geometry-and-trigonometry

[dark sparrow]

are you afraid of simply saying no?

[proper rivet]

yes

[dark sparrow]

why

[proper rivet]

because i don't know

the answer

[dark sparrow]

again why not just say "no i don't know how to find the distance between two points"

are you afraid i'll bite you

the distance between two points can be calculated as $$d = \sqrt{\Delta x^2 + \Delta y^2}$$ where $\Delta x$ and $\Delta y$ are the differences in the $x$ (resp. $y$) coordinates of your points

[somber coyote]

Ann:

[proper rivet]

why would you have x^2 in a square root

[dark sparrow]

it's not x^2, it's (Δx)^2

do the words "pythagorean theorem" ring any bells at all to you?

because this is just the pythagorean theorem in a slightly different form

[proper rivet]

yes a^2 + b^2 = c^2

[dark sparrow]

great, your legs are Δx and Δy, and your hypotenuse is d

[upper karma]

So that will become d^2=Δx^2+Δy^2 (Pythagoras Theorem)
=> d=sqroot(Δx^2+Δy^2)

[upper karma]

um hello

i have a strange geo question

im workin on this for 3 days but still i havent solved it

i really need help

it asks the alpha

[runic beacon]

Can you please write the question in English?

[upper karma]

yea ABC is a triangle

and

AB+BK=AC

and the angle of BAK is 30 degrees and BKA is 70 degrees

its asking for alpha angle

Rotating ABK over B seems a good idea

umm how?

if its possible could you draw it?

,rotate

[upper karma]

Now AK'C is isosceles

I rotated ABK around B, 100 degrees

Such that AK is a line

if you moved how did you move the alpha

Alpha is still there

whats the next step then?

Idk

It looked a good idea tho

yea

but it should continue

lol

If K', A, and C were collinear, it would be awesome

cant we use the Z rule

with A C K' A'

What?

just tryin to move the angles lol

your way looks so good but

i cant continue

thanks for the idea

I tried

Try rotating something else

Or reflecting

[silent plank]

you could also apply sine law and sum-prod identities

[upper karma]

That's actually a good idea

But using trig in such a problem is 🤢

Useful but 🤢

[acoustic jungle]

alpha=30

[upper karma]

@acoustic jungle how

[acoustic jungle]

I bashed it, I'm looking for another solution rn.

if you refer to HOBO's picture, and extend K to meet K'C at W. and prove that K'W=WC, then it can be proven.

but I can't seem to find a way.

you can also prove it if you get AWK'=90.

[upper karma]

it seems so complicated

oof

thanks again

[upper karma]

Hey

Can anyone tell me what's the answer?

I'm stuck between A and B

Everyone tells me sth different

[earnest echo]

,w calculate √((130-118)^2+(210-151)^2)

[somber coyote]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by The Godfather#1908

[earnest echo]

Your answer is B

[upper karma]

I thought it was B too, but in the answer key and my teacher, they said that I find the hypotenuse of the big triangle and then the hypotenuse of the small one then I subtract

The answer key also said that

This would give us A

I did it like this

But apparently it's wrong

Maybe because they asked what's the minimum?

Idek

[earnest echo]

To me it looks like a pretty simple coordinate geometry problem,
Maybe I'm missing something

@dark sparrow could you check this,
I can't seem to find my mistake

[dark sparrow]

the minimum is the straight line distance

[earnest echo]

That's what I did and I'm getting 60.2

[upper karma]

Ann could u try to do it plz

[dark sparrow]

the correct answer is 60.2

your teacher's method can be shown to be obviously absurd if we replace the points with say (400, 0) and (0, 300)

the straight line distance is obviously 500 miles but your teacher's method would give 100

which is BS

[upper karma]

@dark sparrow no that's not her method

She said 2 right triangle would be formed

The hypotenuse of the big one- the hypotenuse of the small one would give us the distance

Idk if that's right tho

[dark sparrow]

it isn't

you're basically trying to find the distance by computing the distance from each point to (0,0) and then subtracting those

this is less than or equal to the straight-line distance

https://www.desmos.com/calculator/cn7ptraf9m

[upper karma]

Yeah so its B

Tyty

[dark sparrow]

you can drag the points around here

to see just how wrong your teacher is

[upper karma]

Ok lol

Also I have another question

[dark sparrow]

like it's possible to get D_0 (the teacher's answer) to near zero while still keeping D_1 (the correct answer) pretty big

yes?

[upper karma]

A polygon is inscribed in a circle. If some diameter of the circle divides the polygon into two regions of equal area, which of the following must be true:
1- the polygon is regular
2- the center of the circle is inside the polygon
3- the polygon is symmetrical about some diameter

The answer choices are :
A. none
B. 1 only
C. 2 only
D. 3 only
E. 2 and 3

First of all, the second choice is definitely yes

Yeah

Because the diameter won't pass through the polygon let alone divide it equally if the center of the circle isn't inside the polygon

Wait

What if it's like this

Yes, you are right

So this disproves the second choice is definitely correct

Hmm does 3 always have to be true

It doesn't... right?

I don't think it always has to be right

Because what if the triangle didnt have equal sides

It cut it in half

It wouldn't be symmetrical

Right?

Yes

Now I am sure, the third one doesn't always have to be true

Wait but if it cut it into 2 regions of equal area, does it mean that both have the same side measures?

Wait let me give a visual representation

so far, we know that the second option must not always be true

so you can exclude that out

Yeah

and for the third option

let's take a right angled triangle

And also the first option isnt always true

it's very rough but you get the idea

Yeah lol

it doesnt have to be symmetrical but can still be divided into equal areas by a straight line

Oh so the answer is none

yes

Thanks!

Welcome 😄

[fresh pike]

would this be false? I was thinking it was false but I have doubts

[upper karma]

Like

The S indicated seems like a point and not actually labelling the plane

[fresh pike]

no it's not a point

[upper karma]

Seems like so

Whatever

Why do you think it's on the plane S

[fresh pike]

I said i thought it's false

[upper karma]

It is false indeed

[fresh pike]

thx

why would the answer true be false? Can someone explain to me?

[upper karma]

@fresh pike you still need help?

[fresh pike]

nah I figured it out after re reading some stuff

[nova bone]

If I understand what you are asking, can you take the coordinates of each of the vertices and multiply them by two to get the vertices of the new triangle and draw it like that?

[olive mortar]

Ah yeah, ok

I understand. Thank you!

[nova bone]

you're welcome

[twin void]

Hi , I wanted to ask why is it if i have tan-1(2+sqroot(3)) = 75degrees in the first quadrant

for example

the other answer is -105 in the third quadrant or -180 degrees + 75 = -105

[acoustic jungle]

because tan's period is 180.

by the way, -180 +75 is the same thing as 180+75.

(for unit circle)

[twin void]

so i am loking at this image, is this the way to analyse it for sin cos tan inverse

where arcsin answers are in first and second quadrant

arctan are in first and third quadrants

arccos are in first and fourth quadrants

for a positive initial angle

[silent plank]

arctan isn't a multivalued function
arctan(2+sqroot(3)) only has 1 value and that is 75° (or 5pi/12 radians)

however the solutions to tan(x) = 2+sqrt(3)
are x = k*180° + 75°

[twin void]

take for example this question

so there are 2 answers for arcsin, one of which is in first quadrant, second answer is in second quadrant

[silent plank]

bad wording.

there are two values for theta

arcsin(w/R) gives the angle in the first quadrant
pi - arcsin(w/R) gives the angle in the second quadrant

[twin void]

so there are 2 answers from this question?

[silent plank]

depending on context there may be more

[twin void]

so these are just 2 of the possible values (within 0 to 360 degrees)

outside of 0-360 degrees there may be more possible values?

[silent plank]

within 0 to 360° yes

[twin void]

Got it, thanks!

[long totem]

so ik i have to memorise the first row for exams, but would it be worth the time to memorise the 2, 3 & 4 rows?

[silent plank]

learn the periodic/phase shifts and/or compound angles and derive as needed

the top row is pretty much the complementary nature of sine and cosine
and tan and cot

[long totem]

learn the periodic/phase shifts and/or compound angles and derive as needed
@silent plank sorry what are periodic/phase shifts? - is it referring to the symmetry of the circles, so when you reflect along a certain line you get its complementary?

are periodic/phase shifts this?

sorry, i'm really bad with terminology fkjhkjh

[silent plank]

pretty much

eg adding pi to the arguement gets you in the opposite quadrant and the sign may change depending on the trig function

[long totem]

ohhhh okk, so once you know the periodic shifts theres no point memorising the table above?

[silent plank]

odd/eveness helps too

yeh, no point

same with the unit circle

just need to know the first quadrant

and derive the rest as needed

(using reference / related acute angles)

[long totem]

oooo ok thank you for the tips

[silent plank]

which reduces it to learning around 5 key ideas
instead of a whole page of formulae/identties/values

[long totem]

yeaa it makes it a lot easier to remember now,,, i'll make sure to be confident with it before my exam

[night snow]

I find many people become nervous and obsessed with memorization

When if they learn the content the content that needs to be memorized becomes naturally understood and intuitive

[long totem]

"find all the solutions to:"

how would you find a solution to this question?

[upper karma]

What have you tried so far

[long totem]

oh wait,,,, i forgot root3/3 = 1/root 3 🗿

nvm ik how to do it now

but hypothetically if it didn't correspond with an exact value, is there a method to do by hand?

[azure reef]

@long totem arctan!

or by noticing that value is near some known and can be represented as tan of some sum

[keen goblet]

Hey i have a question

how does $2\pi r = 2\pi$

[somber coyote]

MeIsNotGoodAtMath:

[paper vale]

it doesnt bruh

[keen goblet]

ok

so, r = 1

idk, might be stupid

but i always see r = 1

[paper vale]

well obviously in this special case, but in general it doesnt hold

[keen goblet]

In this case

What is r ?

r = 1 right?

[upper karma]

What

[keen goblet]

idk

[glad veldt]

if it is a unit circle, then yes

[paper vale]

so u cant just assume the radius for no reason

[glad veldt]

most likely it is a unit circle, otherwise the question is impossible

[keen goblet]

yes its a unit circle

i drew the circle

[glad veldt]

yeah then the radius = 1

[versed river]

if its a unit circle, r is defined to be 1

[keen goblet]

ohh makes sense

[long totem]

how come the period changes when n =/= 1? n as in nx

[dark sparrow]

the period doesn't change

the domain does

if x runs from 0 to 2pi

does it not make sense that 2x would run from 2*0 to 2*2pi??

[long totem]

oHHH, sorry for the dumb question heheh,,,

[long totem]

why are they subtracting pi/6 instead of 5pi/6?

[upper karma]

?

$\frac{11\pi}{6}=\frac{12\pi}{6}-\frac{\pi}{6}=2\pi-\frac{\pi}{6}$

[somber coyote]

Al𝟛dium:

[long totem]

i'm so sorry for troubling you with such trivial question o.O

[upper karma]

no i didn't mean that

[long totem]

hhhhh i don't think my brain's working anymore

[upper karma]

i was just confused about what you were saying

[long totem]

no no,, like i know the question idek why i was confused,,,,

[upper karma]

take a rest and come back

it'll help you reset

[long totem]

hhhh i think it's time for me to stop revisnig for tonite

yea tyy,,,

[proper rivet]

Hi just wondering how do you find an interval

I’m just not getting it

[upper karma]

wdym?

[long totem]

an interval is just the 2 points in which the function goes through is it not?

i believe the interval for that function would be for -1<=x<=5

[proper rivet]

Sorry I meant midpoint

[upper karma]

oh okay

[long totem]

oHh

[upper karma]

then

$AB_{\text{midpoint}}=(\frac{x_A+x_B}{2}, \frac{y_A+y_B}{2})$

[paper vale]

it is trivial

[upper karma]

do you know what the variables mean and how to use them to get the problem?

it is trivial
ugh again?

[proper rivet]

No I don’t understand the variables

[upper karma]

may i repeat that saying "this is trivial" doesn't help at tall him to solve plus no one cares?

No I don’t understand the variables
okay

so $x_1$ and $x_2$ represent the x-coordinate of points A and B respectively while $y_1$ and $y_2$ represent the y-coordinate of points A and B respectively

[somber coyote]

Al𝟛dium:

[upper karma]

maybe you understand the formula better this way:

[proper rivet]

Yes I do

[somber coyote]

Al𝟛dium:

[proper rivet]

Yes this makes much more sense now thanks

[proper rivet]

how do you find an equation for this

[dark sparrow]

for what

[upper karma]

Try graphing the points

[proper rivet]

ok

[dark sparrow]

there are many forms for the equation of a straight line.

[proper rivet]

i have graphed the points

[dark sparrow]

one thing you might find useful to know about a line is its slope.

or gradient, if you're from the UK

[proper rivet]

so you just find its rise/run

[dark sparrow]

i'm not saying "so you do this". i try not to do that

i'm merely suggesting that you do it.

[proper rivet]

i understand

[golden oxide]

Sorry, this is a dumb question, but if I have some angle ABC, is there a name of the "connection" of the two lines of the angle, in this case, the point B

[paper vale]

didnt u just answer ur own question?

the name is point

[golden oxide]

well yeah, but I mean more generalized

like is there a mathematical name for the kind of point that B is

[paper vale]

what do u mean kind of point

[golden oxide]

like if I have some arbitrary angle

is there a term for the point that is in the middle

[paper vale]

middle of what

[golden oxide]

the middle of the angle

like AB is a line

and BC is a line

is there a "name" for the type of point that B is

sort of like how the term for the side opposite a right angle is always the hypotenuse

[paper vale]

the line is called the angle bisector

well obviously it depends on the point

some points have names

[golden oxide]

sorry, I don't think I'm explaining this well

oh I'm dumb

I couldn't remember the word vertex

[upper karma]

I understand what you are trying to say @golden oxide

As far as I know, there is no standard mathematical name for such a vertex, you can just refer to it as it is labeled for eg. (B)

[slate oar]

you can say vertex of <ABC

[paper vale]

that isnt what he meant he just forgot what a vertex was, however i have no idea what he was talking about

[slate oar]

oh lol

[arctic vortex]

mmm geometry i remember this as if it was 10 years ago anyone need help

[fresh pike]

can someone explain to me what the heck this means?

the explanation is kinda duckery to me

r/explainlikeimfive

[little osprey]

@fresh pike What part confuses you

[fresh pike]

AB+BC=AC is true, where AB, BC, and AC are the distances between points A and B, B and C, and A and C, respectively

like where did AB+BC=AC come from?????

and what does it mean by AB, BC, and AC are the distances between points A and B, B and C, and A and C, respectively

it might be a stupid question because all I have to do is read it but i just simply dont understand what im reading

[little osprey]

like where did AB+BC=AC come from?????
@fresh pike this is kind of like saying 4 + 5 = 9

and what does it mean by AB, BC, and AC are the distances between points A and B, B and C, and A and C, respectively
@fresh pike It just means that its not going somewhere else or curves

[fresh pike]

huh

so did they combine A, B, c or something?

[little osprey]

Try and visualise it

If points A B and C were points on a line

and B was the point inbetween A and C

logically AB + BC = AC

[fresh pike]

not abc?

lmao

that's weird

[little osprey]

ABC is the name of the line

Its easier to say AC

Since you know that B is inbetween

Imagine saying

ABCDEFGHIJKLMNOPKQRSTUVWXYZ instead of AZ

@fresh pike

[fresh pike]

ahhhh

i seee

so it's like a {A,...,Z} thing

[ashen brook]

anyone know why these aren't correct?

[versed river]

i mean cos(theta)<0

is given

and you clearly havent fulfilled that

for a start

[ashen brook]

im new to trig and the video for the section wasnt really helpful sorry

[versed river]

i mean you used the pythagorean identity to get cos(theta) right?

[ashen brook]

yeah

[versed river]

note that both cos(theta)=4/5 and cos(theta)=-4/5

fulfill the pythagorean identity there

and you're given cos(theta)<0

(if you dont know how i got cos(theta)=-4/5 pls ask)

and since 4/5>0

it can't be that

so it must be -4/5

[ashen brook]

how do u get the negative

[versed river]

$(\frac35)^2+\cos^2(\theta)=1$

[somber coyote]

Sneaky:

[versed river]

$\cos^2(\theta)=\frac{16}{25}$

[somber coyote]

Sneaky:

[versed river]

give me a bit im in league game

[ashen brook]

youre fine take your time ty for helping me in the first place

[versed river]

now im gonna go on a weird tangent here and ask you what you would answer if i asked you to solve $x^2=4$

[somber coyote]

Sneaky:

[ashen brook]

would it not just be the square root of both sides to get x

so 2

[versed river]

you sure thats the only solution?

[ashen brook]

well and -2

now i see

[versed river]

so you get how -4/5 is right now?

[ashen brook]

yeah

ty

[versed river]

and tan(theta)'s correctness should follow from tat

and cot and sec

[fresh pike]

can a plane only contain 2 points?

if so why can't it contain 3 collinear points?

how are a,c,d, and e coplanar? any explanation?

[opaque ruin]

If anybody know the answer, please tell me...

[upper karma]

@fresh pike coplanar simply means that the points are all on the same plane. Since they make up the rectangular base of this object, which is a plane, they are all on the same plane.

[fresh pike]

huh

[upper karma]

?

[fresh pike]

never thought about it like that

i thought each point was dedicated to one of the triangular planes

+1 knowledge thx

[upper karma]

lol

They are part of both planes.

Depending on the points in question

[fresh pike]

yeah once i read "they are all on the same plane" it clicked

[upper karma]

Well, I am glad I could help.

Tell me if you need any other help with things like that.

[fresh pike]

I wish i could just lay on my notes and let my brain absorb information

yeah definitely will

[upper karma]

XD sometimes I feel the same

alright

Well*

Have a good night/day

[fresh pike]

same to you

[upper karma]

😁👍

[paper mauve]

YO PLEASE

HELP ME

WITH THIS ASSIGNMENT

[hasty plover]

YO

BET

LETS SEE IT

[paper mauve]

OH BET

[hasty plover]

oh lemme read

[paper mauve]

yes please help

[silent plank]

not geo/trig

[paper mauve]

its geo assignment

I dont know why my teacher gave it to us

she is trolling

[hasty plover]

geography?

[paper mauve]

no geometry

she is trolling

[hasty plover]

[paper mauve]

bro like wtf is this

how am supposed to solve

[silent plank]

logic puzzle

[paper mauve]

yeah

please help me

this is a major grade assignment

[silent plank]

repeatedly go through the list of conditions and rules, and eliminate options from the table

[paper mauve]

yeah I did that

[silent plank]

leaving you with a unique solution

[paper mauve]

for 2 hours

then realised

there is no fucking way

to do that

they give like 3 direct clues

then it's basically impossible

[silent plank]

some clues give you more information than you may realise

[paper mauve]

hUh

AM I MISSING A PAGE

TF

[silent plank]

uh show me what you have so far

[paper mauve]

yeah here is the thing

I dont want to wake up my mom

so I didn't show my work

and just trying to do it in my head

[silent plank]

how's that related to not having any work?

this is NOT something you'd be able to do in your head (unless you had an eidetic memory)

[paper mauve]

maybe your right

I'm going to print it out tomorrow then

then can you help me

[silent plank]

it's an assignment, most of the work should be yours
show some serious effort and someone may be able to provide some additional pointers

[paper mauve]

[dark sparrow]

tf are you tryna do in your head

[silent plank]

einstein riddles

[dark sparrow]

[paper mauve]

how is this

even geometry

[north vortex]

first thing i read einstein riddles

lmao

[paper mauve]

thats what the zebra puzzle is called

[fresh pike]

@paper mauve that profile picture is from somwhere, where's it from?

[upper karma]

reminds me of Studio Ghilibi

[fresh pike]

a ray goes in a certain direction right? does that mean this is false?

[paper vale]

yea but they go in the same direction so it is true

[fresh pike]

whaaaa

Which direction is cb going?

[paper vale]

bruh

look at the arrow above CB

[fresh pike]

yeah?

[paper vale]

that shows its direction

[paper mauve]

I think it was from that mecha anime

forgot the name

[fresh pike]

guilty crown?

no that wasnt it

is this wrong because s isn't in all planes? I thought it was touching the tip of the triangle so it was in all plans

and how are the 3 points in this image cooplanar can someone explain?

@upper karma

i should prob ask squid for help

[paper vale]

1 is false

2 is true

any 3 points are coplanar so it isnt really that interesting

[fresh pike]

what?

is it because s is a line?

@paper vale

[paper vale]

?

[fresh pike]

for this one ^

[paper vale]

no need to repost

S is a point....

[fresh pike]

and how is it false. Explanation?

[paper vale]

it is quite clear

[fresh pike]

well to me it isnt

i am quite the uneducated person

how many planes is s in

[paper vale]

well in the plane through 3 of them, in order for all 4 to be coplanar, the other one must by in that plane

and the plane through any 3 doesnt contain the 4th one

[fresh pike]

"well in the plane through 3 of them" is that a typo oorrrrrr

[paper vale]

no

[fresh pike]

the other one meaning "s" right?

[paper vale]

not necessarily

just any 3

[fresh pike]

well in this situation?

well in this situtation for all 4 of them to be coplanar "S" would have to be in the same plane right?

[paper vale]

what do u think......

[fresh pike]

...

i am quite the uneducated person
@fresh pike

nut

What do the numbers "NU=1 SU = 2, SN = 3" signify?

i already know the midpoint is "U"

[paper vale]

the length of the segment

[fresh pike]

ahh

i see

wait so why is NU=1 then?

[paper vale]

this question is laivirt

what do u mean why, because it is

[fresh pike]

wouldn't the length of it be 2? Like how SU is?

[paper vale]

no, because it isnt

[silent plank]

represent that information on a diagram

i already know the midpoint is "U"
U isn't the midpoint

just because a point is between two things doesn't make it a midpoint (of those things)

[fresh pike]

figured that out

After reading to question again

i missed some segments

is it all the boxes?

i got this one wrong

[paper vale]

all of them work

[upper karma]

@fresh pike notice how they’re not on a plane brother. S is part of the bottom of the figure which is a square. R and T are part of the triangular planes.

answering the question you pinged me on

Sorry for late response

[fresh pike]

all's good m8

[upper karma]

Mega oversleep

Thonks brööther

[fresh pike]

S is not part of any other plane? it touches the tip doesnt it?

[upper karma]

S is the center of the triangle on the bottom plane.

[fresh pike]

this is for the 2nd question right?

[upper karma]

hold up

What

Yea I think so

[fresh pike]

gonna repost

[upper karma]

Ok

[fresh pike]

i dont see how it's true

R S T, are coplanar? how so? which common plane do they share?

[paper vale]

any 3 points share a plane

i said earlier

[livid moss]

Three points are always coplanar

[silent plank]

S looks like its supposed to represent a line

[fresh pike]

that's what i thought too ^

[paper vale]

i dont think it is

[fresh pike]

but i guess a line is just a set of points

[upper karma]

I mean the plane isn’t on the figure that they’re coplanar on... I suppose you could draw a plane through them all.

Ima just take S as a point

[livid moss]

Oh, it does look like a line

[paper vale]

wait actually it is

the other one have a blue point

[upper karma]

a line would be SB

[fresh pike]

so i could name any 3 points from that figure and it would just be coplanar?

[silent plank]

lines can be labelled by a single variable

[paper vale]

do u know what coplanar means

[fresh pike]

on same plane?

[upper karma]

why would they do that though

[fresh pike]

3 points?

[upper karma]

If they can be on the same plane then they are coplanar

The plane would connect them all

[fresh pike]

a set of 2 or more points all on plane?

^that's what the lesson said

[upper karma]

I think that any 3 points can be coplanar.

So

[fresh pike]

so this image is False because s is only on the bottom square plane?

[upper karma]

They give you 3 points (or if not, a line and 2 points.) which are coplanar, and no matter what point on that line, it will still be coplanar with the other two.

But idk

[fresh pike]

so any set of 3 points is automatically coplanar. <<<<< final verdict?

[upper karma]

Yus

[fresh pike]

so that image above is not coplanar because s doesnt share the same plane with a,r,c

[silent plank]

you mean A,R,C

[upper karma]

I don’t think you can connect all 4 with a plane. And so, it’d render it non-coplanar.

[silent plank]

also not the image, (points/lines are not co-planar)

[fresh pike]

はい

si

yes

well on to geography and history assignments

thx

for help

[upper karma]

No problemo

[paper mauve]

I tried now

can you help me

is this correct

I'm confused when it says parks at 1st

does this mean

that mirata is in 1st

or just parked at it

I'm confusion please help and review answers

[upper karma]

I’m sorry I have no idea what that is...

Would help if I could

[silent plank]

they'd mean the same thing?

[paper mauve]

I mean for this worksheet from yesterday

it's either this 1st yellow 2nd blue 3rd red 4th green and 5th white

or 1st green 2nd white 3rd yellow 4th blue and 5th red

but the words are trippy and say mirata 1st parked and doesn't specifically say that mirata belongs to 1st

[silent plank]

its implied

why would someone part at a house that isn't theirs

[paper mauve]

I mean my neighbors park on our house alot

because they dont have anywhere else to park

also when I tried the 1st yellow formation

it didnt work

this one

zucchini bird and hummer dog doesnt work

[silent plank]

can you repost the full table

[paper mauve]

ok

the other side is the same as the top

both sides same

doesn't matter which way you do it

[silent plank]

do you have the also the full image of your table with explanations

[paper mauve]

yeah

oh wait

my table?

the ones on the bottom can be translated to the top

both on top and bottom are the same

[silent plank]

you should mark the info in all locations

[paper mauve]

mark info how

like write explanation how I got it?

[silent plank]

most of the table is symmetric

[paper mauve]

wait wut

I'm confused

[silent plank]

eg using the existing markings,

those could also be filled, blacking out all the invalid combos can also make it easier to identify things

there shouldn't be any need for guessing

seeing as you have miata associated with the yellow house which isn't the first, you've messed up somewhere

[paper mauve]

maybe I did

this is the other graph for other combination

[silent plank]

which also conflicts with the other marking saying its also associated with the 1st green house

[silent plank]

like you should really use the whole table

[paper mauve]

I am astronomically confused

[silent plank]

that's why its there

[paper mauve]

I tried to use all of the table on paper

then I just got even more confused

and just gave up on that

[silent plank]

like you'll probs need to go through the list like at least 15 times or something

[paper mauve]

I just need you to confirm one thing then I can finish it

[silent plank]

examples of how you'd use the table:
family that plants eggplants next to family with cats

means eggplant and cats are mutually exclusive

and you can black out that combo on the table

[paper mauve]

is the order 1st yellow 2nd blue 3rd red 4th green 5th white

[silent plank]

without knowing how cats and egglants relate to other things

i haven't solved it

[paper mauve]

oh

[silent plank]

its can be very time consuming

like your table should pretty much be fully blacked out

[paper mauve]

well

sounds like a hassle

[silent plank]

you should also highlight the stuff like
miata with miata
and most things along that diagnoal

the purpose of the table is to show the relationship of EVERY single pair

and if you're not indicating them, you aren't gonna get anywhere

[paper mauve]

every single pair?

[silent plank]

yes

[paper mauve]

I dont think my teacher will need to see the table so if I understand it enough to solve the question I think blacking out that portion is good enough

[silent plank]

i don't even know how you managed to get that far without doing that

i mean its the first and third part worth 30% ea

[paper mauve]

stupid einstein riddle

98% of population cant solve this my ass

[vale beacon]

Is this correct?

[silent plank]

no

[vale beacon]

Where did I go wrong?

[silent plank]

you aren't reading the question

[paper vale]

you wrote down what theta equals in terms of a and then b

[vale beacon]

Oh shit

How do i approach this correctly?

[paper vale]

also the a=theta =b should start to make you think that you are not right

[silent plank]

start with what's sin(theta)

and then solve for a

[vale beacon]

Sin(theta) a/21?

[silent plank]

sin(theta) = a/21

[vale beacon]

How do I solve for a from there

[silent plank]

algebraic manipulation

don't overthink it

[vale beacon]

I literally don’t know

[silent plank]

can you solve something like
2x = 2 for x?

[vale beacon]

x =1

[silent plank]

what about x/2 = 5

[vale beacon]

10

[silent plank]

apply exactly the same idea here

[vale beacon]

How do I set it up or what do I input to my calculator

[silent plank]

you don't input anything

seriously don't overthink it

how did you solve: x/2 = 5 (for x)

[paper vale]

i think what he is confused about is solving in terms of theta, but it is sin(theta)

[silent plank]

sin(theta) is just an expression, you don't have to evaluate it or anything

just leave it as it is

eg 5 times 🍌 could be expressed as 5🍌 (without knowing the explicit numerical value of 🍌 )

[vale beacon]

21a = sintheta , is that how I would set it up? I’m sorry I’m just a little confused to how I solve for a in this situation

[silent plank]

no

sin(theta) = a/21

$\sin(\theta) = \frac{a}{21}$

[somber coyote]

ramonov:

[silent plank]

is where you would start

[vale beacon]

so how exactly am I supposed to proceed after getting there

[silent plank]

how did you solve: x/2 = 5 (for x)

[vale beacon]

well intuitively you would know 10/2 is 5

[silent plank]

what about
solve x/y = 5 (for x)

[vale beacon]

X would have to be 10 and y would have to be 2

[silent plank]

separate question

[vale beacon]

?

[silent plank]

solve x/y = 5 (for x)
x and y here are unkown
rewrite it in the form x= stuff

ok there are major gaps in algebra here.
apply the same operations to both sides of the equation to work towards isolating the variable you want

using x/y = 5 as an example,
to get x by itself, you can multiply both sides of the equation by y

which will result in x = 5y

for x/2 = 5,
you could multiply both sides by 2 to get
x = 5 * 2 = 10

and applying the same concept to this question

to isolate a, get a by itself, you can multiply both sides of your equation by 21

$21 \times \sin(\theta) = 21 \times \frac{a}{21} $

[somber coyote]

ramonov:

[silent plank]

(which gives you what you want after simplification)

👻

[paper mauve]

I figured it out

are you proud of me

[paper vale]

[main thunder]

**Can someone possibly provide some guidance on what I maybe doing wrong here?
**
I'm trying to calculate 5km*cos(40) and I'm getting two different results on different calculators.
Result 1 = -3.33469 (TI-NSpire and TI-84 Plus CE)
Result 2 = 3.83022 (Symbolab)
Entry on all devices: 5cos(40)
Is there a setting I maybe missing or messing up?

[silent plank]

radians vs degrees

[main thunder]

Ah wonderful, thank you for the guidance! I'll check my settings.

[fresh pike]

can i have an explanation for this?

[upper karma]

For what?

[fresh pike]

The image

Ah whatever

I figured it out any way

[naive sonnet]

does anyone know a good geometry book for me (i'm doing competitions but i'm terrible at geometry) i'm 9th grade but my teacher hasn't even taught us triangle congruency.

[agile rain]

A pair of parallel interstate gas and power lines run 10 meters apart and are equally distant from relay station A. The power company needs to locate a gas-monitoring point on one of the lines exactly 12 meters from relay station A. Draw a diagram showing the locus of possible locations.

How would I go about answering this question?

[half latch]

How do I solve this?

[earnest echo]

Remember sin(x)=cos(90°-x)

@half latch

[half latch]

Ooo

Does the fact that the cos is squared change anything

[earnest echo]

Cos^2(x)=(cos(x))^2

So no, it doesn't change anything

[half latch]

Oh ok tyty

[supple wedge]

i hate geometry

[upper karma]

How about angle AEB

AEB shares the same segment as ADB

[supple wedge]

ah i see

[paper vale]

use the fact that it is cyclic quad so that AEB=ADB

oh hobosas already said that

[dark sparrow]

what have you tried and where are you stuck

[upper karma]

want the honest awnser

i just woke up and forgot i had a test this shit is normally easy accept midpoints i suck at those 100

im doing in now lol

[runic beacon]

do you still need help with that?

[upper karma]

hold up

[dark sparrow]

accept != except?

anyway, these are two supplementary angles

[upper karma]

solveing for x

[dark sparrow]

have you written down an equation to solve

[upper karma]

thats what im doing

[dark sparrow]

these are two supplementary angles, they add up to 180°.

[upper karma]

im aware

i figured that out first glance

[vale nimbus]

then whats the issue

[dark sparrow]

^

[upper karma]

me trying to solve for x

[runic beacon]

have you made the equation for that?

[dark sparrow]

have you written down an equation to solve

you said that's what you were doing, and now you say you're having trouble solving for x, which means you already have an equation but have not yet shown it to us. yes?

[quiet mason]

Uhhh

[upper karma]

i did an problem wrong i feel like an ideot now!!!!!!

x=14

[runic beacon]

that is right

x=14

[upper karma]

shoot i need to stop sleeping all day

[upper karma]

Drink ☕ like me 😉

[lament shell]

I need some1 rn

for two geometry questions

is that a yes?

[upper karma]

yes

[lament shell]

https://gyazo.com/ca9db3d6d184ed1e1509c952b8dad197

[upper karma]

I am sure someone would help you, there are many people in this server so you can expect a quick response almost every time

[lament shell]

https://gyazo.com/c2081f141e34c66295443713cf615af1

well

its timed for 5 min so

can you pls help me

[upper karma]

in the first question

what have you tried so far?

you are given 2 angles, and you have to find the third angle

[lament shell]

I have 1 min

[upper karma]

I don't think I am allowed to help you for a test, that breaks a rule in this server

I can only discuss 😦

[lament shell]

this not a test

but ok

its finsihed

holt crap

i got both right

lets go

[upper karma]

lol

ok do you still wanna discuss it?

maybe it will clarify some things up

[lament shell]

I just subtracted the two angles

[upper karma]

perfect

thats what u needed to do

[lament shell]

and the first one i put false

[upper karma]

You have an angle RST = 161 degrees. As you can observe from the diagram, both angle RSY and YST lie within angle RST and together make up angle RST. So adding them both gives angle RST. This implies that if you subtract angle RSY from angle RST you get angle YST and if you subtract angle YST from angle RST you get angle RSY.

[lament shell]

Right

The second one was easy

I just panicked lol

[upper karma]

cool glad you got them correct and understood

[lament shell]

Is someone telling you the answer to a hw assignment not allowed on the server?

[upper karma]

oh it was an assignment

then telling the answer is fine, as long as you explain it properly and discuss, because the point of this server isnt to get answers, but to learn

[tacit sparrow]

hey im writing geometry problems for the class my brother's making and i want to know if there's an easy way to figure this out without drawing this second perp bisector and noticing that it creates a 180 degree angle through the center

like, is it obvious that triangle BOA is equilateral ?

how would you get that OBA is bisected by the line

it's been a while since i did this stuff

[paper vale]

all u need to do is note that BOA is isosceles with legs OB=AB, but OB=OA=r, therefore all are equal

(it is isosceles as B is on the perpendicular bisector of AO)

doing what the hint says is silly

[tacit sparrow]

oh i see

yeah i changed that

[upper karma]

can someone explain how to do 4 c)

[paper vale]

write it as cos/sin

and you know the values for cos and sin at pi/4 right?

[upper karma]

yea

im just confused on how the anwser is cot 3pi/4

[paper vale]

also u can just use the symmetry to work out the numerical answer

[upper karma]

bro cot is confusing

[paper vale]

there is a differece of pi, so both are negated, but the overall effect is the same

not really

[upper karma]

what is related acute angle again?

[silent plank]

the answer shouldn't be cot(3pi/4)

related acute angle is the acute angle between the terminal arm and the x-axis

[paper vale]

that is obtuse yea

[upper karma]

ahhh ok thank u

[paper vale]

but i was just saying that the value is still equal

[upper karma]

idk the anwser at the back of the textbook says cot(3pi/4)

[silent plank]

in this case, rac would be pi/4,
and the answer should be something like
-cot(pi/4)

[upper karma]

yea thats what i wrote before

[silent plank]

then it good

well I mean you could explicitly write
cot( pi - pi/4)

which isn't the same as writing cot(3pi/4)

though technically cot(3pi/4) is in terms of the rac since pi/4 is in that expression

the wording is vague, but i'd interpret it as having the rac (alone) for the argument (which you did)

[upper karma]

Ok thank u

[paper vale]

what is rac

[upper karma]

https://gyazo.com/ca9db3d6d184ed1e1509c952b8dad197
@lament shell btw why is there a m before the angles, I know it means measure of the angle but seems arbitrary because even without that nothing changes

[paper vale]

have u tried thinking about it

[upper karma]

Well does the m serve any purpose?

[paper vale]

you dont need to put the m

most people dont

[upper karma]

Yes I had realised that

so it is arbitrary right?

[paper vale]

what u mean

it is just a notation

[upper karma]

I know but it isn't necessary at all right?

[paper vale]

yea

[ashen brook]

what is the reciprocal of -12x

nvm

[foggy beacon]

hey guys

can someone assist me in solving for this

i got to

can someone explain this to me

[silent plank]

the general solution for cos(t) = 0 are the odd integer multiples of pi/2
(or t=pi/2 is a solution and from properties of cosine, there'll be another solution every pi in either direction)

[upper karma]

There are points A,B,C,D on a straight line find point O on the same straight line such that OA:OB = OC:OD ?

I don't really know how to start

<@&286206848099549185>

[silent plank]

is there more context?

[upper karma]

I don't think so

[fallow rampart]

@upper karma do you have to draw the line im assuming with point O?

I'm assuming you do i'll try to guide you a little

Create your first line we have points (ABCD) , Since we have to make the distance of O from A to B the same as C to D I'd make the order A - D - B - C <-- this is our first line

Drop down about an inch from this line and create a parallel mirror of the same line name this A' - D' - B' - C'

Now (using a ruler so you make sure you have precise measurements and accuracy) connect the lines DB' through a diagonal and C'A

The diagonal where these two lines cross can be marked n

Now if you take a line through n vertically (passing through both the ADBC and A'D'B'C' lines) you have your O point

You can put an O' point too just to keep the pattern

If you get confused through the process lmk, I drew up the picture but I might be going to sleep soon nearly 4am just @ me and i can dm tomorrow if i sleep

[thorny bough]

how do i work with restrictions on a variable properly?

[dark sparrow]

too vague. what do you mean by "work with"?

[upper karma]

anyone want a complex geo problem

Sure

[thorny bough]

@dark sparrow how do i do this properly?

i am not good at math

i ignored the restriction on vt

i don't know how to reason about it

[dark sparrow]

wait, what are you trying to do exactly

[thorny bough]

solve sin(t)=sin(vt) for t

[dark sparrow]

and what's known about v?

[thorny bough]

umm. I guess any real?

[dark sparrow]

do you have the problem statement in front of you?

[thorny bough]

i made the problem

[dark sparrow]

...ok fine

[thorny bough]

sorry 😭

[dark sparrow]

anyway you're going about this in a way that is inefficient at best

[thorny bough]

what should i do instead?

[dark sparrow]

perhaps you could write sin(vt) - sin(t) = 0, and then apply the sum to product identity for sine...

[thorny bough]

if it’s any use, algebraic solver gives:

which seems to be right, i just wanted to know how to solve it myself

ok i'll try that

@dark sparrow i can see where the v+1, v-1, comes from but i still don’t know how to solve 😂

thank you tho

[thorny bough]

so when a product is equal to 0 you can divide from both sides getting rid of one or the other?

[livid moss]

What?

[thorny bough]

I have 2xy=0
can i divide the 2 and get xy=0 ?

[paper vale]

yea

[livid moss]

Yes

[thorny bough]

but can i divide the x and get y = 0?

or divide the y and get x = 0?

[livid moss]

But that's because you know 2 is not 0

[paper vale]

no

[livid moss]

You cannot do it with x or y unless you already know they are not 0

[paper vale]

lol why would u be able to do that

[thorny bough]

i have no idea that's why i asked

[paper vale]

u literally just contradicted yourself right there

[livid moss]

If you have xy = 0 then x = 0 or y = 0 (at least one of the factors must be 0)

[thorny bough]

So i can split it like that?

I remember doing that when i was younger

[livid moss]

You can say x = 0 or y = 0

[thorny bough]

the OR is important

ok

[livid moss]

But it does not come from dividing

[paper vale]

you "showed" that it implies x=y=0 even though that isnt necessarily true

[thorny bough]

@livid moss where does it come from?

[livid moss]

The only way to multiply numbers and get 0 is if one of the numbers is 0

[paper vale]

if one is 0 then the product is also

[livid moss]

It comes from that fact

[thorny bough]

true

and that's true even if i have variables involved?

[livid moss]

Yes

[paper vale]

of course

[livid moss]

The variables are representing real numbers

[thorny bough]

ok sweet

i know how to solve it then!

thank you

[sullen canopy]

Please help

[paper vale]

just use (1/4)^n times 128

[sullen canopy]

Is that a rule?

[paper vale]

well the medial triangle is 1/4 of the reference triangle

[sullen canopy]

Wow thanks

[paper vale]

and there are 5 layers deep, so n=5

also do u know why that it is 1/4, it is easy to prove

[sullen canopy]

Probably just look up google and memorize the rule lmao

[paper vale]

no that is definetely not want u want to do

😐

[upper karma]

and there are 5 layers deep, so n=5
Isn't it n=4?

[paper vale]

yes, oops

[sullen canopy]

Area is 1/4 perimeter is 1/2

Got it

[paper vale]

to be fair it isnt that easy, ill give u clue, basically prove that all the 4 triangles formed are congruent

so implies they are all a quarter

[thorny bough]

is this true for cos (with arccos instead of arcssin)?

[paper vale]

yea cos also has a period of 2pi

[thorny bough]

ye but the pi shift also?

[dark sparrow]

no

the other family of solutions will be just y = -arccos(x) + 2πk

[thorny bough]

just that one?

hmm how did the algebraic solver get 4 equations 🤔

[sullen canopy]

If f(x) is a graph

f(x-2) will do what to the graph

I keep forgetting left or right

How about

2f(x)

I remember the shifting horizontally is opposite of common sense

So it is probably right yeah

[paper vale]

wait actually it is right

[sullen canopy]

Do you know what 2f(x) do ?

[paper vale]

2 f(x) just multiplies everything by 2

[sullen canopy]

I remember something about making it narrow or wide

I forgot these graphs and geometry concepts 😦

[paper vale]

making it narrower is doing f(2x)

2f(x) will just stretch everything out

[sullen canopy]

Right

Thanks

Shift to the right is - c

So you were right

[paper vale]

it means that f(x) occurs at a later value of the input than it normally has, so the output now shifts to an input further to the right

i.e like u need a greater input to get the same output

[fresh pike]

would this be symtric postulate or transitive? Im having trouble figuring out if 1/2 counts as a third number which would make it transitive

[dark sparrow]

this has the form of "If A=B and B=C, then A=C" so that's the transitive postulate

[fresh pike]

got it

thx

which one would this be? I assumed it was transitive but I guess it was wrong

[sullen canopy]

How

[paper vale]

use 1/2(sin(x)ab)= area

in EQD as x

then you can use cosine rule to work out ED