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[delicate idol]

Forces 𝐹1and 𝐹2 act on a particle at an angle of 50 to each other with |𝐹1| = 220 N and |𝐹2| = 130 N. Determine the magnitude and direction of the resultant.
i got 319.5 N at 32 degrees

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Please don't occupy multiple help channels.

[delicate idol]

closed

[gritty rose]

.close is the command

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[fallow widget]

this is completely ilegal right? 💀

[plush egret]

its not clear what youve done

[fallow widget]

i mean is:

y=1.8+x
y/x=1.8

[glass crystal]

yep this is completely illegal

[plush egret]

https://tenor.com/view/415базаответье-базаответьте-котсмигалками-кот-полиция-gif-19759294

[fallow widget]

thanks!

[plush egret]

do you see why

[glass crystal]

if you want to divide both sides by x do so, but apply the operation correctly

[plush egret]

[fallow widget]

yeah just was a dumb doubt that i had :)

!close

[woven snow]

.close

[fallow widget]

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[supple token]

How can you confirm that a Oblique isotope crosses the vertical isotope

[muted verge]

wait what

what is an isotope

do you mean asymptote?

[supple token]

lol ya auto correct

[muted verge]

ah okay

so

2 lines cross if they arent parallel

and oblique asymptotes arent parallel to vertical asymptotes because theyre slanted

so they will cross

[supple token]

sorry, i didnt see your msg

okay but how can i mathematical prove it

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[sand stone]

<@&268886789983436800>

[slender onyx]

.close

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[harsh halo]

hello, I need some help on how to solve this

[kind lynx]

is this a exam?

[wise wyvern]

Exam police

[calm sphinx]

whatve you tried

[rough plaza]

well, we have been through this yesterday, what is still giving you trouble?

[harsh halo]

exam? this is a khan academy task

I can't figure out how to solve this one

[rough plaza]

as we have gone through yesterday, the numbers in the answers are representing the speeds

which you'll just have to compare them with the speed of Usain Bolt

which is around 10.44 as you have found yesterday

[harsh halo]

but I don't understand how I can compare the speed of usain bolt to the other times

<@&286206848099549185>

[torn jolt]

speed=distance/time

[harsh halo]

yeah yeah

I have calculated the speed

but I don't have the time of the other values so I can't compare it

[torn jolt]

if d=10t, what is the speed

ie what is d/t

[harsh halo]

d = 10 * t

I have no idae what the speed is

[torn jolt]

speed is d/t

try dividing both sides by t

[maiden karma]

distance = 10 times the time

so speed = 10

supposedly

[harsh halo]

but I don't know the distance

[maiden karma]

you said it's 10*t

so you know none of the variables ?

[harsh halo]

I don't know whta t is

[maiden karma]

you have t = 9.58s

so use this

D is the answer :

100m ran in 9.58s

d/t = v : 10.438
d = 10.438t

[harsh halo]

yes I have calculated the speed

of usain bold

but I don't know how I can figure out the speed of d = 10t

<@&286206848099549185> could someone please help me? would be much appreciated

[maiden karma]

you only need to find which of the answers is > 10.43t

so only D if i'm correct

[harsh halo]

Yeah but I want to be able to understand this problem

[maiden karma]

the problem is : find something greater than d(usain-run)/t(usain-run)

input the numbers and you find : 100/9.58 = 10.43m.s^-1

[harsh halo]

how can I calculate d = 10t so I can later compare it to usan bolt

[maiden karma]

you don't need to calculate d = 10t, just compare it with what you found before

you found that d(u)/t(u) = 10.43
then just divide by t so you find d(u) = 10.43t
then you know that d = 10t is < to d = 10.43t

[harsh halo]

but I need to find out the speed in order to compare my calculation

[maiden karma]

i'm telling you how to do bro

[harsh halo]

no you are telling me the answer without explaining it and that way I won't learn this

[maiden karma]

I just explained how i found it mate

but i'll re-explain one last time

[harsh halo]

yeah if you just explain it one time would be enough

[maiden karma]

Your inputs are : t=9.58s ; d = 100m
then you calculate speed ( c ) out of these two : the formula is s = d/t
so you calculate Usain's speed :
s(usain) = 100/9.58 = 10.43m/s

[harsh halo]

why is is c and not s?

[maiden karma]

so you calculate the same data as in the question out of your result :
d = s(usain)*t

therefor you can calculate that Usain's distance is d = s(usain)*t
<=> d = 10.43*t

then you can compare it with the rest

a : d = 10*t so this is lower than d = 10.43*t

You can walk the other way around and pick the d/t = s
with a it means s(a) = d/t = 10

[maiden karma]

Sorry i'll change to s

[harsh halo]

I don't understand this

the first part I got

[maiden karma]

Where is it stuck ?

[harsh halo]

"d = s(usain)t"

[maiden karma]

the distance Usain has travelled in the t time is expressed by d = s(usain)*t

[harsh halo]

the distanse is s * t

[maiden karma]

yeah because you can just switch the formula the way around like you can say with s = d/t that d = s*t

[harsh halo]

yeah I know how to calculate all of them, speed, time and distance. But I can't compare usain bolts time against d if I don't know t

[maiden karma]

You don't need to calculate the result to compare it with another formula

okay let's say

s = Usain's speed is 10.43
d = Usain's distance is 100m
t = Usain's time is 9.58s

Then you can put this as : s = d/t
d = st
in Usain's case it's d = 10.43t ( for all t )

And you have something that is d = 10*t you can say the distance will be lower than Usain's distance in the same time

you take a specific t that's the same for both Usain's run and the answers in the question, therefor you can make the speed comparison

I think that's what was missing for you, sorry for the bad explanations i'm pretty bad at maths in english because i study them in another language

[harsh halo]

how do you get that?

[maiden karma]

that's what we were told from the question itself

https://cdn.discordapp.com/attachments/903486480985489478/1023238445151297618/unknown.png

[harsh halo]

in Usain's case it's d = 10.43t ( for all t )

[maiden karma]

read the beginning, these are your initial values

[maiden karma]

because whatever t you have, the distance is proportional to the speed * the time it takes

in this case it doesn't cause any problem to change t because d will change proportionally to it

Try to calculate it, let's say :
t = 5 and s is the same as Usain

[harsh halo]

I don't understand what you mean by that? d is relative what both s and t are

[maiden karma]

then do the same with t = 9.58 and then 20

[maiden karma]

yes but s is determined so we don't need to care about that

so it's one changing number relative to another, it's fine then

[harsh halo]

but how can I get the speed of d = 10 * t?

[maiden karma]

In mathematics, two sequences of numbers, often experimental data, are proportional or directly proportional if their corresponding elements have a constant ratio, which is called the coefficient of proportionality or proportionality constant. Two sequences are inversely proportional if corresponding elements have a constant product, also called the coefficient of proportionality.

[maiden karma]

you don't need its speed

the speed is 10m/s

all the answers are arranged as " d = s*t " so you just replace the value with s

but you only need to use d and t proportionality to guess what's the answer

[harsh halo]

how do you replace it if you don't know what it is

[maiden karma]

you know what it is

because it's d = 10*t

idk i can't explain that, it's almost logical for me

maybe someone else could explain better why we find out that the speed is that

but it's basically the formula for speed and the only missing variable is s, so by elimination you pick that s = 10

[harsh halo]

but you only need 2 of the values to figure out the 3rd

[harsh halo]

how do you know what this is

[maiden karma]

The formula is d = st
the answer is " d = 10t "
so d = d, t = t
right ?

then s = 10

[harsh halo]

how can u calculate what s is if you don't know t?

[maiden karma]

I don't calculate it

i recognize it in the formula given by the answer

[harsh halo]

well how can you figure

out its value then

[maiden karma]

" d = 10*t " " d = s*t "

By elimination : s = 10 because it's the only missing number in the formula

[harsh halo]

but by elemination it should just be 10, not the speed

and how can you eliminate the other values

[maiden karma]

i'm just trying to recognize which value is what in the formula

if s = 10 then d = 10*t right ?

[harsh halo]

yes that part is clear

[maiden karma]

well then you have the answer

just go reverse

[harsh halo]

but I don't know the value of t so how can I take s * t

I just don't understand the comparisons

[harsh halo]

how can I figure out the values of them?

[maiden karma]

don't figure the values

you have to keep it as it is

so d = 10*t

we agree on the fact that the 10 is the speed ?

[maiden karma]

then just look at all these examples,
a : " d = 10t " < " d = 10.438t "
b : " d = 10.2t " < " d = 10.438t "

To remind you, we found that 10.438t is the distance Usain can travel for t time

[harsh halo]

how can you get that?

[maiden karma]

i told you before, we recognize it in the formula as the only missing variable : s

but whatever, let's say you are using the multiplying factor for these two

if i pick d = 10t ( a ) and d = 10.438t ( usain )
i divide a by ( usain )

d(a)/d(usain) < 1 => d(usain) > d(a) and for the same t
s(a) < s(usain) because d and t are proportional

[harsh halo]

don't understand how you can divide by usain

[maiden karma]

mate, at this point, just open your lesson on proportional numbers

everything must be written in it

i'm picking Usain's distance parcoured and Usain's speed

which we calculated as 10.43m/s just before

[harsh halo]

I don't have access to that anymore that was over 8 years ago

I'm just trying to understand how I can solve this problem

[maiden karma]

idk how you can't solve it since i could in 10s

[harsh halo]

because I don't know how

I was hoping I could get some help

[maiden karma]

i tried to explain everything to you tho

[harsh halo]

but I didn't understand

[maiden karma]

mb then

i'm a bad teacher

[harsh halo]

I never said that

but I believe when you explained to me you assumed that I already knew necessary information for the task

[maiden karma]

probably

i'm sorry i can't find a way to help you understand the problem

[harsh halo]

no worries, I appreciate you taking the time. Have a great rest of the day

[maiden karma]

thanks mate, i'm only gonna start working on my math problems lmao

[harsh halo]

goodluck

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@harsh halo Has your question been resolved?

[rough plaza]

hello!

seems " Shadow was trying really hard to explain and Norahc don't seem to understand
it's okay, sometimes math is hard to understand

i think i can use another approach to help you understand this question

@harsh halo
i remember you saying you cannot find the speed of you don't know what the distance and time are, is that correct?

[harsh halo]

hello @rough plaza yes I don't know how I can figure out d = 10 * t and then compare it to the speed I got from usain bolt

[rough plaza]

ok, so let's go through this
d = 10 * t
one by one.

what is d?

hint: you can find it in the question

[harsh halo]

That's what I am having trouble with I don't know

[rough plaza]

ohhhh, lemme circle it for you

so, again, what is d?

[harsh halo]

100 meters

[rough plaza]

nope
another hint: just answer in words, no need numbers

(sometimes we don't just use numbers to explain in maths)

[harsh halo]

I really don't understand

[rough plaza]

it's okay, it's always hard to start

[harsh halo]

I feel like this is pretty basic, I'm surprised it wasn't explained in more depth on khan academy

[rough plaza]

Q: What is d?
A: d is "distance in meters".

maybe did you skip the chapter of variables?

[harsh halo]

no they have videos explaining each segment they go through and I even rewatched all the video for rates and proportional relaationships this morning

[rough plaza]

i see, that's very hardworking indeed, you did well

anyways, let's head back to our question.

[rough plaza]

do you understand this?

[harsh halo]

I'm not sure what you mean by that, but I have calculated the speed of usain bold. I just don't know how I can calculate the values to compare it with

[rough plaza]

if you wanna know how to calculate the values to compare it with, you will have to know what is d and what is t

or else you dont even know what are the uses of ,"d=10t", those answers.

[rough plaza]

and what i mean by this is that,
I was asking you "What is d?"
and i help you by answering "d is 'distance in meters'. "

[harsh halo]

okay

[rough plaza]

so do you know what is d now?

[harsh halo]

well in the first option d is 10t

[rough plaza]

very good, but d has more than one meaning.

d is also a "distance"

so we have

[harsh halo]

yeah I'm aware

[rough plaza]

let's call it Distance A, since it's from answer A

so we have

Distance A = 10 t

does this make sense to you?

[harsh halo]

yes

[rough plaza]

very good

first step done

second step

What is 10?
I'll answer that, it's a number, and for now we will just leave it alone.

third step

what is t?

(your turn)

[harsh halo]

we don't know the value of t

[rough plaza]

nah, again, we are not finding the value

we are finding an explanation in words for t

hint: it's written in the question

[harsh halo]

t just represents the time in seconds

[rough plaza]

very good!

time in seconds, that's what we are finding!

since it's answer A, we call it Time A

so we shall rewrite d=10t into:
Distance A = 10 * Time A

all good till here?

[harsh halo]

yes

[rough plaza]

so, next step is hard

[harsh halo]

ok

[rough plaza]

we divided both sides by "Time A"
so that the equation remains valid

[glossy valve]

OldBiscuit

[harsh halo]

in d = 10t is 10 the speed?

and is every number the speed?

[rough plaza]

yep!

you got it!

[harsh halo]

so they are giving us the speed in the question and d and t is irrelevant here

[rough plaza]

you can say that, but d and t needed to be there to show that the numbers are the speeds

[harsh halo]

alright I believe I understand now, thank you

[rough plaza]

It is never easy to start with variables.

but once you understand it, it will flow like water

[harsh halo]

well I have done algebra so this was hardly starting

now I am doing y=kx

[rough plaza]

Trying to understand it in words are harder than just using it as a tool

you did a great job understanding them

[harsh halo]

.close

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[deft star]

Yall i forgot how to find the equation to something

[deft star]

could someone explain it real quick

Since i can't remember anything currently

😭

[smoky wing]

What equation

[deft star]

these

[iron portal]

bruh

[deft star]

Don't judge me

[smoky wing]

Ok so you have to find the gradient and intercept

[deft star]

Ofcourse you do

[smoky wing]

Pick two points

Change in y over change in x

That’s gradient

Then (y-y1) = m(x-x1)

Or y=mx+c

[deft star]

Alright i understand the X

But the Y is getting me confused

[smoky wing]

What do you mean

[deft star]

There is an X

And a Y

[smoky wing]

Right

y is just y

It’s the value on the vertical axis

The output

x is the input and the value on the horizontal axis

[deft star]

so the answer here is 11?

right?

[smoky wing]

How is the answer 11

I thought you were trying to find the equation of the graph

Ok so firstly tell me what value you got for the gradient

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@deft star Has your question been resolved?

[atomic blade]

Giggity

[plush seal]

well uhh y = mx +c where m is tan of (theta that it makes with x axis) and c is the value of y when x =0 which is referred to as the y-intercept

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[fallow kayak]

can anybody help me get reciprocal function of f

[fallow kayak]

Domain is ]-inf;0]

i tried to solve f(y)=x but it's too long

[torn jolt]

reciprocal or inverse?

reciprocal is 1/f(x)

inverse if f^-1(x)

[atomic blade]

The inverse requires quadratic formula

And it's quite the uh

Equation

[fallow kayak]

inverse

[fallow kayak]

yeah but look

we know that f is increasing from f'

and f continuous and f(]-inf;0])=]-1;0]

I get delta of the quadratic equation negative if x is in ]-1;0]

[atomic blade]

(-1, 0], yes

But deriving it is gonna be a pain

First swap x and y around

$$x = \frac{\sqrt{y^2 - 2y}}{y-1}$$

[glossy valve]

Umbraleviathan

[atomic blade]

Then solve for y

@fallow kayak you can start by multiplying by y-1, and then squaring

[fallow kayak]

that's excatly what I did

i'ma try again

nvm I miscalculated that's why

thanks tho

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[severe basin]

Suppose that the number of customers visiting a KFC on a particular day is $N \sim \text{Poisson}(5)$. Assume that each customer purchases a Classic Chicken Zingers with probability $0.3$, independent of other customers and independent of the value of $N$. Let $X$ denote the number of customers who purchase a Classic Chicken Zingers in a day. Let $Y$ denote the number of customers who do not purchase a Classic Chicken Zingers. Find P(X=3,Y=3).

[glossy valve]

QuantumBee

[severe basin]

nvm

I got it

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[torpid hemlock]

(PROBABILITY/STATISTICS) i dont know what this means ,,

[eager violet]

What have you tried

[torpid hemlock]

nothing cuz idk what it means

idk where to start

I know and is like

multiplying rule

I guess

[eager violet]

Do you know how to calculate P(A or B)?

[torpid hemlock]

I'm not sure what that means

[eager violet]

It means the odds that event A or event B occurs

Like, the odds I roll a 1 or I roll a 2

[torpid hemlock]

is A or B same as E and F?

[eager violet]

A, B, E, and F are just names

[torpid hemlock]

like the same thing just diff variables

mkayy

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[near lance]

Hello

[near lance]

Does anyone know how to solve #3 based on #2?

I know how to achieve an upper bound through the Remainder Estimation Theorem, but I've never tried to do so with an integral.

[full forum]

@near lance Has your question been resolved?

[near lance]

<@&286206848099549185>

[plush egret]

well you just need an upper bound right

[plush egret]

what is the relationship between $\int _a ^\infty f(x) \dd x$ and $\sum _{n=a} ^{\infty} f(n)$

assuming convergence

[glossy valve]

jan Niku

[full forum]

@near lance Has your question been resolved?

[near lance]

If the integral converges, the series also converges.

f(x) has to be positive, continuous from a to infinity, and increasing.

[plush egret]

sure, but does it make sense how that means there is bounding happening

[near lance]

Sorta...

No

Not really

I'm kinda lost rn

[plush egret]

think about something like this

[near lance]

Area under the curve?

[plush egret]

is the sum of the area of the rectangles or the area under the black curve gonna be greater

[near lance]

Area under the black curve

[plush egret]

yea

[near lance]

Ohhh

[plush egret]

this isnt always true

i mean for riemann sums in general

but in the specific case that you have a positive, decreasing function

[near lance]

Yeah

Ok

So I get what you're saying now.

But how would I show a clear connection between the two?

Could this work?

[plush egret]

yea i think so

idk how much argument youre required to provide for like

the fact that the integral is greater

if a picture is cool then it seems fine

[near lance]

It shouldn't be anything crazy.

Well, thank you so much for opening my mind 🤣

No, seriously

Thanks a bunch

Have a nice day/night

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[iron sand]

How do i make a direct proof that this statement holds for all natural numbers n

[iron sand]

I tried this

Hope it makes sense

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[toxic zenith]

Luis earned ₱2500 on the first week of selling fruits and ₱3500 on the second week. Find his total earning in four weeks
by using the arithmetic series

[robust slate]

direct formula substitution

[toxic zenith]

ok thanks

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[toxic zenith]

.reopen

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✅

[toxic zenith]

.

[finite dagger]

.help

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Commands:
clopen: .close, .reopen, .solved, .unsolved
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factoids: .tag
help: .help

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[finite dagger]

.reopen

[light sonnet]

Please read #❓how-to-get-help

[light sonnet]

Why did you reopen the channel?

[toxic zenith]

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[toxic zenith]

nvm

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[toxic zenith]

Luis earned ₱2500 on the first week of selling fruits and ₱3500 on the second week. Find his total earning in four weeks
by using the arithmetic series

am i right the answer is 5008?

[smoky wing]

Answer shouldn’t be that

First term is 2500

The earninf in 4 weeks is 2500+3000

So 5500

[torn jolt]

..

[smoky wing]

Wth

[full marsh]

A small problem here

<@&268886789983436800>

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[signal solar]

f(1/a)=((1/a)-1)((1/a)-5)

[signal solar]

I understand algebra rules I just don't entirely know how to reduce that

other than multiplying them together i guess

[torn jolt]

just substract the things that needs to

and multply

or if u want to find f(a)

notice that f(a)=f1/(1/a)) = (1/(1/a) -1) *(1/(1/a) -5)

=(a-1)(a-5)

so f(a)=(a-1)(a-5)

[signal solar]

I understand f(a) but I don't know how to reduce f(1/a)

I have another problem with (x+∆x)^2+2(x+∆x)+1 -(x^2+2x+1)

I want to reduce it without doing too much work but I'm not entirely sure what works algebraically or not

[full forum]

@signal solar Has your question been resolved?

[full forum]

@signal solar Has your question been resolved?

[simple totem]

which one are you doing nino

the first or second

[signal solar]

the first

i mean im doing both i want to understand both but its probably better to understand the first before the seoncd

[simple totem]

$f(\frac{1}{a})=(\frac{1}{a}-1)(\frac{1}{a}-5)$

does this look right

[glossy valve]

maximo

[signal solar]

yep

[simple totem]

what do you want to do with it

what's your goal

[signal solar]

oh wait its +5

1/a +5

but yeah I want to simplify it

[simple totem]

it's pretty much as simplified as it gets tbh

all you can really do is expand it out

[signal solar]

the books answer is (1-a)(1+5a) all over a^2

i wonder is there an easy way to expand it or would i have to multiply them together

[simple totem]

to get where the book takes you start by multiplying the whole thing by a^2/a^2

so

$(\frac{1}{a}-1)(\frac{1}{a}-5)\cdot \frac{a^2}{a^2}$

[glossy valve]

maximo

[signal solar]

ooo

how'd u figure that out

i wanna know how to find shortcuts like that to simplify stuff other than all out expanding

[simple totem]

well this isn't exactly simplification in my book, but the idea here is to change the (1/a -1) and (1/a -5) into (1-a)(1-5a)

to do that we want to multiply each of the () bits by a, but to do that we need to divide by a as well to keep the expression equal

[signal solar]

yea idk why they chose to have it in that way in the book

ig it turns it into one singular expression that's why?

[signal solar]

and how can i easily simplify this without having to expand it and all that

[simple totem]

$(x+\Delta x)^2+2(x+\Delta x)+1 -(x^2+2x+1)$

[glossy valve]

maximo

[simple totem]

damn texit not having it

this one i'm pretty sure you need to expand

[signal solar]

hm idk

[signal solar]

so you're sure?

[simple totem]

yeah i can't see anything right away that makes it easy to compute

[signal solar]

oh ok

im just gonna double check with helpers to see if maybe there is idk if not i wonder why the book is making me expand it instead

eventhough its pretty simple so its not a lot of work actually it's fine

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[autumn anchor]

What is tan(3pi/4), if tan(pi+v)= tanv

[modern sentinel]

tan(3pi/4)=tan(pi+(-pi/4))=tan(-pi/4)
tangent is odd function so
=-tan(pi/4)=-1

[autumn anchor]

How Did you come up with this

[woven snow]

with what?

[autumn anchor]

Like How to think

[woven snow]

hmm

the -pi/4 part?

[autumn anchor]

Yeah

[woven snow]

,w pi+x =3pi/4

[glossy valve]

Results provided by WolframAlpha

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Requested by Deep.#0001

[woven snow]

thats it

thats how you come up with -pi/4

rest is just trig right

?

umm do you get it?

[autumn anchor]

No

Like what is the formula from

Also where goes 3

[woven snow]

like we saw

tan(3pi/4) = tan(pi + (-pi/4))

and you know tan(pi+v)=tan(v)

[autumn anchor]

where does Tan(pi + (-pi/4)) come from

[woven snow]

,w pi +(-pi/4)

[glossy valve]

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[woven snow]

like i said here

[autumn anchor]

Do you use calc to figure that out

[woven snow]

uhh not really

(3/4)-1

isn’t hard to calculate

thats -1/4

[autumn anchor]

Yeah that’s 3/4

Huh

[woven snow]

hmm

[autumn anchor]

(3/4)-1 should be -3/4

[woven snow]

why

(3/4) -(4/4)

as 4/4 =1

so we have same denominator

so we get (3-4)/4

[autumn anchor]

Wait can you write this in latex

[woven snow]

okay

$\frac 34 - 1$

[glossy valve]

Deep. (kawaiiCat for emoji)

[woven snow]

= $\frac 34- \frac 44$

[autumn anchor]

So we arent using parenthese?

This I can understood if we use without parenthese

[woven snow]

okay

well

[autumn anchor]

Because -4/4 is -1

[woven snow]

then lets remove it

[glossy valve]

Deep. (kawaiiCat for emoji)

[woven snow]

okay so that will be

[autumn anchor]

Yes that’s -1/4

[woven snow]

okay cool

so now

do you get why -pi/4

[autumn anchor]

No sorry

[woven snow]

we want something in the form of pi +v =3pi/4

yes?

[autumn anchor]

Right

[woven snow]

okay so cool

we have a equation

can you solve for v

?

[autumn anchor]

In that way we get a angle right?

[woven snow]

yes

[autumn anchor]

V is pi3/4

[woven snow]

hmm 🤔

is it?

pi is same as 4pi/4

so 4pi/4 + v = 3pi/4

we want to solve for v sol lets take 4pi/4 to rhs

so we get

[autumn anchor]

Do we figure out what V is then put it in orgin equation

[woven snow]

v = 3pi/4 - 4pi/4

[woven snow]

yes

[autumn anchor]

So we subtract the Pi from both sides

[woven snow]

so from here do we not get v = -pi/4

[woven snow]

yes

[autumn anchor]

Then we have V=3pi/4 -pi

[woven snow]

yes

[autumn anchor]

Put it in v in (pi+v) ?

[woven snow]

umm not yet

[woven snow]

can you not simplify it?

[autumn anchor]

In a parenthese?

[woven snow]

= $\frac {3\pi}4- \frac {4\pi}4$

[glossy valve]

Deep. (kawaiiCat for emoji)

[woven snow]

…

[autumn anchor]

Oh

[woven snow]

do you remember something like this?

so what do we get v=

[autumn anchor]

-pi/4

[woven snow]

correct

[autumn anchor]

How is this simplified

[woven snow]

so do you see what we did here?

[autumn anchor]

Because we want the angle to be less?

[woven snow]

well yes

because we know tan from 0 to 90 (also known as pi/2)

[autumn anchor]

Yeah and 180/270

[woven snow]

hmm

cool so now

do

you

get it

?

hmm

[autumn anchor]

Then we put it in (pi +v)?

[woven snow]

yes

[autumn anchor]

Because that is 0-90

[woven snow]

so we know tan(3pi/4)=tan(pi+(-pi/4))

well not exactly, but we can workaround a bit

[woven snow]

you get this now?

[autumn anchor]

Yeah

[woven snow]

okay cool

[autumn anchor]

Can you give me more question like this my book only gave 3

[woven snow]

hmm 🤔

[autumn anchor]

Oh we not done?

[woven snow]

you can maybe ask in #geometry-and-trigonometry

[autumn anchor]

Ok

[woven snow]

i am not very resourceful generally

[autumn anchor]

That is ok

What do we next

Oh we get the angle from 0-90 in tanv now

Which is the number in unit circle

No something is wrong

Doesent have -pi/4

How is this -1

Oh it Applies to another rule but this unit circle doesent say -1 in pi/4

[autumn anchor]

Deep?

[woven snow]

-pi/4 is same as 7pi/4

because added 2pi(rotating 360°) lands us to same angle

[autumn anchor]

😮

Yeah tan only has 180!!!!

Thank you!

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[distant brook]

Can anyone help me with the question 1.d)?

[deft zodiac]

i think its taylor series

have u done that

[distant brook]

No I'm still stuck on it

@deft zodiac can you help me?

[deft zodiac]

ok whats ur

ans for the prev parts

u can prob combine em to get part c

https://tenor.com/view/cute-transformers-gif-8173495

[distant brook]

Can you explain this in more detail?

[deft zodiac]

ok so

uve the

appx of those 2 terms

for

till x^3 term

so u can use

n itll prob just add up

[nocturne creek]

You have excellent handwriting...

[deft zodiac]

OMG YES U DO HAHAHA

[distant brook]

@deft zodiac hey thanks a lot for the help I did the math 😊

[deft zodiac]

yayyy

❤️

[distant brook]

@nocturne creek and @deft zodiac thank you so much both of you but I don't think it is that good I have never gotten any compliments from my teachers

[deft zodiac]

HAHAHA

TEACHERS 2 TIRED FROM MARKING TOO MUCH

[topaz valley]

from having to mark your assignments D:

[deft zodiac]

WOW

NO

MY ASSIGNMENTS ARE BEAUTIFUL N SHORT

[topaz valley]

[deft zodiac]

unlike urs

40 pages

[topaz valley]

that was

necessary

[deft zodiac]

JAHAHHA

YESS

SURE

[topaz valley]

everyone had just as much

[distant brook]

Yeah it's true 😅

[deft zodiac]

HAD HALF AS MUCH

[topaz valley]

and didn't finish the qs

so got 0 for everything

mmm

[deft zodiac]

HAHAHA

[topaz valley]

makes my life easier as a marker

[deft zodiac]

HAHHAHA

YESS

[distant brook]

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[austere herald]

A bag of mixed nuts contains cashews, pistachios, and almonds. There are 2000 total nuts in the bag, and there are 300 fewer almonds than pistachios. Cashews weigh 1 g, pistachios weigh 2 g, and almonds weigh 4 g. If the bag weighs 2.5 kg, find out how many of each type of nut is in the bag. thats my question i am confused on the weights and quantity portion if someone could help me with clearing that up I would appreciate it

[full forum]

@austere herald Has your question been resolved?

[torn jolt]

Alright so you want to link the quantity and weighs

We know that the bag weighs 2500g

If we take C,P,A as the numbers of respective nuts in the bag

"Cashews weigh 1 g, pistachios weigh 2 g, and almonds weigh 4 g"

What equation can we deduce with C,P,A ?

@austere herald

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[torn jolt]

I just need help trying to understand the basis of these questions

[torn jolt]

I’m at the point where I’m struggling at every one only to find a key component I was missing

🥹

Would also like help with this

To my understanding f-1 means an inverse of y

Thinking I might just be math illiterate because when I break it down these questions don’t seem super difficult

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[deft zodiac]

which Q

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[pliant violet]

i need help with 5) b

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[pliant violet]

<@&286206848099549185>

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[dusty crag]

Hi, I have a question about notation

[dusty crag]

for high order derivatives i frequently use f^n(x) to denote the derivative (i find this better than doing f'''''(x) for instance)

however the same notation is used for function composition

i'm wondering whether there is an alternative notation to denote repeated function composition so that i do not cause confusion between the two

[atomic blade]

Usually $f^{(n)}(x)$ is used for nth derivative. Parentheses matter

[glossy valve]

Umbraleviathan

[dusty crag]

so without brackets on the n would denote function composition?

[atomic blade]

Well I don't know how having f^2 would denote composition, unless that means f of f

[dusty crag]

yes f(f(x))

[atomic blade]

Maybe the parentheses then

[dusty crag]

ok

thank you

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[torn jolt]

ok

[torn jolt]

..close

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[plush hill]

need help

[plush hill]

anyone there to help

[barren wagon]

Ping helpers

Im to dumb to solve this sowwy

[plush hill]

who are the helpers

<@&286206848099549185> need help

[torn jolt]

Hi still need help?

@plush hill

[plush hill]

yes

[torn jolt]

Alright

You're looking for a linear fonction

Do you know which form they have?

If you don't you can try to give me one randomly

[plush hill]

no

[torn jolt]

A linear function is of the form f(x) = ax + b where 'a' and 'b' are real numbers.

So we know that S(x)=ax+b, we now have to find a and b

Do you have an idea of how to do it?

[plush hill]

no sorry

[torn jolt]

it's alright

Let's say the sales person doesn't make any sale

How much does he makes? What can we deduce about S(x)?

[plush hill]

nothing

[torn jolt]

He makes nothing?

so he doesn't get paid?

You should read the problem again

[plush hill]

oh wait 400

[torn jolt]

Yes

[plush hill]

my bad

[torn jolt]

So if x is the number of sales and it's 0 and S is the salary

Can we deduce something about S(x)=ax+b

[plush hill]

yes

[torn jolt]

And what do you deduce?

if you replace x by 0

[plush hill]

the 11 percent

[torn jolt]

no but that's an idea

Rewrite S(x)=ax+b replacing x by 0

[plush hill]

so it will be S(x) 0.11x+400

[torn jolt]

Yeah

Well you found it directly that's nice

[plush hill]

what about part 2

[torn jolt]

S(x)=0.11x+400 according to you

What if we plug in 6000

[plush hill]

what happens when we do that

[torn jolt]

Well since they're asking what is S(6000) we can calculate it

by replacing x by 6000

[plush hill]

then what next

[torn jolt]

how much did you find for S(6000)?

[plush hill]

how do i do that

[torn jolt]

by replacing x by 6000

in S(x)=0.11x+400

[plush hill]

so by replacing 0.11 with 6000 right

[torn jolt]

no

replacing x by 6000

you don't touch the 0.11

[plush hill]

so 6000=0.11x+400 right

[torn jolt]

no

That's S(x)

S(1)= 0.11 * 1 +400

S(2)= 0.11 * 2 +400

S(3)= 0.11 * 3 +400

S(6000)=?

[plush hill]

im i choosing one of those

[torn jolt]

no

replace x by 6000 in S(x)=0.11x+400

That means S(6000)=0.11 * 6000 +400

Can you see it?

[plush hill]

so this is how i caculate it correct

[torn jolt]

yes

[plush hill]

where can i put this type of equation

[torn jolt]

Well

S(6000)=0.11 * 6000 +400 = ?

Check the value of 0.11 * 6000 +400

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[paper lagoon]

Can someone help me with 29

[viral vigil]

.rotate

[paper lagoon]

.rotate

can someone help me

[viral vigil]

well this isn't very different from the other problems

so if you've done them then it's the same method

[paper lagoon]

can you walk me through it still

cause I cant cancel stuff out like 27

so im confused

[viral vigil]

ok

so s+t

you want the greatest common denominator

[paper lagoon]

yea

[viral vigil]

ok

so do you have that?

[paper lagoon]

uh

no

[viral vigil]

ok

so

you want to multiply s by (2-x) on the top and bottom

and multiply t by (x^2 - 9) on the top and bottom

and add them together

to be able to add them together the denominator needs to be the same

[paper lagoon]

can you show me how that would look

[viral vigil]

ok

sorry for the bad quality

[paper lagoon]

do I always do this

when I have something like this

[viral vigil]

wdym

like if you want to add two 'fractions' then that's the way to go

[paper lagoon]

so If I add fractions I have to do this

[viral vigil]

yes

[paper lagoon]

what is this called

[viral vigil]

uh

adding fractions?

[paper lagoon]

no I mean like this rule

of mutiplying them'

[viral vigil]

you're adding them

OH

ok

it's just called adding fractions

or finding the gcd

[paper lagoon]

ok

[viral vigil]

like 1/2 + 3/4

[paper lagoon]

now that I have this do I just mutiply them

[viral vigil]

you add them together because you want (s+t)(x)

[paper lagoon]

ok

what do I do now

[paper lagoon]

with this

[viral vigil]

well that's (s+t)(x)

so then you have to simplify

[paper lagoon]

ok

how do I do that

[viral vigil]

have you taken algebra 1?

[paper lagoon]

yea

but I forgot everything

I took it 3 years ago

[viral vigil]

ok

so you expand the numerators of both fracttions

leave the denominators as they are

[paper lagoon]

ok

how

[viral vigil]

for the left numerator

you have (x-2)(2-x)

so use FOIL

and you get 2x - x^2 - 4 + 2x

[paper lagoon]

ok

now do I do the same for other fraction?

[viral vigil]

yes

it won't be the same value

but it's going to be x^3 - 9x - 3x^2 + 27

[paper lagoon]

yea I got that

now what do I do

[viral vigil]

you add the two together

or add like terms

[paper lagoon]

ok let me do it rq

-5x-4x^2+x^3+23

is that right?

[viral vigil]

yep nice job!

and thats all over

(x^2 - 9)(2-x)

[paper lagoon]

yea

[viral vigil]

ok

[paper lagoon]

is that it

[viral vigil]

welll

[paper lagoon]

or we have to simplify more

[viral vigil]

thats fine for now

well thats it basically

do you need help with the domain

[paper lagoon]

no

[viral vigil]

ok cool

[paper lagoon]

I just checked the answer in the book and it gave me something else

[viral vigil]

.

[paper lagoon]

what did we do wrong

[viral vigil]

nothing

we just didn't expand the botto

we don't want to expand the bottom

because its easier to figure out the domain that wya

[paper lagoon]

can we do it

also their numerator is diff

[viral vigil]

expand the bottom?

how so

ohh

ok gimme a minute

[paper lagoon]

alr

[viral vigil]

ok so when you subtracted

we left out the parentheses

and thats why we got -5 instead of 5

because double negative is a positive

[paper lagoon]

when did we subtract

[viral vigil]

the two fractions

wait hold on

uhh

i think there's a book error im not gonna lie

nvm

ok

so

i messed up

and multiplied by the wrong thing

i did x-2

instead of 2-x

but those are the correct steps

[paper lagoon]

so was your mistake

[viral vigil]

yes

sorry

[paper lagoon]

where im confused

[viral vigil]

can we talk tmrw?

[paper lagoon]

na

I have my test tmrw

[full forum]

@paper lagoon Has your question been resolved?

[paper lagoon]

.close

[full forum]

Channel closed

Closed by @paper lagoon

Use .reopen if this was a mistake.

Available help channel!

Send your question here to claim the channel.

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

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

[full forum]

Please don't occupy multiple help channels.

[rapid laurel]

what is this inequality called

[native flicker]

more than or equal to

how u playin apex for 13 hr

[rapid laurel]

cause im 崩溃ing

😳

[rapid laurel]

no

this entire thing

why is this inequality true

[light sonnet]

Don't open multiple channels, even if you have different questions

[rapid laurel]

im not chris hu

im another person using this account, dualism

🐓

[light sonnet]

?

[rapid laurel]

help 2 is chris hu

just realized its CS inequality

[light sonnet]

And there is two channels labeled with "chris hu" hence multiple channels

[rapid laurel]

nono, but the chris hu are different

[light sonnet]

Yeah.... no

[rapid laurel]

nono, a guy named snow duplicated chris hu profile

[light sonnet]

If it's different, why would the bot post this?

[rapid laurel]

the bot is a dumbass

anyway my question is solved,

.close

[full forum]

Channel closed

Closed by @rapid laurel

Use .reopen if this was a mistake.

[light sonnet]

Why are the name and tags the same?

Everyone has a unique tag

[full forum]

Available help channel!

Send your question here to claim the channel.

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

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

[torn jolt]

How to solve the highlighted question

[wise widget]

Idk the answer but what website is that? American math competition?

[rapid laurel]

AOSP