help-10

[frank monolith]

#book-recommendations

[sweet grotto]

Khan academy, Pearson

[hoary sleet]

they do for SAT only right?

[frank monolith]

no

high school too

[hoary sleet]

oh got it

thanks

[obtuse pebble]

@hoary sleet Has your question been resolved?

[obtuse pebble]

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[timid silo]

<@&286206848099549185>

If I want to learn number theory from scratch what should I do ?

[sacred root]

You should study

[high lily]

first ensure you are competent in basic algebra

[timid silo]

what u really mean by number theory?

[verbal geyser]

books on number theory, youtube

[errant lark]

That does not include linear algebra. Does it?

[wicked copper]

Study?

With Books or watch youtube videos ...

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

Do you know any good youtube playlist in number theory ?

[verbal geyser]

https://www.youtube.com/watch?v=qvxKlbdRUyM&ab_channel=TheMathSorcerer

[timid silo]

I think I need to revise that too, do you know any good youtube playlist for that?

[timid silo]

Thanks alot ❤️

[verbal geyser]

nppp

[runic void]

Burton is a good book

I studied from ‘ Elementary Number Theory’ by Thomas Koshy

I don’t know if that is famous but it’s very elborative

[obtuse pebble]

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[rugged escarp]

An introduction to number theory book

[rugged escarp]

Or if u want to learn algebra from basic including number theory then go for higher algebra by hall and knight

[haughty coyote]

#book-recommendations has something, surely

[obtuse pebble]

@rugged escarp Has your question been resolved?

[obtuse pebble]

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[north smelt]

Let the painting speed of the pedro be 600x

And Juan's speed is 400x then

and Pilar's speed is 500x

right?

or lets say 60x pedro's speed

Juan's speed 40x

And Pilar's speed is 50x

60x+40x+50x = 4 hours

[final owl]

how did you get 40 50 & 60?

[north smelt]

ratio

only ratio

could have been 4,5,6

Pedro paints in 6y duration

Juan paints in 5y duration

Pilar paints in 4y duration

Pedro is 50% faster than Pilar

4y+4y×1/2 = 4y+2y = 6y = Pedro's painting time

butt

there is a problem

I missed it

fast paints in less time

For example, if I paint in 10 minutes and you paint in 20 minutes

I'm 50% faster than you

right?

[final owl]

yes I understand

but

there is no given time for Pedro

[north smelt]

ok i'm just saying it randomly

for example Pedro paints in 96y time

then Juan paints in 192y time

because Pedro is 50% faster

am i right?

[final owl]

yes I understand

[north smelt]

but wait a minute

50% difference is not double right?

It should be 3/2 difference.

because, for example, I can eat 10 eggs, you can eat 15 eggs

you eat 50% more than me

but you are 3/2 times me

if you were eating 100% more then i, it would be double

because 15/10 = 3/2

[final owl]

I understand it really does make sense

[north smelt]

okay so

if Pedro paints at 40x speed, then Juan paints at 60x speed

[final owl]

yes

[north smelt]

3/2 times 40x = 60x

so

what was the other man lol

Pilar

okay then

[final owl]

Pilar 8

[north smelt]

20% more means 12/10 times

[final owl]

80

[north smelt]

40×12/10

must be 48

[final owl]

oh yes

you add it to 40

[north smelt]

If I can eat 10 eggs and you can eat 12 eggs

you are 1.2 times

[final owl]

sorry it must be 8 the 20% of 40

[north smelt]

yes

yes

Pilar's speed 48y then

Pedro = 40y
Pilar = 48y
Juan = 60y

We have to add them all because they paint all together

the question says so

[final owl]

they are all equals to 4 hours

[north smelt]

60y+40y+48y = 148y

= 4hours

148y = 4 hours = 240 minutes

then y = 240minutes/148 right?

[final owl]

yes

[north smelt]

If we calculate for Pedro

40×240minutes/148

because Pedro was 40y

= 960minutes/148

[final owl]

64.86

oh wait in minutes

[north smelt]

yes but

it's getting faster and it's impossible

I knew it must have been a mistake

I think we would add bases of -1

i mean

1/40y+1/60y+1/48y ?

[final owl]

yes

[north smelt]

because speed problems are inversely proportional

uhh, its boring lol

[final owl]

wait I'm a little confuse, you multiplied the equation to 10?

[north smelt]

I reversed

If I paint in k time, you paint in 2k time

and if it takes 60 minutes in total

wait

bro i'm confused

frankly i would solve it if i tried but i have to go

bad timing..

[final owl]

sure thanks

[north smelt]

i paint at k speed

you are 2k speed

but you are faster now

speed = m/s

bruh

paint/second

okay its better

[final owl]

there's no speed in the problem

[north smelt]

i paint 1 paint per second

ok but about that

I'm just trying

let's talk about it later

i will write dm

[final owl]

Pedro is 50% faster than Juan
20% faster than Pila

= 4 hours

[north smelt]

you try to solve it with someone else for now

[final owl]

okay sure thanks

I will close it thanks a lot : ))

.close

[obtuse pebble]

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[rough stratus]

Factors of $\cos{4\theta} - cos{4\phi}$ are

[warm shale]

therealtdp

[rough stratus]

I tried using cos C - cos D, but failed

[hearty cove]

how about trying the formula for cos 2 theta?

[whole dock]

Can you show what you got

[rough stratus]

,rccw

[rough stratus]

@whole dock

[whole dock]

Yeah wait

$-2\sin(2\theta + 2\phi)\sin(2\theta - 2\phi)$

[warm shale]

ColdTee

[whole dock]

Where did the other term come from

You missed a negative sign too

[whole dock]

Yeah but you should try this

[rough stratus]

I missed a -ve sign

Shit

[rough stratus]

I expanded both of them using sin2A

[whole dock]

Try this

[rough stratus]

One sec

This right?

,rccw

[whole dock]

Seems correct

You could also use $1 - 2sin^2\phi$ to get rid of that 1

[warm shale]

ColdTee

[obtuse pebble]

@rough stratus Has your question been resolved?

[obtuse pebble]

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[fluid snow]

Could someone give me some harder problem(s) on solving inequalities with products please? This will come up in an university examination, so it should be something on competition-math level, probably

[high lily]

i can whip up a question, but its not gonna be comp level
that stuff is just whack

[fluid snow]

Sure, thank you!

[high lily]

try have a go at

wait

[severe reef]

Well

I saw that

[high lily]

gimme a minute,

lol

[severe reef]

How's this one

[high lily]

have a go at

$(|2x-3| - 3)(|x - 5| - 7)(3x +7) \ge0$

[warm shale]

ℝam()n()v

[fluid snow]

lol thanks! Where did you get that from?

[fluid snow]

Thank you!

[severe reef]

It's from a JEE prep book

[fluid snow]

Alright

I will close this for now, thanks!

.close

[obtuse pebble]

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[obtuse pebble]

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[trim trail]

Can someone please check my solution:

[trim trail]

Typing it here

As $p \equiv 1~mod(~4), 4|(p-1). \therefore$ there are $\phi(4)$ distinct integers whose order $(mod~p)$ is $4$. Therefore, there is a distinct integer $q$ such that $q^{4} \equiv 1~(mod~p)$. As $q^{2}-1 \equiv 0~(mod~p)$ is not a solution since $ord_{p}(q) = 4$, $q^{2} \equiv -1~(mod~p)$ is a solution. Further, as $a^{2} \equiv a^{2}~(mod~p)$, $a^{2}q^{2} \equiv -a^{2}~(mod~p)$. Therefore, $(aq)^{2} \equiv -a^{2}~(mod~p)$. So, $aq$ is a solution

[warm shale]

StatisticalCat

[trim trail]

seems too simple to be the right answer

also ik i have to prove it the other way round assuming if we alr have solutions. im doing it rn

but is this first part correct?

[rotund willow]

The first part is indeed correct, but proving it the other way might be difficult.
Have you already proved which numbers can be the sum of 2 squares ? Because it makes the problem much easier.

[trim trail]

hmmm is the first part correct tho? It seems too easy to be correct lmfao.

Have you already proved which numbers can be the sum of 2 squares ? Because it makes the problem much easier. No I haven't proved this...

I think that's the point of this problem I suppose?

Also, a future problem is

isn't this literally just what is proved in the earlier part?

[rotund willow]

Yeah, makes sense, the next problem just helps set up a criterion based on the prime factor decomposition of the integer

You might want to show that the existence of a solution with p = 4k+3 causes a contradiction

[trim trail]

for the second part of the first q i sent right? Yeah im trying to do that

thanks a lot for the help

im not closing this chat i'll send u a sol if i get it to check or i'll just ask for some slight help

[trim trail]

wait wait wait if i use this to prove

[trim trail]

this

then it wont work cause it says (a, b) = 1

i'll have to write a new proof?

[rotund willow]

the next problem will be easy, you'll just have to say that if p = 4k+3 then it's impossible for gcd(a,b) to be 1

[trim trail]

but how would this prove that gcd is 1 if p = 4k+1

like in the sol to the first question i'm writing aq as a solution

but gcd of aq and a^2 is not 1

[trim trail]

oh I got it NVM

thanks

lemme solve...

[rotund willow]

I have to go, but if you want another way to do this, you can use quadratic reciprocity to solve the problem. I'll be back in an hour so you can ask someone else if you still need some help, or you can DM me and I'll check back. Good luck.

[trim trail]

ohhh ok sure. thanks for your help : ).

idk quadratic reciprocity... haven't learnt that yet...

will try it with fermat's theorem and other primitive roots theorems....

[obtuse pebble]

@trim trail Has your question been resolved?

[obtuse pebble]

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[rustic yew]

I've been stuck for hours.. I can't seem to get a rational function that has a y intercept at (0, -2), and instant rate of change of 0.123 at x=2

[rustic yew]

I have the trig function: g(x)=0.3915sin(pi(x))

so i need to get the rational function to intersect with it at x=2

[polar fossil]

,calc 0.3915 * sin(pi * 2)

[warm shale]

Result:

-9.5889844373238e-17

[polar fossil]

ok so 0

[rustic yew]

This is the best I came up with, but I cant prove how I got here allgebraically and neither contains the digit "3" unless we use the 0.3915 as that

[obtuse pebble]

@rustic yew Has your question been resolved?

[rustic yew]

<@&286206848099549185>

[polar fossil]

ok well 0.3915 definitely includes the digit 3

instead of doing a very small secant line to show slope just take the derivative

[rustic yew]

the what? O.o

[rustic yew]

what are you implying?

[polar fossil]

oh if you don't know what a derivative is don't worry about it

[rustic yew]

that is a big word and i am scared

[polar fossil]

that's why i said not to worry about it

[wintry swift]

does this function meet criteria d)?

[polar fossil]

yeah

[rustic yew]

yes

[obtuse pebble]

@rustic yew Has your question been resolved?

[obtuse pebble]

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• Show your work, and if possible, explain where you are stuck.
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[hasty flume]

Hi can someone help me with these this is my last set of homework for the week I'd really appreciate it if I could get help.

[fringe rivet]

ok we will start with 1

easy enough

Both graphs will start at 0 amd end up at 270

Well start with f(x)

what do you thing is the max

and min

Also how far do you think they are spaced from the information given

which will be your period

[hasty flume]

I see this

[fringe rivet]

Of so what do you think the height is

2sinx

Since we dont have any stretch factor besides 2

[hasty flume]

Wouldn't it be 2?

[fringe rivet]

yep

thats the maximum and minimum

[hasty flume]

Great

[fringe rivet]

Also you dont have a horizontal stretch or compression

so

[hasty flume]

How would I sketch it?

[fringe rivet]

now we have to find the period

you need a couple of info first

[hasty flume]

Oh before we sketch it?

[fringe rivet]

ya

[fringe rivet]

this

so what do you think the period will be

[hasty flume]

Alright I see

[fringe rivet]

also do you know how these graphs are supposed to look like

?

[hasty flume]

Yes like waves

[fringe rivet]

yep thats right

they are waves that repeat

[hasty flume]

This section reminds me of physics because do it as well but that isn't the point

[fringe rivet]

yep

so to find the period

we can use this as a hint

sin(x)=1

since we dont have a factor that would affect this

[fringe rivet]

This isnt always the case tho

it works for this instance

[hasty flume]

I know it has 2 py in there... if I am not mistaken

[fringe rivet]

2 pi is a full revolution

an entire 360 basically

[hasty flume]

I am following

[fringe rivet]

so what number do you plug in for sin

to get 1

if you plug in 360 it would give you 0

[hasty flume]

Yeah this is the part I don't get

[hasty flume]

I agree with you

[fringe rivet]

You can try to use a calculator

and plug in

arcsin(1)

and that will give you your anwser

[hasty flume]

When I plug this in I get pi/2

[fringe rivet]

ok do you know the

mmm

this

[hasty flume]

Yes I know this I've seen it before

[fringe rivet]

also thats wierd that you got pi/2

no nvm

also

you dont need that mb

[fringe rivet]

?

how

oh your using radian

ok

so ya

[hasty flume]

3.141.....for normal pi

[fringe rivet]

ya

divide by 2 then covert 2 degrees

[hasty flume]

There's another way to do it what's is it called again?

[fringe rivet]

use degrees

it should be easier

for beginners

ok

[warm shale]

HimpLimpDip

[fringe rivet]

this will give you

also pi is 180 degrees

dont forget that

so if you divide 180 by 2

u get

[hasty flume]

Ah yes thank you that's the one I'm very familiar with

[hasty flume]

90 degrees

[warm shale]

HimpLimpDip

[fringe rivet]

so thats your period

[hasty flume]

Alright I'm following

[hasty flume]

90 degrees?

[hasty flume]

Or this?

[fringe rivet]

ok

so since you have nothing

that makes

a

difference in the period

thatll make

you try to get 1 pi

which is 180 degrees

thats your period

180

is half the

period

ill show you an example

mb

[hasty flume]

Oh so my period for f(x) would be 90 degrees? Or is it 180 degrees

[fringe rivet]

oh for sin 1 its 90

[hasty flume]

I would appreciate an example please

[fringe rivet]

There are your graph

see how

its 2 pi for an entire period

from your begging to max in 90 degrees

thats your sin 1

thats from the beggining to half of the period

[hasty flume]

Oh okay I'm starting to get the gist of it now

[fringe rivet]

no that was wrong mb

dont worry about values of sin

you dont need that yet

just worry about

the entire thing

if there is no horizontal stretch

its always an entire reevolution

360

[hasty flume]

I am following

[fringe rivet]

ok so you can start graphing

[hasty flume]

Also I've got a question about the period of f(x) as my final answer would I say sin 1= 90 degree or just 90?

[fringe rivet]

start from 0,0

[fringe rivet]

niether

a period

is ill show you

see how it starts and end at the same time

[hasty flume]

Oh so my period is 0,0? For f(x)?

[fringe rivet]

your period for this will be 360

[hasty flume]

For f(x)?

[hasty flume]

Or this?

I'm kinda confused sorry

[fringe rivet]

The period of a sinusoid is the length of a complete cycle

a complete cycle is

you start off

at the sinusiod axis

which in this is 0

and will end at

the sinusiod axis

If you dont know what that is

its the middle of the graph

also use desmos graphing calculator

to help you out

Also forget everything above you dont have to worry about all that

you just need to understand that a period

is a complete cylce

it starts off and the middle line which in this intance is 0

and end off at 0

[hasty flume]

Oh okay I'm following let me sketch f(x) now

[fringe rivet]

ok

[hasty flume]

The part where you mentioned "end" is this the 270 degrees part?

[fringe rivet]

no it should be all the way to 360

mmm

If i was you I would close this chat and make a new one with the same question so that you dont get confused

there is a lot to intake

So 270

is a restriction

[hasty flume]

Oh but since my question stated 270 degrees would my waves for f(x) end there?

[fringe rivet]

Im not sure

[hasty flume]

I'm following

[fringe rivet]

it shouldnt although

thats why you might need someone elses opinion since I think it shouldnt end at 270

[hasty flume]

I mean for my question if I'm not mistaken

[fringe rivet]

ill check one sec

[hasty flume]

Alright thanks I appreciate it

Alright since we are both confused with how I am supposed to sketch f(x) on the graph... let's skip that question and only come back once we have done the other ones

[fringe rivet]

alright

ya

[hasty flume]

Great your back

[fringe rivet]

im not sure exactly what the teacher is asking

for that one

ok can you start a new help and ill help you with everything besides graphing since im not sure

myself

I can do 2 3 4 5 6

with you

[hasty flume]

Yes please help me with those

[fringe rivet]

I dont want to give you wrong anwsers thats why

ok

alright

[hasty flume]

It's alright thank you for helping me though

[fringe rivet]

Ok

lets start all over again

well start with 3

[hasty flume]

Sure

[fringe rivet]

since its the easiest

[hasty flume]

Alright

[fringe rivet]

ok do you know what the amplitude is

[hasty flume]

No I don't

Any hints?

[fringe rivet]

ya

its the distance between your middle to the max or min value

[hasty flume]

Okay I am following

[fringe rivet]

y = A·sin(B(x-C)) + D

also this is your formula

for sin

its funny enough that they give you the amplitude

A=amplitude

[hasty flume]

I am still following

[fringe rivet]

So what is your amplitude for this

y=2sin(x)

[hasty flume]

The amplitude is 2

If I am not mistaken?

[fringe rivet]

thats correct

[hasty flume]

Yay!

[fringe rivet]

Yep that works

look

[hasty flume]

Can we move on to question 3? Oh wait but we can't we must find the amplitude lf g(x)

[fringe rivet]

ya

so you have -cosx+1

[hasty flume]

Beautiful actually slowly understanding this

[fringe rivet]

yep

[fringe rivet]

ok so what do you think the amplitude for this one is

-cos(x)+1

[hasty flume]

Is it 1?

[fringe rivet]

ya

thats correct

[hasty flume]

Great

[fringe rivet]

okay

we can move to 3

or 4 mb

Do you know what range is

[hasty flume]

Alright

[fringe rivet]

Range is what your y values can be

so what can they be

for sin(x)

take to an account

[hasty flume]

I am following

[fringe rivet]

that max and min values are

-2 and 2

so what do you think the range will be

[hasty flume]

Sorry to disturb but would writing my amplitude like this be wrong or is it fine

[fringe rivet]

Ya that should work I assume but where did the 3 appear from

?

[hasty flume]

It's another example I did before I requested for help with but let me do the correct ones now

[hasty flume]

I am lost here

[fringe rivet]

ya that should work but specify that a is amplitude

[fringe rivet]

ok

i can explain this

[hasty flume]

Thanks

[fringe rivet]

We know 2 thing here

from 2sin(x)

we have a max and min of -2 and 2

and that y can be all real numbers

so how you would write that as

R:{yER} to specify that y is all real numbers

and now your going to have to add the restrictions

[hasty flume]

I am following

[fringe rivet]

ok so how do you write that y is smaller and equivalent to 2 and larger and equivalent to -2

[hasty flume]

Yeah this is part that I always get wrong like I never know how to write it out-

[fringe rivet]

ok

you can do this

Your anwser is the green thing

thats your restriction

and also you can see that

the y can be all that green but dosent extend lower or higher than

[hasty flume]

I am following

[fringe rivet]

so to write out range completetly

its

$\left{yER\left|-2\le y\le2\right\right}$

wait one sec

nope thats wrong

here

just dont add the line after the 2

[warm shale]

HimpLimpDip
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[fringe rivet]

like this

[hasty flume]

Oh so i type out my final answer like this

[fringe rivet]

yep

[hasty flume]

Thanks bro

Alright we can move on to g(x) of the question now

[fringe rivet]

alright

so try g(x) out

so we know the max and min

[hasty flume]

How f(x) range looks in my book

[fringe rivet]

Ya thats correct

make the E

next time

like

∈

since that represents something

E dosent

[hasty flume]

oh alright let me scratch it out and re write it

[fringe rivet]

no you dont have to

you can just round in a little bit

[hasty flume]

Oh alright

Okay I fixed it

We can move on the g(x)

[fringe rivet]

yep attempt it on your own and tell me where you think you made a mistake

[hasty flume]

Alright

This is my g(x)

[fringe rivet]

lets check if thats right

Does that look correct?

[hasty flume]

It looks correct

You can double check but it looks good

[fringe rivet]

It aint lol

[hasty flume]

Mine?

How?

[fringe rivet]

you forgot to keep in mind that hte graph was shifted

cosx+1

[hasty flume]

Haha I thought I got it right

[fringe rivet]

If the graph has been shifted once upward

which is the cos(x)+1

part

youll need to add 1 for each

one you did

so -1+1=0

and 1+1 will be 2

thats your actual restrictions

[hasty flume]

I am following

So it become cosx+2?

[fringe rivet]

No you dont change

the equation

your restrictions were false since you didnt keep in mind

that the graph was shifted upwards once

[hasty flume]

Oh okay

[fringe rivet]

so what are your new restrictions

[hasty flume]

What I am getting now

@fringe rivet sorry to tag you but are you still there? We are nearly done

[fringe rivet]

ya

alright we are on 5

mmm

I dont know this part

[hasty flume]

Great

[fringe rivet]

Your going to need the help of someone else for 5 and 6 and 2

since i dont know what the period will be

[wet moss]

do you know the addition formula?

[hasty flume]

Oh alright thanks though for helping me with the other questions

[hasty flume]

Hi could you explain that formula to me please

[hasty flume]

I am following

[wet moss]

when you sub in the values of f(x) and g(x) into number 5 you get the equation 2sinx + cosx = -2

you can use the addition formula (or compound angle formula as it is known) to put 2sinx + cosx into either just sin or just cos

so that you can solve the equation

[hasty flume]

This is for question 5 correct?

[wet moss]

yes

[hasty flume]

I am a bit confused how do I put the 2sinx+ cosx into the R sin(x+a)= R(sinx cosa + sin alpha cosx)?

[wet moss]

i chose to use the sin version here

using the cos version would still get you the same answer

by expanding out the left hand side, we can equate that with what we are trying to get on the right hand side

for example we can equate the coefficients of sinx since both 2 and Rcos(alpha) are both constants

[hasty flume]

Okay I'm following with what you did on the left hand side of the page

[hasty flume]

I am following

[hasty flume]

What you did on the left looks like it wil be the final answer thanks I appreciate it

[wet moss]

well there is still a bit to go after the final line

do you think you can solve it from there?

the important thing is that there are no more cosx terms

[hasty flume]

Oh I thought it was the final answer oh no-

[wet moss]

well it wants you to solve that and find the value of x

[hasty flume]

Let me try and calculate it from here...

Update I'm not winning

[wet moss]

first try and get sin(x+26.57) on its own

[hasty flume]

If I do that I will just end up expanding sin(x+26.57)...

Unless I'm wrong

[wet moss]

as in just get that entire sin term on its own without any coefficient

[hasty flume]

Just like this "sin(x+26.57)"

[wet moss]

yeah

[hasty flume]

When I try solve that on it's own I just end up expanding it...

[wet moss]

so when you get this dont try and solve it for x

try to solve it for x + 26.57

in that case you dont have to expand it

or you could do something like let a = x + 26.57 to visualise it better

then you have sin(a) = -2/√5

[hasty flume]

Can I do this step right now or can I not?

[wet moss]

?

i dont know what you mean

[hasty flume]

Sorry it was a typo on my end it's literally 01:30am and I'm so tired I just wanna finish this though so baldy

[wet moss]

i can send you the last steps if you want

or do you want to do it yourself?

[hasty flume]

Can you please send the last steps because I am really tired and we still have to do question 6 as well

[hasty flume]

I would really appreciate it sorry that I can't do it right now I'm just really tired

[wet moss]

the reason x cant equal -90 is because it isnt in the range of 0 to 270

those are the only values of x within that range

otherwise there are technically infinite solutions

[wet moss]

also why are you up at 1:30 doing maths

[hasty flume]

No rest for high schoolers unfortunately

Thank you so much i appreciate it

[wet moss]

😭

np

time for 😴

you need sleep

[hasty flume]

Bro can you help me find the period of f(x) and g(x) and question 6

[hasty flume]

I wish

[wet moss]

now?

[hasty flume]

I still have to do Chemistry after this

[hasty flume]

Yes bro please

[wet moss]

ok can you post the questions again please

i just dont want to keep scrolling up

[hasty flume]

Alright

There you go :).

[wet moss]

ok we can start with number 2 i guess

[hasty flume]

We are left to do question 2,6 and 1

[hasty flume]

Sure

[wet moss]

i thought you did number 1

[hasty flume]

Unfortunately we didn't the other guy was unsuccessful in helping with question one but we wil, come back to it let's focus on question two now

[wet moss]

ok we'll do question 2 first

[hasty flume]

Great

[wet moss]

so the period of a graph is defined by the distance between 2 repeating points on a graph

[hasty flume]

I am following

[wet moss]

so notice how the graph repeats at each green point

it goes up to the maximum then down to the minimum and repeats continuosly

[hasty flume]

I am noticing that

[wet moss]

the period is just the distance between 2 of these points

you could measure this from anywhere you want on the graph, so long as it is at a repeating point

you could do this for example

the distance doesnt change

this is the graph of 2sinx

so it gives the answer to the first part of number 2

so lets try and find the distance between the first one i put up

[hasty flume]

I am still following

[wet moss]

so for this we want to know where y = 0

and take every other value

since between the first 2 green lines, the graph crosses the x axis another time

[hasty flume]

I am still following

[wet moss]

so that shows every point to where the graph crosses the x axis

dont focus on the axis since they arent in degrees

so for this you want where x = 0 and then the point after the next

so you want where x = 0 and x = 180

and so the distance is just 180 - 0

[hasty flume]

I am still following

[wet moss]

so the "period" is 180

you can measure the distance from any of those points on that graph and the distance will always be 180

basically the graph has gone through 1 "revolution"

[hasty flume]

Alright we got f(x) now great

[wet moss]

lemme quickly just get the graph of g(x) now

[hasty flume]

Alright

[wet moss]

ok so same thing here

we want the distance between these 2 points

since the graph is repeating at this point

so once again we solve for the graph being equal to 0

give me a moment while i show the working

[hasty flume]

Alright np

[hasty flume]

I am following

[wet moss]

since you can see that the graph doesnt go through the x axis again between these 2 points, you can tell that we only need the first 2 solutions

so the green points are at x = 0 and x = 360

so the distance between them is 360 - 0

and the period is therefore 360

[hasty flume]

Ah I see now thank you.

Sorry for slow reply I was digesting everything

[wet moss]

nah its np, take as long as you need

just tell me which one you want to do next when you're ready

[hasty flume]

Quick question do I say degress for both of the periods or not?

[wet moss]

yes

180 degrees and 360 degrees

[hasty flume]

Alright in that case we can move on to question 6 thank you so much for helping me as well

[wet moss]

do you want to do number 1 last then

[wet moss]

np

[hasty flume]

Yes I'd like to do that question last it that is fine

[wet moss]

ok

[hasty flume]

Must I send the question again or you okay?

[wet moss]

nah its ok

so we'll start with f(x)

[hasty flume]

Alright

[wet moss]

since i dont know how to do the shading thing on desmos ill just do it on paint

[hasty flume]

Alright that's fine with me

[wet moss]

ok so ive put the coordinates of the points where the graph crosses the x axis on there

the question wants you to figure out when is that graph less than or equal to 0

[hasty flume]

Alright I'm still following

[wet moss]

so it wants you to know the shaded region

[hasty flume]

Oh okay I see

[wet moss]

ok so it only wants it in the range of 0 to 270 so i put a line there to show that we dont want the 2nd shaded part

so if you were doing it as an inequality, what inequality of x would show the first shaded region?

[hasty flume]

Alright I am still following

[hasty flume]

(xER (90°_< x _< 180) this should be correct now

[wet moss]

so in this case we are discussing the domain and not the range

if you think about using y for when there is height and using x when there is horizontal distance

the inequality itself is correct if you just switched y for x

[hasty flume]

so I should use an x and not a y?

[wet moss]

yeah

[hasty flume]

Oh alright

Let me edit my answer

[wet moss]

easier to visualise that you are finding horizontal ranges

rather than vertical

[hasty flume]

I ahbe edited this now

[wet moss]

tbh i dont know why they do this but do you notice in the question when they state the range for x in the other questions

they use square brackets

[0,270] rather than (0,270)

there is a difference in the meaning

with square brackets, it means that the values there are included so x is between 0 and 270 AND CAN EQUAL 0 or 270

but with usual round brackets it means x is between 0 and 270 but CANNOT EQUAL 0 or 270

so it wants you to find the parts in the graph where y is less than or equal to 0

but as you can see

when x = 270, y = 0

therefore there is another point in the range [0.270] where f(x) is less than or equal to 0

since it is equal to 0 at x = 270

so it just means there are 2 regions you have to consider

[hasty flume]

Bro I am back sorry my tablet died just put it on the charger

[wet moss]

oh lol

ok just read through what i have just wrote

tell me if you understand all of it

[hasty flume]

Alright I'll read through the messages

I've read through the chats and I understand

Thank you so much bro I really appreciate it

[wet moss]

nah its np

luckily its easier for g(x) though

[hasty flume]

Let me write this down in my book as the final answer

[wet moss]

ok

[fringe rivet]

still going at it I see

[hasty flume]

Agreed

[hasty flume]

No rest for us maths people fr lol

[fringe rivet]

Yep stayed up until 4 am yesterday doing math

miserable day

[hasty flume]

This is deep

I still have to do chemistry as well-

[fringe rivet]

you have school?

I thought it was online?

[wet moss]

1:40 we keep up the grind

[fringe rivet]

no need for sleep

I would recommend 2h of sleep every week

[wet moss]

yep

[hasty flume]

It is but it's a lot

These teachers don't care about our health

[fringe rivet]

so summer school?

[hasty flume]

Today I wrote maths paper 2 like at 7am till 9am then I've been doing math work that was overdue

[hasty flume]

No I am from South Africa

It's like 02:42am here lol

Grind goes on and on

[fringe rivet]

TODAY IS MY LAST DAY DOING SUMERRRRRRRRRRRR SCHOOL

so happy

[hasty flume]

Anyways yall have a good night I'm about to have to best sleep of my life fr

[hasty flume]

Happy for you bro

Alright I'm closing the channel thanks for your help guys

[wet moss]

dont you want to do g(x)

[fringe rivet]

Gn

[wet moss]

or number 1?

[hasty flume]

Oh wait you are right

[hasty flume]

I completely forget about question 1

[fringe rivet]

welp no sleep for u

gl

[wet moss]

g(x) part can be done in like 1 min though

[hasty flume]

Thanks

[wet moss]

so this is g(x) with points 0 and 360 put on the graph again

and roughly the line of x = 270

[hasty flume]

So I start sketching my waves at 0 and I end at 270° as what my graph showed in the activity?

[wet moss]

yeah for number 1 you do

[hasty flume]

Alright thanks let me go do that brb

[wet moss]

that will roughly be what you sketch for g(x)

you might want to plug in x = 270 into g(x) so you stop sketching at an accurate place

[hasty flume]

I'm doing the sketching on paper I'll show you how it looks once I'm done

[wet moss]

all you are doing though is flipping the graph of cosx in the x axis and shifting it up by 1

[wet moss]

ok

[hasty flume]

Black pen is g(x)
Blue pen is f(x)

[wet moss]

ok ill start with black

theres nothing too badly wrong with it but the labels at the y axis interceptions are wrong and the shape should be less of a steep curve going up

i would recommend doing this

instead of this

as for the intersections it should be at 0,360, 720 and so on

instead of 0,90,180,270 ...

but the fact that it doesnt go below the x axis is correct

as for the blue one of f(x)

the intersection points with the x axis are correct

the shape once again is the same problem as before

but in this case remember that since it is 2sinx, the graph goes 2 times higher than the g(x) graph

since the g(x) graph has its peak at y = 1, but the f(x) graph has its peak at y = 2

[obtuse pebble]

@hasty flume Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[viral tree]

I tried to multiply both equations by 100

but my result is wrong

[high lily]

show work

[viral tree]

one moment I will draw it

[royal basin]

arithmetic errors befall everybody.

take it as a rule: EVERY time you come here with a question, ALWAYS show your work.

BEFORE getting asked for it.

[viral tree]

I will next time

[royal basin]

35x - 60y + 80x - 60y is not equal to 115x

adding the equations would not help you, as you would get 115x - 120y = 110

[viral tree]

but I have -60y in both equations

oh thats why I need to subtract

[royal basin]

adding -60y to itself gives -120y and not 0.

[viral tree]

I need -60y - - 60y

[royal basin]

sure

[viral tree]

which is equal to -60y + 60y

.close

[obtuse pebble]

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• 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.

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• Show your work, and if possible, explain where you are stuck.
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What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[royal basin]

can you clarify a little

what natural number do you claim is the identity element under the minimum operation?

@white basin

[zenith raft]

and also maybe post the original problem

[obtuse pebble]

@white basin Has your question been resolved?

[obtuse pebble]

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[royal basin]

bruh

[obtuse pebble]

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[robust rampart]

how do i do this

[shadow tangle]

What exactly are you doing to it?

Isolating x?

[robust rampart]

finding value of x

[shadow tangle]

Ah ok

[timid silo]

subtract both sides with x and subtract both sides with 3

[robust rampart]

so 0 = 3 + x

and then

-3 = x

oh

thx

[timid silo]

yea there you go

[shadow tangle]

Nope

[robust rampart]

thx

[shadow tangle]

Wait nvm

[robust rampart]

??

[shadow tangle]

I've been up for a bit and can't read. Disregard lol

[timid silo]

Could you help me in help-4?

[robust rampart]

how do i find value of x

??

[gloomy python]

add both sides with 6-x

[obtuse pebble]

@robust rampart Has your question been resolved?

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[royal basin]

that's...

you realize that's not how the concept of an identity WORKS at all right

yes, such that FOR ALL a it holds that a*e = a

no!

note it must be ONE element that works this way FOR ALL a!

[obtuse pebble]

@white basin Has your question been resolved?

[obtuse pebble]

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Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[wise hedge]

https://imgur.com/wXcaQyl

[wise hedge]

Why is this question in a course for trigonometry. It looks more like it's checking your equation solving skills.

I don't even understand how to process this question.

[versed stratus]

looks like a trignometric equation

[wise hedge]

It is, exactly.

But it seems to be asking more a question like, "How many of these are the same thing"

What am I supposed to be learning here?

[royal basin]

no two of these look 'the same' to me

[wise hedge]

Okay, so there are 2 right answers I guess is what you are saying.

I don't have a clue to be honest. I just marked 2 as guesses.

[royal basin]

no

if i wanted to say "the right answer consists of exactly 2 options" i would have said "the right answer consists of exactly 2 options"

[wise hedge]

And here's the thing, it's not in a standard form of a trigonometric function. That would be: Acos/sin(Bx + C) + D

[royal basin]

if you're chasing after a standard form, the lhs IS in it...

30 cos(30x + 0) + 16

but you do not even need that there specifically

for the purposes of solving the equation

[wise hedge]

Is the first step solving for x then?

[royal basin]

no, solving for x is the goal

it's strange to treat it as "the first step"

[wise hedge]

Isolating 'x' is how it's done

[royal basin]

what i would consider the first step towards isolating x is subtracting 16 from both sides to get 30 cos(30x) = -30

[wise hedge]

That's what they teach you in 7th grade so why isn't isolation of the x variable the first step?

[royal basin]

isolation of x is a task that itself takes several steps

[wise hedge]

Ok

But your first transformation above is in an odd form also

[royal basin]

???

what transformation?

[wise hedge]

to get 30 cos(30x) = -30

[royal basin]

and in what sense do you consider it "odd"?

[wise hedge]

And also, can't we just say that 30x is really 15 cycles or just 2Pi?

[royal basin]

30x is 30x, you're overthinking it.

[wise hedge]

This is the most bizarre question I've come across in this course for as long as I've been doing the course.

[royal basin]

i haven't received a straight answer to "in what sense do you consider the transformation of 30cos(30x) + 16 = -14 into 30cos(30x) = -30 odd?"

[wise hedge]

Because I don't know what that is even supposed to mean. The answer is -14?

[royal basin]

...no?

[wise hedge]

I have a question, since this is an infinite wave that goes in cycles, how can there not be an infinite number of answers for x?

[royal basin]

there IS an infinite amount of answers for x.

but we've barely even started on the journey towards finding them.

you're overthinking a simple algebraic step here.

[wise hedge]

So, what they want is maybe just a few specific answers for X where you end up with -16 on the right side..

[royal basin]

????

no

again

you're overthinking it! so hard! right now!

would you like me to try and explain with a simpler example?

[wise hedge]

Yes, please

[royal basin]

do you know how to solve linear equations?

[wise hedge]

Of course

[royal basin]

right

so when faced with an equation such as 8x + 11 = -21

what would your first step be

[wise hedge]

8x = 10

Oops

Subtract 11 from both sides

8x = -32

[royal basin]

you'd subtract 11 from both sides, right.

and then divide both sides by 8.

[wise hedge]

Yes

[royal basin]

i'm doing the EXACT SAME THING HERE just with different numbers.

the presence of the cosine function has NO EFFECT on the validity of these actions or the content thereof.

you shouldn't get hung up with "forms" and "standards". from my pov, you seem to be treating them as some kind of dogma.

[wise hedge]

Only to guide me if I am

[royal basin]

well here they don't guide you at all but instead obstruct you

like

with the equation
30cos(30x) + 16 = -14
there is absolutely nothing wrong, weird, strange or illegal about subtracting 16 from both sides to get
30cos(30x) = -30

[wise hedge]

I know that, I never said illegal, that just basic step of solving a linear equation.

[ripe terrace]

hmm cos(30x) is just the cos wave of period pi/15 so you just need to tell when it's equal to -1 (the crest/lowest point of the wave) the first point will be at pi/30 (as in period 2pi wave -1 is at half the period i.e at pi) now add npi/15 to get to all the lowest points on the graph

[wise hedge]

They have thrown me way off base by asking a question like this in trigonometry, that was my intial point. Maybe it's so easy I don't understand why it's even in this course.

[royal basin]

⌛