geometry-and-trigonometry

[iron rain]

Is it vector b + 1/4 vector BT?

[idle bloom]

yup

so now you gotta find those vectors but that's the right path

[iron rain]

b = (6 6 0) and BT = (-3 -3 8)

(6 6 0) + 1/4 (-3 -3 8) = (5.25 5.25 2)

So P = (5.25; 5.25; 2) ?

[hexed kraken]

sup guys

i have not done trig since my freshmen year of highschool, so this is easy sin cosine and tangnt stuff, can someone help me refresh my memory?

[weary drift]

https://www.khanacademy.org/math/trigonometry

[hexed kraken]

i need help wish basics basics.

but thanks. In triangle ABC, let AB = 34.1, LaTeX: m\angle A:=:62^\circm ∠ A = 62 ∘, and AC = 31.8. Find the area of the triangle. <-- thats a problem i need help with then ill remmeber everything

if someone could add me/ help me id be greatly appreciated!

[hexed kraken]

ok

im hurt.

[hallow rose]

Anyone?

[cerulean tundra]

find BC

then the area is easy

m²

if cm² there

so cm.cm

/2

because a triangle is a square

/2

@hexed kraken @hallow rose

[hallow rose]

Random pings?

[cerulean tundra]

you said "anyone"

[hot pumice]

Does an unchanging, infinite series like this converge and if so at what value?

[upper karma]

No

[somber coyote]

N/𝔄:

[hot pumice]

hmmmmmm

Don't really fully understand that, sorry

[upper karma]

If you have a sequence whose members are gonna be the summands of your infinite sum and this infinite sum converges, then this sequence must converge to 0

That means no constant sequence other than the sequence that is 0 everywhere is allowed there

[hot pumice]

Ahh right, it doesn't diverge either though right?

[upper karma]

If it does not converge it diverges

[hot pumice]

Got it, ty

[idle bloom]

@hot pumice think about it

you're infinitely adding up 11/12

all converging series at some point you add up stuff that tends to zero

Now just cause your terms tend to zero it doesn't mean you converge

but if your terms don't tend you zero you definitely diverge

[rare pollen]

Have an upcoming test and me and my friend are working through revision books etc. we had this one question which we thought we had the answer and yet the answer in the booklet had something completely different hoping you guys could help?

A box in the shape of a square prism has a base 12 cm by 12 cm and is 40 cm tall. Find to the nearest whole number:

a) the length of the longest diagonal ( we got this right, and the booklet matched)

b) the angle the longest diagonal makes with the base (This we think we have right, didn't match the book)

[jade valley]

what are your answers first?

[old ferry]

can someone help me with this? i dont seem to make any progress

[midnight trout]

I'd probably use atan2 on ba, then bd, then subtract one from the other.

[turbid garden]

@old ferry I highly suggest drawing it then placing in all the numbers you know, then working from there

you also know each of the three angles of ABC is 60 degrees (It's an equilateral triangle)

I find that finding all of the angles that I can at the time, even if they don't help me in the end, can be helpful.

Here's something to get you started:
BCD=6
CBD=12
BDC=180-BCD-CBD -> 162

Knowing CBD, we can also know ABD - it's just 60-CBD -> 48

[old ferry]

i did all those, but didnt progress after that

[eager pendant]

@turbid garden you won't be able to solve something like this just using simple angle chasing

[turbid garden]

Oh
I mean you'd use that to start out

[eager pendant]

@old ferry try trig

[old ferry]

trigonometric form of ceva's theorem didnt get me anywhere

[midnight trout]

What happened when you tried atan2?

[eager pendant]

with ceva you'd have to extend those lines and that seems a bit unwieldy

[midnight trout]

I'm curious why it would've failed. It might help me to know.

[old ferry]

no i mean trigonometric ceva

sinDBCsinDCAsinDAB = sinDBAsinDCBsinDAC

[turbid garden]

this is wack

[sharp patio]

Is there a channel for tri dimensional geometry

[dark sparrow]

dunno but it'd probably go here

[old ferry]

i've just solved it

[old ferry]

can i post the solution here?

p.s i didn't know the solution before asking it here

[turbid garden]

... what year of hs is this

[old ferry]

3rd

[turbid garden]

Wait multiple years of geometry?

[old ferry]

not the US

[eager pendant]

yay nice construction

most of these types of problems involve some type of construction then some cyclic quad / similarity: what not

or you can draw the diagram accurately, get the angle using a protractor and verify that it’s right (ceva would work)

[upper karma]

I want a circle between 0,0 and 1,1. what is the equation

[dire rampart]

[upper karma]

no im serious

I need this for something I'm working on

what equation or system of equations or whatever

[dark sparrow]

what do you mean by "between (0,0) and (1,1)"

do you want the segment joining those points to be its diameter?

[split geyser]

or do you want one to be the center? or just an arbitrary circle that passes through those points?

[dark sparrow]

@upper karma

[upper karma]

@split geyser @dark sparrow I mean that its centered between those points, and the edges go to the edges of the square between those points

[dark sparrow]

what

do you mean that it's supposed to be inscribed in the square?

[upper karma]

yes

the square between (0,0) (0,1) (1,0) and (1,1)

@dark sparrow

[dark sparrow]

ok great

(x - 1/2)^2 + (y - 1/2)^2 = 1/4

[upper karma]

wow that was fast

so inside the circle, will it be less than 1/4? @dark sparrow

[dark sparrow]

yes

[upper karma]

perfect

i am making a shader

i will share it here with you

[gleaming creek]

Hey, could someone help me with some problems?

[upper karma]

@dark sparrow this is what it does. thank you.

[quick otter]

hey guys, does a dice become less equal as if its not a cube?

[tribal wind]

usually yea

[quick otter]

classifying the symmetry can someone explain what that means

is just the rotational and reflections

[tribal wind]

yea just those

[quick otter]

im trying to express in words have a cube has 24 symmetrie

but I don't know how without just copying someone online

i can describe it with an actual cube though

im trying to express in words have a cube has 24 symmetrie
@quick otter i mean 48

[tribal wind]

uhh I'd just say it's fully decided by the orientation of the top face

so like you have 1-6, 4 rotations around the top, and a mirrored version, giving 6*4*2=48

[quick otter]

so does a cube have 24 rotations, and 24 reflections?

[drifting barn]

Hello.

is
sin5*cos25+sin25*cos5
sin(5+25)=sin(30)=1/2?

Just wanted to check, not sure if it was correct or not

[dark sparrow]

what's that * right before the +

and are you measuring angles in degrees

[drifting barn]

Yes, in angles

and that is multiplication

Sorry, that made no real sense

I know about the formula
sin(a+b) =sina*cosb+sinb*cosa

[dark sparrow]

well

what you wrote is an instance of it

with a = 5 and b = 25

[drifting barn]

So it's correct?

Is all of that equal to sin30

[dark sparrow]

you are telling me you know the formula sin(a+b) = sin(a)cos(b) + sin(b)cos(a), and are asking if it remains correct if you insert a = 5 and b = 25

of course it does lmao

[drifting barn]

Okay, good, just wanted to be sure

The exercise itself is quite easy, just scared me because there are 10 of those xd

[lethal narwhal]

How would I work out for 0 <x < 360 degrees:
3sinx = 4cosx

[silent plank]

what have you tried?

[lethal narwhal]

trial and error

[silent plank]

how does trial and error even work here...

consider tan(x) = sin(x)/cos(x)

[lethal narwhal]

thanks

[tall flower]

can anyone help me complete this online test?

[silent plank]

#❓how-to-get-help rule #6

[crisp sparrow]

no help on tests

[surreal ingot]

How you do number 41?

[cinder portal]

what have you learned that'll help you solve this

[surreal ingot]

Area

Law of sines

[cinder portal]

go use that

[surreal ingot]

Use area?

Or law of sines?

[cinder portal]

you're going to have to set up equations properly

set up equations here and there

and then see if that get's you anywhere

[surreal ingot]

👌

Is this so far looking right?

Oh shoot I forget 1/2

Oh wait

I set up a better equation

Not quite sure what to do next

Ohh

Turn sin2ø to 2sincos

[silent plank]

you used the incorrect substitution

[surreal ingot]

Oh

[silent plank]

but yes, apply the double angle identity after fixing those

[surreal ingot]

Sin cancel each other

Never mind I figure out

Xd

[ruby pulsar]

Hello?

Can someone help me with my online hw?

[dark sparrow]

i'll bite

what's giving you trouble here

(but also don't multipost)

(i've deleted your post in #help-0)

[ruby pulsar]

Sorry.

I don't know how to do these problems, @dark sparrow

[dark sparrow]

define "these problems"?

do you know how to solve basic trigonometric equations, i.e. ones of the form sin(x) = a, cos(x) = a or tan(x) = a?

[ruby pulsar]

Yeah, but with the intervals, I do not.

[dark sparrow]

where a is a constant

ok wait

if your problem didn't say "on the interval [0, 2π)", would you be able to do it

[ruby pulsar]

Nope, lol. The interval thing is complicating me.

[dark sparrow]

no, that's not what i'm asking you

[ruby pulsar]

Would I have to crunch it down with identities?

[dark sparrow]

if you were just asked to solve $\sin\paren{\frac{\pi}{6} + x} + \sin\paren{\frac{\pi}{6} - x} = \frac{1}{2}$ without any mention of an interval to solve on, would you be able to do it?

[ruby pulsar]

Uhw hat

[somber coyote]

Ann:

[dark sparrow]

there we go

[ruby pulsar]

Like I mentioned above, I am not able to.

[dark sparrow]

and yet you said immediately afterwards that "the interval thing was complicating you", making it seem as if the interval was the issue

[ruby pulsar]

I require step-to-step assistance on that matter.

Yeah, it's making me more confused.

[dark sparrow]

and if there WASN'T an interval, you would still be unable to do the problem?

did i get that right?

[ruby pulsar]

Ok, nvm\

I got it from someone

Thank you for trying to assist me.

[dark sparrow]

is that a way for you to say "fuck off, i wanted a quick answer and you refused to provide and i don't want your help anymore you idiot"

[white cradle]

usually I'd say you're overreacting

but nah, this time you're right lmao

[white cradle]

it just makes your own life harder, later on

oof

if they were too easy then you should've been able to solve it without wasting much time anyways

the server isn't for asking aid for graded tests or papers anyways

i probs wouldn't enjoy it per se, but I did do those stuff

and maybe unbeknownst to me it helped me gain confidence in those basic stuff

[formal hamlet]

Find the exact value of tan Θ , given that Sin Θ = 1/2, and Θ is in quadrant 2.

$$-\frac{\sqrt{3}}{3}$$

[somber coyote]

DeadEye:

[formal hamlet]

Is that right?'

Since Tan is negative in quad 2

[dark sparrow]

yup

[deft sleet]

idk if this is the correct place to put it so if this is the wrong place please show me where to ask.

We got a task to create this graph which went fine

but then we were asked to read the crossing points of h with the x axis which i think was okay

however, the next task was to calculate the crossing points of h with the x axis

i dont know how to do that

[round isle]

?

again with the x axis?

[deft sleet]

i can send you the entire thing but its in norwegian and i tried to translate as well as i could

[round isle]

I think you meant y axis

for the second one

[deft sleet]

nope :/

[round isle]

????

[deft sleet]

b) read the crossing points of h with the x axis

c) calculate the crossing points of h with the x axis

[round isle]

what is the difference between read and calculate here?

[deft sleet]

Thats what i dont understand

[round isle]

Is this something special in norwegian polynomials?

[deft sleet]

well read is just to look at it and see where it is

calculate is to calculate the point

[round isle]

that does make sense

[hard gale]

i mean in a) they ask you to graph the function i guess

[deft sleet]

yes

[round isle]

maybe first it wants you to find crossong points by drawing

[hard gale]

well yeah just look at the graph

[round isle]

and in the next one they want you to calculate it

[deft sleet]

Okay well i already drew it

and made a value sheet

but i dont know what the meaning of calculating the crossing point is

[round isle]

equate it to 0 and solve

[deft sleet]

can you give me an example?

[round isle]

do you know how to solve a quadratic equation of the form ax^2 + bx + c = 0

[deft sleet]

yes i believe so

using the quadratic formula?

[round isle]

do this here by equating h(x) = 0

at crossing point with x axis, the y values will be 0

[deft sleet]

uhh i dont think i understand

[round isle]

h(x) = 0

left hand side of equation becomes 0 at crossing point

put a 0 on LHS and solve it

would be much easier and faster if you factorize it

quadratic formula looks overkill here

[deft sleet]

I hate homeschool due to corona

I still dont understand sadly

[round isle]

-x^2 -4x + 5 = 0

I hope you understand why I did that

the points at which any graph crosses the x axis are the points whose y value will be 0. Here y value for any point is h(x). Any point A on this graph has coordinates (x,h(x)). Any point B that is a crossing point on the x axis has coordinates (x,0)

Just imagine h(x) as y

[deft sleet]

okay

but how does -x^2-4x+5 equal 0?

[round isle]

are you asking me how to solve this?

[deft sleet]

i guess so?

[round isle]

hmm, I must ask you what grade are you in

[deft sleet]

upper secondary school first grade in norway

[round isle]

did your teacher show you how to solve equations of this type?

if you are uncomfortable with factorizing, you can use the quadratic formula. However, I would highly advise you learn how to factorize since that is a useful trick in maths in general

[deft sleet]

Yeah he did a week ago but we were supposed to go more in depth this week however due to the corona virus, there was no more school except for this homeschool type

[round isle]

well first thing you should do is multiply both sides with -1 to make the coefficient of the 2nd degree variable positive

[deft sleet]

okay

so it turns into x^2+4x-5=0?

[round isle]

yes

now

you need to break down 4x into a sum of two numbers

but the two numbers must be factors of 5

do you know what a factor is?

[deft sleet]

We have different terms in norwegian but would it be 4= 2^2?

[round isle]

what are the factors of 5?

yes the idea is correct

what are the factors of 5?

[deft sleet]

i dont know

[round isle]

what two numbers can you multiply to get 5

[deft sleet]

1 and 5?

[round isle]

yes, there you go, those are called factors of 5

[deft sleet]

okay

[round isle]

now

4x = -x + 5x

replace 4x with that

hopefully you are able to proceed from that point

[deft sleet]

okay just one last question i guess

why does 4x have to be a factor of 5?

[round isle]

4x is not a factor of 5

we are breaking down 4x into a sum of numbers

4x can be written as a sum of any two numbers

but 4x = 1000x - 996x doesn't really make sense here now does it

However 4x = -x + 5x does make sense here because you have two numbers who share something common with the left and right hand side numbers

I think you should wait for your teacher to explain this to you in more detail

No point in rushing like this without proper explanation

[deft sleet]

okay well i think you helped me atleast a little bit

Would the quardratic formula work here aswell?

even if it is overkill

[round isle]

of course but how do you know the quadratic formula but not factorizing?

[deft sleet]

no i know factorizing

but we have different terms in norwegian

so i was confused

thats all

[round isle]

I see

try to do by factorizing. Always look for the easy way out

that is literally how maths developed

people got tired of using lengthy formulas

so they looked for shortcuts and better ways

[deft sleet]

Cool. I liked your way by factorizing but i couldnt really wrap my head around it i think

[supple wedge]

@deft sleet quadratic formula works everywhere

[round isle]

I remember my teacher told us a step by step procedure for factorizing when I was your age

obviously I don't remeber it now

[supple wedge]

if u can factorize factorize it

[round isle]

It's now muscle memory

[supple wedge]

imo quadratic formula is last resort

[deft sleet]

Well thanks for the help and showing me other ways :D. I'll try to do my task now

[round isle]

good luck

[ionic bluff]

factors of ac

add to equal b

i mean it's really that simple

[deft sleet]

Can you explain with the equation that was given? @ionic bluff

[ionic bluff]

what eq?

[round isle]

@deft sleet multiply the coefficient of x^2 with the last number in your equation

[ionic bluff]

this one?

x^2+4x-5=0

factors of 1*5

which is plus or minus 1, 5

add to equal 4

so plus 5, minus 1

(x+5)(x-1)

[round isle]

I think some exercises in factorization would clarify this to you

[deft sleet]

The graph gave -5 and +1

[ionic bluff]

yes

[round isle]

yes that is correct

[deft sleet]

no i really understood now

but it was still not correct?

[round isle]

no harm in practice

[deft sleet]

true

[ionic bluff]

(x+a) is a negative root

(x-a) is a positive root

[round isle]

build up that muscle memory in your hand and your confidence

[deft sleet]

okay but shouldnt it be (x-5)(x+1) to fit the graph?

[round isle]

no

x-5 = 0

x = 5

[deft sleet]

huh

I guess i have to watch some videos on it then

[round isle]

I suggest you ask your teacher

[ionic bluff]

(x+a) is a negative root
(x-a) is a positive root

[round isle]

has your teacher explained all of this before?

[ionic bluff]

8

[deft sleet]

yeah we had all this (a+b)^2 stuff but i dont understand what you guys are getting at

[round isle]

(x-5)(x+1) = 0

how did your teacher solve this?

[deft sleet]

x^2+x-5x-5

[round isle]

?????

what???

[deft sleet]

x^2-4x-5?

[round isle]

are you doing?

no no

[ionic bluff]

no that's fine actually

[round isle]

(x-5)(x+1) = 0
what are the values of x in the above?

[ionic bluff]

that's how you factor things by grouping

x^2+x-5x-5

[round isle]

how will you find the value of x then?

[ionic bluff]

x(x+1) -5(x+1)

(x+1)(x-5)

[round isle]

yes I gave him that originally

and asked him to solve for values of x

[ionic bluff]

(x+1)(x-5)=0

@deft sleet

solve that

[round isle]

yes

@deft sleet please solve that and tell us what are the values of x

[deft sleet]

uhm

[round isle]

how did your teacher solve it in class?

makes no sense for you to do these exercises if your teacher didn't show you how to do it

[deft sleet]

i remember that he did

[ionic bluff]

ok

you need a more conceptual understanding

[deft sleet]

but i guess i forgotr

[ionic bluff]

if i have two numbers, a and b

[round isle]

I think you should review your lecture notes

[ionic bluff]

and i say that a * b = 0

[deft sleet]

yes

[ionic bluff]

what does that imply

[deft sleet]

they can be whatever as long as one is 0?

[round isle]

not really

it means that a = 0 or b = 0 or both are 0

[ionic bluff]

yeah. it says that either a or b MUST be 0

[deft sleet]

thats what i said

[ionic bluff]

(x+1)(x-5)

(x+1) is just a number like a or b

so if (x+1)(x+5)=0

[deft sleet]

oh my lord im so dumb xd

-1 then

[ionic bluff]

yes.

what's the other solution

[deft sleet]

-5

[round isle]

think of the expressions inside brackets as numbers

and manipulate them as you would with numbers

[deft sleet]

yeah

now i remember it

[round isle]

do you have a maths textbook?

[deft sleet]

we dont

[round isle]

that cannot be possible

[deft sleet]

?

[round isle]

there must be a textbook

how do you study at home then?

[deft sleet]

he prints out tasks

and hands them to us

[round isle]

when I was your age, we had a thick textbook and we would go home and do 100s of sums

[deft sleet]

but i remember now

yeah we dont xd

[round isle]

no handouts or anything

opened a big ass textbook and did sums back home. Call me old fashioned but that stuff built a lot of muscle memory that I don't think I would ever forget

[deft sleet]

Hahahah

yeah but remember we have different school systems

[round isle]

your professor should give you dozens of trivial sums and exercises to help you build your muscle memory with basic tasks like factorization

[deft sleet]

he did

and i did lots of them

[round isle]

can you show me an example handout from your professor?

[deft sleet]

sure

[round isle]

you should be able to do this stuff if you did lots of exercises

[round isle]

lol

what is this supposed to be ????

[deft sleet]

tasks?

[round isle]

why so few?

[deft sleet]

ask my teacher

[round isle]

norway is supposed to have the best education system, either I am missing something or norwegians are natural born mathematicians who don't need to do as many sums as we do

[deft sleet]

hahaha

that was just for 1 day

we got more papers

[round isle]

hmm ok

get in as much practice as you can

that's all you need to do

practice

[deft sleet]

I agree

[round isle]

also try to understand the theory too

[ionic bluff]

hey rainlinkz wanna see something cool

[deft sleet]

sure

[deft sleet]

yup

[round isle]

ahhhhhh

[deft sleet]

we had that

[round isle]

I remember this

classic proof

[ionic bluff]

that's what (a+b)^2 is

[round isle]

this and the Pythagoras proof made me fall in love with maths as a child

[ionic bluff]

i had to figure that out on my own because my teachers would just say yeah it's a^2+2ab+b^2

[deft sleet]

no my teacher gave it to us

as a task

and lots of others like it

[round isle]

good

pay attention to the proofs

[ionic bluff]

idk if it's just my school but it feels like there's too much random info without any reason why

[deft sleet]

he wants us to understand the concepts and proves everything he shows us

[ionic bluff]

like memorize this and that

[round isle]

theory is as important as doing sums

[deft sleet]

he goes deep into it

[round isle]

do you know the proof of the quadratic formula?

[ionic bluff]

wait is there a geometric proof

[deft sleet]

yes

[round isle]

I used to complain about completing the squares

[deft sleet]

he showed us that aswell

[round isle]

until I saw how that was used to get the quadratic formula

good good

[deft sleet]

found it

he is a great teacher tbh but sometimes hes not

thanks for the help @round isle and @ionic bluff

[drowsy pond]

can someone summarize special right triangles in an understandable way? we are doing them in class this week and i have no clue whats going on except something about 30, 60, 90 and 45, 45, 90

[drowsy walrus]

30-60-90 triangles and 45-45-90 triangles

[dark sparrow]

those refer to the angle measures @drowsy pond

[drowsy pond]

okay

[drowsy walrus]

it’s basically Pythagorean theorem

[drowsy pond]

okay

[supple wedge]

@justindoan#6225 those are special angles

lol where did he go

[onyx basin]

@drowsy pond

[proper solstice]

How do I explain the relationships here with words/formulas?

<@&286206848099549185>

Did I do the right ping? :3

[rich wolf]

,rotate

[stoic steeple]

The second one(if you know the first one... Let me know)

[golden panther]

I need Halp

[supple wedge]

[round isle]

Usually you should follow that with your question

[golden panther]

its my first day here

[round isle]

what is your question

[golden panther]

sin2x/2sinx=cos^2x/2-sin^2x/2 after a couple steps i get to this cosx=cos^2x/2-sin^2x/2 what do i do now

[round isle]

cosine raised to the power of 2x?

sorry but can you write this on a piece of paper

[olive plover]

why is secant negative in third quadrant if tangent is positive there and tangent is sin/cos

[golden panther]

I cant because im on a laptop

[round isle]

then you need to find a way to write it down properly

[golden panther]

wth

[round isle]

maybe use paint

please write down the equation in a proper way so it makes sense. At the moment, it is very hard to understand what your equation is exactly

@olive plover well secant is geometric inverse of cos

[golden panther]

i cant believe this

@round isle

[round isle]

ok

[golden panther]

im at this part : cosx=cos^2x/2-sin^2x/2

[round isle]

are you trying to make x the subject of the above equation?

what is your end goal with this equation?

[golden panther]

no im trying to verify

prove

[round isle]

I see

right

RHS is a trignometric identity

(cosx)^2 - (sinx)^2 = cos(2x)

please solve now and the equation is proved

[golden panther]

how the heck did you get that

[round isle]

?

please go through your class notes on trignometric identities to verify

[golden panther]

are you using half angle identity formula

[round isle]

you can verify this by expanding cos2x

now please use the trignometric identity on RHS to verify the equation

[golden panther]

There is no cos2x

[round isle]

(cosx)^2 - (sinx)^2

that is equal to cos2x

here it is x/2 and not x

so make the appropriate substitution

[dark sparrow]

im at this part : cosx=cos^2x/2-sin^2x/2
parentheses

[round isle]

the RHS is equal to cosx

cosx = cos(x/2 + x/2)

[dark sparrow]

how do you know whether cosx/2 refers to cos(x/2) or cos(x)/2 and how do you know you won't forget what you actually mean

the answer is you don't so you gotta put those parentheses there

and ideally you should just always put parentheses around the inputs of trig fictions

[golden panther]

wth. My Apologies

[round isle]

obviously it should be clear to you now

[golden panther]

No

[round isle]

what is not clear?

cos(x/2 + x/2) can be expanded using the cosine formula and you would get the original RHS

best you review trignometric identities again

[dark sparrow]

cos(2t) = cos^2(t) - sin^2(t)
now replace t with x/2

[golden panther]

is that it ^

am i done with the problem after i do that

[round isle]

well RHS will be equal to cosx

so yes, proved

[dark sparrow]

uh yeah that just gives you the thing you were stuck at

[golden panther]

thanks ..i guess

[upper karma]

so my mcq exams are giving me problems such as if 3 i + 2 j + a k and 4i -3j + k are perpendicular to each other, what is the value of a?

(it's a vector problem so i,j,k are vector co-ords)

if they are A and B respectively, then the formula is A × B = 0

[weak shoal]

i,j,k are not vector coordinates, they're unit vectors.

[upper karma]

yeah, sorry, that

[weak shoal]

There's a simpler way to approach this with the scalar product.

[weary drift]

standard inner product on R^3

[upper karma]

how should i go about it?

[weak shoal]

In particular:

$\overrightarrow{A} \cdot \overrightarrow{B} = 0$

[somber coyote]

Abhijeet Vats:

[upper karma]

ohhhhhh

right right right

[weak shoal]

Jintarou

I swear to god.....

[upper karma]

my dumbass forgot about dot product

[weary drift]

abhi, don't swear at god or He will smite you

[weak shoal]

Lul

Don't get me wrong

[upper karma]

don't swear at god because the dude don't exist

[weak shoal]

You could have done it with the cross product

It's just a more painful way to do it.

[weary drift]

find $a$ that maximizes $\norm{A\cross B}$. this is painful

[somber coyote]

RokettoJanpu:

[upper karma]

A x B = AB, right?

no wait

abs( A x B ) = AB

[weak shoal]

Yes.

$||A \cross B|| = ||A||\cdot ||B||$

[somber coyote]

Abhijeet Vats:

[weak shoal]

WHAT THE FUCK

Oh

[upper karma]

is that the latex programming language?

how does so many people know all the syntax to use this bot

[weary drift]

experience

[upper karma]

well said

thanks, my dudes

[weak shoal]

No u

You're welcome.

[fleet roost]

hey guys can anyone help me pls?

[silent plank]

what have you tried?

though this sounds like it should be in calculus

[round isle]

Yes

It's also a very vague question

The volume limit is not enough

[silent plank]

it should be

[round isle]

I mean technically you can keep decreasing the base and keep increasing the height

While maintaining the same volume

So height can potentially be infinite with the base area close to zero

[silent plank]

after a certain point the total SA would start increasing

[round isle]

How so?

If I keep increasing the height and decrease the surface area, the volume would remain the same

So ideally I could bring the surface area down to a very small value and the height to a very large value

[silent plank]

you're making a very bad assumption

what evidence do you have to backup
"increasing height decreases the SA (at large values of h)"

[round isle]

Take a very large height and divide the volume with that

You will get the surface area

And that surface area would be really small

[silent plank]

uh what?

[round isle]

Cylinder volume = pi * radius * radius * height

We know the cylinder volume

[silent plank]

yes

[round isle]

We want to find the smallest surface area for this volume

Pi * radius * radius = cylinder volume / height

Keep increasing height

Increase height to infinity

The base area becomes 0

[silent plank]

gets close to 0 but ok

[round isle]

Exactly

[silent plank]

how does that decrease the total SA of the cylinder?

[round isle]

I think he is asking for the base area

[silent plank]

you're ignoring that middle section (and possibly the top) for some reason

no

[round isle]

Ah sorry

Now I read it again

[silent plank]

SA of a cylinder is not the same as the base area

[round isle]

The total surface area

Hahah

Right, you could take the derivative of the total surface area and find the value of h that gives you a minima for that

[upper karma]

is this true for all cases?

[agile axle]

Could someone tell me how I should calculate this one?

http://prntscr.com/ri9n7p
The line AC is just as long as the cirkels radius. The Angel BAC = 40 degrees.
what angle is v?

[silent plank]

consider constructing AM and CM

[agile axle]

@silent plank Thank! I got the answer 😉

[outer ravine]

My teacher had this on the answer key for us to check our notes, is this right?

https://i.ibb.co/vBVwNkr/opera-a-PTXEj-OXSO.png

[wooden citrus]

I suck at math, I was hoping I could get some help on a simple problem

I want to calculate a slope of a series of pipes. Let's say X1 is (34.05) and I know that I want to have a Y% slope to X2 which is 56 meters away, how would I calcuate thaT?

[round isle]

Can you formulate this problem in a more formal way.

Slope is between two points.

@outer ravine yes it is right

[outer ravine]

can you explain how she did it because I screwed it up

I pretty much screwed up all of my notes 🙃

[round isle]

Well your teacher has written the Formula for area of a sector

Then she just substituted the right values into it

You do know what the Formula of a sector is right?

[outer ravine]

yeah I do

but this part

https://i.ibb.co/bR6L5N6/opera-Kl-SDIv-BMfu.png

I don't get that part

like the way I solved it was you take the 4.5 and multiply 40 by 4.5 then divide by 360... which is wrong

[round isle]

Sorry I didn't understand your procedure. Best you show your calculation

[silent plank]

,rotate

[silent plank]

that looks fine. simplify your fraction

[outer ravine]

wait what

that works?

[silent plank]

multiplication commutes so yeh.

[outer ravine]

oh

also idk why the last 2 problems on my homework just got a lot easier, we just haven't done any algebra for a couple months or so. I kinda forgot a bit of it

[dire yarrow]

Stuck in this question any help would me much appreciated

[weak shoal]

Where are you stuck?

[dire yarrow]

On part a

At the moment

[weak shoal]

Alright, do you have any ideas for an approach?

[dire yarrow]

Turn sec into 1/cosk

And do the same with tan

[weak shoal]

Well

Let me suggest a better approach?

[dire yarrow]

That would be much appreciated

[weak shoal]

So, consider the identity:

$\tan^2(k) + 1 = \sec^2(k)$

[somber coyote]

Abhijeet Vats:

[dire yarrow]

ok

Thanks

[weak shoal]

You're welcome. I do hope you're able to solve it now.

[dire yarrow]

That should help slot cheers @weak shoal

[hot sable]

Hey could someone tell me

how can i find AB from ABC with (<ACB = 90) when i only have P=60cm and S=120cm?

<@&286206848099549185>

[quiet mason]

firstly #❓how-to-get-help

and what the fuck is P and S

[hot sable]

Perimeter and Area

[idle bloom]

Set up some systems of equations

You have 3 unknown variables and 3 equations you can make

[hot sable]

aight

[rich wolf]

Draw a picture

[upper karma]

@hot sable

where did you end up posting your question?

okay i think I've got it

[acoustic peak]

a^2+b^2 != (a+b)^2

[upper karma]

a²+b²=(a+b)²-2ab

[acoustic peak]

Ah I see it

Mb

[upper karma]

np

[acoustic peak]

Ye looks right

[upper karma]

i need help 😫

anime cooch :|

lets start from the center's height

the center of the ferris wheel is 55ft above the ground

so whatever your sine function spits, you'll have to add 55to it

so d=55

now... the radius is 50ft

so the amplitude gonna be 50

so a=50

finally, since f(t) is a function of time, the b is gonna be it's period

which is the total time needed to complete the cycle multiplied with 2π

so b=2π/4min

[idle lynx]

https://cdn.discordapp.com/attachments/269573202018041856/689896978498453515/image0.jpg

can someone check this please

[onyx basin]

well

do you have values for any of those letters

well there's many ways we can calculate y

it might just be confused, but i dont know what you're asking

you asked for the value of y

but you have no values for the others

so we can write expressions for y

e.g. sinA = y/v

sqrt(wz) or sqrt(w) * z

i feel like i've learned this before and my mind is just blanking

[upper karma]

for part b would it be (-3, 7pi/4) ???

like im confused how to find another pair that represents (3,pi/4)

[weary drift]

make it easy for yourself. keep the same radius and just find an angle coterminal with pi/4

[upper karma]

isn't 7pi/4 a coterminal angle with pi/4

[upper karma]

im still confused 💀

help pls 😭

and with part c 😫

[olive plover]

guys I dont understand how to find lengh of an arc of a cicle

[sly marlin]

@olive plover do you know any formulas that may help?

[olive plover]

2pi r times x/360?

[upper karma]

pi describes the length of half a unit circle you should able to deduce more things from there

[weary drift]

@upper karma close. and i suggested you keep the same radius. same radius+coterminal angle describes the same point

[olive plover]

they give me central angle of 80 and diameter of 20

i put 80 in x

but then i dont know about 20

[upper karma]

i put 80 in x
@olive plover what does that mean

@weary drift so would it be (3, -7pi/4)

[olive plover]

2piRadius times (x/360)

?

[weary drift]

@upper karma that's one good answer. ANY angle coterminal w/ pi/4 is ok

[upper karma]

80 degree is your angle so what is that in radians?

The length on the unit circle

[olive plover]

4pi/9

[upper karma]

Right so can you find what the length is in the circle you described?

It scales linearly

[olive plover]

no

[upper karma]

@weary drift ok and then converting it into a rectangular equation what would that be ?

@weary drift is it just sqrt2 / 2 , -sqrt2 / 2 ???

4pi/9 is the arc length with the angle you want on the circle of radius 1. The length scales with the radius of the circle. Do you know how to scale this arc length up to your circle?

[olive plover]

the diameter is 20

do i multiply?

[upper karma]

@weary drift not a rectangular equation i mean to rectangular coordinates***

[olive plover]

@upper karma

[upper karma]

By what?

[olive plover]

4pi/9 times 20?

[upper karma]

No

That is double the size

You have 1*4pi/9 because the circle we calculate radians in is the unit circle

Which means we want to look at the radius

The unit circle has a diameter of 2

[olive plover]

oh its 40pi/9

[upper karma]

Wtf

Radius is half the diameter

[olive plover]

given diameter is 20

[upper karma]

Right

So what is the radius

[olive plover]

i got it correct

[upper karma]

If you say so

[weary drift]

@upper karma always remember the conversion between polar and rectangular. if you have (r,t) in polar then (x,y) in rectangular is given by (x,y)=(rcos(t),rsin(t))

[upper karma]

@weary drift ok thank you

how do you do this ?

is there a formula or something

[rich wolf]

@upper karma ok

So i want you to ignore all the context of the problem

[upper karma]

ok

[rich wolf]

And just look at the diagram

What does it look like

[upper karma]

right triangle

[rich wolf]

Good

Now try solving for a side

[upper karma]

for the side opposite from 38 degrees i got 149.179

@rich wolf

[rich wolf]

How

[upper karma]

well since its a right triangle the angle opposite of 450 is 90

and i subtracted 180- 90 - 38 an got 52 for the last angle

then i used law of sines

[rich wolf]

You dont need law of sines lmao, and you got the wrong answer anyway

[upper karma]

oh 💀

then how do you do it 💀

[rich wolf]

Lol

Its just funny to me that you know law of sines

But not SOHCAHTOA

[upper karma]

oh lmao

i completely forgot about that

did you get 277.047

for the side opposite of angle 38 degrees

@rich wolf

[umbral snow]

,calc 450sin(38 deg)

[somber coyote]

Result:

277.04766389655

[umbral snow]

,calc 450cos(38 deg)

[somber coyote]

Result:

354.60483912302

[umbral snow]

@upper karma
Those

[upper karma]

@umbral snow yeah thats what i got

now what do i do

[umbral snow]

Wat u mean? That's the answer

[upper karma]

oh that's it ?

[umbral snow]

Well, they want it in a <x,y> format

[upper karma]

@umbral snow so < 354.604, 277.047> ???

[umbral snow]

Ya

[tepid finch]

yeah people just call it volume

[rich wolf]

@ashen mica what

4D volume

What

Yeah i get that dude

But what the fuck

Why

OMG ITS GRANT SANDERSON

From 3brown1blue

[supple wedge]

heil

[rich wolf]

He needs to do a bsauce collab

[supple wedge]

st. 3blue1brown

[umbral snow]

It is called volume.
"Area" and "length" are the exceptions

[rich wolf]

What does 0 dimensional space look like

Or -1

A point has location

[tepid finch]

you still see area and length called volume sometimes

0 dimensional space is a point

-1d isnt a thing

oops i literally repeated you

[umbral snow]

One way to answer it is with linear algebra. How many vector spaces are zero dimensional? That is, has a basis of zero vectors?

The question doesn't make any sense, there's no 0D vector spaces

[tepid finch]

is {()} a vector space?

[umbral snow]

Nvm I just looked it up

[tepid finch]

() is additive identity and multiplicative identity

[umbral snow]

The zero vector space is defined to have dimension 0

[tepid finch]

and () = 0 as well

its literally just 0 * stuff = 0 or 0 + 0 = 0, 0 + 0 = 0 + 0 etc

[umbral snow]

So you have exactly one

It is the space of one element

[tepid finch]

yea

[jolly geode]

Hey Vsauce!

Michael Here!

Where are your fingers?

D-Don't touch your face!

Go wash your hands for 20 seconds.

[golden panther]

how does sinxcosx+sinx = sinx(cosx+1)

Please

ive been trying for two hours please

[silent plank]

distributive property / factorisation

the lack of parentheses is a little disturbing

[golden panther]

dude i did that

[silent plank]

$\sin(x)\cos(x) + \sin(x) = \sin(x) (\cos(x) + 1)$

[somber coyote]

ramonov:

[silent plank]

ab + a = a(b+1)

[golden panther]

is that correct

[silent plank]

is what correct?

[cinder portal]

factor out sin(x)

lmao

[golden panther]

how does it turn to a +1

this isnt a joke bro

[silent plank]

do you agree that:

ab + a = a(b+1)

[golden panther]

i guess I thought i woud be using a trig IDentity

[silent plank]

don't overthink it

no trig identites needed at all

recognise when they are/aren't needed

[golden panther]

i cant believe this

i stayed up for 2 hours for this

[cinder portal]

you're factoring a term

that's all

[rich wolf]

@golden panther it can be helpful

To introduce new variables

Like a or b

And set them equal to parts of the equation

[viscid ginkgo]

if I want to find s when v = 21 mi/hr and t = 20 min

I do 20/60 * 21 mi/hr to get 7 mi

how does the /hr get canceled out?

(20/60hr) doesn't make sense

[round isle]

Convert t to hrs

[viscid ginkgo]

I can say 1/3 of an hour

[round isle]

Yes

[viscid ginkgo]

1/3hr?

[round isle]

Yes

[viscid ginkgo]

seems so wrong, because I'm kinda saying 3 hours

[round isle]

????

[viscid ginkgo]

it would look right if it was hr/3

1hr/3

20 mins is 1/3 of 1 hour

so it makes sense logically

[round isle]

Yes

1 min = 1 hr / 60

So 20 min = 20 hr / 60

Just multiply both sides by 20

All of this becomes second nature soon with practice

[viscid ginkgo]

well I'm calculating to find the distance traveled

if it's 20hr/60 then isn't that 7mi/hr²

[grim wharf]

please help;
is this a Yes or No?

[dire rampart]

yes

[vale nimbus]

i dont know if this belongs here since its a physics problem but i have cos(a) = (x)/(y*z) (x,y,z are actual numbers in the problem)

i have to find what angle a is

i think i have to use Arccos or something for it but we havent covered that in math class yet

[vital sedge]

So what you can do is use arccos at both sides

a = arccos((x)/(y*z))

Is the angle 0deg<a<360deg or are you looking for multiple answers?

because if you're just looking for one answer then hitting cos^-1(x/(y*z)) should be enough

@vale nimbus

[vale nimbus]

was it really that simple

thanks man

[vital sedge]

@vale nimbus np mate

[static kiln]

I need help

[upper karma]

@static kiln DM = 4r + r + 5

@static kiln what can you do next

[static kiln]

5r + 5

[upper karma]

no i meant what else do you know about DM

[static kiln]

It’s 60

[upper karma]

so what can you do

[static kiln]

Is the value of r 30

[crisp phoenix]

guys

[upper karma]

i don't know, is it?

[static kiln]

I think it is

Am I wrong

[upper karma]

why do you think it is 30?

[static kiln]

Because dm is 60 and it is split in 2 and if u divide it it’s 30

[upper karma]

what does that have to do with r, though

[static kiln]

Wait is it 11

[upper karma]

i don't know, is it?

[static kiln]

Because 4 times 11 equals 44 and 11 plus 5 is 16 and 44 plus 16 is 60

[upper karma]

@static kiln are you guessing the answer?

[static kiln]

No

I looked at the choices

And I saw 11 and did the math

At first I didn’t even look at the choices so that’s why I said 30

Is 11 wrong?

Okay thanks for answering me

[onyx basin]

first off people have lives

secondly, you can check it yourself

[static kiln]

I’m leaving this discord y’all can’t help

[onyx basin]

lmfao okay cya

[upper karma]

Lol

[halcyon coyote]

[upper karma]

what

i went to eat

and i asked him if he was guessing the answer

so i suppose the answer is yes

[onyx basin]

i dont think he guessed

[upper karma]

he did

he said "i saw 11 and did the math"

so he thought that looked like the one that is the most right lol

[onyx basin]

oh

he had multiple choice

well then

yeah he guessed

lmao

[crisp phoenix]

can someone please help me with this quickly

[onyx basin]

ok let's think about it

you know the base

you know the area

A = base * height / 2

for now, we're solving for height

h = 2 * A/b

now we know the height, and we know the base

if we drew in the height, we'd find that the isosceles triangle splits into two equal right triangles

divide the base by two to find the base for one right triangle

use pythagorean theorem to solve for length of the hypotenuse

and that's your leg

[viscid ginkgo]

if we have omega = 4 radian / second, r = 2 in and t = 5 sec

doesn't the second become sec²

which is (1/60)²

we get 4 rad/second = s / 10 inches / second

so 4 / sec * (10 in. / sec)

40 in. / second²

[gritty sail]

How these equal

Going from top to bottom

A+B+C=180 btw

This too

[viscid ginkgo]

nvm I found my answer. 60 ^2 seconds/ 60^2

[brazen depot]

How would I do question 6 or 7? I could not solve it at all 😂

[viscid ginkgo]

@brazen depot do you still need help with this?

[brazen depot]

No i have solved it after asking my classmate! Thank you though :)

[viscid ginkgo]

ok np

[quick mesa]

This is just a review but I've honestly completely forgotten how to do segment proofs

What I'm having trouble with is at #5 because I cant tell whether I should use definition of midpoint or angle bisecter

An explanation is also much appreciated 😁

[novel flax]

Transitive Property @quick mesa

because 4 is PQ = NM and 3 is PN=NM so when you combine them you get PN=NM=PQ or PN=PQ

[mellow flicker]

hey

[round isle]

yes

[golden panther]

guys whats the best way to find the exact answer to y=tan^1(1) without using a calculator

[rich wolf]

@golden panther