PLS HELP Solving Triangles with the Sine and Cosine Law | Mathematics | Page 1

fading marten May 26, 2023, 3:11 AM

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i hav a lot of questions b/c i wasnt there for the lessons and need help with hw questions

muted anchor May 26, 2023, 3:47 AM

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Sin function stays between -1 to 1

fading marten May 26, 2023, 3:51 AM

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muted anchor Sin function stays between -1 to 1

but how do i get the equation

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like i dont understand how to solve this

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ik what u mean by sin f^ stays between -1 n 1

muted anchor May 26, 2023, 3:55 AM

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Ampltitude is 6 units means the peak will be of 6 units height

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Period here means how long until 'matching points' repeat at the same level

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For a basic sin(x) function, period is 2π

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Means the same level,type of point will come back after 2π radians (360°)

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Here you have 60°

Hence, sin(6x)

fading marten May 26, 2023, 3:58 AM

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muted anchor Means the same level,type of point will come back after 2π radians (360°)

im sorry i dont understand

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so a normal period would end at 340 but with this one it ends at 60?

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so a full period would be 60?

muted anchor May 26, 2023, 4:00 AM

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fading marten so a normal period would end at 340 but with this one it ends at 60?

*360°

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Normal is 360, yes

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In your question, they're asking to make it 60°

fading marten May 26, 2023, 4:01 AM

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ooh

muted anchor May 26, 2023, 4:01 AM

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You can make it by multiplying 6

fading marten May 26, 2023, 4:01 AM

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so 60x6?

muted anchor May 26, 2023, 4:01 AM

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Yes

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X = 60

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Will make it 360

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6x

fading marten May 26, 2023, 4:02 AM

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oooh

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so then it would be sin(6x)?

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sorry but why am i x it by 6?

fading marten May 26, 2023, 4:03 AM

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fading marten sorry but why am i x it by 6?

is it b/c the max height is 6 so im x it by my period?

muted anchor May 26, 2023, 4:04 AM

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We have to make the inside of sin such that it becomes 360 when we multiply the period by something

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Here period is 60

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We have to multiply 6 to make it 360

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Hence 6x

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It is a coincidence that the amplitude is also 6.

It could've been 4 too but the inside would be 6x still

fading marten May 26, 2023, 4:05 AM

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so if we has a period of 30 we would have to x it by 12?

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so it would be 12x?

muted anchor May 26, 2023, 4:06 AM

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fading marten so if we has a period of 30 we would have to x it by 12?

Yes

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You got it

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Now the amplitude comes in

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Normal sin function equation is like this:

y = A sin (w×x + phase) + C

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A here is amplitude

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w = 360°/Period

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Phase means the starting angle from 0

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C is a constant to give the graph an offset

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General sin(x) graph

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I ACCIDENTALLY TOLD YOU ABOUT THE PHASE

C is how much the graph will lift/sink in the Y-axis

fading marten May 26, 2023, 4:11 AM

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im sorry are you able to join vc and explain

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i dont really understand the wording 2 much

muted anchor May 26, 2023, 4:12 AM

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fading marten im sorry are you able to join vc and explain

I'm taking a dump rn

fading marten May 26, 2023, 4:12 AM

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LMAOOO \

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HAHHAA

muted anchor May 26, 2023, 4:12 AM

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😆

lofty widget May 26, 2023, 4:12 AM

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muted anchor I'm taking a dump rn

may god have mercy on your soul

fading marten May 26, 2023, 4:12 AM

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muted anchor I'm taking a dump rn

are u able 2 join after ur dump XD

muted anchor May 26, 2023, 4:12 AM

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Check this.

This explains the role of C in the equation

fading marten May 26, 2023, 4:13 AM

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oooh

muted anchor May 26, 2023, 4:13 AM

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fading marten are u able 2 join after ur dump XD

Won't promise but ok

fading marten May 26, 2023, 4:14 AM

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so instead of the original that starts off at 0 it shifts up by 2

muted anchor May 26, 2023, 4:14 AM

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Yes

fading marten May 26, 2023, 4:14 AM

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and starts at 2?

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omg thank u

muted anchor May 26, 2023, 4:14 AM

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Everything rises 2 units

fading marten May 26, 2023, 4:14 AM

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ahhh

fading marten May 26, 2023, 4:15 AM

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muted anchor w = 360°/Period

so then what do u mean by this?

lofty widget May 26, 2023, 4:15 AM

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fading marten oooh

muted anchor May 26, 2023, 4:15 AM

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60°

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6x

fading marten May 26, 2023, 4:16 AM

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y=a sin(6x+idk)+4?

muted anchor May 26, 2023, 4:16 AM

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Phase

muted anchor May 26, 2023, 4:17 AM

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fading marten y=a sin(6x+idk)+4?

Amplitude is 6

So first A becomes 6, that we know

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6x we found out

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The max is at (0,4) meaning the peak point is at that

fading marten May 26, 2023, 4:18 AM

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how would i find the phase?

muted anchor May 26, 2023, 4:18 AM

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Ok

muted anchor May 26, 2023, 4:19 AM

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muted anchor The max is at (0,4) meaning the peak point is at that

First find out this, you got this?

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What can you find using this info?

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0,4 means the peak is at 4

Normal sin graph has peak at 1

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You need to lift it by 3 units

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Normal sin x curve has the peak at π/2 (90°) on x axis

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Here it is given that the peak is at 0 on x axis

fading marten May 26, 2023, 4:20 AM

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sorry these terms ur using are a lil different then the terms my teacher uses

muted anchor May 26, 2023, 4:21 AM

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Which ones?

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I'll write the answer here :

Y = 6 sin(6x - π/2) + 3

fading marten May 26, 2023, 4:21 AM

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we say stretch or compress

muted anchor May 26, 2023, 4:21 AM

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fading marten we say stretch or compress

Ok, we stretch by 3

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I guess? despair

fading marten May 26, 2023, 4:22 AM

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b/c we went up by 3?

muted anchor May 26, 2023, 4:22 AM

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If you mean going up by 3 as stretch then yes

fading marten May 26, 2023, 4:22 AM

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oooh

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okok

muted anchor May 26, 2023, 4:22 AM

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muted anchor Normal sin x curve has the peak at π/2 (90°) on x axis

Then this

fading marten May 26, 2023, 4:22 AM

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so what does the pie/2 mean?

muted anchor May 26, 2023, 4:22 AM

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See the 1st peak on right of origin

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It is at π/2 on x axis

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We need to shift it to 0

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Hence - π/2

fading marten May 26, 2023, 4:23 AM

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oooooh

muted anchor May 26, 2023, 4:23 AM

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troll

fading marten May 26, 2023, 4:23 AM

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okok im starting 2 understand thank you

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so we are compressing it by -2?

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so we could make the first peak on the origin?

muted anchor May 26, 2023, 4:24 AM

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Compress mean?

fading marten May 26, 2023, 4:24 AM

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like moving it ish

muted anchor May 26, 2023, 4:25 AM

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Yes, you can say that we held the peak point and moved it left side by π/2 units

fading marten May 26, 2023, 4:25 AM

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ahhhhh

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so thats y we did -2

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cuz we moved our peak to the origin which is 2 units back

muted anchor May 26, 2023, 4:26 AM

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Where did I do '-2'?

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thonk

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I did - π / 2

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Or -90°

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π means 180°

fading marten May 26, 2023, 4:27 AM

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ooooh

fading marten May 26, 2023, 4:27 AM

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muted anchor π means 180°

sorry we dont use that term XD

muted anchor May 26, 2023, 4:27 AM

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Which country is it?

fading marten May 26, 2023, 4:27 AM

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canada

muted anchor May 26, 2023, 4:27 AM

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India here

fading marten May 26, 2023, 4:27 AM

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ooh v nice to meet u

muted anchor May 26, 2023, 4:28 AM

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You too

fading marten May 26, 2023, 4:28 AM

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didnt know they use such hard terms in india

muted anchor May 26, 2023, 4:28 AM

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Which ones?

π?

fading marten May 26, 2023, 4:28 AM

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we kinda made it more simple by kinda changing the words but keeping the same def

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yeah pie

muted anchor May 26, 2023, 4:28 AM

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Oh

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Ok

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Then -2 terms

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I guess you've understood 😂

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I have to wash my thing now

fading marten May 26, 2023, 4:29 AM

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LMAOOO

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yeah but one more question when ur done XD

muted anchor May 26, 2023, 4:30 AM

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Okok, I'll be back then 🫡

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Ttyl

fading marten May 26, 2023, 4:30 AM

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okok take ur time

fading marten May 26, 2023, 4:31 AM

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muted anchor I did - π / 2

why did we do -180/2?

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and is that the correct way of writing it?

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y=6sin(6x-180/2)+3?

muted anchor May 26, 2023, 4:59 AM

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Back

muted anchor May 26, 2023, 4:59 AM

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fading marten why did we do -180/2?

Because the normal sin graph has it's peak at +90° on x axis

fading marten May 26, 2023, 4:59 AM

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hii

muted anchor May 26, 2023, 5:00 AM

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I'm bringing it left till origin (because it is given in question) by subtracting 90° on x axis

muted anchor May 26, 2023, 5:00 AM

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fading marten hii

Hello

fading marten May 26, 2023, 5:00 AM

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muted anchor I'm bringing it left till origin (because it is given in question) by subtractin...

so y the 2 tho?

muted anchor May 26, 2023, 5:01 AM

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fading marten and is that the correct way of writing it?

If you want to write like your teacher did, you can do it.

Just know that we're subtracting 90°

muted anchor May 26, 2023, 5:01 AM

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fading marten so y the 2 tho?

Do you use '2' to denote 90° and '1' for 45°?

fading marten May 26, 2023, 5:02 AM

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muted anchor Do you use '2' to denote 90° and '1' for 45°?

wym by denote?

muted anchor May 26, 2023, 5:02 AM

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Denote as if alias

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I will call you elon instead of eloo

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Kind of thing

fading marten May 26, 2023, 5:02 AM

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KMAOO

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ok idm XD

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wait so is it ok if i write y=6sin(6x-90)+3

muted anchor May 26, 2023, 5:04 AM

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Yes if it is applicable according to your teacher

I would write '90°' to avoid confusion

fading marten May 26, 2023, 5:04 AM

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yup idk how 2 do that on keyboard XD

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but yeah will do

muted anchor May 26, 2023, 5:04 AM

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Oh

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Ok

fading marten May 26, 2023, 5:04 AM

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are u able to help me with one more question?

muted anchor May 26, 2023, 5:04 AM

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Here, copy and paste it

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°

muted anchor May 26, 2023, 5:05 AM

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fading marten are u able to help me with one more question?

Sure

fading marten May 26, 2023, 5:05 AM

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sorry on the right it says the

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im not good with finding stuff through word problems XD

muted anchor May 26, 2023, 5:06 AM

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Draw a diagram

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It says wave pool

Meaning the water is like a wave at surface

fading marten May 26, 2023, 5:07 AM

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muted anchor Draw a diagram

how would i draw that?

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like what would i draw

muted anchor May 26, 2023, 5:07 AM

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I mean just rough

muted anchor May 26, 2023, 5:07 AM

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fading marten like what would i draw

Draw a pool container

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Like a big width beaker

fading marten May 26, 2023, 5:07 AM

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mhm

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wait r u able to vc?

muted anchor May 26, 2023, 5:08 AM

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I'm not the best at speaking hence I'm refraining from it

fading marten May 26, 2023, 5:08 AM

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oooh okok dw ab it

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so then what els would i do?

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after drawing the diagram?

muted anchor May 26, 2023, 5:09 AM

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Show me

fading marten May 26, 2023, 5:09 AM

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my cam is broken on my phone XD

muted anchor May 26, 2023, 5:10 AM

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Ok, I'll send

fading marten May 26, 2023, 5:10 AM

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okok thank you

muted anchor May 26, 2023, 5:12 AM

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Looks like this

fading marten May 26, 2023, 5:12 AM

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oooh okok

muted anchor May 26, 2023, 5:13 AM

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The difference between top and trough is 0.6

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Hence the amplitude will be 0.3

fading marten May 26, 2023, 5:14 AM

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ooh ok

muted anchor May 26, 2023, 5:15 AM

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We need to find the coordinates now

Based on h-t graph

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H on y axis

t on x axis

lofty widget May 26, 2023, 5:15 AM

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but isn't he on a trough before he travels 1.8 m from the bottom of the pool?

muted anchor May 26, 2023, 5:16 AM

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lofty widget but isn't he on a trough before he travels 1.8 m from the bottom of the pool?

Elaborate

fading marten May 26, 2023, 5:16 AM

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LMAOOO IM SO CONFUSED despair

muted anchor May 26, 2023, 5:17 AM

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I think they mean he reached the trough

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Which is at 1.8m height

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Look at the bracket sentence

fading marten May 26, 2023, 5:18 AM

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idk what it means by trough/bottom of the wave

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ooooh

muted anchor May 26, 2023, 5:18 AM

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Either way,

They take 5 seconds to reach bottom to top.

Hence, it would take 2.5 seconds to reach the x axis

fading marten May 26, 2023, 5:18 AM

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ok nvm i understanf

fading marten May 26, 2023, 5:18 AM

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muted anchor Either way, They take 5 seconds to reach bottom to top. Hence, it would take 2...

oooh okok ic

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so how would we determine the equation of sin f^

muted anchor May 26, 2023, 5:20 AM

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I'm figuring that out

fading marten May 26, 2023, 5:20 AM

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oh sorry take ur time

muted anchor May 26, 2023, 5:20 AM

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Sin goes from 1 to -1

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Here it is going from 1.8 to 2.4

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The person needs to go only 2 seconds to reach the bottom, from starting line

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It should take 2.5 seconds by calculation

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Hence, the graph is offset leftside by 0.5 seconds

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So phase = -0.5

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Let's find period

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Period means the time/unit until the same point repeats

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That would be 10 seconds

(Starting from bottom,5 seconds to reach top, 5 seconds to reach bottom again)

fading marten May 26, 2023, 5:25 AM

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oooh

muted anchor May 26, 2023, 5:25 AM

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Now we have A, phase, Period

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w = 360°/period

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So 36°/second

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We now have w too

fading marten May 26, 2023, 5:27 AM

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omg u r fucking smart asf

fading marten May 26, 2023, 5:27 AM

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muted anchor We now have w too

ok

lofty widget May 26, 2023, 5:28 AM

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anything else?

muted anchor May 26, 2023, 5:28 AM

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Normally thr graph goes from -1 to 1

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I'm figuring out if C should be there

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The height difference is 0.6

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But they asked us to denote the height w.r.t time

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Ok, if we take blank statement

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I currently got this equation

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Let us put x = 2

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I have a feeling that we must convert time to degrees or vice versa thonk

fading marten May 26, 2023, 5:32 AM

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what is the thing on the left of -0.58?

muted anchor May 26, 2023, 5:35 AM

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Where

fading marten May 26, 2023, 5:35 AM

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the circle wit the line through it

muted anchor May 26, 2023, 5:35 AM

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Phi

fading marten May 26, 2023, 5:36 AM

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is that the period?

lofty widget May 26, 2023, 5:36 AM

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no

muted anchor May 26, 2023, 5:36 AM

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Phase

fading marten May 26, 2023, 5:36 AM

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ahhh okok

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thank you

fading marten May 26, 2023, 5:37 AM

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muted anchor I have a feeling that we must convert time to degrees or vice versa <:thonk:7220...

i dont understand XD

muted anchor May 26, 2023, 5:37 AM

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Ok let's start beginning.

I'll walk you through

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QUESTION

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we make diagram and we write stuff beside

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finding the stuff itself

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(i) We find Amplitude here.
Amplitude means the height of the wave from the x axis

That is, A = (2.4 - 1.8) / 2 = 0.6/2 = 0.3

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(ii) We find the Period here.
Period is how much time/unit it takes to repeat a particular point.

Period = 5 seconds × 2 = 10 seconds
(5 seconds from bottom to top, 2 seconds from top to bottom)

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(iii) We use Period to calculate 'w'

w = 360°/Period = 360/10 = 36° per second

fading marten May 26, 2023, 5:43 AM

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oooooh

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sorry theres a GAINT fucking bug rihg tnext 2 me

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but keep going

muted anchor May 26, 2023, 5:46 AM

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(iv) We now find the C or offset value of this particular question's graph.

Normally we start at y = 0.
Here, we're starting from 1.8 + 0.3 = 2.1 m
Also can be written as, (1.8+2.4)/2 (Min + Max)/2= 4.2/2 = 2.1m

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Hence we lift / stretch it by 2.1m too

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(v) We find out the phase (phi) now.

Normally it is in degrees or radians(π)

Here we have in time.

Hence, we have to convert x into time

It takes 2.5 seconds to reach top/bottom from x axis.

But here, the person reach bottom just at 2 seconds.

Hence, the graph if shifted leftside by 0.5 seconds (-ve)

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We have everything now

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Y = A sin(wx+phi) + C

fading marten May 26, 2023, 5:51 AM

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omg

muted anchor May 26, 2023, 5:52 AM

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Y is h/d here (height/distance)
X is t here (time)

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despair

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36° *

fading marten May 26, 2023, 5:55 AM

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muted anchor 36° *

LMAOO \

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XD

muted anchor May 26, 2023, 5:55 AM

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I guess you've understood now 4am

fading marten May 26, 2023, 5:55 AM

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wait lemme read this

muted anchor May 26, 2023, 5:56 AM

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Ok

fading marten May 26, 2023, 5:56 AM

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muted anchor (iv) We now find the C or offset value of this particular question's graph. Nor...

ooooh

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can u explain the .5?

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i dont understand how u got it

muted anchor May 26, 2023, 5:59 AM

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See that we need 5 seconds to reach from bottom to top

fading marten May 26, 2023, 5:59 AM

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mhm

muted anchor May 26, 2023, 5:59 AM

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Hence, we should be needing 2.5seconds to reach the middle point/x-axis

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?

fading marten May 26, 2023, 6:00 AM

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i kinda understand ish

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idk its kinda confusing

muted anchor May 26, 2023, 6:00 AM

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I meant the x axis like this

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The x axis for the question would be the starting height of the person

fading marten May 26, 2023, 6:01 AM

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which is 2.1m?

muted anchor May 26, 2023, 6:01 AM

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Yes

fading marten May 26, 2023, 6:01 AM

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ahhh

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okok so how would i show my work to get .5?

muted anchor May 26, 2023, 6:02 AM

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I'm explaining that😂

fading marten May 26, 2023, 6:02 AM

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LMAOO MB

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im super tired rn

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n i gotta get these questions done

muted anchor May 26, 2023, 6:03 AM

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It should take 2.5 seconds to reach bottom to starting height according to the calculation

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But the question has told us that it takes 2 seconds instead

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Hence, the graph is shifted 0.5 seconds to the left to be able to do that

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Let me draw

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So the person is already sliding down the hill, according to the question

fading marten May 26, 2023, 6:06 AM

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ok

muted anchor May 26, 2023, 6:07 AM

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,rccw

iron burrowBOT May 26, 2023, 6:07 AM

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muted anchor May 26, 2023, 6:07 AM

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The person starts from x = 0

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Upper graph is what it should be

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The question is telling us about the lower graph

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We shifted the whole graph ⬅️ by 0.5 seconds

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Hope you got it this time

fading marten May 26, 2023, 6:09 AM

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OOOOOOH

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I SEE

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so we started at the origin n we shifted .5 back b/c hes alr falling???

muted anchor May 26, 2023, 6:10 AM

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Yes

fading marten May 26, 2023, 6:10 AM

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ahhhhhhh

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omg

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thank you so much

muted anchor May 26, 2023, 6:10 AM

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You're welcome my man

fading marten May 26, 2023, 6:11 AM

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omg ur a atcual really fuckign smart

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actually

muted anchor May 26, 2023, 6:12 AM

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😂 I was actually learning with you.

I didn't solve questions of this kind before.

But the wave part was in my Communication system chapter

fading marten May 26, 2023, 6:12 AM

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LMAOOO

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so we both helped each other💀

muted anchor May 26, 2023, 6:12 AM

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Yes

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bonk

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How old are you?

fading marten May 26, 2023, 6:12 AM

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Im 16

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Hbu?

muted anchor May 26, 2023, 6:12 AM

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18

fading marten May 26, 2023, 6:13 AM

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Dammm

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N u snart asf

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Man good for u

muted anchor May 26, 2023, 6:14 AM

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Since 16, I didn't pay attention in class tbh 😂

All day Call of Duty Mobile with friends or LifeAfter

Now I took one year to learn most that I can and get into a college that I can obtain

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Anyways, have a good night.

Sleep early and good luck☺️

fading marten May 26, 2023, 6:15 AM

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Thank you so much man

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LMAOO FOR ME ITS VALORANT

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you too

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It was nice meeting you

#PLS HELP Solving Triangles with the Sine and Cosine Law