since you have 10 toppings and for each its a binary operation whether its on the pizza or not. you can also do 2^10. should be the same result
i apologize for making it more complicated than neccessary
Wait what
That's only 1024
woeful summit
Hello there :) I'm not sure if this question fits the server, but it's linear alg so why not.
I'm doing 3d graphics programming and am trying to convert 3d world coordinates to screen coordinates, i.e. project the world onto the screen.
Available parameters are the camera angle in degrees, the camera position in world space, the fov, the viewport (width, height) and obviously the position of the point in worldspace I want to project onto the screen.
x and y are horizontal, z is vertical.
angle_x represents up and down movement of the camera (pitch), where moving down increases the angle -> rotation around the y axis
angle_y left/right movement (yaw), where moving left increases the angle -> rotation around the z axis
angle_z roll -> rotation around the x axis
I'm not so sure how I can express this in more mathematical terms, I guess then I would get more help as this is a pure math discord, but I hope someone still understands what I'm trying to do.
rich basin
@woeful summit I thought modern game engines took care of stuff like that?
woeful summit
if i would use a modern game engine, yes. but where is the fun in that?
rich basin
Well, I wrote code for that in 1998, which I am looking at right now.
novel spruce
@woeful summit do you know any linear algebra?
like matrix multiplication dot products or projection?
woeful summit
yeah a little i guess. this is what i tried (glm is a math / graphics library for cpp, not sure if you know how to code)
glm::vec3 world_to_screen(glm::vec3 pos,
glm::vec3 cam_pos,
glm::vec3 cam_angle) {
glm::mat4 projection = glm::perspective(
glm::radians(FOV), (float)SCREEN_W / (float)SCREEN_H, NEAR, FAR);
glm::mat4 model(1.0);
model = glm::translate(model, cam_pos);
model = glm::rotate(model, glm::radians(cam_angle.x),
glm::vec3(1.0f, 0.0f, 0.0f));
model = glm::rotate(model, glm::radians(cam_angle.y),
glm::vec3(0.0f, 1.0f, 0.0f));
model = glm::rotate(model, glm::radians(cam_angle.z),
glm::vec3(0.0f, 0.0f, 1.0f));
glm::mat4 view = glm::inverse(model);
return glm::project(pos, view, projection,
glm::vec4(0, 0, SCREEN_W, SCREEN_H));
}
idk what the project function does
woeful summit
it should project it correctly, modelview matrix and projection matrix.
and as model should be identity (i guess) in this case i can just pass view mat
i suspect that something with my rotation is wrong
novel spruce
idk computer graphics but i hope someone else can help you
rich basin
Well, I seem to have neglected to comment any of my code, unfortunately.
It's an example rotating a cube.
In Java...
woeful summit
you could send it to me anyway (or at least the relevant part)
but i guess my problem is constructing the view matrix, not projecting as that's something glm does for me
small helm
If a direction vector is lets say t(1,2,3), then would be able to find the slope of the line?
cause if it was in 2D we could just do y/x to get the slope
rich basin
Here's the Java code.
I have an older one from 1993, in C, also rotating a cube but using only integer math and precalculated trig tables.
When floating point processors were rare...
woeful summit
thanks a lot but honestly i don't think that helps me. it's cool to look at (i wasn't even born in 1996) but not really something i can adapt in my code
rich basin
Nah, that code looks better commented though.
Anyway, the java code has a function "perspectivize" that I believe calculates a projection from an intended set of eyes onto the screen coords.
Looks like my "world" is expressed in terms of an orthonormal base, and rotation is done by rotating that base, and everything else falls into place.
novel spruce
||that ryme fell into place||
woeful summit
||
||
yeah i'm currently looking into your world renderer class so thanks already
maybe someone spots a trivial mistake in my code though. it's kinda working btw. if the camera and the object don't move, only the angle changes, it works.
rich basin
What does inverse(model) do?
So, glm already has methods for translation, projection, etc?
faint flame
woeful summit
So, glm already has methods for translation, projection, etc?
and yes.
everything simd optimized etc. so makes really no sense to do it myself
oak chasm
@alpine sable Exactly how much of a circle is the part inside the lines from the center?
oak chasm
OK, so what's the area of the circle?
alpine sable
5pi cm squared
oak chasm
Right, so what's a quarter of that?
alpine sable
Divide it by 4?
oak chasm
Yep.
alpine sable
1.25
alpine sable
6.25
oak chasm
Right.
So, you have the area of the quarter circle.
Now you need to subtract the unshaded part of that. What is the unshaded part?
alpine sable
How do I get the shaded part?
oak chasm
It's the quarter circle minus the unshaded part of the quarter circle, right?
oak chasm
You want the shaded part of the quarter circle.
oak chasm
The shaded part of the quarter circle plus the unshaded part of the quarter circle is the entire quarter circle.
Right.
So, simplify.
alpine sable
12.5
oak chasm
OK, what units?
alpine sable
Cm
oak chasm
Almost.
alpine sable
Squared
oak chasm
Right.
oak chasm
So, what's 6.25 pi cm^2 - 12.5 cm^2?
No, be precise here.
It wasn't 6.25, it was 6.25 pi cm^2.
oak chasm
No, if you get a negative area, something went wrong.
What went wrong was it's not 6.25 cm^2 for the quarter circle.
Go back to what you answered for that part.
oak chasm
[7:14 PM] .Asante: So 25 pi squared?
[7:14 PM] Chai T. Rex: 25 pi cm^2 (units are cm^2 for area).
[7:14 PM] Chai T. Rex: Then you quarter it.
[7:15 PM] .Asante: 6.25
You answered 25 pi cm^2, then you quartered that, which is what?
alpine sable
6.25 pi cm ^2
oak chasm
Right, now subtract the answer you got for the triangle's area.
alpine sable
Do I solve 6.25 time pi
oak chasm
Yep.
oak chasm
Yeah, but when they ask for that, round only at the very end.
We're not quite at the end yet.
alpine sable
19.62
oak chasm
OK, what's 19.62 - 12.5?
alpine sable
7.12
oak chasm
OK, and don't forget the units.
alpine sable
,w 19.62 - 12.5
ocean sealBOT
oak chasm
@alpine sable Yes, and now we're at the end, so round.
oak chasm
Right.
alpine sable
Thanks
oak chasm
No problem.
oak chasm
@alpine sable There's no rule that deals with a subtraction inside a log.
ocean sealBOT
square
alpine sable
oh, so would it be e to the x over lnx?
novel spruce
wait hang on
alpine sable
oh, i forgot to mention, im doing diff. equations
alpine sable
i just tried multiplying it out to each term
but i forgot that it works diff. with logs
yea
it would be
$\sqrt{test}$
thx
ember stream
jovial talon
Any help on this
errant tangle
what are you trying to solve here
limpid spade
x and y
errant tangle
oh ok sorry
limpid spade
Does that square thing at A mean it's a right angle?
errant tangle
@stray salmon can you stop pinging
i'll only give you hints but i wont give u the full answer
ok
why are you so desperate to know the answer
use y = mx + b
limpid spade
Use Thales
limpid spade
Thales' theorem, did u learn it
jovial talon
Any help on this
Any help on this
limpid spade
Search Thales' theorem
errant tangle
Any help on this
im pretty sure y = 0
jovial talon
Yea and how are supposed to find x
limpid spade
<@&268886789983436800> 2 ppl to 
chilly hatch
@stray salmon stop spamming
glass lichen
who's the 2nd person?
chilly hatch
yeah, they did
limpid spade
Cuber*
errant tangle
Yea and how are supposed to find x
are there any other details listed in the question or is this it?
jovial talon
We are supposed to find the area
errant tangle
oh
limpid spade
Well u can find the area of the left triangle
Does the square on A mean it's a right angle?
limpid spade
It doesn't look like a right angle to me
errant tangle
most math diagrams aren't to scale
jovial talon
Okay lemme try
jovial talon
We cant solve for x right?
errant tangle
yeah maybe it's because you don't stop spamming and are impatient
how about you try solve the problem urself
because you keep spamming
im trying to help someone right now
with a problem
i gave you a pretty good hint actually
limpid spade
Please do a favor and leave this server
limpid spade
errant tangle
clever actually
fringe trout
B is 26.0
limpid spade
Dunno if angle A of the right triangle is 45
fringe trout
:oooo how did u do it
because 0,0 to 4,8 is 10 units
and pythagorean triple
10, 24, 26
where 10 is the shorter leg
limpid spade
<@&268886789983436800> pls ban cuber
fringe trout
lmfao
chilly hatch
thanks again!
fringe trout
np
limpid spade
Np
errant tangle
because 0,0 to 4,8 is 10 units
how is it 10?
fringe trout
how is it 10?
4^2 + 8^2
limpid spade
So there was an easy way to do it while we were doing a hard way lol
fringe trout
yeah
fringe trout
yh
limpid spade
To find the base of the right triangle we can use tan45=x/8
errant tangle
8*1?
limpid spade
U calculated?
limpid spade
Mh 8 then
errant tangle
if we rearrange x=(tan45)*8
yea
but that's assuming angle CAB is 45 tho
the question didn't state it
limpid spade
Now just Pythagoras or cos45=8/x
limpid spade
If you split a right angle in 2 angles perpendicurarly won't the 2 angles be 45
oak chasm
@limpid spade What is perpendicular to what?
limpid spade
Well we didn't need to find the hypothemuse of the right triangle
errant tangle
it wanted the x and y coordinates didn't it?
errant tangle
oh
oak chasm
No, only in a 45-45-90 triangle will a line perpendicular to the hypotenuse split the 90 degree angle into two equal portions, but it doesn't appear that that's been decided yet.
For example, draw a right triangle where the left leg is much, much shorter than the other. If you draw a line perpendicular to the hypotenuse up into the right angle, the left portion of the right angle will be much less than the right portion.
errant tangle
true
limpid spade
Mhhh then how is it possible to find the area
errant tangle
not all instances of a line bisecting a right angle will always end up with two perfect halves (i dont think that made any sense but u get the point)
we can solve the length AB in terms of x
and then find the area in terms of x
it never said we had to find the numerical value of AB
or the area for that matter
limpid spade
He said he needs to find the area
limpid spade
That would be ((4-x)8))/2
errant tangle
oh
tardy sluice
can someone help me with permutation functions?
tardy sluice
does that mean f:A>A?
actually not really 😦
i do understand how cycle permutation works but that doesn't apply to the question right?
naive parrot
anyone know how to prove that 3^500+5 is divisible by 14? I'm confused to how this whole mod thing works...
ocean sealBOT
tired axle
show that rational and use basic proof techniques for example thats its an integer and its divisible by 14 LOL
@alpine sable not like literaly lol
in proofs
hahah
alpine sable
i mean
naive parrot
@alpine sable it is divisible
alpine sable
isnt every number divisile by 14 then
naive parrot
well no
tight locust
ok
tired axle
isnt every number divisile by 14 then
????
tight locust
$3^{500} + 5 = 0 (mod 14)$
naive parrot
i've gotten given an example to work with but its confusing me
ocean sealBOT
EndTimes
tight locust
what can you do with this congruence
alpine sable
$3^{500} + 5 = 0 (\mod 14)$
ocean sealBOT
square
tight locust
$3^{500} = -5 (\mod 14)$
ocean sealBOT
EndTimes
tight locust
$3^{500} = 9 (\mod 14)$
ocean sealBOT
EndTimes
tight locust
that should be very simple now
naive parrot
This is how to prove 5^100 − 5 is divisible by 19. I just don't lnow how to use this to prove that 3^500 + 5
*know
tight locust
look at what i just did
swift shore
Find the angle between the lines given by $$2x^2 + 2y^2 = 5xy.$$
ocean sealBOT
abs_0
wild shard
**abs\_0**
Solve for y, you should get two equations
use tangent and the slopes of the lines to find the angle
vast lance
would part c be 0<x<50 or 0≤x≤50? but if its 0≤x≤50 i wouldnt have rectangle no more because there is no width..
^ping me pls
solar cradle
@vast lance Yes, the width would be 0 < x < 50, for exactly the reason you stated. A little more precise would be to note that if x= 50, length = 0, and A(x) = 0 and vice versa.
hollow flare
@solar cradle can you help me with a question
vast lance
alright
solar cradle
@hollow flare what exactly are you studying, you can do this with a Riemann sum
solar cradle
perfect, that is literally the definition of Riemann sum without sigma notation lol
Just use $$\lim_{n \rightarrow \infty} f(x) \Delta x + f(x+ \Delta x) \Delta x + \cdots + f(x+ n \Delta x) \Delta x$$ where $\Delta x \rightarrow 0$.
hollow flare
u see i have to use definition 2
ocean sealBOT
Billy Clintorus
solar cradle
Just define $x = 4$ and $x + n \Delta x = 7$
ocean sealBOT
Billy Clintorus
solar cradle
yeah, its exactly the same thing
solar cradle
Yeah exactly!
Some early calc exercises are shallow like this, just try not to overthink it
hollow flare
do u know logic proofs too?
comp sci related lol not really relevant to what we talking ab but jw
solar cradle
I've never taken a logic course and a bit rusy on the notation so I probs can't help you on that lol
hollow flare
ah its fine lets try to finish this problem tho haha
@solar cradle would this be the final answer without evaluating?
solar cradle
yep looks good
hollow flare
thank you
alpine sable
how would i put this into an augmented matrix to solve for x, y, and z in terms if a0, a1, and a2?
daring chasm
alpine sable
wouldnt i still be able to put it into a matrix in terms of the rows equating to the t^2 coefficient, t coefficient, and constant?
example from yesterday
my professor found a way to get x and y and z in terms of a0 a1 and a2 but im so confused on how he did it
ahh wait nvm i think i got it
errant tangle
have u tried solving it
what did u do
oooo ummm
that's not
how u do it
have u learnt factorisation
what is this for
like what class and stuff
is this hw?
a test?
just random
?
i got the answer btw
ok
have you learnt completing the square?
for quadratic equations
what lvl of maths r u doing rn
i have no idea how to explain this
well i can't just give you the answer you won't learn
no there is definitely a solution
i already have the answer
are u australian wtf?
ohhh ok
are u like yr 10 rn?
oh
13 and you're completing the square for non monic trinomials?!
what the hell
thas weird
no just doesn't sync with the nsw syllabus
or the vic or qld one
alr fine i'll give u the solution
basically rearrange the equation so that it equals to y
how-
wdym you dont know how???
that's not the answer
but you need it in this form
then you factor the -6 out from -6x^2-12x
?????
bro are u sure youre not messing with me
well that's what i mean
when i said factor the -6 out
-6 times 2 is -12
because i factored out the -6 from the -12
so the result is 2
see how it's in brackets?
yes
oh god how am i gonna explain completing the square?
you complete the square for what's in the brackets
istg you're trolling
there's no way you could be doing this lvl of maths and not know what completing the square is or even brackets
what do you mean this year
we've only started school 2 months ago!
you-
oh
i though you lived
nvm
im dumb
anyway
fine i'll give you the solutions
hold on im writing it down
here
the solution is the bottom red box
yw
thorn kindle
what is u
errant tangle
:)))
thorn kindle
alpine sable
@viscid tangle this might help: https://www.youtube.com/watch?v=pwITxyUghV0
thorn kindle
$ax^2 + bx + c = a(x+\frac{b}{2a})^2 + c - \frac{b^2}{4a}$
ocean sealBOT
AMD
errant tangle
i'll help you out a little more
thorn kindle
it's just a formula. plug in for a, b and c
errant tangle
a = -1 b = 12 c = -40
the formula will help you dw
it works
you plug numbers into the formula to get the equation
thorn kindle
if i tell you that 2+2 = 4, then that means that any time you see a 2+2 in an equation, you can replace it with 4
now if i tell you that
$ax^2 + bx + c = a(x+\frac{b}{2a})^2 + c - \frac{b^2}{4a}$
ocean sealBOT
AMD
thorn kindle
that means any time you see "ax^2+bx+c" you can replace it with "a(x+b/2a)^2+c-b^2/4a"
errant tangle
because it gives you the answer
thorn kindle
stop freaking out lol
this is a basic rule of arithmetic
called the "transitive property"
you should know what that means
if a=b, and b=c, then a=c
doesn't it?
if 2+2 = 4 and 4 = 3+1
errant tangle
bro
thorn kindle
then doesn't 2+2 = 3+1 ?
both sides of the equations are just numbers
every expression is just a number
that can be evaluated for a certain value of x or whatever variable you have
what is (2+2) + 3?
hint: there's a formula for what 2+2 is
that i just gave you
right
ok
standard form of a quadratic:
y = ax^2 + bx + c
it's a polynomial of degree 2
sums of powers multiplied by coefficients
i literally gave it to you
multiple times lol
if you have an equation in standard form:
y = ax^2 + bx + c
then the vertex form of that equation is y = a(x+b/2a)^2+c-b^2/4a
so just take the a, b, and c values and evaluate
can you make this equation look like y = ax^2 + bx + c
it will
errant tangle
why are you so adamant on getting the answer
it's very simple if you just powered through the formula
stoic hound
Dragon :)
thorn kindle
here's the answer. good luck on your test
i tried
but i guess this isn't something i can teach you
write this down line for line:
y = ax^2 + bx + c
y = a(x + b/2a)^2 + c - b^2/4a
y = -(x-6)^2 - 4
there
copper prawn
In a row echelon form, should the pivot point row never be swapped?
Need this to avoid my algorithim utterly evaporating the determinant
thorn kindle
can you just use the wolfram alpha api?
i mean it requires an internet connection
but mathematica is way better at this sort of stuff
copper prawn
never heard of those
im using c++
and its more of a learning experience than anything
ive been stuck with this determinant thing for 2 days now
just gotta know this and im good
thorn kindle
you've never heard of wolfram alpha
do you live under a literal rock with no internet
copper prawn
just don't care is all
tight locust
@copper prawn you can just google that question lol
copper prawn
<@!288465420011438080> you can just google that question lol
bet
ionic jewel
just look up a correct implementation for RREF in your choice of programming languages
or at least pseudocode and implement it into your own
copper prawn
but thats booooooring
ionic jewel
if its for learning rref, really just do it by hand, if its for hard matrices use an existing implementation thats faster
copper prawn
its fun figuring the algorithims out yourself
oh well
best thing to do is just run the program
copper prawn
if i was working for a tech company
yeah
id be fired and kicked out the door by the ceo personally
but its just for fun
ionic jewel
yea fair
fair fossil
hello, I was wanting to be pointed in the right direction. I have a question about statistics but I'm not exactly sure how to google it (and then watch videos to learn about it.
Pretty much pretend I'm hitting x bricks with a sledgehammer at the same force, and my hypothesis is that 10% of them will break. When can I be certain that I've broken enough bricks that my 10% claim is either correct or incorrect?
does this make sense, I can explain further if I worded it weird
thorn kindle
ideally the number of bricks you break should be infinite
because as you break more and more bricks you get a more and more precise experimental probability
so just a reasonably large number should work
fair fossil
I'd want to be able to specify what p value i'd want, normally the cut off is 5% right?
thorn kindle
yeah
fair fossil
so just a reasonably large number should work
Yes, I was wanting to figure out how to calculate how much that would exactly be. For instance, let's say these bricks are expensive. I'd just want to break as little as possible while still reaching the 5% threshold, or any threshold i'd set
if that makes sense
brittle drift
help
fair fossil
hello, I was wanting to be pointed in the right direction. I have a question abo...
<@&286206848099549185> hey could anyone help me out with this?
winter bay
ah this is a pretty fun problem
i may not know how to do it tho but ill give it a shot
first i think we should find the length of the arc that is over the shaded region
alpine sable
first i think we should find the length of the arc that is over the shaded regio...
I don't think we need that for finding the area though
it's just the radius I'm trying to find
winter bay
just multiply each coord by the dilation factor'
upper ember
is the answer 416.67?
alpine sable
is the answer 416.67?
idk...?
winter bay
i think thats what hes wondering buncho
alpine sable
just multiply each coord by the dilation factor'
whats tht?
winter bay
oh for lavishes thing
alpine sable
I'm in grade 6 so I don't know what u mean...
well in grade 7 but failed grade 6
so back in grade 6.
fair fossil
o
upper ember
idk...?
oh, lol, well what i did was,
See the equilateral triangle? It is divided in 3 equal parts, now area of an inscribed equilateral triangle is (3*sqrt3)/4 *r^2, so i calculated that, and then, calculated the area of the segment and then added them both
alpine sable
oh, lol, well what i did was,
See the equilateral triangle? It is divided in 3 ...
..........
whats a sqrt?
fair fossil
square root
upper ember
sqrt=square root
winter bay
how do u just know the area of an inscribed equilateral triangle
upper ember
i studied it for olympiads
upper ember
idk of any way simpler than this
alpine sable
idk of any way simpler than this
oh
upper ember
like anything else would be more complex, with trignometry, or some wacky geometry properties
ig
alpine sable
lmao
oh @upper ember is there a way to find the area of a triangle without the base?
upper ember
well, there can be
like there is a formula, area of triangle=1/2 ab(sIn(C))
but u will need to know one of the lengths
then u can use some neat tricks to find the area
upper ember
like there is a formula, area of triangle=1/2 ab(sIn(C))
this formula uses trigonometry, btw so dont be confused if u dont get it
forest wasp
Not sure if this is correct but I feel like you can prolly just find the area of the circle and then divide by 3
Because if you look at the image the unshaded area is actually just the same as two of the shaded area
alpine sable
Not sure if this is correct but I feel like you can prolly just find the area of...
tht wouldn't work i think
forest wasp
why not?
alpine sable
cause it'd be like 3 pieces of a pie then
I could find the area of the circle then triangle then subtract them and divide the answer by 3 tho
forest wasp
But isn't a part of the triangle also shaded in?
alpine sable
But isn't a part of the triangle also shaded in?
i can find that after dividing the triangles area by 3
forest wasp
ok
stoic hound
Technically speaking couldn't the situation be like this?
https://share.sketchpad.app/21/20c-5280-1b50bf.png
The question doesn't actually say anything about symmetry
forest wasp
I think that it's pretty safe to assume that the diagram provided is at least accurate if not to scale
alpine sable
do i set the determinant to 0 for this?
stoic hound
do i set the determinant to 0 for this?
That would make one eigenvalue zero
For repeated eigenvalues you'd probably set the discriminant of the caharcetrsistic equation to 0
alpine sable
i mean discriminant not determinant sorry
alpine sable
k well that answer is wrong
stoic hound
One possibility is how you're entering the answer.. These autograders can be really eccentric
alpine sable
nah it entered correctly
stoic hound
Well, that was my last idea.. Sorry
fading shadow
I have a question
alpine sable
what
fading shadow
d/dx lnax is just 1/x right
alpine sable
yes
fading shadow
So it doesn't matter what the coefficient is
stoic hound
d/dx ln(ax) = 1/ax * a right?
fading shadow
Wait hold on yea by chain rule
stoic hound
Because after all, ln(ax) =ln(a) +ln(x)
alpine sable
d/dx ln(ax) = 1/ax * a right?
oh your right
stoic hound
And ln(a) disappears
alpine sable
fuck
stoic hound
Lmao
fading shadow
dln(ax)/d(ax) × d(ax)/dx
robust palm
flat gust
Base times height
jagged imp
well if u=2x+y, du/dx=2+dy/dx, so dy/dx=du/dx-2. then, du/dx-2=u after subbing everything in. The resulting diffeq in u is seperable
round hawk
Ohh got it! Thanks a lot!
small helm
Can I get some help with question 12
Since I have the symmetric equation of the line it's parallel to, I know what the direction vector is
But not sure how I would find x_0, y_0, z_0
serene jacinth
hey, could somone help me out with these equation ? Whats the reason or definition of multiplying the transpose x with x and the inverse of it ?
i also would appreciate if you suggest somethin that i can study that on
fading zephyr
that's the solution to a least squares problem @serene jacinth , you can find it from $\min_{\theta}\Vert X \theta - y \Vert_2^2$ by taking the gradient and setting it equal to 0
ocean sealBOT
Edd
fading zephyr
you can look at multivariable calculus, linear algebra, optimization, signal processing, and/or machine learning to read about it
the "reason", from the linalg perspective, is to project the vector y onto the row space of the matrix X, since that bunch of matrix operations yields an orthogonal projection matrix
stoic hound
Do you know how the derivative is defined
green marsh
i dont understand what youre asking
ik how to find the derivative of like
2x^2 or something like that
but not when its like 1+ 2x^2
fading zephyr
but do you know what the derivative means
green marsh
yes
alpine sable
the derivative of a number is just 0
alpine sable
then what's the problem
green marsh
idk how to do the problem