#help-26

226100 messages · Page 251 of 227

hazy pumice
#

No, what would?

#

You are solving for "dy/dx"

tiny ginkgo
#

to isolate dy/dx we need to take them to opposite sides of each other?

hazy pumice
#

No

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Both terms with dy/dx in it are already on the same side

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Factor it out of both terms

tiny ginkgo
#

so itd be 3x^2+4y=2x

hazy pumice
#

Ok, let's assume I'm too distracted to recognize your genius

#

I'm trying to get there hang on

tiny ginkgo
#

4x(dy/dx)+3y^2(dy/dx)=2x-3x^2-4y

hazy pumice
#

3x^2 + (dy/dx)(4x + 3y^2) + 4y = 2x

dy/dx = (2x - 3x^2 - 4y)/(4x + 3y^2)

#

Yes, you were on it in your last post

tiny ginkgo
#

is it possible to isolate dy/dx from 4x(dy/dx)+3y^2(dy/dx)=2x-3x^2-4y?

#

is it possible to get dy/dx = (2x - 3x^2 - 4y)/(4x + 3y^2) from 4x(dy/dx)+3y^2(dy/dx)=2x-3x^2-4y?

hazy pumice
#

What are you talking about, its just factoring

#

It's up there ^

tiny ginkgo
#

why is (2x-3x^2-4y) on top and not the other one

hazy pumice
#

The terms without dy/dx as a factor will be on top, you can try this experiment

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...on this problem, I mean

#

Or I guess

2x - 1 = 6, solve for x

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Term without x in it on top

tiny ginkgo
#

would you multiply dx/dy on both sides

#

also we dont end up using the points for anything is that alright?

#

.close

topaz sinewBOT
#
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stark thicket
topaz sinewBOT
stark thicket
#

how to prove they are equal without using calculator

neon iron
#

factor both equations

stark thicket
#

didnt work

neon iron
#

are you trying to find the solution or prove they're equal?

stark thicket
#

prove they are equal

mystic cobalt
#

hm

neon iron
#

wtf they aren't equal though

mystic cobalt
#

interesting

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let me see it for a bit

stark thicket
neon iron
#

OH

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so find the solution

mystic cobalt
#

u have to find these solutions?

stark thicket
#

i have to prove they are equal

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without using solutions

neon iron
#

no you're not proving they're equal you're proving they intersect/the equaiton has a solution

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it isn't equal for all v

stark thicket
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its not possible to go from left

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to right?

neon iron
#

multiple the four by each term

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then subtract the common terms from each side

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make it a quadratic

stark thicket
#

i tried everything m8

neon iron
#

UHHHH

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ill help

stark thicket
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they intersect in 2 points

mystic cobalt
#

well

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i think

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you must find some solutions and make a table for common answers

thorny flameBOT
#

kaynsu

neon iron
#

i messed up

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32 v^2 + 36 v +4

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that's the LHS

stark thicket
#

so u telling i can only prove they are the same only when x is equal to 2 solutions

mystic cobalt
#

not quite that

neon iron
#

are you looking for real or complex solutions?

stark thicket
#

not trying to find solutions

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trying to go from left to right

neon iron
#

yes y ouare

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you are trying to find the place where the equality holds

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they aren't equal that doesn't make any sense

stark thicket
#

they are equal in 2 points only

neon iron
#

yes

stark thicket
#

but not in other points

neon iron
#

yes

stark thicket
#

thkx m8

neon iron
#

those are the solutions

empty sail
#

Do you have the exact question?

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Like post a screenshot of it

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Because whatever you are asking makes no sense

stark thicket
#

teacher just gave it in the last minute in class

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told us to right that only

neon iron
#

ok so you're trying to find the solutions

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just trust me on that

stark thicket
#

ok

mystic cobalt
#

let me get some paper

neon iron
#

multiply the four on the LHS

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then combine like terms

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set it equal to 0 and use the quadratic equation

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that's the game plan

stark thicket
#

i understand u

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i made that

neon iron
#

let me see

stark thicket
#

25v^2+21v+2=0

neon iron
#

now use quadratic equation

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what class are you in

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algebra 2?

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college algebra?

stark thicket
#

idk

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my school dont go with that system

neon iron
#

have you learned about complex numbers

stark thicket
#

yes a year ago

neon iron
#

ok so you may have two complex or one complex or no complex solutions

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just use the quadratic equation

stark thicket
#

kaynsu

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i want to ask question

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last question

neon iron
#

ok

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shoot

stark thicket
# stark thicket

this is true only if x is in solutions of the combined = 0 thingy

neon iron
#

if the RHS =0, then you can use the quadratic equation

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RHS = right hand side

mystic cobalt
#

check this out

stark thicket
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i didnt undestand last part

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all other i understand

mystic cobalt
#

which part?

stark thicket
#

aaaa

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u drew them

#

i understand

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thanks for ur time

mystic cobalt
#

all gucci

topaz sinewBOT
#

@stark thicket Has your question been resolved?

topaz sinewBOT
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gloomy needle
topaz sinewBOT
gloomy needle
#

i need help plz

wary frost
#

anyone able to do 5th grade math?

gloomy needle
wary frost
gloomy needle
#

question 13 is 72

#

its 2(length+width)

wary oak
gloomy needle
wary oak
#

The formula is written there

empty sail
wary frost
#

oh sorry im new

empty sail
gloomy needle
empty sail
gloomy needle
empty sail
#

Plug in the P values into T(x, y) equation given

gloomy needle
#

k thx

#

got it

topaz sinewBOT
#

@gloomy needle Has your question been resolved?

gloomy needle
#

?

#

.close

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neon iron
topaz sinewBOT
devout halo
topaz sinewBOT
#

@neon iron Has your question been resolved?

neon iron
#

Help him

#

He’s dumb

arctic plank
#

hey be nice

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some people arent as smart as u

neon iron
empty sail
#

Two, don't be rude

arctic plank
#

u can help him instead of beating him down

#

im sure he'll appreciate ur help

empty sail
arctic plank
#

.close

neon iron
topaz sinewBOT
#
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neon iron
#

Nah

topaz sinewBOT
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neon iron
topaz sinewBOT
arctic plank
#

can u not

empty sail
#

Because stop

arctic plank
#

am i allowed to ping a mod

neon iron
#

No that was an accident

#

Calm ur tits

#

.close

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empty sail
#

Fyi, don't ping specific mods

arctic plank
#

k

empty sail
#

That's why the mod ping exists

neon iron
arctic plank
neon iron
empty sail
#

<@&268886789983436800> Can you deal with this user? Being rude to others and seems very trollish

arctic plank
#

.close

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fading cypress
#

Can someone please explain this limit law, I don't understand what it means

sudden parcel
#

simply put x equal to a

#

this law literally means to limit the observation of a function to the point 'a'

fading cypress
#

could you give an example?

sudden parcel
#

let's say, we take the limit of a function: f(x)=sin(x)/x

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at 'x' = 0

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that basically implies that we are observing what the function returns when the value of x becomes 0

keen venture
#

All continuous functions do this.
Like, the limit of 2x
as x approaches 3
is 2(3)

fading cypress
#

ohhh i get it

#

thank you both!

sudden parcel
#

@fading cypress if you are done, close this channel

#

type .close

fading cypress
#

.close

topaz sinewBOT
#
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split solstice
#

Hi I have a question about discrete mathematics

split solstice
vernal vale
#

what have you tried?

split solstice
#

I have tried like finding the pattern with it. Too see if it would be true for every like example but I dont really know how to "prove" it

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or is like all the variatons the proof or is there actually a physical format proof that I need to show

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Im pretty sure its true for every combination of x y z but idk how to prove it unless I should list out every possibility

fluid phoenix
#

how many cases are there though

worldly tendon
#

y and z are interchangeable so assume without loss of generality that y < z
reduces cases to check by 1/2

split solstice
#

I think there are 8 cases

worldly tendon
#

meaning you only need to check x < y < z, y < x < z, and y < z < x

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there are 3 cases

split solstice
#

Why only 3

worldly tendon
#

i just said why

split solstice
#

oh sorry missed that

split solstice
#

so do you think just listing out those variations should suffice

#

thats what I would assume as well but just double checking

#

.close

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frail lion
#

yo

topaz sinewBOT
frail lion
wheat grove
#

test?

frail lion
#

no

#

past papers

#

im doing them for my exam tommorow

wheat grove
#

perimeter is the outer boundary so

worthy storm
#

maybe the simplest way is to recognize that there's a related rectangle with the same perimeter

frail lion
#

i divided the shape

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into two part

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one which is a rectangle

wheat grove
#

then you just need to find two left sides (which are the differences of two sides)

frail lion
#

isnt the other shape a

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square

worthy storm
#

"not drawn to scale"

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just extend the right side so that instead of turning left where it does, it turns left at the bottom of the figure

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you get a rectangle with sides 5x+4 and 3x

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with the same perimeter

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the x+1 and 2x are irrelevant

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weird problem imo

restive inlet
#

the x+1 and 2x are irrelevant
this is only part i)
supposedly they'd be useful in later parts when the area is requested

worthy storm
#

fair enough, then just consider my observation a short cut for part i 😄

#

amusing and somewhat related:

topaz sinewBOT
#

@frail lion Has your question been resolved?

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neon iron
#

so for this question i alreayd got the answer for it but i used trial and error, i was wondering if there is a formula for this type of question or can i only get it out of trial and error.

vernal vale
#

hmm

neon iron
#

How I got it was by 150/10 = 15

fast sentinel
#

the question alone has multiple solutions

neon iron
#

To make it easier

fast sentinel
#

are there any other requirements

soft copper
#

Is anybody here an expert in statistics?

neon iron
fast sentinel
fast sentinel
neon iron
neon iron
fast sentinel
#

im working with a language barrier here so sorry if i dont make any sense

neon iron
#

I don’t understand

fast sentinel
#

ok its fine

neon iron
#

Sry

#

I’m pretty sure what you’re saying makes sense but I’m just stupid and don’t understand it

fast sentinel
neon iron
#

Would it be 2x?

fast sentinel
#

yes

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and how long would the next piece be

neon iron
#

Uh

fast sentinel
#

the piece after the one with length 2x

neon iron
#

2(2x)?

fast sentinel
#

yes

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and what would be the one after that

neon iron
#

2•(2 x 2x)

fast sentinel
neon iron
#

No

fast sentinel
#

you mean 2*2x*2x?

neon iron
#

2 x (2x2x)

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Wait

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I did it wrong

neon iron
fast sentinel
neon iron
#

K

fast sentinel
neon iron
#

I’m still thinking

#

🤔

fast sentinel
#

if the next pieces length is double of the current one (which is 2(2x)) what would be its length

neon iron
#

Wouldn’t it be 2 x (2(2x))

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Cause it’s double it’s length

fast sentinel
#

yes

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assuming you mean 2 * (2(2x))

neon iron
#

Yup

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That was what I was saying the whole time

fast sentinel
#

oh

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so can you see a pattern

neon iron
#

Yup

fast sentinel
#

so the pieces length would be x, 2x, 2²x, 2³x, ... right

neon iron
#

Do I keep going?

fast sentinel
#

no lets see what we have right now

fast sentinel
neon iron
#

Yea

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Wait

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Wtf

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I didn’t see that the whole time

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Mb

fast sentinel
#

now the problem here is that the question doesnt tell us how many pieces there are

neon iron
#

Yup

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It just tells us it equals to 150

fast sentinel
#

which we will see why later

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yeah

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so if we were to assume the wire is cut into 4 pieces what would be x

neon iron
#

15

fast sentinel
#

think again

neon iron
#

X+2x+4x+8x=

fast sentinel
#

yes

neon iron
#

Oh

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Wouldn’t it be 15x

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?????

fast sentinel
#

indeed

neon iron
fast sentinel
#

and what is 15x

neon iron
fast sentinel
neon iron
#

Yup

fast sentinel
#

the answer we get here is still in terms of x

neon iron
#

So it’s the total length or 4 pieces

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OfI

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Of*

fast sentinel
#

yes

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so the total length of the wire is the length of the 4 pieces combined

fast sentinel
neon iron
#

Is it because we got 15?

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15x

fast sentinel
neon iron
#

I don’t understand

fast sentinel
#

right now were assuming the wire is only cut into 4 pieces

neon iron
#

I don’t think they told us the max would be 4 pieces

neon iron
#

What do you mean by that

fast sentinel
fast sentinel
#

that we got in terms of x as 15x

neon iron
#

It’s Double the amount

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Of the first piece

fast sentinel
#

ok lets summarize the information that the question gave us first

neon iron
#

K

fast sentinel
neon iron
#

You want me to do it?

fast sentinel
#

or any constant value

neon iron
#

Yup

fast sentinel
#

what is it

neon iron
#

They told us

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That the wire is 150 long

fast sentinel
#

true

neon iron
#

And that the smallest piece/ first piece is over 9m long

fast sentinel
#

so what did we get for the length of the wire in terms of x a while ago

neon iron
#

15x

fast sentinel
#

so if the question tells us that the wire is 150 long

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and we get that the wire is 15x long

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can we form an equation

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to solve for x

neon iron
#

15x=150?

fast sentinel
#

yes

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and what would be x

neon iron
#

10

#

Oops

fast sentinel
#

so now lets check our answers

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so the four pieces length would be x, 2x, 4x and 8x

#

which would be 10, 20, 40 and 80

neon iron
#

Yup

fast sentinel
#

which adds up to 150

neon iron
#

Yes

fast sentinel
#

now this is the problem

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the question doesnt tell us how many pieces the wire is cut into

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so lets look at it again

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but this time assume that its cut into 2 pieces

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only

neon iron
#

K

#

Then the answer would be 75

fast sentinel
#

what would be the length of the 2 pieces in terms of x

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when x is the length of the smallest piece

neon iron
#

Oh

fast sentinel
#

what do you get

fast sentinel
#

yes

fast sentinel
#

correct

neon iron
#

Yup

fast sentinel
#

and if we check our answers; 50, 100
50+100=150

neon iron
#

Yea

fast sentinel
#

this is why the question has multiple solutions

neon iron
#

OHHHHH

fast sentinel
#

because both the solutions we found still satisfy the question

#

because theres no extra condition that limits it enough

neon iron
#

What the heck

fast sentinel
#

so yeah

neon iron
#

Wtf

fast sentinel
#

thats about it

neon iron
#

So basically the question is still trial and error?

fast sentinel
#

no

neon iron
#

Because there’s no exact formula for it

neon iron
fast sentinel
#

the method i presented is one apparent way of doing it

#

that doesnt involve trial and error

#

the problem here is the question doesnt have enough conditions to only have 1 answer

neon iron
#

But how did u come up with with cutting the thing into 2 pieces

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Or 4

fast sentinel
#

because the question didnt tell us how many pieces its cut into

#

i was demonstrating why thats a problem

neon iron
#

Oh

fast sentinel
#

because normally questions would only have 1 solution

neon iron
#

Yea

fast sentinel
#

and it would have to give us conditions that could only lead to 1 solution

#

but this problem doesnt have that

#

so yeah thats about it

neon iron
#

Ohhhhhh

#

Thanks alot for your time

fast sentinel
#

np

neon iron
#

Imma write this down

#

Then close

#

Or should I close first

fast sentinel
#

but if im going off what they want here they probably want the solution where its cut into 4 pieces because its "elegant" or something if thats the right word (integer sides, not too simple like the 2 pieces case, also satisifies that the smallest piece is more than 9 m long)

fast sentinel
neon iron
#

Thanks a lot😄

#

.close

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waxen storm
#

Why are two diff approach giving me diff answers?

abstract wadi
#

Where is the second approach?

#

You mean the one you have ❌?

#

@waxen storm

waxen storm
abstract wadi
#

It's wrong.

#

$(\log_5{x})^2 \neq \log_5{x^2}$

thorny flameBOT
#

What the hell am I doing here?

abstract wadi
#

What you did would be correct if you had $\log_5{x^2}$

thorny flameBOT
#

What the hell am I doing here?

waxen storm
#

Ah ive got my mistake xd

#

Thanks

#

.close

topaz sinewBOT
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acoustic wyvern
#

hihi! could i please get help with the second question?

acoustic wyvern
#

i dont really understand how to get the perpendicular height of the triangle

#

i know that AB is 5 root 2 from the distance formula

narrow torrent
#

can you find the distance AP

acoustic wyvern
narrow torrent
#

i'll assume that's correct

#

now can you find the distance BP

acoustic wyvern
#

in the solutions, theres a thing like this

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but i dont really understand what its saying-

acoustic wyvern
narrow torrent
#

i never made that assumption

acoustic wyvern
#

how do i find BP if its not right angled?

narrow torrent
#

just the distance formula

acoustic wyvern
#

but i dont know what P is and i only know BP and AP

narrow torrent
#

you do know what P is

#

(p, p^2)

acoustic wyvern
#

aa okieokie

#

root (p^4 -7p^2+4p+20)

narrow torrent
#

now this is going to get a bit messy but it will work

#

let k be the semiperimeter of this triangle, which is one half the sum of all the sides

#

$A = \sqrt{k(k-AB)(k-BP)(k-AP)}$

thorny flameBOT
#

EndTimes

narrow torrent
#

Heron's formula, just to save us from having to mess with all the trig

acoustic wyvern
#

aa okok thank you

#

.close

topaz sinewBOT
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analog osprey
topaz sinewBOT
analog osprey
#

how do i solve this

olive plume
#

The idea of (1,180) is not correct

analog osprey
#

they said a single period

#

imma write this on my paper

analog osprey
olive plume
#

Why do you think that when x is 1, y will be 180?

analog osprey
#

Cause its a single period

olive plume
#

No

#

180 is the number of pages initially he has to read

analog osprey
#

yep he has read it

olive plume
#

Initially here means when time is 0 because he hasnt begun to read it

#

SO it shoud be (0,180)

analog osprey
#

hmm

#

i dont get it

#

can u explain it in other words?

analog osprey
olive plume
#

When he just started to read the pages left is 180

#

So t must be 0

#

If the pages left is not 180, then he must have started to read some time earlier

#

So t cannot be 0

analog osprey
#

oh the word left

#

wait i dont understand

#

the sentence said Conrad read a 180 page book cover to cover in a single session

#

it didnt said left

olive plume
#

But the question mentioned he took 6 hours to read 180 pages

#

So when he just started to read, at t = 0, the pages left must be 180

analog osprey
#

that means he already read it

analog osprey
thorny flameBOT
analog osprey
#

so theres a y intercept

olive plume
#

yes

analog osprey
#

so after 6 hours he read 180 books

olive plume
#

180 pages not books

analog osprey
#

so its 6,0

#

after 6 hours. 0 pages left to read

olive plume
#

yes

analog osprey
#

x and y int

#

and no slope?

#

how do i identify if theres a slope

olive plume
#

slope is the gradient

#

From the question the gradient is not given

analog osprey
#

how do i know if theres a gradient?

#

delta y/delta x?

olive plume
#

Yes

#

so in this question will be (180-0)/(0-6)

#

= - 30

#

but since -30 is not stated in the question, so the slope is not given

analog osprey
#

how did u find that slope

#

give me a sec ill see if i can find the slope

analog osprey
#

i got 30 instead of -30

#

i think -30 and 30 is the same for the slope

#

right?

olive plume
olive plume
#

(180-0)/(0-6)

analog osprey
#

thats right

#

oh -6

#

but -30 and 30 for the slope is same tho

#

think about it

#

1/30 1/-30

analog osprey
#

i think ur confused

waxen storm
#

Slope is -30 only

olive plume
#

Slope is (y2-y1)/(x2-x1)

#

x2 is 0 y2 is 180

#

x1 is 6 y1 is 0

#

(0, 180) and (6, 0)

waxen storm
#

Slope wud have been 30 if your y was no. of pages read

analog osprey
waxen storm
analog osprey
#

wait wait wait

#

30 represents the y right?

#

every x it moves 30 y

waxen storm
#

In the question given its moving -30 y

analog osprey
#

how

#

i dont get how its negative

waxen storm
#

Draw the graph

analog osprey
#

ok i see now

topaz sinewBOT
#

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cold sigil
topaz sinewBOT
cold sigil
#

can someone helpp

#

15000 is the principle , 4.5 or 0.045 = interest rate , number of periods the interest compounded per year = 1

#

i supposed we need to use this formula right? mv = p ( 1 + r/n ) nt

topaz sinewBOT
#

@cold sigil Has your question been resolved?

summer dragon
#

do you need help with the formula or have you already tried this question?

cold sigil
#

no i dont know how to do it and which formulae to use

summer dragon
#

where it says per annum I assume it's asking for compounding interest

cold sigil
#

yes

summer dragon
#

the compounding interest formula is A=P(1+r/n)^nt

#

P is the principle amount, r is the rate (0.045) n is the number of times it compounds in a year and t being the number of years

#

so we could solve this by plugging the values in A=15,000(1+0.045/2)^2

cold sigil
#

let me try

#

the question said once every 6 months

summer dragon
#

oh yeah I was solving a

#

do you need help with b?

cold sigil
#

hold on

#

OH YEAH THATS RIGHT

#

thats right

summer dragon
#

it was 0.045/1?

cold sigil
#

no no

summer dragon
#

oh ok do you need help with question B as well? :]

cold sigil
#

sure

summer dragon
#

all you have to do is use the same formula, but change n to 6 since it compounds every 2 months and 2/12=6

cold sigil
#

so i calculated (1+0.045/2)

#

i got 1.0225

#

do i have to take all the numbers of just two numbers after the decimal point?

summer dragon
#

yea

#

I would try to calculate it all together because you need all the digits and then you round after

cold sigil
#

i got it

#

thank you so much for helping

#

:))

topaz sinewBOT
#

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unkempt anvil
topaz sinewBOT
unkempt anvil
#

Anyone tell me (h) and ( i)

topaz sinewBOT
#

@unkempt anvil Has your question been resolved?

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@unkempt anvil Has your question been resolved?

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flint moat
#

I have a 3x3 covariance matrix that describes how xyz values correlate. How can i reconstruct xyz values from the covariance matrix

flint moat
#

scale does not matter.

#

It should be doable

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@flint moat Has your question been resolved?

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marsh mortar
#

let u =1-x

topaz sinewBOT
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topaz lynx
topaz sinewBOT
topaz lynx
#

how to solve

wide berry
topaz lynx
#

all good

#

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neon iron
#

$\int e^{e^x} dx$

topaz sinewBOT
thorny flameBOT
#

Gilgamesh

neon iron
#

Can someone help me?

#

Thats my solution, but at the end we see that we divide by 0

mellow venture
#

u forgot

#

+C

#

and you can pull of the n=0 term from the sum before you take the integral , the n=0 term is just 1, so the integral becomes x + the sum from n=1

topaz sinewBOT
#

@neon iron Has your question been resolved?

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velvet notch
#

how does this make any sense?

topaz sinewBOT
velvet notch
#

i cant understand why the initial velocity cant be expressed as itself

tiny wolf
#

,w 29 yards to feet

thorny flameBOT
velvet notch
#

why must it be expressed as something else

#

oh

mild oasis
#

This is when living with imperial system is like living on hard mode

tiny wolf
#

Supposedly they expect you to use acceleration due to gravity in terms of ft/s^2

#

(Which I have literally never seen)

#

But in order to use this measurement, you need units to agree

#

So velocity needs to be in ft/s

velvet notch
#

ok thx

#

.close

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bold raptor
topaz sinewBOT
bold raptor
#

Help with 29th question please

bitter hemlock
#

Just add the fractions together

#

Common denominator

empty sail
bold raptor
#

If I take a look

empty sail
#

No

#

If you're unsure, you can use it to assist you

bold raptor
#

Hmmmm

#

Alright

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grizzled badge
#

reviewing riemann sums and im not understanding why they're multiply by 2.5 and 4 and stuff

grizzled badge
#

like what i would do for the right riemann sum is f(1)(1-0) + f(2)(2-1) + f(2.5)(2.5-2) + f(4)(4-2.5)

#

finding the areas of these rectangles, right?

#

which is just base*height, with height being f(x) and base being the (b-a) stuff

#

so where does that other term they're multiplying by come from?

#

here's the actual question if you want it

topaz sinewBOT
#

@grizzled badge Has your question been resolved?

topaz sinewBOT
#

@grizzled badge Has your question been resolved?

cosmic salmon
#

the extra term comes from the value of r

grizzled badge
#

ohhhhh

#

so the riemann sum was fine, but it was the question

#

ty

#

.close

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cosmic salmon
#

@grizzled badge ur good, just make sure to read everything carefully

cosmic salmon
#

good luck on the exam!

#

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distant rapids
topaz sinewBOT
distant rapids
#

How to write this out and solve it

mellow venture
#

so they have same area right

#

do you have know area formula for rectangles?

topaz sinewBOT
#

@distant rapids Has your question been resolved?

distant rapids
#

Ayo?

#

.close

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fathom trellis
#

so basically my question is this

topaz sinewBOT
fathom trellis
#

and i figured out this

topaz sinewBOT
#

@fathom trellis Has your question been resolved?

fathom trellis
#

.close

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tiny ginkgo
#

so an equation for the tangent line towards the end of the problem would be y-y1 = m(x1-x)

#

just really not sure how to set this up

#

or why im given f(x)

#

I know that f(x)^x is also xln(x) I believe

#

this may or may not be some form of logarithmic differentiation idk

#

<@&286206848099549185>

knotty ledge
tiny ginkgo
#

wait i forgot f(x) is just y

#

but there has to be natural log somewhere right?

#

so y^x

#

should be xln(y) no?

bitter hemlock
#

well you know what the point is right? just plug in 5 into G(x)

tiny ginkgo
#

so y = y^x then

bitter hemlock
#

G(5) = e^15 thats why you are given f(5) = e^3

#

have you trying getting a derivative of G now to find the slope?

tiny ginkgo
#

not yet no i am not sure where to start

#

would it be something like derivative of e^-12^x

#

why does G(5) = e^15?

bitter hemlock
#

f(5) = e^3 right?

tiny ginkgo
#

yes

bitter hemlock
#

and G(5) = f(5)^5, its how G is defined

#

(e^3)^5 = e^15

tiny ginkgo
#

and 5 comes from the x=5

bitter hemlock
#

ya

tiny ginkgo
#

okay thats established i understand that

#

okay let me check my notes for tangent line

bitter hemlock
#

im trying to figure out how to differentiate that now, its tricky since x is both in the base and exponent, so you can't use either power rule or exponent rule by themselves

#

since those only work if the exponent or base respectively are constant

tiny ginkgo
#

hmmmm maybe its asking for dy/dx?

bitter hemlock
#

yeah we need to get G'(5) thats the slope of the tangent line

tiny ginkgo
#

okay let me attempt that

bitter hemlock
#

remind me how can we rewrite f(x)^x so that its base e instead? multiply by some sort of logs but apparently ive forgotten how logs work : )

tiny ginkgo
#

ln(a)a^x ???

#

a^x = ln(a)a^x

#

e^x = e^x

#

if we used the power rule instead itd be 15e^14

#

but i dont think thats allowed given "e"

bitter hemlock
tiny ginkgo
#

hold on

#

i think we need to multiply both sides by ln

#

because y=g(x)

#

so 5y*ln=xln(e^15)?

bitter hemlock
#

ok i think heres how you need to think of it

tiny ginkgo
#

because im assuming this is logarithmic differentiation

bitter hemlock
#

using $G(x)=f(x)^x$ take ln of both sides

thorny flameBOT
#

Sooshon

tiny ginkgo
#

ahhhh thats probably right

bitter hemlock
#

then $\ln G(x) = x \ln(f(x))$

thorny flameBOT
#

Sooshon

bitter hemlock
#

now you should be able to do some implicit differentiation

tiny ginkgo
#

that has to be it

bitter hemlock
#

and get G'(x) in terms of f'(x) and some other stuff you can find

tiny ginkgo
#

okay i will attempt it

bitter hemlock
#

product rule on the right etc

tiny ginkgo
#

given x=5

#

so would we just say its 5y? or just 5

bitter hemlock
#

5y?

tiny ginkgo
#

because g(5)

bitter hemlock
#

say what is 5y?

tiny ginkgo
#

or just dont think of constants for now

#

g(5) = 5y? or just 5

#

can we agree on the left side of the equation

bitter hemlock
#

im confused about what youre asking, sorry

tiny ginkgo
#

that it should be

#

1/g(x) * dg(x)/dx

bitter hemlock
#

yep

tiny ginkgo
#

okay great let me attempt the right side

#

given f*g' + f'*g

#

okay right side should be x * 1/f(x) + (ln(f(x))*1

bitter hemlock
#

i think you forgot to chain rule the first term

tiny ginkgo
#

its not just x?

bitter hemlock
#

i get $x \frac{f'(x)}{f(x)} + \ln(f(x))$

thorny flameBOT
#

Sooshon

tiny ginkgo
#

so ln(f(x)) is not 1/f(x)?

bitter hemlock
#

and chain rule the inside of the ln

#

so multply by f'(x)

tiny ginkgo
#

because ln is multiplied by f(x) ahhh

#

oh why prime f'(x) though

#

because dy/dx?

bitter hemlock
#

$\frac{d}{dx} (\ln f(x)) = \frac{1}{f(x)} f'(x)$

thorny flameBOT
#

Sooshon

tiny ginkgo
#

hmmm

bitter hemlock
#

just basic chain rule

#

you multiply by the derivative of the inside

#

the inside is f(x), its derivative is f'

tiny ginkgo
#

ahhh very true

#

so ill type equation we have now

#

1/g(x) * dg(x)/dx = x * f'(x)/f(x)+(ln(f(x))) * 1

#

would you say x * f'(x)/f(x) is just (xf'(x))/f(x)

#

and now that we have this format

#

its safe to multiply by G(x) on both sides

bitter hemlock
#

yes

tiny ginkgo
#

to isolate dG(x)/dx

bitter hemlock
#

im going to write this out in latex in outside program since its kind of a confusing one without math notation

#

ill put it here after and see if you agree with my steps

tiny ginkgo
#

yes okay sounds great

bitter hemlock
#

something like this?

#

bigger

tiny ginkgo
#

yes

#

but dont we multiply G(x) on both sides

#

we'd be getting f(x)^x on the right

bitter hemlock
#

multiply by G(x) on both sides at what step?

#

oh you mean by the e^15 yes i did it at the end there

tiny ginkgo
#

1/g(x) * dg(x)/dx = xf'(x)/f(x)+(ln(f(x)))

#

we multiply by g(x) on both sides

bitter hemlock
#

yes, i multip-ied through by g(5) = e^15 we got earlier right at the last step

tiny ginkgo
#

so it'd look like = G(x) * ((xf'(x)/f(x))+(ln(f(x))))

bitter hemlock
#

yeah, whenever you want to do that, i started plugging in values already before that

tiny ginkgo
#

ahhhhh i see okay

#

and the three came from ln(e^3)?

bitter hemlock
#

so point slope form would be i guess: $y - e^{15} = (5+3e^{15})(x - 5)$

thorny flameBOT
#

Sooshon

bitter hemlock
#

yes, if i didnt make a mistake

tiny ginkgo
#

no you're correct

bitter hemlock
#

which isnt entirely unlikely, this problem doesnt want to simplify too nicely : )

tiny ginkgo
#

yeah my teacher will except exact answers and not too simplified

#

you multiplied e^15 on both sides

#

oh wait

#

how'd you get the right side of the equation

bitter hemlock
#

at which step

#

(they are numbered, tell me number of step)

tiny ginkgo
#

(5+3e^15)

#

step 7

bitter hemlock
#

just plugging in x = 5, f(5), f'(5) etc

tiny ginkgo
#

oh i guess after that then

tiny ginkgo
bitter hemlock
#

e^-12 / e^3 = e^-15

#

then when both sides get multiplied by e^15 that just becomes 1

tiny ginkgo
#

it would be e^15 * G'(5) then on the left ?

bitter hemlock
#

we had a e^15 in the denominator on the left right? so the step involves multiplying both sides by e^15 to cancel that out

tiny ginkgo
#

yes

bitter hemlock
#

so left just becomes G'(5)

#

and each of the terms on the right get multiplied by e^15

tiny ginkgo
#

ahhhh canceling

#

yes

#

so why is it y-e^15 now?

bitter hemlock
#

wheres that?

#

oh

#

well we now the slope now right

tiny ginkgo
#

lets just go back a quick sec

bitter hemlock
tiny ginkgo
#

our equation is now G'(5) = 5e^-12/e^3 + 3

bitter hemlock
#

umm

#

no

tiny ginkgo
#

g(x)=e^15 yes

bitter hemlock
#

now its just algebra, you know the point (5, e^15) and you know the slope and have to write the line equation

#

I've got to go eat so good luck : )

tiny ginkgo
#

okay thanks

topaz sinewBOT
#
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knotty fulcrum
topaz sinewBOT
worldly tendon
#

divide numerator and denominator by x

#

x = sqrt(x^2) also

#

so 5x -> 5
while sqrt(x^2 + 3x) -> sqrt(1 + 3/x)
and sqrt(x^2 - 2x) -> sqrt(1 - 2/x)

knotty fulcrum
#

makes sense

worldly tendon
#

you can do this because dividing by x/x is the same as dividing by 1

#

so equality is maintained because x/1 = x

knotty fulcrum
#

ty

#

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dawn cloud
topaz sinewBOT
dawn cloud
#

<@&286206848099549185> pls 👉 👈

topaz sinewBOT
#

@dawn cloud Has your question been resolved?

dawn cloud
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<@&286206848099549185> hope this is allowed

dawn cloud
#

<@&286206848099549185> tell me if / what part of the question is hard to comprehend

topaz sinewBOT
#

@dawn cloud Has your question been resolved?

novel token
#

no youre right

topaz sinewBOT
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bold cloud
#

I dont understand hint b and onwards with this series

topaz sinewBOT
#

@bold cloud Has your question been resolved?

topaz sinewBOT
#

@bold cloud Has your question been resolved?

bold cloud
#

<@&286206848099549185>

novel token
bold cloud
#

sure

novel token
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.close

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topaz sinewBOT
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uncut agate
#

Hi, I don't understand what happens with the log(x+1) :c
why can I write log(x+1) like log(1+1/x) + log(x)?

restive inlet
#

prod to sum law for logs

uncut agate
restive inlet
#

log(ab) = log(a)+log(b)

uncut agate
#

Aah I get it! thanks you! ❤️

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cinder rapids
#

not sure if its b or c

topaz sinewBOT
cinder rapids
#

im leaning towards b tho

#

because "enforce" might be a loaded word

drifting swift
#

this doesnt sound like a math question

#

however

#

what is your defn of an 'unbiased question'?

cinder rapids
#

its from a stats class so peepoShrug

#

ig unbiased question meaning it doesnt lead to biased answers

#

biased data* is probably better

#

eh i'll just sitck with that

#

.close

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lofty elm
topaz sinewBOT
warm finch
#

I got a good idea for this one

#

I would first multiply both sides by cos to get cos^2 on the left and just 1-sin on the right

#

@lofty elm

lofty elm
#

hmm

#

i see im gonna try that

#

@warm finch could you write out the formula

#

equation*

warm finch
#

Idk how to use the bot but I’ll try

lofty elm
#

kk thank u

warm finch
#

$\frac{cos(\Theta)^{2}}{1 + sin(\Theta)} = 1 - sin(\Theta)$

thorny flameBOT
#

VictorLee

warm finch
#

It would look like this

lofty elm
#

Thank you so much

warm finch
#

Then the trick i had in mind is to multiply the 1+sin on both sides

#

And then the magic happens

topaz sinewBOT
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topaz sinewBOT
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fathom girder
#

Pls help

topaz sinewBOT
bitter hemlock
fathom girder
#

pls

#

it’s physic

#

im french

#

it’s like

#

i need to calculate the light of speed

#

Instead of it being in kilometer

#

It need to be in meter

#

in a scientific notation

#

i think it’s

#

300 000 x 1000

#

=

#

300 000 000

#

but in scientific notation

#

ru here

thin oak
fathom girder
#

so

#

It’s

#

3 x 10’8

#

if am right

#

okay thanks

#

how do I close

#

.clode

#

.close

topaz sinewBOT
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topaz sinewBOT
#

@shut obsidian Has your question been resolved?

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livid pelican
#

I've been given this

topaz sinewBOT
livid pelican
#

I would like to do this