#help-17

1 messages · Page 3 of 1

twin meteorBOT
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Basudev

vast shale
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umk

trim walrus
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2=k^(1/p) -(i)
3=k^(1/q) -(ii)
6=k^(1/r) - (iii)
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Agreed??

vast shale
trim walrus
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Multiply i and ii

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You get

twin meteorBOT
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Basudev

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Basudev

trim walrus
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Agreed ??

low lance
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ntse question ahh

trim walrus
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Now compare the power and do some Math and you should get 1

vocal sleetBOT
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@vast shale Has your question been resolved?

vocal sleetBOT
#
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dusky adder
#

hello, can someone please help me with my math homework? ive been stuck at circle and hasnt been able to answer the semi one,
if anyone wanting to help the topic is solving circles and semi circles (angles)

dusky adder
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i tried solving the circle first (finding the x) but im a bit stuck and dont know where to multiply the ten, please do tell me if i did something wrong :)

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btw please excuse my bad english grammar, it isnt my first language ^^

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<@&286206848099549185>

dim junco
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What’s the problem @dusky adder

dusky adder
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im having trouble on the next step :')

dim junco
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I see

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But where’s the actual problem

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Oh it’s above that

dusky adder
dim junco
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Wasn’t it

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5x+15=180

dusky adder
dim junco
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So subtract 15 on both sides

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Then divide by 5

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For x

dusky adder
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im sorry but can u explain what you mean but subtract 15 on both sides?

dim junco
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Absolutely

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So subtract 15 from the left side

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And you get 5x

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Subtract 15 from right side

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And you get 165

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So 5x=165

dusky adder
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hold on, im trying to figure out what you mean, im rlly sorry :')

dim junco
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You want to isolate x

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So if 5x+15=180

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You wanna get 5x by itself

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So you get rid of the 15 on the 5x side by subracting it

mighty walrus
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^
The reason you subtract 15 on both sides is because of the equality you want to make X alone so you can find it's value.

dusky adder
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im sorry but is that for finding the x or finding the measurement of fg?

dim junco
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Finding x

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I thought that was what you needed

dusky adder
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i needed that, but i thought "2x+5" would also be needed so i got a bit confused

dim junco
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No I just put the 2x+5 and 3x+10 together

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To get 5x+15

dusky adder
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ohh, i thought you were talking abt solving the circle

dim junco
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Oh

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Do you need help with that

dusky adder
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i need help with both :')
i didnt understand what our teacher meant and didnt explain it properly

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sorry for confusing you

dim junco
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Could you draw the circle again

dusky adder
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okay

dim junco
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It’s a little hard to understand right now

dusky adder
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tell me if u dont understand thw writing

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okay ^^

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oh

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ow waiy

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yeah

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in the given there were none

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oh

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should we try the semi circle then?

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if you dont feel like it or if ur too busy rn, its alr

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ohh

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wait

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should i draw it?

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done

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omg

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my teacher is prbably sleeping at this hour

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its currectly 12 am abt to be 1 am

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do u think thiw will help?

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thats the only photo sent in our math gc that could possibly help, the others are inscribed angles

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wdym plug in?

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like do i just put x in both 2x and 5?

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ohh

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and may i ask how you found the x?

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yes

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like multiply it by 2?

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ohh

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wait

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im rlly rlly rlly sorry but im still confused

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i mean, on how you solve it, is done in a specific order?

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like do u add it after multiplying it?

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yes

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ohh

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ok hold on

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so after multiplying the two of them do we add them to eachother like this?

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or this?

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wait omg

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i think i misclicked sum in my calc

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do we plus it? if yes r we gonna do sum abt the x?

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im still confused, how do u get 360 from adding 10 to just 40?

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i tried adding it, i just got 50 and multiplying it iis 400

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yeah

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x is 32?

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ahh okay

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just another question

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is the formula we used in circle the same for finding the x in semi circle?

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so, we just add all of them?

merry python
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Can you resend your question

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I am unable to understand that pic

dusky adder
dusky adder
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i founf the x

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all i need are the arc measurement

dusky adder
dusky adder
merry python
merry python
# dusky adder

Okay is the intersection point of chords given as centre?

merry python
dusky adder
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it wasnt in the center

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but idk yeah

merry python
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If it is not given as centre, then it's not gonna be an easy deal finding arc lengths

dusky adder
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wait

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whats a centre

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wait let me search

merry python
merry python
dusky adder
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i easily forget things

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sorry

merry python
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What grade are you in?

dusky adder
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7

merry python
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Do you know angle arc relationship?

dusky adder
merry python
# dusky adder

I am still not sure
Since I is not given as centre of the circle it may require some tricks

merry python
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idk

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It would be better if you close this channel and open new one so as to get more help cuz pretty much no ones comming here

dusky adder
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r u sure thats alr?

merry python
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Yes

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Just save those pics in case you haven't

dusky adder
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okay then

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.close

vocal sleetBOT
#
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vocal sleetBOT
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stable oriole
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could someone help me with the following geometry problem:

stable oriole
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R is the radius of the circumscribed circle

vocal sleetBOT
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@stable oriole Has your question been resolved?

grim swan
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Sounds like there are two steps here:

  1. Finding out the values of the angles in the triangle.
  2. Using the angles and the radius of the circumscribed circle to find the lengths of the sides of the triangle.
    Are you comfortable with those steps?
stable oriole
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yeah sure but how

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oh wait

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im so dumb

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holy shit i cant believe how dumb i am

grim swan
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What's wrong?

stable oriole
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i can just say 12x = 180

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and then find the angles

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and then its smooth sailing from there

grim swan
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Yup! This is because the sum of the angles in the triangle is 180°.

stable oriole
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yeah

grim swan
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Are you comfortable from this point on?

vocal sleetBOT
#

@stable oriole Has your question been resolved?

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molten notch
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hallo

vocal sleetBOT
molten notch
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is this correct?

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idk what i just did tbh

lyric fossil
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what is the problem asking you to do

molten notch
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uhmmm

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we go to the top triangle

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and uhmm

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which equation should i use

lyric fossil
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for what

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can you post the full question

molten notch
# molten notch

i also forgot to add a angle on the top triangle near the 6 ft

molten notch
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oh wait

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let 0 be the angle of elevation of the players line of sight when shooting a free throw to the basketball ring which equation describes the problem?

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and then it ust gives me some tigonometric functions

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@lyric fossil

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<@&286206848099549185>

molten notch
vast shale
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as in theres no angle of elevation?

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oh theta

molten notch
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yea

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so what do i do

lyric fossil
vocal sleetBOT
# molten notch <@&286206848099549185>

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lyric fossil
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your diagram is wrong

molten notch
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diagrm?

lyric fossil
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drawing

molten notch
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how

lyric fossil
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it looks like the 6 and 10 are at the same height

molten notch
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oh

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noo 10 is the whole of the right side

vast shale
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im still confused about what its asking you to solve for

lyric fossil
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can you post the full question

molten notch
lyric fossil
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as a picture

molten notch
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ok

vast shale
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to find what??

molten notch
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there

vast shale
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ohhh

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that makes much more sense

molten notch
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to the questions

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and given

vast shale
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so your graph is correct

molten notch
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niceeeee

vast shale
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but we're focusing on the top triangle

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instead of the bottom triangle right

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so you dont rly need that one ;-;

molten notch
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ok

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the bottom one?

vast shale
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so

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basically youre only finding the line of sight

molten notch
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so on the top triangle we have 15 as the adja and we have 4 as the oppo

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so were missing the hypo

vast shale
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but you dont rly need it

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since youre finding the angle

molten notch
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oh

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ohhhhh

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that's what that evalation stuff meant

vast shale
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so which trig function uses the opp and adj

molten notch
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uhhh

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tan

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cos 0 = oppo/adja

vast shale
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so it is tan

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tan is opp/adj

molten notch
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yea

vast shale
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so what would be the ans

molten notch
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uhmmmmmm

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idk

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dk how to use tan

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ik how to use tan to find a side but not an angle

vast shale
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15 is adj

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4 is opp right

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since 4 is on the opposite side of theta

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and 15 is next to theta

molten notch
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yea

vast shale
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and since tangent is equal to opp/adj

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what would it be

molten notch
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ummmmmm

vast shale
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for example if it opp was 7 and adj was 2 , tan = 7/2

molten notch
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yea

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it would be 15/4

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no wait 4/15

vast shale
molten notch
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so we just divide it?

vast shale
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theres your answer

molten notch
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oh

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OH

vast shale
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you cant divide 4 by 15

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gl :D

molten notch
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ITS A

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thanks bro

vast shale
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np

molten notch
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wait

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but wait

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how do we find the value of the theta tho

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yk the degree

vast shale
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so i dont think you learned this yet

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but later

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you would use inverse tangent to find theta

molten notch
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how

vast shale
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so tan^-1(4/15)

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but you didnt learn this yet i think

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its soon tho

molten notch
vast shale
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oh

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wait what

molten notch
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im stuck on home

vast shale
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ah

molten notch
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cause i cant go to school cause of my foot injury

vast shale
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ill show you it hang on

molten notch
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ok

karmic imp
vast shale
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you understand this right

vast shale
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its b

molten notch
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oh yea its b

vast shale
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since its tan

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anyways

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do you understand this

molten notch
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i kinda dont get it

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nope

vast shale
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so

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sin is opp/hyp

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cos is adj/hy

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*hyp

molten notch
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yea

vast shale
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and tan is opp/ad

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adj

vast shale
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or that

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ig

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sure

molten notch
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agreed

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so whats next

molten notch
karmic imp
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You should watch that video

vast shale
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oh bad handwriting

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its 5

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but yeah watch that video

molten notch
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but i want you to teach me

karmic imp
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It explains most of what you don't understand

vast shale
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nawr oct explains it much better than i do

molten notch
#

thanks

#

.close

vocal sleetBOT
#
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midnight knoll
vocal sleetBOT
midnight knoll
#

Is this correct?

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I have to find the limit of 1/sqrt x using the limit definition

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Oh wait

worthy citrus
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if you times the top of your fraction by $\sqrt{x+h}\cdot \sqrt{x}$ then you have to do the same to the bottom

twin meteorBOT
midnight knoll
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Oh right

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I’ll update it

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@worthy citrus how does this look

worthy citrus
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it shouldn't be 4x on the bottom have another go

midnight knoll
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Alright

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@worthy citrus idk what I did wrong

worthy citrus
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$\sqrt{x}\cdot\sqrt{x} \neq 2\sqrt{x}$

twin meteorBOT
midnight knoll
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Oh wait yeah just saw that

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It’s 2x times sqrt x

worthy citrus
#

the whole bottom is yeah

midnight knoll
#

Alright thanks 🙏

#

.close

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rare wyvern
vocal sleetBOT
rare wyvern
#

using part d) how do i prove part e)

strange crater
#

,rccw

twin meteorBOT
rare wyvern
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<@&286206848099549185>

calm tulip
#

@vocal sleet

vocal sleetBOT
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@rare wyvern Has your question been resolved?

rare wyvern
#

<@&286206848099549185>

vocal sleetBOT
#

@rare wyvern Has your question been resolved?

rare wyvern
#

<@&286206848099549185>

heady ibex
#

hey i don't know if what i did was valid

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but through some what seems to me to be rather vague ideas i got the right expression

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i decided if d is true

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let b = c = d = e = f

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a special case of d

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(d)

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then let a = c = d = e = f another special case of (d)

agile oxide
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What’s this

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Or is it 21

heady ibex
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you should go into a new help channel

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@rare wyvern

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after you find those two special cases of (d) you add them together

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to get the equation

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but i have no idea if that is proving anything or if i'm just fucking with the symbols

rare wyvern
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wym by special cases

heady ibex
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well a, b, c, d, e, and f can be any number > 0

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and the inequality holds

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that's proven in (d)

rare wyvern
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yeah

heady ibex
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you presumably did tha

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t

rare wyvern
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yeah you can assume d)

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yeah cause i proved that alreasy

heady ibex
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a special case of that is where b = c = d = e = f

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and another one is where a = c = d = e = f

rare wyvern
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then a = b

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oh wait

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nah becayse they are two seperate cases

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aight lemme try that

heady ibex
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to avoid confusion i should make it b = c = d = e = f and a' = c' = d' = e' = f'

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but although i get the correct expression at the end

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idk if i just did fucky stuff

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or if it actually proves anything

rare wyvern
#

idk that might be it actually

heady ibex
#

i can give screenshot of what i did

rare wyvern
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though i havent done a proofs question like that

heady ibex
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if you want it

rare wyvern
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yeah would be good thanks

heady ibex
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the second to last line are the two special cases of (d)

rare wyvern
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yeah that works

heady ibex
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which you then add together

rare wyvern
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i dont see a problem with it

heady ibex
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to get the right expression

rare wyvern
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damn

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thanks a lot

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this question was buggin me

heady ibex
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you should ask a prof for clarification because i am not certain 😄

rare wyvern
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i will but thanks again anyways

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how do i close this

heady ibex
#

.close

rare wyvern
#

.close

vocal sleetBOT
#
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thorny storm
thorny storm
#

That was good man, never have I saw a use like that, and I'm going to graduate in maths this month 😂

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umbral cove
#

Hi, the answer to this is P = 2<-13/5, -19/5> + (1, -5) right?

umbral cove
#

My teacher got a different vector and I have no idea how

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I checked my algebra like thrice

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he got P = 2<-18/5, 6/5> + (1, -5)

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idk how he got the 18/5

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wait nvm

#

.close

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vast shale
#

.

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How did my teacher determine that this would be in quadranttwo?

vast shale
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I'm so confused

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Because the triangle we have is in quadrant III

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How did half of the tan end up in QII

icy spear
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Quadrant III is the interval (pi, 3pi/2)

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half of that would be the interval (pi/2, 3pi/4)

vast shale
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We don't use unit circle

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If that's what you're referring to

icy spear
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you have to use the unit circle

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otherwise it doesn't really even make sense to refer to angles being in quadrants at all

vast shale
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How did she do it then

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She like free stuff

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Drew

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You see the blue stuff?

icy spear
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would you agree that angles in quadrant 3 lie in the interval (pi, 3pi/2)

vast shale
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I know 3pi/2 is a coterminal angle in quadrant 3

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I guess those are coordinates?

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I've never been allowed to use a unit circle

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She doesn't like it

icy spear
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not coordinates, this is an interval

vast shale
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What do you mean by that though

icy spear
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wdym not allowed? how do you even define the tangent then

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fine alright how about this.

vast shale
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Or 1/cotx

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Those are identities though

icy spear
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you see that's not really a definition because it tells you nothing about how to find the tangent as the function of an angle

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like if i told you to find tan(2) you probably would have no way of knowing how to do that

icy spear
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nope

vast shale
#

That's 1/2

icy spear
#

tan(2). not tan(x) = 2.

vast shale
#

Oh

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What the heck is tan(2)

icy spear
#

the tangent of 2 radians

vast shale
#

Tan^-1

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Inverse trig functions?

icy spear
#

the tangent is a function that takes in an angle and returns a number

vast shale
#

Or would that not work either

icy spear
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you really do need to use the unit circle, i'm guessing you just haven't gotten to that yet.

vast shale
#

We're almost done with precalculus entirely

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She said we'd never use it

icy spear
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well unfortunately for you she's 100% wrong

vast shale
#

I feel like she makes everything harder than it should be

icy spear
#

let's focus on the whole quadrant thing for a moment

vast shale
#

I understand it now

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It's just splitting the quadrant system in half

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And going from there

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Sorry for taking your time up

#

Thank you for helping me though

#

.close

vocal sleetBOT
#
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vocal sleetBOT
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brave ruin
vocal sleetBOT
brave ruin
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Ignore the slash

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Anyone see my mistake?

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The solution is:

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Assume Cal 1 knowledge

outer warren
#

you had issues with the application of product rule for

brave ruin
#

Isn't it
d/dx[x]*y + d/dx[y]x = y + dy/dx * x ?

outer warren
#

yeh, but you didn't have that in you work

brave ruin
#

Isn't it right below that part?

#

hmmm

#

I''m gonna rewrite it

#

it's very sloppy

outer warren
#

you're missing the x in the second term

brave ruin
#

ahhhh

outer warren
#

and you should also have parentheses around that whole part

brave ruin
#

I rewrote it

#

Hopefully that's easier to read

#

I stopped at 4

outer warren
#

same issue again

brave ruin
#

no way

#

can you point to the number

outer warren
#

again you somehow wrote
y dy/dx + 1
which isn't
the y + dy/dx x which i confirmed to be correct

#

(1), your work for the derivative of xy

brave ruin
#

shit

#

okay

#

I see that

#

is that the only error you see

outer warren
#

rewrite it, i didn't look at any of the work that involved the result of the wrong derivative

brave ruin
#

okie

outer warren
#

yeh

#

looks ok now

brave ruin
#

so

#

can I combine the two terms on the lhs

#

then on the rhs, I could subtract x^2 dy/dx to get it on the lhs

#

The idea is to isolate dy/dx

rough cairn
brave ruin
#

bruh

brave ruin
outer warren
#

after isolating dy/dx and simplifying you should get the result

#

show your attemp

brave ruin
#

right

#

well that's the thing

#

The mess I got , i'm not really sure

#

I'll show you

#

<@&286206848099549185>

outer warren
#

this isn't any different from isolating a certain variable in any other linear equation

vast shale
outer warren
#

separate terms with dy/dx from terms without that

vast shale
outer warren
#

would you be able to solve
(a + bc)(1/d) = e + fc
for c?

brave ruin
#

Ummm

#

For that I can divide (1/d) from the lhs

#

Oh

#

Wait

#

(1/d) = (e + fc) / (a + bc)

#

Hmmm

#

Yeah I can't figure it out here either

#

What's the algebra property here that I'm forgetting

outer warren
#

lets make things simpler and reduce this to a question with one variable

#

would you be able to solve
(2 + 3x)/5 = 2 + 7x

brave ruin
#

(2+3x) = 10 + 35x
.
.
(2 + 3x) - 35x = 10
.
.
.
x[(2+3) - 35] = 10
.
X = 10 / -30 ?

brave ruin
brave ruin
#

5 - 35 = - 30

outer warren
#

(2 + 3x) - 35x = 10
x[(2+3) - 35] = 10
that step was invalid

brave ruin
#

Oh

outer warren
#

x isn't a factor of (2+3x)
you can't factor x out like that

vast shale
vocal sleetBOT
#

@brave ruin Has your question been resolved?

rough cairn
vast shale
#

Use cos2x=1-2sin²x

vocal sleetBOT
#
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rough cairn
#

Please check this

vocal sleetBOT
paper depot
#

where's your solution?

vast shale
rough cairn
#

I want to confirm my ans

tidal marlin
#

what is your answer?

paper depot
rough cairn
thin vale
#

Please show your work that got you to the answer of D

rough cairn
#

Hmm wait

tidal marlin
#

isn't z only infinite if either x or y is infinite?

rough cairn
#

Since it maximizing at 2 point so it should be infinite?

tidal marlin
#

Oh mb I read it wrong 😭

rough cairn
#

.close

vocal sleetBOT
#
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storm idol
#

Hi

vocal sleetBOT
storm idol
#

Not sure how to do this

#

Do I multiply both of them individually of their conjugate?

#

<@&286206848099549185>

sweet frost
#

@storm idol
What about taking LCM first?

storm idol
#

Would that be

#

Hmmm

#

How can I do that for m+i and m-i though

sweet frost
#

the LCM of two distinct denominators which cannot be reduced further is equal to their product

#

a/b +a/c
In above case denominators are distinct and their LCM would be bc

storm idol
#

Oh hmm

#

Brb shower real quick

#

Ok

#

Im back

rough cairn
#

I think you should multiply by its conjugate first

rough cairn
#

Yes individually

storm idol
#

Okok

#

On it boss

rough cairn
#

Their denomination will become same

storm idol
#

How do you know that

gaunt pendant
#

Well write it as a single fraction

#

then do some algebra to get it in standard form of a complex number

sweet frost
#

@storm idol are you done with your question?

storm idol
#

Nope

#

Im a bit busy rn

#

9 50 pm NZT

#

4 minutes*

vocal sleetBOT
#

@storm idol Has your question been resolved?

#
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kind zephyr
#

This is what I have so far

vocal sleetBOT
#

@kind zephyr Has your question been resolved?

vocal sleetBOT
#

@kind zephyr Has your question been resolved?

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vocal sleetBOT
vocal sleetBOT
#

@late vessel Has your question been resolved?

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half cloud
#

how to get the inverse of this?

vocal sleetBOT
vocal sleetBOT
#

@half cloud Has your question been resolved?

vocal sleetBOT
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twin meteorBOT
onyx condor
#

Let $p(x) = x^5 + x^2 + \bar{1}$ and $ E = \mathbb{Z}_2 [x]/<p(x)>$
I've shown that E is a field since p(x) is a maximal ideal, the dimension of E is 5 and that the number of elements in E is 2^5 = 32. We have that Z mod 2 is a subfield of E such that we can consider p(x) as a polynomial over E. How can we factorise p(x) over E?

hard atlas
#

do you know one root of p? what do you know about conjugation?

vocal sleetBOT
#

@onyx condor Has your question been resolved?

hard atlas
#

dont ignore the bot while you are typing

onyx condor
#

no havent found any roots in E. Not entirely sure what the roots should look like. Are we looking for an x where x is a polynomial upto degree 4?

vocal sleetBOT
#
Channel closed

Closed due to the original message being deleted

hard atlas
#

and dont delete the original message...

#

get a new channel

onyx condor
#

mb

#

was an error in the tex

hard atlas
#

then edit, dont delete

onyx condor
#

it wouldnt change

hard atlas
#

copy paste

vocal sleetBOT
#
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onyx condor
#

Let $p(x) = x^5 + x^2 + \bar{1}$ and $ E = \mathbb{Z}_2 [x]/<p(x)>$

twin meteorBOT
hard atlas
#

the bot only lets you change the output for a few minutes

#

after that you need to write a new message

#

what is $p(\overline x)$ ?

twin meteorBOT
#

Denascite

onyx condor
#

A polynomial?

hard atlas
#

no, if anything a residue class

#

with overline x I mean the residue class of x in E

onyx condor
#

aha

#

yeah so the elements of E are residue classes

hard atlas
#

yes

#

and each residue class includes a unique polynomial of degree < 5. which we usually use as the representant

onyx condor
#

mhm

#

so we are trying to write x^5 + x^2 + 1 as a product of some representatives of residue classes ?

hard atlas
#

no

#

you said that polynomial is irreducible

#

so how should we write it as a product

#

well ok, trivial products I guess

onyx condor
#

oh ok, thought the irreducibility was dependent on the field

hard atlas
#

well ok yes. we'll get there over E

#

first we want to find a root

#

and I'm asking you to please calculate p(overline x)

onyx condor
#

i dont know what p(overline x) is

hard atlas
#

plug overline x in

#

and use what rules about addition and multiplication you know in quotient rings

onyx condor
#

$\bar{x}^5 + \bar{x}^2 + \bar{1}$ ?

twin meteorBOT
hard atlas
#

yes

#

next?

onyx condor
#

$p(\bar{x}) = 0 \iff \bar{x}^2 = -1(x^5 + 1) \iff \bar{x} = i * \sqrt{\bar{x}^5 +1}$

hard atlas
#

what?

#

what is $\overline a \cdot \overline b$ ?

twin meteorBOT
#

Denascite

hard atlas
#

what is i supposed to be

#

and who says you can take roots in E

twin meteorBOT
onyx condor
#

it woult be a * b mod p(x) ?

onyx condor
hard atlas
#

you are just supposed to follow my instructions for a moment. you are not supposed to solve the equation

onyx condor
#

ok leme go back

hard atlas
#

how do you multiply residue classes in a quotient ring

#

btw we are working mod2, so -1=1

onyx condor
#

(a + N)(b + N) = ab + N

#

is this what you mean?

hard atlas
#

ok we are switching notation but yes

#

$\overline a \cdot \overline b = \overline{ab}$

twin meteorBOT
#

Denascite

hard atlas
#

so what is $\overline x ^2 = \overline x \cdot \overline x$ ?

twin meteorBOT
#

Denascite

onyx condor
#

hmm

#

$\overline{xx}$ ?

twin meteorBOT
hard atlas
#

yes

#

or in more usual notation, $\overline{x^2}$

twin meteorBOT
#

Denascite

hard atlas
#

what about $\overline x ^5$

twin meteorBOT
#

Denascite

onyx condor
#

$\overline{x^5}$

hard atlas
#

{}

twin meteorBOT
hard atlas
#

ok, so now $p(\overline x) = \overline{x^5} + \overline{x^2} + \overline{1}$

twin meteorBOT
#

Denascite

hard atlas
#

next, how do you add residue classes

onyx condor
#

$\overline a + \overline b = \overline{a + b}$

twin meteorBOT
hard atlas
#

yes

#

what do you get if you apply that

onyx condor
#

$p(\overline x) = \overline{x^5 + x^2 + 1}$

twin meteorBOT
hard atlas
#

yes

#

and what is that residue class equal to

onyx condor
#

alright

#

how do we go from here?

#

to finding roots in E

hard atlas
#

how about you answer my questions

onyx condor
#

man im blind

hard atlas
#

what is the residue class of p(x) in E

#

what is the usual representant

onyx condor
#

0 ?

hard atlas
#

yes

#

so p(overline x) = overline 0

#

so in E, overline x is a root of p

onyx condor
#

ok

hard atlas
#

ok

#

so we found one root

#

what do you know about field automorphisms

onyx condor
onyx condor
hard atlas
#

no

#

they need more structure

onyx condor
#

i see they are isomorphisms

#

like permutations?

hard atlas
#

iso means bijective, so yes they are permutations

#

but special ones

onyx condor
#

ok, but im still uncertain what the question to factorise p(x) over E even means. Like what exactly are we looking for?

hard atlas
#

we will eventually get a factorisation (x-a)(x-b)(x-c)(x-d)(x-e) where a,b,c,d,e are elements of E

onyx condor
#

aha

hard atlas
#

we found the first factor with a=overline x

onyx condor
#

ohh now i see why it was a root

#

can we divide p(\overline x) by (x-\overline x) to get a 4th degree polynomial?

hard atlas
#

we could

#

but we wont

#

because then we'd have to do all kinds of calculations in E

#

and then just get out some random 4th degree polynomial which will be harder to argue with than with p

onyx condor
#

ok

#

so what now?

hard atlas
#

I was still asking you about field automorphisms

#

so we got that they are isomorphisms from E to itself. isomorphism in what sense. which operations do they respect

onyx condor
#

im thinking that it would map residue classes to residue classes

#

and preserve the addition and multiplication rules we just went through

hard atlas
#

well yes E is a set of residue classes

#

yes

#

did you do none of this in class?

onyx condor
#

this is the very last part of our intro to algebra class, and i missed the lecture they went through this exercise

#

we learned about the division algorithm, and when we get fields from ideals

hard atlas
#

in that lecture that you missed or before that?

onyx condor
#

before that

hard atlas
#

do you have notes from friends for the lecture that you missed?

onyx condor
#

yes, in the first half of the lecture they covered 1. definition of a maximal ideal 2. that an ideal I in R is maximal iff R/I is a field 3. That the ideal generated by p(x) in F[x] is maximal iff p(x) is irreducible over F

#

Also showed that F[x] is a vector space over F and that F[x]/<g(x)> is a finite dimensional vector space for g(x) in F[x] different from 0

hard atlas
#

hmm that is not enough to do this exercise. can you show me the original problem statement?

onyx condor
hard atlas
#

hmmm

onyx condor
#

i feel bad youve helped so much

#

we can stop here if you want to go. i can ask the classmates after easter what they did

hard atlas
#

did you have in class that over F_p, the map x^p is linear?

onyx condor
#

no

hard atlas
#

(a+b)^p = a^p + b^p ? not seen?

onyx condor
#

no, we've seen the binomial expansion but not this

hard atlas
#

hmm

#

well for p=2 its easy enough to see

#

I'm really wondering what they want to hear from you for this exercise

onyx condor
#

sometimes the professors assume we know stuff we dont

hard atlas
#

I guess we can at least factorize p(x)=(x-overline x)*(random degree 4 polynomial)

#

which is a factorization

#

not as good as you can do but well

#

but even seeing that overline x is a root is stuff that I wouldnt expect anyone to come up with

#

at least not within the time constraint that these assignments typically have

onyx condor
#

They said they intentionally include some questions that we aren't ready for yet to get us to think about the questions. It's not expected of us to solve them

hard atlas
#

oh

onyx condor
#

is there material you'd recommend to read up on for solving these kinds of questions?

hard atlas
#

any book on finite fields

#

or I mean, just field theory in general

onyx condor
#

thank you so much for all the help

vocal sleetBOT
#

@onyx condor Has your question been resolved?

#
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oblique stone
#

hey

vocal sleetBOT
oblique stone
#

question

#

how would i go about proving or disproving this. don't want the answer, just the first step

strange crater
#

use the definition of m|n first

oblique stone
#

what is the definition?

#

n=mk?

strange crater
#

you should have learned that if you are asked to prove things about divisibility

oblique stone
#

these are questions that haven't been covered yet

#

*topics

#

also is it assumed that the devisor is the same in all 3 statements?

#

@strange crater

strange crater
#

if m | n then there exists some k such that n = mk. you got that right

#

since the conclusion is a negative statement, it might be easiest to prove by contradiction

oblique stone
#

ah

#

so what would be the first step, assume d|m?

rough barn
#

yeah

strange crater
#

assume $m | n$, and $d \nmid n$ and $d | m$

twin meteorBOT
#

cwatson

strange crater
#

and reach a contradiction

oblique stone
#

mhmm

#

so then i would do n=mk, n !=dk, and m=dk?

#

and then substitute?

strange crater
#

try it, see what happens

#

if you get stuck, come back

oblique stone
#

m!=d

#

ok

#

ok i tried assuming that d|m and ended up getting k!=1

#

i don't think im approaching the question correctly. no?

#

@strange crater

strange crater
#

so you have n=mk as one assumption, and you're also assuming the negative of the conclusion, so that d|m. but that doesn't mean m=dk; i.e., it won't be "the same k" for both necessarily

#

so assume m = dj for some j

#

so you have n = mk, and m = dj

#

then what would you do?

oblique stone
#

rearrange and get n/k=dj?

strange crater
#

no, do it one step at a time

#

but you were on the right track...

oblique stone
#

hmmm

strange crater
#

so, go back. what is the next step after seeing that n=mk, m=dj

oblique stone
#

substituting

strange crater
#

which gives you what?

oblique stone
#

n=djk

strange crater
#

now what does that mean, right there?

oblique stone
#

means m=dj

strange crater
#

you started w/ that already

#

just look at n=djk itself

#

and look back at your starting assumptions

oblique stone
#

oh

#

it breaks the definition of n=mk

strange crater
#

how would it? you used n=mk (along with m=dj) to get to n=djk

oblique stone
#

yes my bad

strange crater
#

no worries. look at all the starting assumptions

oblique stone
#

unsure

strange crater
#

what if it was written like n = d(jk)

#

think of the definitions you used to start the proof

oblique stone
#

i don't know

#

could i do d!|n = n!=gd

strange crater
#

if $m | n \leftrightarrow n = mk$ then what does $n = d(jk)$ tell you

twin meteorBOT
#

cwatson

strange crater
#

remember, we're looking for a contradiction to be reached

oblique stone
#

i don't know, i just get back to m=dj

#

wait

strange crater
#

does $n=d(jk)$ contradict any of the assumptions: $m | n$, and $d \nmid n$ and $d | m$

twin meteorBOT
#

cwatson

oblique stone
#

i think i understand it now but i don't know how to write it

strange crater
#

if you understand, then explain in words

oblique stone
#

actually my line of reasoning didn't make sense, nvm

#

ok i don't know. another hint? @strange crater

strange crater
#

if I tell you that you don't need to do anything more, does that help? you have enough finished to conclude the proof...

#

which of the 3 assumptions have we not used so far?

oblique stone
#

n!=gd

strange crater
#

yes

#

and with the other 2 assumptions we've shown that $n = d(jk) = (jk)d$

twin meteorBOT
#

cwatson

strange crater
#

so what does that tell you?

oblique stone
#

d!=d?

strange crater
#

no, you're not manipulating equations here

#

if I told you "let g = jk"

#

then what?

oblique stone
#

djk!=gd

#

jk!=g

strange crater
#

but we are saying that g = jk.........

#

there's the contradiction

oblique stone
#

why is that something we can assume?

strange crater
#

because j and k are just integers. so their product is another integer. we can just call it "g", or "x", or whatever

oblique stone
#

ah i see fair enough

strange crater
#

so by saying $n = d(jk) = (jk)d = gd$, we are saying that $d | n$, which contradicts our (given) assumption that $d \nmid n$

twin meteorBOT
#

cwatson

oblique stone
#

ok that's where the issue was in my understanding, got to jk!=g and didn't know where to go

#

thank you very much @strange crater

#

.close

vocal sleetBOT
#
Channel closed

Closed by @oblique stone

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vast shale
#

idk how to convert them

vocal sleetBOT
#

Please don't occupy multiple help channels.

vast shale
#

.close

vocal sleetBOT
#
Channel closed

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vocal sleetBOT
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scarlet bough
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how do i solve for 0<x<180? i did tan(3)^-1 to get 71.57 and i divided that by 2 to get 35.78 but one of the other answers is 125.78 and idk how to get that

dull bear
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if 0<x<180 then 0<2x<360 - for these types of questions it can be easier to make a substitution such as u=2x, solve for u first, and then from there solve for x

scarlet bough
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.close

vocal sleetBOT
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vocal sleetBOT
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gentle anvil
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Im trying to determine the function for the sum of this power series

gentle anvil
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Im figuring its something with e^x^2 but the (n+1)n! Part is really throwing me off

rugged vortex
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Hm

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Yeah no that (n+1)! Is tricky

dull bear
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Maybe make a substitution in the sum to change the n+1 into n

river minnow
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Reindex

gentle anvil
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Reindex?

gentle anvil
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Also according to wolfram its

dull bear
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As in your original was
[
\sum_{n=0}^{\infty} \frac{x^{2n}}{(n+1)!}
]
we're suggesting to shift the terms so that the $n + 1$ turns into $n$ in the sum

twin meteorBOT
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@dull bear

rugged vortex
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Yeah that's also what I got

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Well

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Without the -1

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Hm

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Because I let u = n+1

dull bear
gentle anvil
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How would i shift the terms so it would be n?

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I cant see it

rugged vortex
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Well let u = n+1

dull bear
brave ruin
gentle anvil
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Okay so i got, U!

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How does that do anything cuz i dont know where to go from, dont think ive learned this approch looking through the text book

brave ruin
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should i try to explain or share soln, cox soln is easy to look at and understand

rugged vortex
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well they already know the answer

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So showing steps is fine

brave ruin
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cool

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expansion of e^x^2 can be obtained using maclaurin & taylor series

gentle anvil
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Thank you this makes so much sense i got it now!!! ❤️

#

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vocal sleetBOT
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#
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autumn badger
vocal sleetBOT
autumn badger
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what is number of term?

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i found q, she said q is the common ratio

sacred acorn
autumn badger
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?

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u1 = 16
u2=8
u3=4
u4=2
u5=1
u6=1/2
u7=1/4
u8=1/8

sacred acorn
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that's right but you also have to include the 16 at the beginning in your counting so it would be 8

autumn badger
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oh

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thanks

sacred acorn
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no problem 🙂

autumn badger
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jade sparrow
jade sparrow
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is it 15 * 14 * 13 + 10 * 9 * 8?

loud walrus
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yes

vocal sleetBOT
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@jade sparrow Has your question been resolved?

jade sparrow
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ty

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vast shale
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Have I evaluated this correctly?

vocal sleetBOT
desert hornet
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,rcw

twin meteorBOT
desert hornet
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what do you need to calculate?

vast shale
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F'(x)

desert hornet
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not quite

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you would have to multiply it by the derivative of the ineer function

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due to the chain rule

vast shale
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Oh, I thought the chain rule was just for say if it was like integral[5,x^2]

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So would it just be F'= -4x^3tan(x^4)?

desert hornet
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wait

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I'm getting confused

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i think it's best if somebody else helps you

vocal sleetBOT
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@vast shale Has your question been resolved?

vast shale
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my original answer was correct *

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.close

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frank plover
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What math rule allows this?

vocal sleetBOT
frank plover
prime spear
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ithink its fractional exponent

frank plover
#

.close

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blazing depot
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does derivatives mean slope?

vocal sleetBOT