It's a substraction not a multiplication, my apologies
#geometry-and-trigonometry
karmic spruce
pastel anchor
so is it-3i+6i?
karmic spruce
yes, that is correct
pastel anchor
ok here is what i dont get. the answer will be -3i
so is the final answer is 3+3i or 3-3i?
karmic spruce
Yes
pastel anchor
yea idk which one is the right asnwer tho
karmic spruce
which one do you think it is?
pastel anchor
second one
karmic spruce
and how come?
pastel anchor
cuz the answer from -3i+6i is -3i
karmic spruce
what's -3+6 ?
pastel anchor
acutally its 3
karmic spruce
the answer will be -3i
Is this what the answer book says or?
acutally its 3
correct so -3i+6i would be?
pastel anchor
3+3i
pastel anchor
yea
karmic spruce
great, because I suck at explaining lol
paper vale
It is trivial
karmic spruce
everything is trivial apparently
upper karma
It is trivial
... Again?
karmic spruce
https://discordapp.com/channels/268882317391429632/326138757474680852/761604758384410664
just bumping this real quick since I dont want to get it lost in the chat
upper karma
But the point B(2,0) does not lie on the circle then as you have mentioned
karmic spruce
How so?
Could you take a look at the geogebra example I linked with it? That might convey better than my words
But the point B(2,0) does not lie on the circle then as you have mentioned
Apologies, radius is 2, not 4
the diameter is 4
upper karma
(0,2) and (0,-2)
The eqn of the circle is x^2 + y^2 = 4
Using this and the distance formula, take any point (x,y) on the circle and solve them
eager ocean
dark cradle
having a problem, probably user error
i know that the tan(1.7) is 59.53 degrees
but when i plug that into a calc, it's giving me 5.318....
earnest echo
I think you mean arctan(1.7)
dark cradle
lol, ya
earnest echo
,w arctan (1.7)
somber coyoteBOT
somber coyoteBOT
earnest echo
There you have it
dark cradle
so, trying to help my son with his homework
his question is cot(theta) = 0.1051042353
err
fixed
i know to tan both sides
but when i do...
,w tan(0.1051042353)
somber coyoteBOT
dark cradle
cancel out the cot?
earnest echo
No
dark cradle
ah, supposed to be arccot?
paper vale
well u can multiply both sides by tanx/0.105.... if that is what u mean
paper vale
multiplying by tanx removes the cot
dark cradle
i'm afraid i don't know what you mean by tanx
paper vale
clearly tan(theta)
dark cradle
i'm trying to find theta
paper vale
yea so obviouslty inverse tanx after u rearrange
somber coyoteBOT
dark cradle
is that right?
dark cradle
silent plank
take reciprocal of both sides
apply arctan, write general solution if needed
the output will depend whether the calculator is set in degrees or radians
dark cradle
arctan, or tan?
silent plank
$\tan(\theta) = \frac{1}{\cot(\theta)}= \frac{1}{0.1051042353}$
somber coyoteBOT
ramonov:
dark cradle
is there another way, if i don't have arctan on my calc?
silent plank
on your calc it'll use less desirable notation:
$$\tan^{-1}$$
somber coyoteBOT
ramonov:
silent plank
usually accessed from shift or 2nd function of the tan key
dark cradle
dark cradle
degrees, i think
silent plank
convert manually by multiplying by 180°/pi
and/or use a proper hand held sci-calculator
dark cradle
i'm confused. if
$\tan(\theta) = \frac{1}{\cot(\theta)}= \frac{1}{0.1051042353}$
then why isn't
$\tan^1(\theta) = {\cot(\theta)}= \f{0.1051042353}$
somber coyoteBOT
thnkr:
dark cradle
well that didn't come out well
silent plank
cot is the multiplicative inverse of tan
not the function inverse (over a certain interval)
dark cradle
i'm guessing that there is a key difference between something being a multiplicative inverse and a function inverse?
dark cradle
trying to google an explanation of the difference
silent plank
oh I think I see what youre actually asking now
which is a bit related I guess
$\tan^{-1}$ is suboptimal to represent the function inverse for $\tan$ since it can cause confusion
somber coyoteBOT
ramonov:
silent plank
the use of the ^(-1) is an exception and shouldnt be interpreted as an actual power
$\tan^{-1}(x) \not\equiv \frac{1}{\tan(x)}$
somber coyoteBOT
ramonov:
dark cradle
i don't mean to take your time for granted, but trying to help my son. is there some way you can explain the difference between a multiplicative and inverse function, with some example as to why they are different?
so that i can try to explain it to him?
silent plank
x is the multiplicative inverse of 1/x since x * 1/x = 1
silent plank
and it's probably better to look up the formal definition of an inverse function than me explaining it here
dark cradle
ah, i think i got it
silent plank
You may have been taught that notation like $\tan^{n}(x)$ is used to represent $(\tan(x))^n$ \
However there is an exception when $n=-1$. \
The use of $-1$ in that position is used to denote the function inverse.
Due to this source of confusion it is generally better to represent the inverse of trig functions using the \textbf{arc} prefix.
$$\arcsin, \arccos, \arctan$$
somber coyoteBOT
ramonov:
dark cradle
silent plank
and then there's more stuff about them not being true inverses
dark cradle
hmmm. there's still room for confusion in that example
dark cradle
well, the way i'm trying to wrap my head around it is by replacing tan/cot with 2, 1/2
err
silent plank
yes
dark cradle
however, i find that it still carries over to tan/arctan
because if i do tan(x) = n, and replace tan with 2
2x = n. and if arctan n = x, then it still works as a reciprocal somehow, because
(1/2)n = x
silent plank
if $\tan(x) = \frac{a}{b}$ then $\cot(x) = \frac{b}{a}$
somber coyoteBOT
ramonov:
silent plank
applying that to your question:
$$\tan(\theta) = \frac{1}{\cot(\theta)} = \frac{1}{0.1051042353}$$
somber coyoteBOT
ramonov:
silent plank
does that step make sense so far?
dark cradle
ya
silent plank
if they only want the principle solution where -pi/2 < theta < pi/2
then you can apply the arctan function to the tan(theta) and the fraction
$\arctan(\tan(\theta)) = \arctan\br{ \frac{1}{0.1051042353}}$
somber coyoteBOT
ramonov:
silent plank
for -pi/2 < theta < pi/2 (in radians) or
-90° < theta < 90° (in degrees)
arctan(tan(theta)) = theta (from properties of the inverse function)
and the right side will be what the calculator gives you
dark cradle
ah, i think i got a good analogy
whereas 2^(-1) = 1/2
this is more like
(multiply)^(-1) = divide
heady lynx
west basin
pi
full hatch
upper karma
,rccw
full hatch
Anybody got an idea for solving for r? I saw a similar video online with 3 squares but I wanted to give this a try
somber coyoteBOT
full hatch
Its just something I came up with not homework or anything
snow hornet
what is sin60? r/h? @full hatch
full hatch
That's referring to the small right triangle with the base = x and the hypotenuse = h
It may be easier to ignore my work tbh no guarantee its right 😂😂😅 im just messing around
hallow crystal
What am I doing wrong 😀
west basin
you can just get an integer answer when you multiply 16sqrt(2) by itself
you dont need to distribute
hallow crystal
you can just get an integer answer when you multiply 16sqrt(2) by itself
@west basin
Thanks but is it a coincidence that Area = 512 but that’s also what X squared equaled?
late dirge
does anyone know the right channel for this question?
or if anyone could help me solve it
west basin
x^2 is literally the area of a square
hallow crystal
x^2 is literally the area of a square
@west basin
So I didn’t have to do all that? I could’ve just stopped there and gotten my answer? 😭
west basin
no you still have to do it to get x in the first place
west basin
if you know properties of righr triangles its easy
hallow crystal
My answer could’ve just been what x squared equals?
I dunno what those are 😔 lemmie search that up
Hm I know all of that, I didn’t know it had a name. It’s just all the basic facts related to pythag
west basin
well the helpful one is that in a 45 45 90 triangle the length of both legs will be equal to sqrt(2) * hypotenuse
so you can get 16sqrt(2) easily
and use the area of a square formula
covert rune
@late dirge Are you supposed to define it in terms of Z?
covert rune
Alright, one second let me get a drawing up
covert rune
What part are you stuck on?
hallow crystal
well the helpful one is that in a 45 45 90 triangle the length of both legs will be equal to sqrt(2) * hypotenuse
@west basin
Thank you, I will note that down for similar problems like this in the future
covert rune
if you've done any work so far
late dirge
so Ik both are isosceles triangles
and the angle that's uhh forgot the word "opposite?" of z is 180-z
anddd that's kinda it
@covert rune
I think I got it
covert rune
Alright, so in the triangle with z in it we see two angles that should be equal to each other
We know that because it's an isosceles triangle, these angles would be equal to each other
And because we know the sum of angles in a triangle is 180, we know z + 2(a) = 180 where a is one of the unknown angles in the triangle with z in it
late dirge
ah ok
covert rune
When we subtract z from both sides, we get 2(a) = 180-z
Dividing by 2 gives us angle (a)
late dirge
ohh and now we know the 2 angles on the right triangle
covert rune
Right
So let's look at the left triangle now
We know angle PRS = 180-z because they are supplementary angles
We then find the two equal angles on the left triangle in the same way as the right
(180-z) + 2(b) = 180 where b = the unknown angle on the left
late dirge
and then we simplify to get b
covert rune
That's right
late dirge
yoo it makes much more sense now
covert rune
we know that the angle PSQ is a + b so we simply plug in our values to find it in terms of z.
covert rune
Just worked it out and realised that the z terms cancel out, so be careful to not leave any Z terms in your final answer @late dirge
covert rune
what are you trying to find?
late dirge
just to confirm a = (180-z)/2 and b = 180 - 2z?
covert rune
b = z/2
late dirge
oh
covert rune
That's why it's not working out
late dirge
hold up let me see why I got that answer
OHhhh
I added 180 and 180 isntead of subracting
covert rune
dw about silly mistakes like that, still early in the term so once you practice these types of questions you'll be able to minimize mistakes
covert rune
👍 Good luck dude
late dirge
thx
ah so the answer is 90 degrees
wait what
(180-z) + 2(b) = 180
shouldn't z be negative then
2(b) = -z
b = -z/2
@covert rune
sorry for asking so much
hallow crystal
@Star_#1337 Okay so basically the reason that the area gave us the same number as x squared is because in a 45,45, 90 triangle the length of both legs will always be equal to sqrt(2) * hypotenuse
So you just solve for 16|2 with the help of the formula for finding the area of a square which is a^2, which is also the original area formula which is a = l(w) ?
late dirge
ohh nvm I just understood it now, distributive property sorry for the ping
hallow crystal
well the helpful one is that in a 45 45 90 triangle the length of both legs will be equal to sqrt(2) * hypotenuse
@west basin
Please @ me if u reply :
covert rune
np
@hallow crystal Hi, it seems like you accidentally put (32)^2 instead of (sqrt32)^2
Otherwise your work seems to be fine
Wait my bad
didn't read the question properly for a second lol
upper karma
@west basin Okay so basically the reason that the area gave us the same number as x squared is because in a 45,45, 90 triangle the length of both legs will always be equal to sqrt(2) * hypotenuse
So you just solve for 16|2 with the help of the formula for finding the area of a square which is a^2, which is also the original area formula which is a = l(w) ?
if i'm not bothering you, what program did you use to make this drawn?
hallow crystal
haha no worries, but do my statements make sense? I tried to restate what @west basin and figured color coding would help
if i'm not bothering you, what program did you use to make this drawn?
@upper karma
Medibang!1!!1 and it isn’t a bother at all, ping me next time 💖
haha no worries, but do my statements make sense? I tried to restate what @west basin and figured color coding would help
@covert rune
hallow crystal
Looks good
@covert rune
Thank youu
covert rune
One little detail, though
In your explanation, you put the legs of a 45,45,90 triangle will be sqrt2(hyp) but it's the other way around
The hypotenuse of a 45,45,90 triangle will be sqrt2(leg)
hallow crystal
well the helpful one is that in a 45 45 90 triangle the length of both legs will be equal to sqrt(2) * hypotenuse
@west basin
hallow crystal
HAHA yea sleep deprivation from school got me tripping too
Oh which one’s correct? Urs or star’s(which is what I wrote)?
Cuz I’ve never heard of that property before rip
Let me fact check
covert rune
Well if you plug in star's own, you get sqrt2(16) = the leg which is correct
My own was referring to a different equation, but it's also correct
Either one is fine for this problem
hallow crystal
Ohh alright so I can just ignore urs since it doesn’t apply to my problem?
Ohh alright, so I’ll only write star’s down?
covert rune
👍
hallow crystal
covert rune
They're basically the same equation, however, star's own is put in a different form
(multiplied both sides of my equation by sqrt2)
You can choose whichever one is easier to read at that point
hallow crystal
@covert rune It’s true! :D
@covert rune by the way does this property have a title?
Should I just call it “property of 45-45-90 triangle”?
hallow crystal
I have n clue what those are 
covert rune
They're pretty simple
hallow crystal
Do you learn about sin and cos in geometry honors
covert rune
Which class are you in right now?
covert rune
it's usually taught at class/grade 9
hallow crystal
oo i think we’ll be introduced to it towards the end of the year
covert rune
Basically, they're just the ratios of the leg of the triangle and the hypotenuse of the triangle
hallow crystal
Because you need a calculator for sin and cos right? I remember him saying we’ll start utilizing calculators at the end of the year
covert rune
In other words 1/sqrt(2)
Sin and cos can be simplified to fraction form like above
But only for special right triangles
(45-45-90 is a useful example)
You don't need to worry about them too much at this stage
covert rune
The ones which are most commonly taught are 30-60-90 triangles and 45-45-90 triangles
hallow crystal
Cuz I know 30-60-90 is also one
covert rune
There are more, but you usually don't need to learn them
hallow crystal
Oh so u don’t need to memorize them like how u have to memorize squares
covert rune
You only memorize ratios for special triangles
Otherwise, you'd just use a calculator or leave it in an unsimplified form
hallow crystal
Ohh those 6
I see
Alright well I’m gonna start homework now that I’m satisfied with my notes :’)
Thanks for the help again
covert rune
No problem
hallow crystal
For number 2, how do we know that Pat’s house isn’t diagonally in between Moore St and Joe’s House?
Why straight down?
covert rune
Seems like the question is missing information. There are multiple possible values, but since they're asking for a single point we assume it's directly under Joe's house because it is the most simple answer
hallow crystal
Seems like the question is missing information. There are multiple possible values, but since they're asking for a single point we assume it's directly under Joe's house because it is the most simple answer
@covert rune
So -7, -.5 is technically not the right answer?
covert rune
Again, it's a very ambiguous question
-7,-5 Would be "technically correct" but because it seems as though they want you to find the midpoints we assume that it's -7, -1/2
hallow crystal
-7,-5 Would be "technically correct" but because it seems as though they want you to find the midpoints we assume that it's -7, -1/2
@covert rune
Well I mean the -1/2 part is correct but technically x1 can be anywhere on the x axis right 😔
covert rune
For Moore street, yes
covert rune
x1 for the midpoint can technically be anything because Moore street is an infinite line along the x-axis, but we assume it is -7 because it's the simplest option.
hallow crystal
So on a test anything would be right?
covert rune
It wouldn't be the intended answer, so they would likely mark it as incorrect
hallow crystal
Smh...
covert rune
Because there are multiple possible answers the way to go is usually the simplest answer in ambiguous questions like these
hallow crystal
Is there no technical term for it? Isn’t it called all real numbers domain
covert rune
You can express the possible area in which pat's house can be stationed at as an inequality. They seem to be asking for a point though
hallow crystal
Smhhh
Thank you again uwu
I’ll keep in mind to always look for the simplest route when it comes to problems like these
Because I immediately drew a diagonal line
Instead of a straight one
covert rune
By the way did your teacher make this problem?
hallow crystal
Cuz diagonal felt more natural at the moment
By the way did your teacher make this problem?
@covert rune
Yea that screenshot is from the google meet lol
I just emailed him about this problem cuz I’m a lil petty and wanted to make sure I was t missing any information 😀
covert rune
You can probably ask them about it then, if you get to know your teacher's "test-writing habit" you can get a better idea of what they expect of you
👍
hallow crystal
^^^!!!! Yes
covert rune
gonna go to sleep but the first 4 pages only have 2 mistakes, in question 2 (9,-5) needs a different x value and (19,58) needs a different y value
remember to plug your values when you’re done to verify your answer easily
blissful dew
hey peeps can anyone explain how to get "cos 30" without calculator? teacher said we have to be able to get certain sin,cos without using calculator.
crystal charm
draw your unit circle
30° is π/6 so draw a line with an angle of π/6 (one third of the perpendicular)
And you find sqrt(3)/2
Well with this method you have to remember the value sqrt(3)/2, but you don't need to remember the angle
You have only 5 values to remember : cos(0), cos(π/6) cos(π/4), cos(π/3) and cos(π/2). For the values of sin in this quadrant, you just go in the other direction (cos(0)=sin(π/2), cos(π/6)=sin(π/3), cos(π/4)...
And for the other values, it is all very easy (cosx=cos(-x), sin(x)=sin(π-x),... . And with the addition formulas you can get cos(π/12) for example
silent plank
that implies you know the radians equivalent already
you can derive it it from drawing an equilateral triangle,
splitting it down the middle and apply pythagoras
crystal charm
I find the radians equivalent more intuitive
But you can have the same method with 30°
silent plank
i assumed the question was about deriving instead of memorising and reading off a table
crystal charm
It is far too long to prove the values each time you want to use them
silent plank
if for some reason you "forget", its good to know how to get them
crystal charm
If you remember the 5 values I sent above, with a unit circle you can find which one corresponds to each standard value
crystal charm
Well indeed. But try to remember them xD it will be very useful
somber coyoteBOT
cayteg:
signal wolf
by point i mean circle btw sorry
charred jolt
A bit difficult exercise for me guys
signal wolf
$AD$ is the diameter of $\zeta$
somber coyoteBOT
cayteg:
signal wolf
@charred jolt The equation of a tangent line to the graph $f(x)$ at the point $a$ is given by $f'(a)(x-a) + f(a)$. First, calculate the derivative of $f(x)$, by the chain rule this is $2\left(-\dfrac{1}{1-(x^2-2x)^2}\times (2x-2)\right)$. Evaluating this at $x = \dfrac{1}{2}$ we obtain $\dfrac{2}{\sqrt{\dfrac{7}{16}}} = \dfrac{8}{\sqrt7}$, what's left is evaluating $f\left(\dfrac{1}{2}\right)$ which in this case is $2\arccos\left(-\dfrac{3}{4}\right)$. Putting it together we obtain $y = \dfrac{8}{\sqrt7}x - \dfrac{4}{\sqrt7} + 2\arccos\left(-\dfrac{3}{4}\right)$. I may have evaluated something wrong so be sure to check the answer yourself. Also this is more of a calculus question than anything since it involves derivatives, you should prob keep it at the calculus channel
somber coyoteBOT
cayteg:
hallow crystal
in question 2 (9,-5) needs a different x value
Ohh I forgot the multiply -5 by 2
@covert rune what am I doing wrong
cedar sparrow
@hallow crystal for your X coordinate on problem 2,you set it up correctly, but you multiplied the -5 by 2.
It should've remained -5 + X = -4
Thus getting X = 1
hallow crystal
It should've remained -5 + X = -4
@cedar sparrow
But I thought you were supposed to multiply to both sides?
Why else would the (2) be next to the -5+x
hallow crystal
OHHHHH
cedar sparrow
Oop lol, does that mean you got it?
hallow crystal
Yea cuz the denominator is only on the left side gotcha
cedar sparrow
Yee! So it cancels it out.
hallow crystal
yes haha very helpful thank you, but u should finish ur explanation 😏
cedar sparrow
I was just gonna say imagine multiplying a sum and then dividing that new sum by 2. You'll get the original sum. They cancel out.
:p
hallow crystal
Ohh naisu :DD
hallow crystal
I was just gonna say imagine multiplying a sum and then dividing that new sum by 2. You'll get the original sum. They cancel out.
@cedar sparrow
Fixed it and added some notes
gonna go to sleep but the first 4 pages only have 2 mistakes, in question 2 (9,-5) needs a different x value and (19,58) needs a different y value
@covert rune
Is my homework right
covert rune
Plug in your values using the formula to find out
hallow crystal
Plug in your values using the formula to find out
@covert rune
Wait I can do that? :0 I thought my only way to check my work was graphing
brisk holly
how do I rotate 90 degrees clockwise not about the origin?
west basin
doesntr work for arbitrary points
when rotating $(a,b)$ around $(x,y)$ by 90 degrees, $(-(b-y) + x, (a-x) + y)$
cedar sparrow
how do I rotate 90 degrees clockwise not about the origin?
@brisk holly translate the point so that it is around the point, rotate it, than translate it back.
^^^^^^ what Star said.
somber coyoteBOT
Star_:
west basin
sorry forgot that part
brisk holly
and how about counterclockwise?
somber coyoteBOT
Star_:
brisk holly
it works perfectly, thanks so much @west basin
west basin
np
hallow crystal
@west basin could you tell me how to check my work with the midpoint formula 🥺
west basin
wheres the work to check
hallow crystal
west basin
kinda a lot to read but are you trying to prove that the two endpoints have a midpoint of (5, -8)?
show that when you use the midpoint formula on T and your value S that it gives (5,-8)
if i read correctly
hallow crystal
kinda a lot to read but are you trying to prove that the two endpoints have a midpoint of (5, -8)?
@west basin
Yea, I already have my answer but I wanna check my work
I know with the endpoint formula I can just plug in but with the midpoint formula I thought my only way was to graph
west basin
well it gives you the midpoint
you just need to prove that it is actually the midpoint between the given point and your point
hallow crystal
show that when you use the midpoint formula on T and your value S that it gives (5,-8)
@west basin
Oh I know how to check my work for the second half cuz I had to find the endpoint formula for that, but I’m talking about the first half questions where I had to find the midpoint
west basin
im confused
you need to prove the midpoint is the midpoint using the midpoint formula?
hallow crystal
Plug in your values using the formula to find out
@covert rune
;-;
you need to prove the midpoint is the midpoint using the midpoint formula?
@west basin
I just wanna make sure my answer is right by checking my work
Tavior said I could do that by plugging in the values into the midpoint formula
west basin
to find the midpoints use the midpoint formula
thats literally it
if you can do some simple math then your answers should be right
hallow crystal
Plug in your values using the formula to find out
Then what did u mean by this user @covert rune 😭
covert rune
@hallow crystal Plug in your values of x and y in the midpoint and endpoint formulae
For example on the first one, (9 + (-5))/2 = -2
We see that this works out to be 2=-2 which is false
Therefore the x value for that problem needs to be changed
hallow crystal
For example on the first one, (9 + (-5))/2 = -2
@covert rune
What question is that? I don’t see it on my hw
covert rune
umbral snow
@night basin
Can you come up with two functions that, given a y-value, tells the distance to the two points?
night basin
well i did take it all the way through and ended up with with + or - square route of 23.625
but after checking my work again with pythagorean theorem it didn’t really add up
umbral snow
Well, it should satisfy that equation you wrote above
,calc sqrt(23.625^2 + 255) - 3*sqrt(23.625^2 + 4)
somber coyoteBOT
Result:
-42.612894132462
Hmm yeah that's a little off
I imagine you went forward by first squaring both sides. Did you square the 3 as well? @night basin
night basin
yes
umbral snow
y² + 255 = 9(y² + 4)
night basin
yeah i just wrote that exact thing down and was gonna take a photo
umbral snow
y² + 255 = 9y² + 36
219 = 8y²
y = ±√[219/8]
night basin
yoooooo
i fked up lol
nah hold up that 255 i wrote is wrong
it’s supposed to be 15x15 which is 225
umbral snow
Oops yeah that won't help
umbral snow
I didn't check 15² haha
night basin
umbral snow
,calc sqrt(23.625^2 + 225) - 3*sqrt(23.625^2 + 4)
somber coyoteBOT
Result:
-43.143865041432
that’s why i think my fallacy lies in the setup
umbral snow
Even if your setup is wrong, your solution to it should satisfy your setup
hollow raven
I think u gotta consider +- too if its all the points
umbral snow
But your setup looks good
night basin
obviously but we start at y=0 for both points
so the - would just be -y not anything weird
umbral snow
y² + 225 = 9(y² + 4)
y² + 225 = 9y² + 36
189 = 8y²
y = ±√[189/8]
night basin
can we simplify y
hollow raven
189 is divisible by 9
find the largest square i suppose
8 can be simplified into 2sqrt(2)
3sqrt(21) I suppose for the numerator
night basin
the decimal always comes back to 4.860556
but plugging it in is weird ash and like doesn’t work 💀
umbral snow
What?
night basin
so like one side = 15.76784703122148
noooo 🙏🙏🙏😂😂😂
I WAS RIGHT THE WHOLE TIME
appreciate it y’all helped me come to my senses
hallow crystal
https://gyazo.com/5fe58385a0d1a60729c505aaa0d0794c
@covert rune
Ohh, i get what u mean, I used the endpoint formula to check my work for the midpoint :)
hallow crystal
For second one did they mean “find the missing y coordinate” instead? 😀
west basin
yeah
snow hornet
need help? @hallow crystal
hallow crystal
need help? @hallow crystal
@snow hornet
These past days I’ve been catching up on old notes so I probably will in a few hours or maybe even minutes haha
This server is so helpful I’m glad I joined cuz it’s free 🥺🥺
snow hornet
for that problem, just work backward using that same equation
hallow crystal
Yep!
snow hornet
👍
hallow crystal
for that problem, just work backward using that same equation
@snow hornet
Am I supposed to foil next
hallow crystal
Ohh I have to square 10 as well ??
But it doesn’t say that in the distance formula
snow hornet
ofc not but its easier that way, dont need to but it helps understand that
hallow crystal
Ah to cancel the radical out
snow hornet
u want the total sum inside of the square root
hallow crystal
Yea saves time
hallow crystal
to be equal to outside
@snow hornet
Wait so I DONT foil?
https://youtu.be/J0m28OW-tH8
This person foiled
https://youtu.be/XiArEBYMkQk
But this person didn’t
snow hornet
i dont think u need to use foil
hallow crystal
i dont think u need to use foil
@snow hornet
Yea cause
snow hornet
foil is used when ur multiplying two binomials, right?
hallow crystal
I guess foiling is only for expanding expressions that’s why
snow hornet
ye
hallow crystal
Or am I supposed to foil in certain cases?
snow hornet
u only foil when its like
hallow crystal
foil is used when ur multiplying two binomials, right?
@snow hornet
yerp, it’s mostly a polynomials thing
west basin
you can foil to decompose a polynomial
snow hornet
(2x+2)(x-5)
hallow crystal
Yea like to simplify and expand
(2x+2)(x-5)
@snow hornet
Yea but technically (y-3)^2 = (y-3)(y-3) so i was like
Lol this whole problem just had me like that
Oh I missed ur point
west basin
im confused by the problem
hallow crystal
U meant to say u only foil when it can’t be squared
west basin
its already foiled
snow hornet
thats supposed to be equal to 64 already
hallow crystal
Oh my bad I didn’t show u the first image
west basin
(y-3)^2 is already in simplest terms
snow hornet
and ye
hallow crystal
:0
hallow crystal
I thought to find y I’d need to foil it whoops
snow hornet
and then do a lil algebra
and thats how u get x or y
or whatever u were lookin for
hallow crystal
But this is the original problem
snow hornet
ye
snow hornet
thats not needed
hallow crystal
Welp my first instinct upon seeing it was to foil 😔
west basin
should be 11
snow hornet
u see square root 36+(y-3)^2
west basin
foil is for breaking down polynomials man
hallow crystal
Sn but yea I understand it now lmao
snow hornet
i thought it was -5 @west basin
west basin
10^2 = 100
snow hornet
10=sqrt (-6)^2 + (y-3)^2
west basin
100-32 = 64
snow hornet
its 36
west basin
36 i meant
snow hornet
no
west basin
thats what i meant
snow hornet
hes lookin for y or x
hallow crystal
he
west basin
yes y is 11
hallow crystal
hallow crystal
I’ve fooled the online ppl once again
west basin
they are looking for y
hallow crystal
huehuehue
west basin
y is 11
snow hornet
oh wait
hallow crystal
Lmaoo np
west basin
dont confuse foil
hallow crystal
Wait so I square both sides... and then I square root both sides again?
west basin
we dont want to put them back together
you just perform simple operations til you get your answer
hallow crystal
Yea it’d be no point in that
west basin
i think you got confused because you didnt put = 10
if you saw the 10 maybe you would of thought to square both sides etc
hallow crystal
Hmm perheps
west basin
i mean yeah it does because thats how you solve the problem
hallow crystal
Wait y-3 is still supposed to be squared right?
snow hornet
then u would get 100=(4-10)^2+(y-3)^2
hallow crystal
hallow crystal
Lemmie just tell em it’s already in simplest terms
snow hornet
like factors
west basin
$64=(y-3)^2$
somber coyoteBOT
Star_:
west basin
$8=(y-3)$
somber coyoteBOT
Star_:
snow hornet
8=y-3
hallow crystal
Oh they just said they misread the question lmao
west basin
idk why this is so complicated you can do it in your head
snow hornet
👍
hallow crystal
idk why this is so complicated you can do it in your head
@west basin
I’m kinda new to it so I wanted to get used to it 😔 plus these are old notes I’m trying to review bc I bombed the quiz whomp whomp
west basin
hallow crystal
I’ll probably have to move on to the new notes cuz there’s another quiz on Monday ugh
west basin
yeah feel free to ask any more questions you have
hallow crystal
Thank youu this server has been real helpful
along with cum laude tutoring after school
@west basin @snow hornet are my notes right so far y’all
hallow crystal
alrighty tyt uwu
west basin
the length of each INDIVIDUAL leg will be sqrt(2)*hypotenuse
not the sum
maybe i wasnt clear before
hallow crystal
the length of each INDIVIDUAL leg will be sqrt(2)*hypotenuse
@west basin
:0
But I proved what I wrote correct
snow hornet
its 1:1:Sqrt2 ye?
west basin
you proved it yes the directly contradicted it below
hallow crystal
its 1:1:Sqrt2 ye?
@snow hornet
For the first page?
snow hornet
she wrote hypotenuse multiplied by sqrt2?
hallow crystal
you proved it yes the directly contradicted it below
@west basin
huh
west basin
snow hornet
there u go
hallow crystal
what does n stand for
snow hornet
^
west basin
n is length
hallow crystal
oh it’s just the variable
west basin
yeah
snow hornet
so what i was sayin was like 1:1: sqrt(2) bcuz 1 multiply by sqrt 2 is still sqrt2
oop brb
hallow crystal
I don’t get this property
hallow crystal
whats confusing about it
@snow hornet
Like I thought I proved my statement right
But the statement is wrong
west basin
what is wrong about what
hallow crystal
west basin
what statement are you looking at
hallow crystal
It’s not L1 + L2 = |2(Hypoténuse)
It’s L1 = |2(Hypotenuse) and L2 = ~2(Hypotenuse) correct?
Then how was I able to prove it right
Or am I tripping and didn’t prove it right lol
snow hornet
^
west basin
and the product of them would have no relation ot the sum
hallow crystal
16|2 is the length of both legs
32 is the hypotenuse
2(16|2) = 32|2 no?
snow hornet
No
hallow crystal
not sqrt(2), radical 2
That’s what the property says
west basin
if you really wanna explore this
hallow crystal
I didn’t sqrt anything
if you really wanna explore this
@west basin
actually no I don’t think I do!! 😁😁
Sn lmao
snow hornet
LMAO
snow hornet
R u familiar with like
west basin
$x = \frac{32}{\sqrt{2}}$
hallow crystal
But I should probably understand it today
somber coyoteBOT
Star_:
snow hornet
Oh whats it called
hallow crystal
squints
snow hornet
I cant remember what its called rip
snow hornet
$45⁰={sqrt{2}/2}$
somber coyoteBOT
KO7S:
hallow crystal
$x = \frac{32}{\sqrt{2}}$
@west basin
is x the length?
like how n is the length in the previous image u sent
hallow crystal
$45⁰={sqrt{2}/2}$
@snow hornet
Never seen that before 😀
Is that supposed to be a degree
hallow crystal
F
west basin
anything you type will be put in latex
if you enter a message using dollar signs like that
hallow crystal
yeah
@west basin
So these two are the same thing?
west basin
the top is the general case
snow hornet
No
west basin
the bottom is for your problem
hallow crystal
F
snow hornet
The top is just the basic understanding
hallow crystal
Ohh the bottom one only applies to triangles is that why
west basin
the bottom is the answer to each side on your problem
snow hornet
No
hallow crystal
I’m assuming the top one can be applied to other things?
snow hornet
They both apply to triangles
snow hornet
The bottom is the problem tho
snow hornet
The top is basic general info for 45-45-90
west basin
the hypotenuse is the product of sqrt(2) and any non-hypotenuse side
west basin
therefore the hypotenuse/sqrt(2) will be one of the legs
snow hornet
^
west basin
this only applies for triangles with 45-45-90 angle measurements
hallow crystal
the hypotenuse is the product of sqrt(2) and any non-hypotenuse side
@west basin
Oh wait is sqrt(2) the same thing as radical 2 aka |2 ? 🤡
west basin
yes
snow hornet
Yea.
west basin
i dont use |2 tho
because | is also for divides
when you talk about divisors in higher levle math
hallow crystal
Yea I just wish there was a radical on my keyboard rip
somber coyoteBOT
Star_:
west basin
if you learn latex formatting it will make it easier for you
hallow crystal
$(32)\sqrt{2}$
somber coyoteBOT
MapoTofu:
hallow crystal
TeXit
west basin
TeX is extremely popular in math and science
hallow crystal
Ohh :00
west basin
im a uni math student and i use it a lot
hallow crystal
Ight but
I’m gonna fix what I wrote in purple here
you cant just add a sqrt(2) out of nowhere
@west basin
Hold on what did u mean by this
Do I have to put it in parenthesis and multiply?
west basin
no
32 is already there
thats the hypotenuse
which means 32 is the product of radical 2 and some number x
hallow crystal
Yea paranthesis aren’t needed so wym by that
west basin
$32 = \sqrt{2} * x$
somber coyoteBOT
Star_:
west basin
like you cant just add sqrt(2) to 32 because by definition 32 is already a product of sqrt(2) and another number x where x is the length of a leg
hallow crystal
But I thought the property stayed that ?
hallow crystal
Meaning I’d have to multiply $n/sqrt2$ in order to get n
west basin
you are just restating what i stated
somber coyoteBOT
MapoTofu:
hallow crystal
yes it does it states the hypotenuse is the product of n and sqrt(2)
@west basin
Wait the : doesn’t mean = ? 😭
hallow crystal
32 is the product of n and sqrt(2)
@west basin
Ohh omg that’s the hypotenuse length cuz $(16\sqrt{2})sqrt{2}$ = the hypotenuse ??
somber coyoteBOT
MapoTofu:
Compile Error! Click the 
reaction for details. (You may edit your message)
west basin
lets just restart ok
im going to go over how to find the area
with you
step by step
again
ignore all your writing
hallow crystal
I know how to find the area but I’m confused about what the 45-45-90 property is actually stating
alrighty yea let’s restart
ignore all your writing
@west basin
hold on
west basin
if we know the hypotenuse is equal to $\sqrt{2} * n$ and 32 is the hypotenuse, then $32 = \sqrt{2} * n$
somber coyoteBOT
Star_:
hallow crystal
west basin
therefore, $\frac{32}{\sqrt{2}} = n$
somber coyoteBOT
Star_:
west basin
since the area of a triangle is $n^2$ where n is a side length
somber coyoteBOT
Star_:
hallow crystal
if we know the hypotenuse is equal to $\sqrt{2} * n$ and 32 is the hypotenuse, then $32 = \sqrt{2} * n$
@west basin
and n is the length of each leg correct? Which would be the same since it’s a right triangle?
Actually no, since it’s a 45-45-90 triangle
somber coyoteBOT
Star_:
west basin
$\frac{32^2}{2} = n^2$
somber coyoteBOT
Star_:
west basin
square both sides for the area
hallow crystal
Yes, area = x^2
west basin
$512 = n^2$
somber coyoteBOT
Star_:
hallow crystal
Yes only one
west basin
im using n^2 because it defines the area of a square
hallow crystal
Because they are the same length
west basin
of how i solved it using the property
hallow crystal
So basically there’s just three ways of writing the property?
hypotenuse is equal to $\sqrt{2} * n$
$32 = \sqrt{2} * n$
somber coyoteBOT
MapoTofu:
hallow crystal
$\frac{32}{\sqrt{2}} = n$
somber coyoteBOT
MapoTofu:
somber coyoteBOT
MapoTofu:
hallow crystal
west basin
legit the hypotenuse is equal to sqrt(2)n
if the hypotenuse is already a number
then that number is equal to sqrt(2)n
i cant explain it any simpler
west basin
huh
no i dont think its confusing
the hypotenuse is the product of sqrt(2) and a leg length x
when its a number its already in this form
you just divide by sqrt(2) to get the leg length
like i cant explain it simpler
hallow crystal
when its a number its already in this form
@west basin
Is 16|2 a number
west basin
yeah of course
west basin
yes
west basin
well yes and no
west basin
its actually incorrect for x
but it just so happens it yields a correct area
lol
i didnt even notice that
i was looking at the bottom left
west basin
that is area
hallow crystal
So it IS a coincidence?
west basin
yeah basically
hallow crystal
its actually incorrect for x
@west basin
So my answer is wrong?
😧
What did I do wrong
Did I make a mistake in finding the area? The work in purple
west basin
actually it does work itself out
i think the problem is the difference in representation
between how i did it
i think if you just stick to your Pythagoras youll be good
dark sparrow
kinda sus that the LHS is a scalar while the RHS is a vector
are you sure the arrow's meant to be there
dark sparrow
k
$mg \sin(\theta) = F_a \sin(\varphi) \cos(\theta) - F_a \cos(\varphi)\sin(\theta) \ (mg + F_a \cos(\varphi)) \sin(\theta) = F_a \sin(\varphi) \cos(\theta)$
somber coyoteBOT
Ann:
signal hornet
hmm
dark sparrow
$\tan(\theta) = \frac{F_a\sin(\varphi)}{mg + F_a\cos(\varphi)}$
somber coyoteBOT
Ann:
signal hornet
Let me check my identies
crystal charm
This is a nice expression of θ
Usually when I have to find θ with the help of the tangent, I find squares and roots everywhere 
signal hornet
thanks @dark sparrow I understand what you did now
I feel like I am on the wrong bath
because will this is way too hard for a physics problem
signal hornet
ehh
not really
this is for the physics homework
which usually the math is super easy
understanding how to set up the problem is usually the biggest obstacle
also my angle is like 75deg
they are almost never that high
crystal charm
@signal hornet this is a very usual way to find an angle when there are several angles in the system
crystal charm
Oh maybe
molten sierra
Hi, I need some help to determine if these affirmations (or similar ones) are true or false.
wispy valley
hello, do you guys memorise basic identities for trigonometry??
weary drift
$\trig$
somber coyoteBOT
RokettoJanpu:
weary drift
**RokettoJanpu**:
wispy valley
😮
weary drift
some identities are worth memorizing
wispy valley
it feels like im memorizing them without knowing why haha
weary drift
you memorize so you don’t get caught on algebra as much
median fern
Hello
upper karma
Nice
wet citrus
austere mason
Not sure if I’m in the right group for it, but I’m thinking: could the Po Shen Loh’s method of solving quadratics be related somehow to the normal distribution?
fresh galleon
gritty sail
4x+40 = 6x+10
silent plank
show work
silent plank
x=15 would be correct
silent plank
angle sum on a line is: ?
fresh galleon
how do I get angle sum?
silent plank
wdym
fresh galleon
thats what y is right:?
fresh galleon
they have degrees
silent plank
...
fresh galleon
I dont know
silent plank
pretty sure you applied this to the previous question you did
fresh galleon
where I did 4x+40 = 6x+10?
fresh galleon
0
fresh galleon
180
fresh galleon
so every thing has a 180 on the bottom of it?
silent plank
wdym
fresh galleon
like you want me to find that degree
silent plank
i want you to apply that,
to set up an equation and then solve for y since you already know x
fresh galleon
so 180 to x=15
silent plank
no
fresh galleon
2y*15
silent plank
no
consider the line AD or CE
and consider the (small) angles on said line
the sum of those angles would = what?
silent plank
wdym by both
fresh galleon
like they all equal 180
fresh galleon
the lines intersecting