help-0

[lone heart]

Please don't occupy multiple help channels.

[west owl]

with #11 , i thought to simply use trig, but the answer subtracts the answer that i got from 180

[tardy stag]

when you're measuring angles you need to move the vectors so that the tails touch

so sliiiiiide that bottom vector over to the right before measuring the (much bigger) angle to the hypotenuse vector

[west owl]

okok

wait i think i may be confused with the diagram

oh wait i gave them a 90 degree angle

oh my gosh

wait still can’t get it

[tardy stag]

this is the angle you want to measure

[west owl]

okay, so i could still use my strategy then subtract from 180

i just dont seem to understand how you can move it

and if i weren’t to draw it in that way , how would the 4N act on it

[tardy stag]

vectors have a direction and a magnitude
they do not have a specific position

wouldn't it be most natural to draw the force vectors all originating at one point anyway?

since the object is in equilibrium

[west owl]

sure , i can try thay

[tardy stag]

shouldn't the 3 and the 4 be at right angles?

like in your original diagram?

[west owl]

i’ll redraw , lol my brain isn’t working today

[lone heart]

@west owl Has your question been resolved?

[lone heart]

@west owl Has your question been resolved?

[lone heart]

@west owl Has your question been resolved?

[west owl]

.close

[lone heart]

Channel closed

Closed by @west owl

Use .reopen if this was a mistake.

[lone heart]

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[upper sinew]

Heyo i was wanting to convert this to graph notation so that i can write a python function but im lost as to where to start
For this tournament a structure is used where all games are set at the beginning. The
committee has determined that the following properties are sufficient:
• For every pair of distinct players, either they play against each other, or there are at least two
other players that they both play against.
• All players have the same number of games.
So for example, if Alice and Bob don’t play against each other then it’s still OK as long as they both
play against two players in common, say, Charlie and Denise

[lone heart]

@upper sinew Has your question been resolved?

[wooden crag]

What do you mean graph notation?

[upper sinew]

Disregard that, i just dont know where to start

Graph like
def N(V, E, u):
"""Returns the set of vertices in V that are adjacent to u given edges E.

If (V,E) is the entire graph, returns the neighbourhood of vertex u."""
assertIsUndirectedGraph(V, E)
return { v for v in V if (u,v) in E }

def NS(V, E, S):
"""Returns the set of vertices in V that are adjacent to a vertex in S given edges E.

If (V,E) is the entire graph, returns the neighbourhood of S."""
assertIsUndirectedGraph(V, E)
return { v for v in V for u in S if (u,v) in E }

[wraith stratus]

!original

[lone heart]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

@upper sinew Has your question been resolved?

[upper sinew]

I've model the tournament as a graph where each player is a vertex and each game is an edge connecting two vertices. Graph as G(V,E)
where V
is the set of vertices (players) and E
is the set of edges (games).

For every pair of distinct players, either they play against each other, or there are at least two other players that they both play against.
i.e for every pair of distinct vertices, either there is an edge between them, or there exist at least two common vertices adjacent to both. In graph theory, this is known as the property of a strongly connected graph.

All players have the same number of games.
i.e all vertices have the same degree. In graph theory, this is known as the property of a regular graph.

does this seem right?

[wraith stratus]

are you given the set of edges?

and you're meant to determine if the graph satisfies that property?

did i read good

[lone heart]

@upper sinew Has your question been resolved?

Channel closed

Closed by @upper sinew

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[alpine sable]

Can anyone help me with algebra 2?

[sharp gate]

Yeah just send your question

[alpine sable]

well there is a lot.. I have no help, I'm losing it. let me get some.

[spare ocean]

well start with the easiest assignments you struggle with and gradually receive help w all of them ^^

[alpine sable]

you are so sweet thank you.

[spare ocean]

Do you wish for me to explain why, or just the answer?

[alpine sable]

Explain if you could

[spare ocean]

To figure out which confidence interval will have the widest range of values, youll need to understand how confidence intervals work.

So a confidence interval gives a range that likely includes an unknown population parameter. The width of a confidence interval depends on:

- sample size (n)
- the standard deviation (σ), 
- chosen level of confidence chosen.

In your case, the sample size is 450 and the standard deviation is 13, which stay the same for all the intervals. What changes between the different confidence intervals (80%, 90%, 99%, 85%) is the level of confidence. Agreed so far?

[alpine sable]

Okay, I think I understand that part.

[spare ocean]

Are you familiar with something called the Z-score?

[alpine sable]

I am not.

[spare ocean]

Okay, so the confidence level is linked to a critical value from the normal distribution, called the Z-score.

Whats import is that higher confidence levels have bigger Z-scores. When the confidence level goes up, the Z-score gets larger, making the confidence interval wider.

[alpine sable]

Ohhh okay, that makes sense

[spare ocean]

So which of your options would give the highest z-score?

[alpine sable]

wouldn't it be 99% because thats the highest number?

[spare ocean]

Yes, though you reasoning could use some refining that is correct

[alpine sable]

So that means the answer is 99%? and ohh?

[spare ocean]

yes

[alpine sable]

Thank you so much

[spare ocean]

Out of your options 99% will have the highest z-score, and therefore the widest range

[alpine sable]

So the higher the number the wider the range

[spare ocean]

In the case of confidence intervals, yes, the z-score increases as the % goes up, consequently, the range gets wider

what are you studying, AP class?

[alpine sable]

Ohh okay! and no it's just normal highschool Algebra 2

[spare ocean]

mhm, fair enough

[alpine sable]

I am not smart enough for AP classes

Math and me don't go together well, I do okay in everything but math.

[spare ocean]

Math can be quite tough, but everything can be learned :)

okay next question, lets see

[alpine sable]

You are so sweet thank you.

[spare ocean]

My pleasure

[alpine sable]

Yeah these next ones just confuse me

I think the answer is D, but I am very unsure.

[spare ocean]

Well, the first one is def wrong

[alpine sable]

Yeah

[spare ocean]

Well to be honest, im unsure myself but if I'd have to guess it'd be B

[reef pier]

it's B

[alpine sable]

Thank you guys!

My answer was so off haha

[spare ocean]

diversity helps capture the variability in a population, you can achieve such w more sample groups

[alpine sable]

Ohhh! that makes more sense

[reef pier]

here's another way to think about it, this is how confidence intervals are actually calculated

the narrower your interval, the more confident you can be

[alpine sable]

I have never seen that before

[reef pier]

and as n (the sample size) gets bigger, the confidence interval gets narrower

no worries if you haven't seen it, i haven't seen this before just now either lol

[alpine sable]

OHHHH

wait that makes more sense

[reef pier]

i was just curious exactly what the relationship between sample size and confidence was

[wooden pewter]

Isn't this the Margin of ERror formula

[reef pier]

the term after the +/- is the margin of error formula, yes

[wooden pewter]

Oh makes sense, except that I find this format a bit easier

[alpine sable]

can you guys explain this to me too?

[wooden pewter]

True, true, population

[reef pier]

and in general, let's say i have a population of adult men in the usa and i was trying to figure out what the average height of the population was. if i take a sample of 10 men and find the average height to be 5'9, i can be a little bit confident that the actual population average height is 5'9, but it could be a fluke

when i increase my sample to 1000 men and i also get the average height as 5'9, i can be more confident

which means my confidence interval gets narrower

[spare ocean]

True

[alpine sable]

OHHH that makes sense

thank you!

[reef pier]

of course!

[spare ocean]

A census gathers information from every individual in a population, not just a sample. This makes it comprehensive and ensures that the data collected represents the entire population accurately (as a variable). Hence, the statement is true.

[alpine sable]

Thank you so much for making me understand

[reef pier]

this is some hard algebra 2 lol

we never did statistics in algebra class

[alpine sable]

My grade went up to a 58!

[reef pier]

hooray!

[spare ocean]

True, im fairly sure

[alpine sable]

Oh i got that one!

I turned in thr assignment

[spare ocean]

Literally though

[spare ocean]

I cannot believe this is Algebra 2

[reef pier]

ooh these are fun

@alpine sable do you understand what a geometric sequence is?

[alpine sable]

I don't

My school doesn't explain anything to me

They just give it without lessons or anything

[reef pier]

we say a sequence of numbers is a geometric sequence if each number in the sequence can be obtained by multiplying the previous number by some fixed "common ratio"

for example, the sequence 1, 2, 4, 8, 16, ... is a geometric sequence

each number can be obtained by multiplying the previous number by a fixed ratio, in this case 2

[wooden pewter]

Ohh shii cooking it's C

[alpine sable]

OHHH

[reef pier]

so notice that geometric sequences and exponentials relate to each other a lot

instead of multiplying repeatedly by 2, i can multiply by 2^3 to jump 3 steps ahead in the sequence

[spare ocean]

i dont think you were supposed to give a answer just yet xd, though I suppose im guilty of it as well

[reef pier]

does that make sense?

[alpine sable]

yes it does

[alpine sable]

thank you! I am trying to understand though lol

[wooden pewter]

Lol srry 😭

[reef pier]

now in this sequence, what's your common ratio?

[alpine sable]

1

its adding by 1

[reef pier]

try again, the common ratio is what the previous term gets mulitplied by to get the next term

[reef pier]

oh wait are you looking at the n = 2, 3, 4, thing? those just correspond to indices

[alpine sable]

Yeah

[reef pier]

like those are the numbers corresponding to each item in the sequence

as in the 1st term, the 2nd term, 3rd term, and so on

[alpine sable]

I'm confused haha

[reef pier]

that's not the actual sequence

[wooden pewter]

the formula for terms 2, 3, 4.... n should read an = 4/3an-1 , which means the previous term (the an-1) is multiplied by 4/3. The second through 4th terms of the sequence should look like:

a2 = -4/3
a3 = -16/9
a4 = -256/81
The nth term of the sequence should look like:
an = (4/3)n-1

[reef pier]

@alpine sable to clarify, the sequence is given by a_1 = -1, a_n = 4/3 * a_(n-1)

2, 3, 4, ... is not the sequence they're talking about

[alpine sable]

Ohhh

[reef pier]

those are values of n corresponding to terms in the sequence

the first term is a_1

[alpine sable]

I think I sort of understand

[reef pier]

the second term is a_2

so in general the nth term is a_n

[alpine sable]

My brain isn't good with understand math concepts

But I think I am starting to get it

[reef pier]

it's no worries, it comes differently to everyone

[alpine sable]

thank you

[reef pier]

so yeah notice the common ratio is 4/3?

oh okay for this one

[alpine sable]

Yeah! I understood to multiply

[reef pier]

you could multiply 2 by -4 over and over again until you get the 8th term of the sequence

that kind of takes a while though

[alpine sable]

Is there a faster way?

[reef pier]

there is

a much faster way

[alpine sable]

How?

[reef pier]

a way that lets you instantly find any term

for a geometric sequence with first term a_1 and common ratio r

the nth term of the sequence is given by a_n = a_1 * r^(n-1)

[alpine sable]

uhhhh

[reef pier]

think about it, the first term is when n = 1

so the exponent is 1 - 1 which is 0, so you don't multiply by any r's

and you just get a_1 = a_1

[ocean seal]

joren

[reef pier]

when you want the second term, n = 2

you get a_2 = a_1 * r^(2 - 1) = a_1 * r

which is exactly what you'd expect, the second term is the previous term multiplied by the common ratio

[spare ocean]

$a_2 = a_1 \cdot r^{(2 - 1)} = a_1 \cdot r$

[ocean seal]

joren

[reef pier]

if you kept going, the third term would be the second term multiplied by r, and the second term is the first term multiplied by r, so the third term would be the first term multiplied by r^2

[alpine sable]

So I plug in the 2 and the -4?

to find the 8th term?

[reef pier]

make sure you understand this formula first

because this shouldn't be something you have to memorize

it should just make sense as a consequence of repeated multiplication

[wooden pewter]

To find the 8th term of the geometric sequence where the first term a1 is 2 and each term an is defined as -4 times the previous term an-1, we can calculate each subsequent term with that

[alpine sable]

I think I understand the formula

[alpine sable]

ohhhhh

[fresh silo]

Halloo

[reef pier]

so now if you want to find in general the nth term of your sequence

you can plug in a_1 = 2 and r = -4

and you get $a_n = 2 \cdot (-4)^{n-1}$

[ocean seal]

neil

[fresh silo]

Where do i ask doubts about statistics??

[reef pier]

grab any of the unoccupied channels, look on the left

[wooden pewter]

So by that logic we can just:

a1 = 2
a2 = -4 x 2 = -8
a3 = -4 x -8 = 32
a4 = -4 x 32 = -128

until u reach to the 8th term

[wooden pewter]

Or u can just use the help forum

[reef pier]

or if you don't feel like multiplying out the 7 previous terms to get the 8th term, you can directly plug n = 8 into this

this is useful when you're trying to find a term that's super far into your sequence

[alpine sable]

So its 8,192?

[reef pier]

if i asked you for the 100th term, you don't want to sit there multiplying out the previous 99

[alpine sable]

Ohhhhh okay!

[reef pier]

i'm getting -32768

[wooden pewter]

Same

I just did it that way to make it more simple lol but u do u

[alpine sable]

oh?? I missed 1 number

that was my bad

I needed to multiply one more time

[wooden pewter]

Crazy

[alpine sable]

LOL

[reef pier]

another advantage of this shortcut formula is you don't need to count and keep track of how much you're multiplying

[reef pier]

instant answer every time

[alpine sable]

I wrote that down

[reef pier]

so notice the 5th term will be the first term multiplied by the common ratio 4 times

[reef pier]

so the fifth term should be a_1 * r^4 = 24 * (1/3)^4

which works out to 8/27

[alpine sable]

So i got true

[reef pier]

yes

[reef pier]

this one is just repeatedly multiplying by -4 and checking that they did that multiplication correcly

did they do it correctly?

[alpine sable]

No?

yes

[reef pier]

no, they started out multiplying by -4 but they only multiply by 4 after that

[alpine sable]

sorry

Wait?

[reef pier]

you were right the first term

[alpine sable]

2 negatives make a positive

[reef pier]

side note i accidentally clicked your discord thing and i fw nf so hard

[alpine sable]

its okay haha

so its false?

[reef pier]

that one is false, yes

they didn't correctly multiply by the common ratio

and for that last one, i'm sure you could figure it out?

[alpine sable]

I'm gonna try!

wait

but it doesnt have a term I need

[reef pier]

the one where you're trying to find r?

[alpine sable]

yes

[reef pier]

you don't need any more terms, you can get it using just the information they've given you

what do you know

from what they gave you

[alpine sable]

multiply the -1 and 4/3

?

[reef pier]

yeah, and how'd you know to multiply by 4/3?

[alpine sable]

It's the a^n

[reef pier]

yeah it says $a_n = 4/3 \cdot a_{n-1}$

[ocean seal]

neil

[reef pier]

we defined the common ratio as the ratio between the current term and the previous term

as in the number that you have to multiply the previous term in the sequence by to get the next term

this relation tells you that the nth term of the sequence is exactly 4/3 multiplied by the previous term

which means 4/3 must be your common ratio?

[alpine sable]

So the answer would be -4/3?

[reef pier]

not -4/3

[alpine sable]

because you have to multiply the -1?

[reef pier]

-4/3 would be the second term in your sequence

-1 is the first term in your sequence

you multiply by 4/3 to get the next term

so your actual sequence goes -1, -4/3, -16/9, -64/27, ...

but the actual common ratio is what you multiply by each time

which isn't -4/3, it's 4/3

[alpine sable]

OHHHH

Wait that makes sense

[reef pier]

good

to clarify, there's a big distinction between terms in your sequence and the common ratio

the common ratio is the rule that determines what the next terms in the sequence are based on the previous terms

[alpine sable]

You are a literal angel, I have been having mental breakdowns for weeks oveer this.

and that makes sense

[reef pier]

oh i'm sorry this class has been such a stressor

i love helping people learn math though so it's what i'm here for lol

[alpine sable]

Math always is for me, nobody in person has been willing to help,

this was my last resort before giving up

[reef pier]

math discord never fails lol

[alpine sable]

and you are so sweet, will you be on for longer?

[reef pier]

i'll probably be up a while

you can also dm me if you'd like

[alpine sable]

Thank you so much

[spare ocean]

thats the start of a beautiful friendship if I've ever seen one 😂

[alpine sable]

For real

[reef pier]

bonding over math is fr crazy

i've made a couple friends through math though lol

[alpine sable]

Really?? haha

thats crazy

[spare ocean]

isnt it bed time for you americans though, should be about 3am

[alpine sable]

Yeab it's 3 am

yeah*

but I need to pass

[reef pier]

well i'm a math major in university, i kinda have to make math friends

[alpine sable]

or I'm going to keep getting dragged down and freaking out

[spare ocean]

I major computer science

[alpine sable]

and oh?? thats cool!

[spare ocean]

basically maths until 3rd year

lol

[reef pier]

oh that's sick, i'm also a cs major

[spare ocean]

Taconese feeling left out

[wooden pewter]

Y'all have accomplishments in life meanwhile I'm just gonna graduate hs

[spare ocean]

haha dont stress it

[reef pier]

be proud bro, that's an accomplishment in and of itself

[spare ocean]

i miss my HS times, much simpler times

[reef pier]

fr scared i peaked in hs

but there's no way lmao

[wooden pewter]

I'm taking basically the equivalent of SAT exams rn lol

[spare ocean]

where are you from?

[alpine sable]

fr im just trying to graduate

[spare ocean]

SAT is american?

[wooden pewter]

Belize

[wooden pewter]

That's why I said the equivalent

[reef pier]

im just a silly american idk where belize is

or if that's a country or not

like i'm actual dogshit at geography ngl

[spare ocean]

its below mexico

[wooden pewter]

American acitivities and yes it is

[reef pier]

lmaoo

[wooden pewter]

U just like me fr

[spare ocean]

southern of mexico iirc

[wooden pewter]

Exams I taking rn are CXC

[reef pier]

oh god, these things

[alpine sable]

yeah.....

[reef pier]

firstly, that second answer is true

[spare ocean]

No i was wondering tbh, im not familiar with the american education system

[alpine sable]

I'm gonna be so honest I don't even need you to explain these

I won't understand haha

[reef pier]

i don't feel like i'm just giving you the answer for that one since it's a T/F and if you haven't seen it before you wouldn't know

[alpine sable]

I've been trying to learn this since my freshmen year

[reef pier]

okay well you know how you can graph lines?

like y = x

or other curves

[alpine sable]

all of it haha

yeah I do

I think

[reef pier]

let's say instead of graphing y = x, you wanted to graph y > x

what does that even mean?

it corresponds to a region in the coordinate plane

let me show you

[wooden pewter]

The first inequality represents a hyperbola with a solid boundary because it is less than or equal to 1, the second inequality represents a circle with a dotted boundary because it is greater than 36, so that means that the shaded region on the coordinate plane has a boundary that is both solid and dotted so answer is true

[alpine sable]

y is bigger than x?

[reef pier]

yes

it's not just a line now

[alpine sable]

oh wait that actually kind of makes sense

[reef pier]

it's all points (x,y) satisfying y > x

[alpine sable]

ohhhh

[wooden pewter]

[reef pier]

this is how you can visualize these sorts of inequalities

[alpine sable]

ohh is that desmos?

[reef pier]

they correspond to shading regions around graphs

yes

[wooden pewter]

I hate drawing inequalities

[alpine sable]

Ive used that before

[reef pier]

the dotted line means that it's > or <, if it's a solid line it's >= or <=

and think about it, if y > x then y can't equal x, and the line is all points where y = x

which is why the line is dotted

but if y >= x, it would be a solid line

[spare ocean]

took the easy way out with desmos, next time I expect it in LateX

[reef pier]

😭 i just chatgpt my latex

[spare ocean]

oh you one of the lazy ones huh

cant blame you

[reef pier]

checking that a point is a solution to a system of inequalities is significantly easier than fully solving the inequalities

[alpine sable]

huh??

[reef pier]

they give you two inequalities, right? and they give you a point (5,1)

[alpine sable]

yes

[wooden pewter]

To check if a point is a solution to the system of inequalities, we substitute the point into both inequalities. For the point (5,1):

First, substituting (5,1) into y > 2x^2 - 3 gives 1 > 47, which is false.
Second, substituting (5,1) into y < -x^2 + 8 gives 1 < -17, which is also false.
Since both statements are false, the point (5,1) is not a solution to the system of inequalities, so the answer is false

[reef pier]

the point (5,1) is a solution to that system of inequalities if when you plug in x = 5 and y = 1 into the inequalities, both inequalities are satisfied

[alpine sable]

OHHHH

wait how tf am I starting to understand some math

this is crazy to me

[spare ocean]

well math makes no sense until you get it

xd

[alpine sable]

Thats true haha

would this be false?

[spare ocean]

I'd say it gets enjoyable when you've gotten past the initial learning curve tho

[alpine sable]

Yeah??

[reef pier]

does x = 0 and y = 0 satisfy x^2 + y^2 < 9?

[alpine sable]

wait doesn't 0 go with anything?

[reef pier]

not necessarily

what do you get for x^2 + y^2 when you plug the point in?

[alpine sable]

2,0, 0,2?

[reef pier]

are those ordered pairs?

where'd you get those numbers

[alpine sable]

Well if you have 2 and x you add 0?

[reef pier]

ah that might be the problem, x^2 means x to the second power, or x squared

let me format it better

the inequality is $x^2+y^2 < 9$

[ocean seal]

neil

[spare ocean]

and you have point (0, 0)

[reef pier]

if x and y are 0

you have 0 squared plus 0 squared

[alpine sable]

oh yes

its true then?

[reef pier]

it is, since 0 < 9

[alpine sable]

because 0 is less than 9

[reef pier]

but notice 0 isn't always a solution no matter what

what if this inequality was $x^2 + y^2 > 9$

[ocean seal]

neil

[spare ocean]

bet u didnt have to chatgpt this did ya

[reef pier]

hey i at least know a little latex lol

wrote a paper or two a few years back

but i don't remember all the fancy other stuff

[spare ocean]

thats fair, latex can be quite enjoyable when you've got the time

[alpine sable]

this is so cute haha

but uhh true?

😭

[spare ocean]

well plug in the (0, 0) in again and see what happens

[alpine sable]

nothing happens with 0,0

[spare ocean]

so the point we have is (0, 0), correct?

which means both the x and y are zero right?

[alpine sable]

yes

[spare ocean]

$x^2 + y^2 > 9$ replace the x for a zero, and the y for a zero

[ocean seal]

joren

[spare ocean]

literally just swap them out, what do you get?

[alpine sable]

0>9

[spare ocean]

yes

is that true?

[alpine sable]

No

[spare ocean]

Correct

[alpine sable]

wait

[spare ocean]

$x^2 + y^2 < 9$ and for the one you did before

[alpine sable]

isnt it 0<9

[ocean seal]

joren

[spare ocean]

yes

[alpine sable]

so its true

[spare ocean]

he just swapped the < for the > to show you something

[alpine sable]

ohhh

[spare ocean]

but for the question, its $x^2 + y^2 < 9$

[ocean seal]

joren

[spare ocean]

pluggin in the zero's gives you 0 < 9

which is true

[alpine sable]

so its true because 0 is smaller than 9

[spare ocean]

yes

[reef pier]

yeah sorry, in your problem it's true because 0 < 9

[alpine sable]

its okay haha!

I was just confused

[reef pier]

i only brought up the switching the inequality to show you that 0 isn't always a solution

it depends on the actual inequality

[spare ocean]

true

[alpine sable]

ohhhh

that makes sense

and true?

[reef pier]

yeah and this is just what i told you about how the shading and solid lines and stuff are represented

[alpine sable]

OHHH

I HAVE A 59

only 11% more to go

[wooden pewter]

Tbh I'm surprised that they even give true or false questions for Math

[reef pier]

why is 70 the goal?

[spare ocean]

shes applying for AP classes

duh..

neil ure slow

[alpine sable]

70 is passing

and no

[spare ocean]

ah

nvm

[alpine sable]

no Ap haha

70% is just the passing grade in PA

[reef pier]

also do you get multiple attempts on these

[wooden pewter]

Lmao

[spare ocean]

might be cus its 9am here

[wooden pewter]

Last year my ahhh got an F in math mid semester

[reef pier]

where are you?

[alpine sable]

and yes I get multip,e attempts

[spare ocean]

Netherlands

[alpine sable]

I failed 2 quarters of classes already

[wooden pewter]

Lucky

[alpine sable]

so I can fail another one

[reef pier]

ah sick i've always wanted to visit

[alpine sable]

or I fail the year

[spare ocean]

for the weed or?

[wooden pewter]

Yea the studying is worth it then

[alpine sable]

exactly

[wooden pewter]

Yummers

[spare ocean]

ure too close to columbia

no wonder

[wooden pewter]

Lmao

But nah I never had weed before

[wooden pewter]

Gl bro fr

[spare ocean]

eh you can keep it that way, take it from me

its quite, boring?

[wooden pewter]

Ngl I'd rather be an alcoholic

[spare ocean]

oh nah

and here I thought you were a responsible individual

alcoholic, fss

[wooden pewter]

I'm here in Math procastinating when I have an exam tmmr

What u expect lol

[spare ocean]

ive got an exam tmmrw as well

[alpine sable]

OH GOOD LUCK GUYS!!

on the exams

[wooden pewter]

Rip

[spare ocean]

and im stuck on a partial integration in my private programming project

[reef pier]

i have returned

[spare ocean]

:D

neil u got some more

[alpine sable]

welocme back!

[spare ocean]

to answer

[reef pier]

slide the integral

i love integrals

[alpine sable]

only if you want haha

[reef pier]

it's unhealthy

how much i like integrating

[alpine sable]

oh.....??

[spare ocean]

integrating is lovely

im afraid though this problem ive ran into isnt a math problem

but rather

I cant decide the proper way to execute it

[reef pier]

teaching you this right here is def a little tricky if you haven't seen it before

you'd have to understand the unit circle and what the graphs of these functions look like

[alpine sable]

You don't have to teach it then, this is the only assingment like this I think

either way I am okay with it

I just prefer to learn haha

[wooden pewter]

So here on the interval (0,2pi), the highest point on the graph of f(thetha) = sin(thetha) is 1, which occurs at thetha = pi/2 so Ig answer is b

[reef pier]

would you like me to demonstrate how to solve them instead lol

rather than teach

[alpine sable]

yes that works haha

[reef pier]

ig demonstrating is sorta teachin

[alpine sable]

it is

[reef pier]

yeah sin(theta) ranges from -1 to 1

so sin(theta) = 1 is the highest point

[wooden pewter]

Yea

[spare ocean]

careful neil about to drop his paypal.me 👀

[reef pier]

and you can solve that equation for theta on this interval to get theta = pi/2

[wooden pewter]

Btw off topic but theta has the same pronounciation of female chest in spanish

[reef pier]

me gustan las tetas

[wooden pewter]

Real

[alpine sable]

huhhhhhhhhh

oh my god

[reef pier]

took spanish 5 for a reason

[alpine sable]

HAHAH

[reef pier]

and it was to be lewd in multiple languages

[alpine sable]

thats so real

[reef pier]

but yeah your max is (pi/2, 1)

[alpine sable]

okay

[wooden pewter]

Ong

[reef pier]

@alpine sable are there more

[alpine sable]

yes

[reef pier]

this should be 2

cosine is 2pi periodic, the interval has length 4pi so 2 periods

[wooden pewter]

Wait is it 2?

I thought it was 4

[reef pier]

what are they defining as a cycle

,w graph cosx

[ocean seal]

Results provided by WolframAlpha

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

Requested by nightshade5107

[wooden pewter]

Since aren't there like 2pi units every full period

Oh wait

[reef pier]

cycle is like when it starts repeating itself

so if you start at 0, it doesn't look the same again until at 2pi

[wooden pewter]

[reef pier]

i think they're using cycle and period interchangeably

[alpine sable]

so its repeated

[reef pier]

yeah, the graph repeats itself every 2pi units

and your interval of x values is from -3pi to pi which is 4pi units wide

which means your graph repeats itself twice

[alpine sable]

ohhhh

[reef pier]

this one is 1.5 cycles of sin

[alpine sable]

so 1/2?

[reef pier]

it repeats itself once from -pi to pi, and then accomplishes half of that cycle from pi to 2pi

no

1 and 1/2

[alpine sable]

i was about to type that haha

i missed the `

1

[reef pier]

ah okay

[alpine sable]

so it repeats that?

[reef pier]

this is just 0, pi, 2pi

[reef pier]

wdym by repeats that

[alpine sable]

like it repeats by 1 1/2

[reef pier]

when it asks how many cycles there are, yeah it's basically like how many times does the graph repeat itself

[alpine sable]

and that was my guess actually haha for the 3rd one

Ohhhh that makes sense

[reef pier]

oh that's good, if you take some time when you get a chance to watch a video on the unit circle these questions will make so much more sense

[alpine sable]

and the last one is false I think?

and where would i find that at?

[reef pier]

and that looks like the right graph to me

[reef pier]

just search youtube unit circle trig functions

and solving trig equations

[alpine sable]

ohh okay!

[reef pier]

those two searches will give you everything you need

khan academy has some good stuff

[alpine sable]

Ill write that down

[alpine sable]

how so??

it goes above 3.14 I think?

[reef pier]

would you be able to send that problem separately

or try to zoom in on the graph

i can't really read the units

[alpine sable]

I cant zoom in 😭

I cant even read the numbers

[reef pier]

from what i see, the y axis units are at intervals of 0.5

and the x axis has intervals of pi/2

[alpine sable]

ohh so it would be true??

[reef pier]

it looks like it

let me pull up a graph rq

[alpine sable]

you are right

I got a 100%

OH MY GOD

MY GRADE IS AT A 60%

[reef pier]

this is good

[alpine sable]

OH MY GOD

IT HASNT BEEN THAT HIGH IN MONTHS

YOU ARE A LITERAL ANGEL

[reef pier]

i'm happy to help

but please don't forget about actually learning this stuff

future classes will build on this

[alpine sable]

I know! I wrote down the khan academy

[reef pier]

good

and i don't check my discord too often but if you message me i'll be able to answer any questions you have

[alpine sable]

Thank you so much

[reef pier]

probably not this late at night usually though lol

[alpine sable]

Thats okay! I'm not normally on this late either

[reef pier]

okay well i'll take this as my sign to head to bed then

good luck!

[alpine sable]

Sleep well!

Thank you so much!

if anyone else is here and able to teach me!

[reef pier]

ah i haven't left yet

do you want me to handle these as well rq

[alpine sable]

It's okay, you need sleep! it is important!

[reef pier]

i lied lmao i can never fall asleep on time anyway so i was just planning on infinite scrolling

[alpine sable]

oh hahqa

haha*

then sure!

[reef pier]

i'll try my best to explain my reasoning

but it won't mean much to you if you haven't seen these before

[alpine sable]

thank you

and yeah I hasvent seen any of this before, I'm just going through all the retakes I need that I failed.

[reef pier]

so sin(2x) = 2sinxcosx

which means $sin(2x)cosx = 2sinxcos^2(x)$

[ocean seal]

neil

[spare ocean]

@reef pier you mind me popping in a small question while ure at it, im super tired and prob overlooking smth silly af

[reef pier]

then you bring the expression on the right to the left to get $2sinxcos^2x - sinxcos(2x) = 0$

[ocean seal]

neil

[reef pier]

sure i can check it out

[alpine sable]

ok I think I understand so fa

far*

[reef pier]

then you factor out a sinx to get $sinx(2cos^2x - cos(2x)) = 0$

[ocean seal]

neil

[reef pier]

then if the product of two things is 0, at least one of them is 0

which means either $sinx = 0$ or $2cos^2x - cos(2x) = 0$

[ocean seal]

neil

[reef pier]

on the interval [0, 2pi), sinx = 0 means that x = 0, pi

then to solve $2cos^2x - cos(2x) = 0$, you can rewrite $cos(2x)$ as $2cos^2x - 1$

[ocean seal]

neil

[reef pier]

then $2cos^2x - cos(2x) = 2cos^2x - (2cos^x - 1) = 1 = 0$

[ocean seal]

neil

[reef pier]

whcih has no solutions in x

so your only solutions are x = 0, pi

,w sin(2x)cosx = sinxcos(2x), 0 <= x < 2pi

[ocean seal]

Results provided by WolframAlpha

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

Requested by nightshade5107

[reef pier]

@alpine sable good with that?

[alpine sable]

That is very confusing, but I undertsand most of it I think

[reef pier]

a lot of it is trig identities and solving trig equations

[alpine sable]

yeah, and I have no clue what trig is haha

[reef pier]

a couple other things you should learn is trig double angle formulas and pythagorean identities

just add those to the list

[alpine sable]

writing it down

[reef pier]

im gonna copy and paste the current problem im on so i don't have to keep scrolling

[alpine sable]

thats okay

[reef pier]

cos(pi/2 - x) is the same as sinx

so it becomes $sinxtanx - sec(-x) = 1$

[ocean seal]

neil

[spare ocean]

Given I have $f(x) = \frac{3}{2} \sin(2x) - \cos(3x)$ and $g(x) = \frac{1}{2} \sin(2x)$, I need to find specific coordinates that are displayed in a graph (ill show in a sec).

So i simplify to: $\cos\left(\frac{\pi}{2} - 2x\right) = \cos(3x)$

and find these two solutions:
$x = \frac{1}{10}\pi + k + \frac{2}{5}\pi$ \
$x = -\frac{1}{2}\pi + k \cdot 2\pi$

Now, these are correct solutions, however only the first solution yields the right results.

[alpine sable]

WHAT IN THE

[reef pier]

then $tanx = sinx/cosx$ and $sec(-x) = 1/cos(-x)$

[ocean seal]

joren

neil

[spare ocean]

ill wait until neil is done my fault

[alpine sable]

No no you go first its okay

[reef pier]

all good, let me solve this current one and i'll work with this

are you solving for the intersections of f and g?

[spare ocean]

ye

[reef pier]

what's the interval you're on

or do you want all sols

cos(3x) is disgusting lmao

[spare ocean]

so im supposed to get the coordinates of abcde

$x = \frac{1}{10}\pi + k + \frac{2}{5}\pi$ \

[ocean seal]

joren

[spare ocean]

gives me them properly

[reef pier]

the other one doesn't?

[spare ocean]

literally though

[reef pier]

does this generate all five of those sols?

[spare ocean]

yes

the coordinates of all of them are out of that solution

[reef pier]

yeah so you got sin(2x) = cos(3x) and you're solving that

hm

and you rewrote the sine, did you just solve pi/2 - 2x = 3x?

[spare ocean]

i rewrote to cos

$f(x) = \frac{3}{2} \sin(2x) - \cos(3x)$ and $g(x) = \frac{1}{2} \sin(2x)$

[ocean seal]

joren

[reef pier]

also, is this formatted correctly?

because you have pi/10 + 2pi/5 and you didn't combine them

and you're just adding k instead of k times some multiple

[spare ocean]

it should be a *

not a +

[reef pier]

okay so you got pi/10 + 2kpi/5?

[spare ocean]

wrongfully formatted

$\cos\left(\frac{\pi}{2} - 2x\right) = \cos(3x)$

[ocean seal]

joren

[spare ocean]

this is when I simplified the f and g

to cos, this is correct

[reef pier]

yeah i followed up to here

[reef pier]

walk me through how you got this

[spare ocean]

I got it on paper, is quicker, let me show u

[reef pier]

oh i see it

pi/2 - 2x = 3x + 2kpi

so 5x = pi/2 - 2kpi and x = pi/10 - 2kpi/5

and you just changed the -k to a k

[spare ocean]

yes

since it shouldnt matter

here the - is shown, the left solution

so granted these solutions are correct, I have two solutions that show the intersect between f and g correct?

[reef pier]

yeah i'm trying to see why your right solution didn't work

[spare ocean]

the two solutions are correct

but the right one is, not used at all?

all the coordinates you see at the bottom of the answers are from the PI/10 solution

[reef pier]

i think both answers are correct and it has something to do with specifically A, B, C, and D

[spare ocean]

Yeah

I think so as well but im unsure what

[reef pier]

so you're between 0 and 3pi/2

ah

k is an integer

[spare ocean]

yes

[reef pier]

the second solution also generates intersections

but k = 0 gives you -pi/2 which isn't in your range

and k = 1 gives you 3pi/2

which is E

[spare ocean]

bruh

[reef pier]

so obviously A, B, C, and D can only be generated by your left solution

[spare ocean]

yep no, that's it

[reef pier]

yay

[spare ocean]

that was dumb

[reef pier]

@alpine sable still awake?

[alpine sable]

yes

I have been watching haha

[spare ocean]

its funny cus this is basically worth no points

lol

[reef pier]

ah still, happy to help

there's this small masochistic urge to solve a math problem

i think it's mental illness

[spare ocean]

thanks for your insight ;)

[spare ocean]

ive got no doubt

freak..

[reef pier]

😭

[alpine sable]

im dead

[reef pier]

sorry i got to here

and we had sinxtanx - sec(-x) = 1

which you can rewrite as $sinx \cdot sinx/cosx - 1/cos(-x) = 1$

[ocean seal]

neil

[reef pier]

cosine is even so $cos(-x) = cos(x)$

[ocean seal]

neil

[reef pier]

and you get $sin^2x/cosx - 1/cosx = 1$

[ocean seal]

neil

[reef pier]

then $sin^2x = 1 - cos^2x$

[ocean seal]

neil

[reef pier]

so you get $(1-cos^2x) / cosx - 1 / cosx = 1$

[ocean seal]

neil

[reef pier]

multiplying through by cosx, you get $1 - cos^2x - 1 = cosx$

[ocean seal]

neil

[reef pier]

which becomes $cos^2x + cosx = 0$

[ocean seal]

neil

[reef pier]

which becomes $cosx(cosx + 1) = 0$

[ocean seal]

neil

[reef pier]

solving $cosx = 0$ and $cosx = -1$ on [0, 2pi) gives x = pi/2, 3pi/2 and x = pi

[ocean seal]

neil

[reef pier]

except that's not an answer choice

fuck

what did i do

[alpine sable]

confusion

is it D?

[reef pier]

sin^2x / cosx - 1 / cosx = 1 --> sin^2x - 1 = cosx --> -cos^2x = cosx --> cosx(1 + cosx) = 0

which gives me exactly what i got

which is apparently wrong

okay so now maddie i'm going to introduce you to my favourite problem solving technique

it's called the wolfram alpha method

[alpine sable]

okay??

[reef pier]

,w cos(pi/2 - x)tanx - sec(-x) = 1, 0 <= x < 2pi

[ocean seal]

Results provided by WolframAlpha

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

Requested by nightshade5107

[reef pier]

just pi is crazy

[alpine sable]

oh??

[reef pier]

idk what i could've fucked up lmao

[alpine sable]

I have no idea

[reef pier]

well

your answers pi :/

[alpine sable]

I guess so

what is wolframalpha

[reef pier]

can't solve them all 😭

it's a computational math engine thingy

way smarter than any of us

great way to check your work on messy computation

[alpine sable]

ohh

[reef pier]

also a great way to get caught for cheating

it's just nice because of the bot in here that lets me directly query it without having to open another tab

[alpine sable]

oh??? thats cool though

[reef pier]

i'll keep trying to solve the rest though

maybe i don't screw these up

so cos(pi/2 - x) = sinx and cos(-x) = cosx by what i explained before

this equation becomes $\sqrt(3)sinx = cosx$

[ocean seal]

neil

[reef pier]

then you have $sinx/cosx = 1/\sqrt3$

[ocean seal]

neil

[reef pier]

so $tanx = 1/\sqrt3$

[ocean seal]

neil

[reef pier]

from the unit circle that solution is x = pi/6 and x = 7pi/6

on our interval [0, 2pi)

and confirming using wolfram

,w sqrt3 * cos(pi/2 - x) = cos(-x), 0 <= x < 2pi

[alpine sable]

I thought it was just c, I am so bad at this

[ocean seal]

Results provided by WolframAlpha

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

Requested by nightshade5107

[reef pier]

don't worry about it, everyone gets better with practice and experience

some of these have tricks to them that aren't too obvious at first

[alpine sable]

Thats true

[reef pier]

and you figure them out by seeing enough of these

[alpine sable]

Thats true

ugh I wish I had a mathematical brain but I underdtand words better than numbers haha

understand*

[reef pier]

i think these are the last two

[alpine sable]

correct

I am falling asleep so badly

[reef pier]

same lol

[spare ocean]

makes three of us

[alpine sable]

😭

[reef pier]

why is bro still here 😭

[alpine sable]

frrr

sleep!

[spare ocean]

cant even solve basic shit anymore

[alpine sable]

after I turn this one in im out

[reef pier]

not that we don't want you here but idk if you're just watching me solve trig equations lmao

[alpine sable]

^

[spare ocean]

well I havent slept for about 36 hours, so im just mindlessly starting at my assignments without doing them

watching you solve trig equations isnt the worst

[alpine sable]

same dude 😭 i havent been sleeping ive been to stressed

[spare ocean]

staring*

https://tenor.com/view/sleepy-sleeping-sleepy-dog-perritodormido-dormido-gif-16542296809354104671

neil tonight

after solving the last two

lmfao

[reef pier]

so you have $cos(x + pi/4) + cos(x - pi/4) = 1$

[ocean seal]

neil

[alpine sable]

fr me to

[spare ocean]

homie is going to sleep thinking about his trig solutions

ait ill be quiet again

[reef pier]

imma do something weird here and let u = x + pi/4, then x = u - pi/4

[alpine sable]

you are okay joren haha

and ok

thats comfusing

confusing*

[reef pier]

just trust me here it's useful

maybe not a commonly taught trick

but making substitutions like these are useful later on in math like calculus

and they're also useful when solving annoying trig equations

[alpine sable]

ohh okay

[reef pier]

so then cos(x + pi/4) becomes cos(u)

and cos(x - pi/4) becomes cos(u - pi/4 - pi/4) = cos(u - pi/2) = cos(pi/2 - u)

the last part where i switched the terms inside is because cosine is even

then i get the equation $cos(u) + cos(pi/2 - u) = 1$

[ocean seal]

neil

[reef pier]

so then that becomes $cos(u) + sin(u) = 1$

[ocean seal]

neil

[reef pier]

hm i forgot exactly how we solve this but im pretty sure this is only true when either cosu = 0 and sinu = 1 or when cosu = 1 and sinu = 0

[alpine sable]

confusion

[reef pier]

so that means either u = pi/2 or u = 0

honestly i'm not sure how exactly how to show why this is the case

i know it's true

but

also eepy lmao

[alpine sable]

thats not an answer though

[reef pier]

no i know

[alpine sable]

thats why I am confuzzled

[reef pier]

that's an answer in terms of u

[alpine sable]

ohh

[reef pier]

the original problem didn't have a u

but u = x + pi/4, so x = u - pi/4

fuck

i didn't change the interval when making the substitution

because when i got u = pi/2 and u = 0

that means x = pi/4 or x = -pi/4

and -pi/4 isn't in the interval

alright here me out

it's a multiple choice

pi/4 is definitely one of the answers so it's either A or B

[alpine sable]

can we use that bot to check it some how?

[reef pier]

when we try 3pi/4 from A, we get cos(pi) + cos(pi/2) which is -1 + 0 which isn't equal to 1

so by elimination, the answer should be B

x = pi/4, 7pi/4

and if i ask wolfram

[alpine sable]

I am so confused haha

[reef pier]

,w cos(x + pi/4) + cos(x - pi/4) = 1, 0 <= x < 2pi

[ocean seal]

Results provided by WolframAlpha

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

Requested by nightshade5107

[reef pier]

this is actually extremely hard for algebra 2

[alpine sable]

it is??

I'm only a junior in HS 😭

[spare ocean]

well it requires quite some prior knowledge

and a solid understanding

[alpine sable]

and I have ni prior knowlege

no*

[reef pier]

yeah this being your first exposure to this stuff and then asking questions at this depth requires way too much understanding

some of those stats questions would get asked in an intro stats class, these trig questions might come in a separate trig/precalc class

but shoving all this in algebra 2 is crazy

[alpine sable]

Thats the WSSD for ya, they just dont care about their students

[spare ocean]

I have these questions as 2 pointer

in uni

[alpine sable]

WHATTT

[spare ocean]

you basically need to do them correctly

to do the rest

[alpine sable]

oh

[spare ocean]

its the "free points" type of questions

[alpine sable]

luckily this is the last math class I will ever have to take

[reef pier]

i mean depending on what you go on to study at college this may or may not become either extremely easy or extremely difficult

[alpine sable]

in pa we only need 3 math classes to graduate

[reef pier]

oh wow that's chill

im from fl, the requirements are also pretty relaxed here

[alpine sable]

oh??

thats good

[reef pier]

but the school i went to was one of those weird competitive schools

[alpine sable]

ohhhh

[reef pier]

where everyone did ap and ib and dual enrollment and stuff

[alpine sable]

yeah hell no

[spare ocean]

numerous fixus?

or whatever its called

[reef pier]

not sure what that is

sounds like a harry potter spell ngl

[spare ocean]

basically you

[alpine sable]

fr

[spare ocean]

do an entree exam

u get a ranking

[spare ocean]

and the top 400 gets in

[alpine sable]

last one

[spare ocean]

or however many spots they offer a year

[reef pier]

oh that's actually kind of what it was

it was an international baccalaureate program

[spare ocean]

I had that for TU delft

u might know about the uni actually

[alpine sable]

y'all are smart 😭

I will never be on that level

Im a writer not a mathmatician

[spare ocean]

ah I was worse than u

at that age

trust

[alpine sable]

I can't even spell im so sleepy haha

[spare ocean]

i wasnt doing much

[reef pier]

aight solving this rq, sin(pi/2 - x) = cosx

[alpine sable]

oh??

[spare ocean]

dont underestimate your ability to learn fast and adapt

[reef pier]

so it becomes $2cosx \cdot sinx/cosx = 1$

[alpine sable]

thats sweet thank you

[ocean seal]

neil

[reef pier]

which becomes 2sinx = 1

sinx = 1/2

which very nicely solves to pi/6 and 5pi/6 on our interval

and i think you should get A?

[alpine sable]

oh shit yeah

[reef pier]

,w 2sin(pi/2 - x)*tanx = 1, 0<= x < 2pi

[ocean seal]

Results provided by WolframAlpha

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

Requested by nightshade5107

[reef pier]

shit

no

wait

that's what i got

yay

[alpine sable]

still at 60% but thats better than what it was

thank you so so so sooooooooooooo much

[reef pier]

happy to help lol

[alpine sable]

and I learned stuff haha

which I am so happy about

[reef pier]

if you have other questions about stuff, i'm also way better at explaining this stuff when i'm not typing it out at 4:30 am

lowkey ong one day im becoming a math teacher

shit will be fun

[alpine sable]

Thank you so much, will you be on tmr?

and yeah??

I'd happily be in your class haha

[reef pier]

i'll probably be on

[alpine sable]

hell yeah

thank you so much

[reef pier]

like i said if you message me i'll get a notif on my phone

i don't keep any other discord notifs on

[alpine sable]

Perfect!