help-0

[teal vessel]

yeah

[fathom sequoia]

no I dont think so

its very hard my dad said

[wary stream]

No we are

[fathom sequoia]

ok

[wary stream]

So the problem stated 3 distinct roots, meaning that it can be set up like this $$y = (x - x_1)(x - x_2)(x - x_3)$$

[ocean seal]

dldh06

[wary stream]

You also have $$y = x^3-12Px+R$$

[ocean seal]

dldh06

[wary stream]

You can set the two equal $$ (x - x_1)(x - x_2)(x - x_3) = x^3-12Px+R$$

[ocean seal]

dldh06

[wary stream]

Expand the left side fully

The x^2 terms on both side match and same with constants

If that makes sense

[fathom sequoia]

what does the x-x1 mean

and x-x2 and x-x3

[wary stream]

x1, x2, and x3 are the roots of the graph

[fathom sequoia]

why are you subtracting them again

[wary stream]

It can be plus, doesn't matter

Process is still the same

[fathom sequoia]

ok so can we figure it out now

[wary stream]

Just opposite signs

[fathom sequoia]

oh yeah I get it

then what would we do

[wanton beacon]

So, for 53, I’m pretty sure I get it, but just to make sure, at some point do you multiply both sides by 3, or does the 9b come down?

[wary stream]

What did you get when you expanded the left side?

[fathom sequoia]

ok I will do it

it will take me time

Can I replace $\left(x-x_{1}\right)\left(x-x_{2}\right)\left(x-x_{3}\right)$ with $\left(x-a\right)\left(x-b\right)\left(x-c\right)$

[ocean seal]

TJ89899889

[fathom sequoia]

k its j ust easier for me to work with that

[wary stream]

Yes

Because x1, x2, and x3 are different values

[fathom sequoia]

$\left(x-a\right)\left(x-b\right)\left(x-c\right)$ expands to $x^{3}-cx^{2}-bx^{2}+bxc-ax^{2}+axc+abx-abc$ correct me if im wrong

[ocean seal]

TJ89899889

[fathom sequoia]

i also checked and they give me same result

[north bridge]

@teal vessel

[teal vessel]

yes?

[teal vessel]

piamon? or emergency food?

[north bridge]

emergency food 😄

[wary stream]

Group all the x^3, x^2, x, and constants

[teal vessel]

[fathom sequoia]

ok

[north bridge]

lol can u help me with smth

[teal vessel]

so yeah u need somethin?

[north bridge]

on stream

ye

[teal vessel]

sure

[fathom sequoia]

you mean rearrange

[obtuse sluice]

genshin impact player!!

[north bridge]

yup

[teal vessel]

whm i am

[teal vessel]

send the prob

[north bridge]

nah same problem

just

y was 2b

1.88<x<4.78

[teal vessel]

yes

do u need me to explain?

[fathom sequoia]

do you mean rearrange

[wary stream]

Yeah that

[fathom sequoia]

k like this $x^{3}-ax^{2}-bx^{2}-cx^{2}+bxc+axc+abx-abc$

[ocean seal]

TJ89899889

[merry willow]

hi guys i have a question

why is *0 not an option for *1+*2

*1+*2

[wary stream]

Now factor the GCF

So for instance the x^2 terms, the common factor is x^2

[fathom sequoia]

ok

[fathom sequoia]

easy right

haha jk

[keen trail]

can someone show me how to start off these two i'm having a hard time on doing logically equivalences

*logical

[wary stream]

It's multistep

[fathom sequoia]

yeah I think ik how 2

what I'm confused aobut, don't these terms have no common factor:

[wary stream]

-abc is the constant term so that's fine

[fathom sequoia]

ah ok

[wary stream]

But the other has a GCF of x

[fathom sequoia]

so it would be $\ x^{2}\left(x-a-b-c\right)+x\left(bc+ac+ab\right)-abc$ I assume

[ocean seal]

TJ89899889

[wary stream]

There's something wrong with the beginning

[fathom sequoia]

k let me see

[wary stream]

With the way you typed it

Not sure about written though

[fathom sequoia]

yeah i rushed let me fix it

k now officially I checked the answer is $\ x^{2}\left(x-a-b-c\right)+x\left(bc+ac+ab\right)-abc$ Idk what I was doing before

[ocean seal]

TJ89899889

[fathom sequoia]

🤦‍♂️

[wary stream]

I don't think you fixed it?

[fathom sequoia]

how

I'm getting same result:

[wary stream]

I see

Leave the x^3 alone

$\ x^{3}+x^2\left(-a-b-c\right)+x\left(bc+ac+ab\right)-abc$

[ocean seal]

dldh06

[wary stream]

That's what I wanted you to get at

Because recall $$y =x^3-12Px+R$$

[ocean seal]

dldh06

[wary stream]

The original equation in the problem

You want the same form as that

[fathom sequoia]

makes sense

👍

never learnt this at school but still interesting

[wary stream]

Also recall $$ (x - x_1)(x - x_2)(x - x_3) = x^3-12Px+R$$

[ocean seal]

dldh06

[fathom sequoia]

k I recall it

[wary stream]

So therefore $$\ x^{3}+x^2\left(-a-b-c\right)+x\left(bc+ac+ab\right)-abc = x^3-12Px+R $$

[ocean seal]

dldh06

[wary stream]

After expanding and factoring

[fathom sequoia]

yeah I follow

[wary stream]

Out of curiosity, what software is this? That let's you know that both are equal like that?

[fathom sequoia]

desmos

you can also copy and paste equations to latex

[wary stream]

Interesting

[wary stream]

.

Think you can handle it from there?

Comparing P and R?

[fathom sequoia]

k how would I do that

if you tell me how I can get it from there

[wary stream]

$x\left(bc+ac+ab\right) = -12Px$

[ocean seal]

dldh06

[north bridge]

anyone

anyone know this

[fathom sequoia]

so you just cancelled the stuff out

[wary stream]

Not canceled but set them equal to each other

Because balance the sides

[fathom sequoia]

ah K

[fathom sequoia]

What happened to the R sorry fi its a stupid question

[wary stream]

R is a constant so set that equal to the LHS constant

[fathom sequoia]

k

i would've never gotten this myself

[nimble fiber]

i got 2sqrt(2)

but it is wrong

oh my god

im so stupid

i didvided it by 2 cuz i thought it was a triangle

[keen trail]

@dark granite I posted two other questions that i'm struggling on starting off

[dark granite]

write out the truth table for each of these. That's always a surefire way to determine/verify equivalence

[keen trail]

Okay, but I don't think my professor would want that lol but isn't the truth table more like an alternative method?

[wary stream]

These

One of those works

[dark granite]

I don't know if I'd call it an 'alternative method', but yeaa it really depends on how your prof wants you to do that problem. If they didn't say/mention in any way that you couldn't use truth tables, then you can totally use truth tables unless they say otherwise.

[keen trail]

yeah because i dont think my professor would prefer the truth tables

[dark granite]

okay then go with what @ dldh06 suggested. For problem 35, use the fact that (a -> b) is equivalent to (~a v b)

[keen trail]

ill start off from there and for 36?

[dark granite]

I don't see a 36

[wary stream]

There's no 36?

[dark granite]

I only see 31 and 35

[dark granite]

I see this^

[dark granite]

and this^

[wary stream]

Enlighten us on q36

Because it no exist

[keen trail]

oh my bad hahaha lol

[wary stream]

Figment of our imagination?

[keen trail]

thanks everybody i'll start off from there and i'll see by double checking using truth tables at the end

[dark granite]

you're welcome

[crystal quest]

hi can someone help me?

[alpine sable]

anyone good with asymptotic functions?

[crystal quest]

can you give some real life function?

[dark granite]

wym real life?

[crystal quest]

real life function examples

[dark granite]

I mean you can write a function whose graph is population vs time

so like P(t)=t^2 could be the growth rate of some species

[crystal quest]

wym time?

[dark granite]

where t is in some units of time and P is some unit of popultion (like hundreds or thousands of turtles for instance)

[dark granite]

you don't know what time is?

[crystal quest]

ik

oh i get it

thanks hehe

[dark granite]

You're welcome

[slow girder]

Yo how to write [-8,-2.5) in inequality symbols

[alpine sable]

$-8\leq{x}<{-\frac{5}{2}}$?

[ocean seal]

jswatj

[slow girder]

Thanks

I can change the fraction to decimal right?

[alpine sable]

if u want yes

[slow girder]

OK cool thanks

"x is greater than or equal to -8 but less than -2.5" is this the right sentence for it?

[past prism]

does anyone know why the remainder is (ax+b) to the degree of two?

Working out: P(x)=(x+1)(x+3)Q(x)+ax+b

[past prism]

<@&286206848099549185>

@jagged imp Could u please help?

@vale wigeon pls help i dont understand why the remainder is ax+b

[vale wigeon]

don't ping people out of the blue like this

[past prism]

sorry

[tall wing]

please read #rules and #❓how-to-get-help

@past prism

do not ping people specifically asking them for help

it is rude

[past prism]

sorrrry

[pastel schooner]

Just to make sure. Is the kg 6.94 x 10^4 kg?

and lbm is 1.39 * 10^5 lbm

[keen trail]

@dark granite am I doing this correctly?

[dark granite]

No!

p implies r is equivalent to ~p or r

Use that fact and the distributive law

[pastel schooner]

<@&286206848099549185>

[keen trail]

So like

(~p or r) and (q or r)

*(~q or r)

[quaint trout]

How did you go from p implies r and q implies r to not(p) implies r and not(q) implies r?

Are you saying those are equivalent?

[dark granite]

Yes @keen trail that is correct.

He made an error @quaint trout

[keen trail]

And then from there

By doing distribution law

i get

~p and ( ~ q or r) or ~r and (~q or r)

Right?

[dark granite]

Uhh

Where is this ~r coming from?

[keen trail]

Oops

• r and(~q or r)

Right?

[dark granite]

Hang on a sec

I’m doing this from my phone rn so it’s kinda hard to see shit

[keen trail]

Its fine i can wait

[dark granite]

Okay I just had a thought @keen trail

[keen trail]

Yea

[dark granite]

About how to do this whole thing easier

Start with (p or q) implies r instead

It’s much easier

[keen trail]

Okay

[dark granite]

You’ll have to use demorgans law and the distributive law

And of course the implication law

My proof for it is only 3 lines long

[keen trail]

So i should start off with the implication law

[dark granite]

Yes

Then demorgans

Then distributive

Then implication

And voila!

[keen trail]

So p or q implies r

Turns to

~(p or q) or r

Right?

[dark granite]

Yes

Now use demorgans

[keen trail]

~p and ~q or r

[dark granite]

Yea but use proper parenthesis

(~p and ~q) or r

[keen trail]

(~p and ~q) or r

[dark granite]

Yes

Now use distributive

Law

[keen trail]

(~ p or r ) and (~Q OR R)

[dark granite]

Yes

Now use implication

Law

[keen trail]

Back how it was in the beginning?

[dark granite]

Yup!

[keen trail]

So p implies r and q implies r

Ah

[dark granite]

Yes but use proper parenthesis

[keen trail]

(P implies r) and (q implies r)

[dark granite]

But yea this way is way easier isn’t it?

[keen trail]

Yeah very

How can u tell it was easier is there a trick to it?

[dark granite]

And that concludes the proof

Well just from experience I knew the other way would get quite messy

[keen trail]

I just started discrete math and logic puzzles throw me off

[dark granite]

The other way would’ve required absorption law

As well

[keen trail]

Interesting

[dark granite]

Here’s how I did the other way

Ignore the stuff I scribbled out

And now here’s the shorter way...

Ignore the scribbled stuff

[keen trail]

How does absorption law works again

[dark granite]

Which way you like better @keen trail? 🤣

[keen trail]

Obviously the shorter way 🤣

[dark granite]

(p and q) or p is equivalent to p

It’s easy to see this just by thinking that if p is false, the other statement is false and if p is true, the other statement is true

So the two are equivalent

[keen trail]

I see

[dark granite]

Dope! Aight I’m gonna sleep now it’s 12am here haha

Have a good day/night!

[keen trail]

Night! Ill be asking for more help soon!

[dark granite]

Feel free to dm me your questions. I’ll get back to ya as soon as I can

@keen trail

[tight locust]

what is the algorithm for exponentiation by hand? if i give you for instance, 3.58^9.61 and tell you not to use a calculator how would you go about that

[white swallow]

fellas

my professor keeps turning (x+1)^2 into |x+1|

what's happening here?

[tight locust]

sqrt(x^2) = |x|

[white swallow]

is it like root?

[tight locust]

(x+1)^2 does not equal |x+1|

[white swallow]

that's what's confusing me xD

(x+1)^2 < 9 => |x+1| < 3

instead of a normal (x+1), he puts it into module

[alpine sable]

Hi can i ask the difference of rule method and roster method

[upper aspen]

Can someone help me with my homework?

[upper aspen]

This question got me stuck

[white swallow]

maybe try using the given values instead of 'a'

[upper aspen]

A,B,C,D are multiple choice answers

[vagrant cobalt]

Multiply and compare the coefficients

[chrome skiff]

Hello. Im good at matrixes but they combined it with cosine and sine and i dont know what to do. Welp

[upper aspen]

Right ima try that

[vague iris]

should parabolas be parallel to the slant height of the cone?

[vagrant cobalt]

Put theta equals (2n+1)pi over 3

[upper aspen]

Yep got the answer. If i use FOIL and the multiply the coefficients. Equaling the equation. Resulting the answer being B) -3

[rugged lily]

I'm not sure how this step is split into partial fractions

Does anyone mind explaining this?

I just assumed that it would be written as A/(ax+1) + B/(x^2+1)

[vapid oak]

seeing as the term x^2+1 is quadratic, the numerator of the partial fraction is not necessarily constant, so they have split up the partial fraction further into the linear and constant parts

if that makes sense....

[rugged lily]

yeah it sort of makes sense

how would i split up that into partial fractions though?

[vapid oak]

sorry what?

you mean how would you do it yourself?

[rugged lily]

like the factor x^2+1

yeah

[vapid oak]

ok so when all the factors are linear, the numerators are constant, and you make then A and B

so in this case you would make the numerators Ax + B and C

and then in the example they split it up into 3 fractions, Ax, B and C

[rugged lily]

would the denominators be (ax+1) and 2 (x^2+1)'s

[vapid oak]

yes

frankly if I were doing it myself, I would keep the entire Ax + B factor on top of one denominator to be organised, but it doesnt change a thing

[rugged lily]

would the Ax+B be over (x^2+1) right

[vapid oak]

yep

[devout sigil]

Find 32/35 - 5/7 first

[stable wind]

0.2

[devout sigil]

Then multiply by 5 to get the missing value

[kindred hull]

do you know what ur actually doing

if you have an equation, both sides are of the exact same value, meaning you can do the same operation to both sides and the equation remains true

so ur subtracting 5/7 from both sides first,

then multiplying by 5 to clear the fraction

giving you an equation where the unknown is the subject

[lunar condor]

@stable wind 7

[lyric hedge]

can i also post a question?

[vapid oak]

yes it seems like theyre done

[lyric hedge]

thank you

this one i am stuck a bit

[vapid oak]

ok im going to write something out tell me if it makes sense

[lyric hedge]

ok..

[lunar condor]

I don't like maths , but I need it to crack JEE

[lyric hedge]

why u dont like it ;-;

[vapid oak]

let the number = 10+b. the reverse of the number is 10b+a. 10a+b+10b+a=11a+11b=8. Dividing by 11 gets us that a+b=8.

try and work out what a and b are yourself now 🙂

[lunar condor]

@lyric hedge because I don't get it , it's just that I don't understand it , can you please help me

[vapid oak]

hey guys, if you want to have a conversation maybe don't do it while a question is trying to be answered

[lyric hedge]

ok thank you..

[vapid oak]

if you need the answer: ||a=2 and b=6. The other way round also works.||

[small trellis]

What do you think is the best way to display the answer for the roots of a quadratic equation?
e.g. "x = 3, y = 2 x = 5, y = 7"?

do I throw in an "and" or an "or" in between?

[kindred hull]

dont u display it as coordinates

[vapid oak]

well if y doesnt equal 0 then i dont think those are the roots

[small trellis]

it equals to 0

in this case

[kindred hull]

it doesnt equal 0 tho cos y is 2

[small trellis]

Whoops

forget the Ys then

[trail perch]

if cos y = 2, y is undefined

[small trellis]

funny

[kindred hull]

bro what

[small trellis]

I can't tell if he's making a joke or not

[kindred hull]

hes trying to confuse u bro ignore him

[small trellis]

it's because you said cos

but it was as in because

not cosine

anyway

[kindred hull]

oh

i see

[vapid oak]

go onto channel 5, its not being used 🙂

[small trellis]

the mark scheme shows this for solving a simulatenous equation

so I guess I can just list them

but idk why the comma separates the Ys

I would imagine it to be 1 y, the other x

[kindred hull]

u said roots of a quadratic equation

[small trellis]

and the 2nd y, and the 2nd x

next to each other

[small trellis]

forget it

I'm just thinking in general

how to display it

[alpine sable]

blocked

[kindred hull]

it doesnt matter that much

[small trellis]

I guess if I can clearly show which Y belongs to which X, then I'll get marks

yeah

[kindred hull]

huh

[small trellis]

🤦‍♂️

it's another joke dude

[kindred hull]

u can write it as coordinates too

[small trellis]

I guess

[kindred hull]

cos its the point where the two lines meet

on a graph

[small trellis]

yeah

this is literally 6 marks 😂

I hope I get this in my exam

[alpine sable]

??? lol blocked

[vapid oak]

subsitute x into the second equation

[small trellis]

yeah

very simple

I was just showing how nice it is for this to be 6 marks

[kindred hull]

im reporting u to joe biden

[winged citrus]

hello

is it correct that for any infinite set cardinality is either equal to the cardinality of the set of all natural numbers if it's countably infinite or to the cardinality of the set of all real numbers if it's uncountably infinite

[placid zinc]

Depends on who you ask, haha

I think for a lot of people "uncountable" is any infinite set with no bijection to N

In that case, no you have sets that are uncountable, and also larger than R

For example, the power set of R is larger than R

[kindred hull]

isnt unlistable a better word

than uncountable

[placid zinc]

But some people might take "uncountable" to be any set with a bijection to R

So, ya know, depends

[winged citrus]

thanks

uhh this might be a dumb question but

if we took the set of all natural numbers and added something that isnt a number to it

does its cardinality become greater than the normal cardinality of the set of natural numbers?

[jagged imp]

If that something else is any one element, consider the map that takes that "something else" to 1 and every other number n in your modified naturals to n+1

its a bijection

This is the same as asking if the set of natural numbers including 0 has the same cardinality as the set of natural numbers excluding 0

[winged citrus]

so no?

wait i mean yes

[jagged imp]

Their cardinalities are the same.

[winged citrus]

thanks

[warm tartan]

It is given that x:y = 7:12 and x+y=152, where x and y are non-zero constants. Find x and y

can someone help me

[winged citrus]

if you still need the answer,

[warm tartan]

ok thanks

[jade birch]

@winged citrus don't give out answers, this is not that type of server

[winged citrus]

but its with a solution?

or do u mean because its a school test or something

[jade birch]

No

They're here to learn, or are supposed to be, even showing the full solution without explaining it first and making sure they understand is kinda bad

[winged citrus]

oh, sorry

i thought it would be intuitive with this one

[solemn moth]

Simplify 100mmcube : 25cm cube
Anyone can help me?

[loud jay]

what is sinA/cosA

pls

help

i need it

ok fuck you guys yall are dumb

[alpine sable]

Any help? I havent been paying attention lmao. Confused asf

i prolly sound dumb as hell

[wispy tangle]

ughg

[alpine sable]

This is my first time even touching my geometry work all year

idek wtf a conjecture is

what is nth representing there? are those just variables that they gave?

[solemn moth]

yes they are just variables

[winged citrus]

wouldnt it be B because thats the only one that gives 1 dot at n =1

[alpine sable]

OH

[winged citrus]

also 3 at n = 2

[alpine sable]

it would be B

but

because n(n+1) 1+1=2

then every layer after that follows the same thing

[winged citrus]

yes

[solemn moth]

btw can anyone help me out

[alpine sable]

loll

[winged citrus]

100mm and 25cm for volume?

[solemn moth]

no

[winged citrus]

side length?

[solemn moth]

it is 100mm100mm to 25cm25cm

*100mm^100mm to 25cm^25cm

and simplify it

[winged citrus]

but its a cube

[solemn moth]

I can't figure out the correct way to simplify it

^ is times

[winged citrus]

the incorrect part is * 10

it should be 25 * 100

[solemn moth]

why 100?

[winged citrus]

because its square millimeters and centimeters

[solemn moth]

the difference of squremm and square cm is 100?

lol I am so stupid

[winged citrus]

if 1 cm = 10 mm you take the square of 10

for square units

[solemn moth]

bruh I don't understand

[winged citrus]

1 normal cm = 10 normal mm

[solemn moth]

yes

[winged citrus]

if you take 1 square cm and square mm you have to take the square of 10 also

for cm2 to mm2

[solemn moth]

ok thanks

[hidden pike]

I've a question

If a|1, prove that a=+-1

we can write it as 1 = a*k where k is some integer

Now what should I do ?

Anyone?

[solemn moth]

any photo

[hidden pike]

Leave it I got my answer

wait let me tell you @solemn moth

[warm tartan]

lol niceee

[hidden pike]

This is what I wanted to know

I got my answer.

[solemn moth]

k and I don't understand one bit of your calculation b'cuz i am too stupid

[warm tartan]

we haven't even learn that

[solemn moth]

no casual talking in here lol

[hidden pike]

oh

@solemn moth

[fathom sequoia]

wow that looks hard

[hidden pike]

that's easy

[fathom sequoia]

what is it

wht grade do you learn this

[hidden pike]

I proved there that
a divides 1, then a=+-1 for quotient to be a integer

[hidden pike]

I learnt it in 10th grade

self feed

[fathom sequoia]

are you from india

or soething

something*

[hidden pike]

India

[fathom sequoia]

ah ok, in new zealand we are a couple of grade behind

[hidden pike]

that's from Number Theory

[fathom sequoia]

in nz grade 10 like grade 8-9 in India

[hidden pike]

oh

[fathom sequoia]

yeah

[hidden pike]

ohhhh

[hidden pike]

@fathom sequoia

[fathom sequoia]

👍

Good job

[hidden pike]

a|b => b=ak

The above thing is read as a divides b

[fierce frigate]

how do i find this

my answer is wrong

i dont know how i found it

[alpine sable]

divide it into 2 right triangles

[fierce frigate]

done, so u do the soh cah toa thing right?

[alpine sable]

yeah

[fierce frigate]

yea but the answeer isnt the same with what i calculaateee

[glass lichen]

what did you get for the height of the triangle?

[fierce frigate]

sin 60 = op/11
0.8660254038 x 11 = opposite
9.5 cm

[glass lichen]

approximately, yes

so then find x

[fierce frigate]

ohhhhhhhhhhhhhhhhhhhh

i did the wrong thing

[glass lichen]

Ok, also dont do intermediate rounding

[fierce frigate]

sin 40= 9.5 / x
0.64278... = 9.5/x
0.64 x X = 9.5
X= 9.5/0.64
=14.77

[glass lichen]

no

you still did some intermediate rounding, so you're off

[fierce frigate]

thats what th teacher

wait no nvm

[glass lichen]

$h=11\sin(60) \ \sin(40)=\frac{h}{x} \implies x=\frac{11\sin(60)}{\sin(40)}\approx 14.82$ (2DP)

[ocean seal]

Mosh

[fierce frigate]

yea found it

im confusede with this on

ill tr by myself first

[glass lichen]

that should've been the first thing you did...

[fierce frigate]

i just put the question here first

[alpine sable]

Use soh cah toa

[fierce frigate]

i know

[glass lichen]

read all of it

[fierce frigate]

i think i misscalculated

[alpine sable]

and add the remaining 1.6

[fierce frigate]

last time

[glass lichen]

@alpine sable if you're going to help, actually read

[alpine sable]

read what ?

[fierce frigate]

sin 40= op / 28.5
(sin 40) x 28.5= op
op = 0.6427876097 x 28.5
=18.31944688
= 18.32

not yet

• 1.6

19.91
or
19.92

[glass lichen]

not sine

you have the 2 legs

[fierce frigate]

JESUS CHRIST

[glass lichen]

They said they wanted to attempt it first.

[fierce frigate]

isnt that opposite and adjcent

daammit

[glass lichen]

yes

[fierce frigate]

i cant

read

its taan

stupid

[glass lichen]

yep

[alpine sable]

Sorry . . .

[glass lichen]

everything else is correct bar the intermediate rounding

[finite lichen]

Linus no work so sad no sex tip today 😩 😋 😋 😋 😋

😫

[glass lichen]

not math related, fuck off

[finite lichen]

Ur mom

[fierce frigate]

tan 40= op / 28.5
(tan 40) x 28.5= op
op = 0.8390996312 x 28.5
=23.91433939 + 1.6
-25.514

[glass lichen]

yes

[fierce frigate]

ill takee myy time to memorize soh cah toa

wait

im a moron

its in it already

[glass lichen]

then whatever rounding is wanted, likely 1DP since everything else is to 1DP

[fierce frigate]

STUPID

soh cah toa

why dont

im

a

moron

[glass lichen]

ok...

[fierce frigate]

smh

how did i not know that

it couldve made my life easier

[glass lichen]

know what...?

[alpine sable]

Would you know where i could find a lot of practice problems for polynomial factoring and limits ?

[glass lichen]

google

[fierce frigate]

i knew soh cah toa eexist, i just didnt know it stands for
sin oppositee hypo
cos adj hypo
tan opposite adje

[alpine sable]

okay

[fierce frigate]

stupid

T_T

[glass lichen]

Yeah... that should've been explained by your teacher

[fierce frigate]

didnt pay attention

online class things

how is this 15.86....

my calc sys its 15.93

tan 30 = 9.2/x
tan 30 x X = 9.2
X= 9.2/tan 30
x= 9.2 /0.5773502692
x= 15.93

tried all ways possiblee

its 15.93

@glass lichen im right or wrong?

[glass lichen]

which length? z or x?

[fierce frigate]

x

im looking for x

[flat vale]

ur right

the answer is wrong

[glass lichen]

,w calc 9.2cot(30)

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by moshill1#9771

[fierce frigate]

the one on the picture (is my psat nswers)

[fierce frigate]

okok

thx

[wary stream]

Also, to let you know it's not ideal to use x as multiplication sign since x is a variable too. Use * instead

[fierce frigate]

ye ik, just lazy to do extra shifts, myy quiz is gonna bee on paper so yeea

the aask me to print it

thx tj=ho

[frosty whale]

Hi in relation to part (ii), when using squared trigonometric ratios(sin^2Θ, cos^2Θ etc.), how do i know which quadrants has positive ratios? Is it all four?

[pastel wyvern]

pls help me out

[forest sedge]

Need help rearranging for r, working out would be appreciated.

[frosty whale]

is angle y RPQ?

[pastel wyvern]

no

[frosty whale]

my bad ,what is 'y' referring to in your drawing?

[pastel wyvern]

we need to find y

[frosty whale]

yes but is y an angle

or a line

[forest sedge]

I would think that RPQ is y

[frosty whale]

he said it isnt though so im a little lost

[forest sedge]

Maybe it is the slope of that line

[pastel wyvern]

im not sure btw '

this is a practice sheet i found

[frosty whale]

it should be the angle considering the rest of the equations are all asking for angles

[pastel wyvern]

ohk

you can take it as prq

[tawdry sphinx]

y = 180 - 73 - 60

[frosty whale]

so for y, first you need to find SPQ which can be done since adjacent angles in a parallelogram are complementary(both add up to 180)

so for example SPQ + PQR=180

then from there you can subtract 73 from SPQ to get y

[tawdry sphinx]

the sum of the angles in the triangle PQR has to equal 180 deg

[frosty whale]

yep

[tawdry sphinx]

that would be another way as you know QRP is 73 as well

[frosty whale]

yep by alternate angles

both methods work

for z first you need to find SRP which can be done by subtracting 180 by x and 73 since sum of angles in a triangle(SPR) is 180

then from there, subtract 180 by SRP to find z adjacent angles on a straight line add up to 180

[tawdry sphinx]

and you can find x by the same principle like you found y

[pastel wyvern]

x=107?

y=47

[tawdry sphinx]

x should be 60 right?

y is 47 yes

opposite angles of parallelograms are the same

[alpine sable]

Is this allowed?

[forest sedge]

Are you looking for the limit sum?

Cause there is a formula for it

And it is 1

[flat vale]

he's trying to proof that..

[noble sinew]

Yep it is

[flat vale]

kinda implying that -inf/2 = -inf tho

it's true but 🤔

[noble sinew]

The only place there might be a problem is 1st line that you assume it exists

Could look at partial sum instead (or prove it is finite)

[flat vale]

adding on to that, try searching for proof of geometric series

[alpine sable]

Thanks because my teacher says it isn't.

[tawdry sphinx]

this is allowed yes as long as n is not equal to infinity

[alpine sable]

And just for argument sake. What title do you guys have?

[tawdry sphinx]

this should be enough to convince a teacher tbh

[alpine sable]

Thanks!

[flat vale]

you mean n is infinity right?

[tawdry sphinx]

it cannot be infinity

[flat vale]

no it must be

[tawdry sphinx]

that's why you typically write it as a limit

[flat vale]

try doing n = 5

[tawdry sphinx]

waaait a minute

[flat vale]

n must be infinity for this to be true

I suggest you guys to dive into ‘infinite geometric series’

[tawdry sphinx]

the problem arises tho if it isn't?

i'm so sorry i made a mistake haha

[flat vale]

from the question we can assume the original question asks for n->inf

[tawdry sphinx]

i guess so yes

[flat vale]

the formula is prob given (Sn)

[tawdry sphinx]

but now i would really like to know why it doesn't work for n of R

[alpine sable]

Are you guys mathematicians??

[flat vale]

It’s like saying why 1+1 != 3

it needs to approach infinity in order to become 1

[alpine sable]

Because my teacher doesn't believe me

[violet flare]

some of us

[flat vale]

there’s a geometric proof of this as well

[tawdry sphinx]

yeah ok now i know what the problem is: as long as n is not infinity after subtracting 1/2 and multiplying by 2 you will not get the originial series

so if n is infinity this is fine

sry for the confusion

[tawdry sphinx]

this is actually a nice image to show it. I like it

[pastel wyvern]

Someone pls

[lilac lantern]

is the diagram given to scale and proportional or it is an arbitrary depiction?

[tough hatch]

this is not an infinite series, assuming n is a natural number.
x = 1 does not hold. 2(1/2)^n is not equal to (1/2)^n

take n=1. then the sum is equal to 1/2

[foggy onyx]

hi. is this channel busy rn?

[loud cedar]

(180-115)/2=∠PQO
{360-2(115)}/2=∠SOP or ∠ROQ so minus that from 180 and /2 you get ∠PSO and ∠ORQ prob

[loud cedar]

they afk i think

[glass spoke]

Probs this

how do you solve this again

like since the triangle got circle on it that also form miniature segment that resembles oval do we just (area of triangle) - (area of segment/oval) then times it 3 to get the full area of remaining triangle?

[steady trout]

Ya

Area of triangle - area of circle = the rest inside triangle

[glass spoke]

what if it were to be only known radius or only known bottom

[steady comet]

So , the numbers dont add up right

[glass spoke]

is this sets

i forgot

[steady comet]

how can the intersect of A and B be 9 , if A is 0.6 and B is 0.7

this is venn diagrams

[glass spoke]

ah so it is sets

[glass lichen]

Probability

Hence the P..

[glass spoke]

what

[steady comet]

yes

probability

[glass spoke]

im confused

[steady comet]

but we are instructed to use venn diagram

[glass lichen]

Axiomatic probability uses set notation since events are just elements of the sample space's power set

Aside done

[steady trout]

Idk lol

[glass spoke]

sad 😔

[steady trout]

I think something with diameter

Since its drawn perfectly fitting

[steady comet]

Guys, english please

[glass lichen]

Mine wasn't directed at you, just dispelling set theory vs probability

[steady comet]

back on topic of this question

[glass lichen]

However I'd just use inclusion-exclusion over vent diagrams

Which can be derived by vent diagrams

[steady trout]

That calculus?

[steady comet]

Sets

A.K.A Venn Diagrams

[steady trout]

Oh aight

[glass lichen]

P(AUB)=P(A)+P(B)-P(AnB)

[steady comet]

my fricking man

thanks

[glass lichen]

Prove inclusion exclusion for yourself with a venn diagram

It's not hard

[surreal lily]

,rotate

[surreal lily]

need help with the first one

lowest I got was -78 using -9, -6, 6, and -4 but I don't know if that's right

[pastel wyvern]

Can someone pls check my sum

Pls check this

[steady trout]

Looks good

[solid sage]

If all queries here get complete pls come to #help-1

[pastel wyvern]

Guys is this correct

[brazen yoke]

are vertical stretch by a factor of 5 and horizontal compression by a factor of 1/5 the same

im talking function transformation here

[pastel wyvern]

Plsss tell me

[brazen yoke]

u are

wait hol up

nvm yes

also one question

[craggy sonnet]

yo can anyone join vc and help with some math work

[brazen yoke]

whats the transformation for y=5|x-3|-4

my answer is right 3, down 4, vertical stretch by 5

dk if its correct

[celest sand]

what about the abs

[violet flare]

and all negative points are reflected from the x-axis

or something along the lines of that*

[brazen yoke]

what

[brazen yoke]

wym by that

[celest sand]

absolutes

[brazen yoke]

nothing about it

its just an absolute function

original is y=|x|

[celest sand]

oh ok that makes sense

[brazen yoke]

so im correct then

[celest sand]

yep

[brazen yoke]

im guessing a vertical stretch by 5 and horiOntal shrink by 5 are the same too

[ionic tartan]

hey, I'm trying to learn how to calculate low level math in my head, i.e roots, powers, multiplication, addition, subtraction. does anyone have a good class/tutorial for that?

[brazen yoke]

do more math and memorize it?

[celest sand]

isnt it compressed by factor of 1/5

not 5

[brazen yoke]

oh this a dif question

visually they look the same idk

[celest sand]

im pretty sure its only the same for a parabola with vertex at origin

with cubics they are not the same

^thats just 1 e.g.

[brazen yoke]

it works for absolute function

[celest sand]

as you can see here, the function with the vertical stretch by 5 and the function with the horizontal compression by √5 is the same (red and black overlap)

but for cubics it dont work

[brazen yoke]

ur using root btw in the 2nd

[celest sand]

so u cant generalise it to all functions

yeah its a root bc its a horizontal compression by √5

rather than a vertical stretch by 5

the factor is INSIDE the ()^2

which makes it a horizontal compression

[brazen yoke]

oh damn

i got it now thanks

[celest sand]

all g

[verbal gull]

calculations of the full surface area and volume of the prism

[alpine sable]

im pretty sure this is easy stuff but im jus back from a long break and mind been off.
can someone please tell me the way of factorizing these ?

[covert mist]

im pretty sure this is easy but if you have a 3minute time glass and a 4 minute timeglass how do you calculate 5 minutes

[devout sigil]

They said taking out common factor, that means for example, if my expression is a-a² the common factor is a, so I can factorise a and get a(1-a), common factor can be a number or a variable.

[devout sigil]

Start both timers together, when 3minute time glass runs out only 1 minute is left for 4minute time glass to run out. After 4minute time glass runs out (1minute later) immediately start the 4minute timer again to get a time of 5 minutes.

[covert mist]

can you explain how you calculate this or is it just trial and error

[devout sigil]

There are some practice questions online but for these type of questions usually u need a time difference between the two timers

[covert mist]

alright

[devout sigil]

For example another type of question would be to get 7minutes from 3min and 5min time glasses respectively

In this case time difference is 2minutes so I just need to add another 5minutes to get 7minutes

Btw I found this problem online lol

[covert mist]

ok

[unique fjord]

this is a yes or no question, is this correct?

[alpine sable]

ty Aspiring mathematician/physicist

[unique fjord]

aaaaaaaaaaaaa

im just gonna pass it

i changed the discriminant to 81

ok i also changed number 2's general form to x^2-15+36

i accidentally wrote 2 x squareds

[frosty whale]

if a <@&286206848099549185> could aid me with this query id greatly appreciate it

[alpine sable]

would 2x^2 +6x be 2x (1x+3)

[tight loom]

anyone know how to use SPSS ?

[alpine sable]

Lim ( 2x-3)/sin^2 *x when x goes to 0?

HELP how 2 Factorize the given expressions using identity/formula.
m2 + 8m + 16
4x2 – 4x + 1

never saw this in the 13 y7earrrrs uof my7 lifes

[harsh nimbus]

Do you just need help factorizing the two equations?

[alpine sable]

yes pls

[harsh nimbus]

Do you know the quadratic formula

[alpine sable]

$$-\sqrt{a^2 + b^2} \leq a\sin \theta + b\cos \theta \leq \sqrt{a^2 + b^2}$$
so for your question its
$$-\sqrt{5} \leq 2\sin \theta + \cos \theta \leq \sqrt{5}$$
$$0 \leq 2\sin \theta + \cos \theta \leq 5$$
so greatest value is 5
about quadrants
$$2\sin \theta + \cos \theta = +/- \sqrt{5}$$

no

[ocean seal]

Spica

[alpine sable]

what is it

[alpine sable]

Ok and what to I do with this?

[alpine sable]

nuo idk

whuoa what was tat

cuonfiuosiuon

[harsh nimbus]

Bad picture sorry

[alpine sable]

its - infinity

[alpine sable]

nuo its guouod

[alpine sable]

Thanks what did u thought?

[alpine sable]

huow duo i duo m2 + 8m + 16
4x2 – 4x + 1 wit tat?

[harsh nimbus]

So in your case
M^2+8M+16
A=1
B=8
C=16
You can plug it in to find :
-4
Then you can write it like
(x-(-4))(x-(-4))
Which would finally equal to
(x+4)^2

[alpine sable]

its not any intermediate form so putting x\to 0
is just tends to -3/0 aka -infinity

[alpine sable]

damn

[alpine sable]

ima try7 tuo duo it than ty fuor explaining

[alpine sable]

Yea but how do u know if it's-oo or +oo

[alpine sable]

cause its '- (3/0 )'

[alpine sable]

Yes but x/0 = +- 00 so

[alpine sable]

If it's-00 it goes +00

[alpine sable]

Thanks but why +00?

[alpine sable]

x/0 = infinity if x>0
x/0 = -infinity if x < 0

[alpine sable]

So I write that and I'm done?

[runic flower]

cause its a negative number over 0+
which negative number × +oo
Which is +oo

[alpine sable]

you just have to put x = 0 and you're done just like nop did

[runic flower]

yes this limit doesnt require any method

[alpine sable]

Wait

[alpine sable]

so like (1) m2 + 8m + 16

m2 + 4m + 4m + 16

m ( m + 4 ) + 4( m + 4 )

( m + 4 ) ( m + 4 )

?

[harsh nimbus]

Yes that’s the factoring method

[alpine sable]

uoh

ty7 fuor helping

[harsh nimbus]

You split the 8m into 4m and 4m and then partnered m^2 +4m, 4m and 16

[alpine sable]

uoh

i thiunk i can duo nuo 2 tuouo

[alpine sable]

Like this?

i cant ty7pe

Also ημ is sin

In Greek

im uone handed

[alpine sable]

is 2 like this?
(2) 4x2 - 4x + 1

4x2 - 2x - 2x + 1

2x ( 2x - 1 ) - 1 ( 2x - 1 )

( 2x - 1 ) ( 2x - 1 )

[harsh nimbus]

Yes perfect that works

[runic flower]

no no its +oo for x->0
No need to split cases of x->0+ and 0-

[alpine sable]

That's what I don't understand

• infinity is the answer

I'm confused

just differentiate both numerator and denominator

as long as the answer is not 0/0

[alpine sable]

thanks!!

Ok that's what I did

Then I don't take cases?

[alpine sable]

you are acting just like your name but that's not any intermediate form ><

[alpine sable]

u made me uonderstand it better

[runic flower]

Yes no need cases

[alpine sable]

Why 0+ it says 0 only

[runic flower]

cause

Wait i will write

[alpine sable]

Oof I'm too dumb for that

[runic flower]

You can see it in this way

[alpine sable]

Oh

[frosty whale]

thank you kind sir

[alpine sable]

OH

Or

[runic flower]

no
Youre good
these things happen sonetimes

[alpine sable]

I can say that too?

[harsh nimbus]

Idk if I am helping but I would approach this problem this way

[runic flower]

no bbecause lnx times x is not equal to ln(x^2)

[alpine sable]

Ok thanks

[runic flower]

yee

[vivid fulcrum]

i cant

what

[stuck jolt]

Lol, pH calc

Advanced chemistry in high school I suppose?

[vivid fulcrum]

its actually

in my math book

in the logarithm

chapter

[stuck jolt]

Why would they do that

[runic flower]

yeah its a nice problem involving chem concepts
Awesome

[vivid fulcrum]

i have no idea, thats why im confused

[stuck jolt]

I remember I used to do this for fun

Forgot everything tho

Perhaps I should read my old books

[faint nest]

Hi pwease help idk how they go from this first step to that second step

[stuck jolt]

Ah yes, eulers constant

[harsh nimbus]

Oh it’s (a+b)(a-b)=a^2-b^2 for the numerator

[stuck jolt]

Same thing for denominator

This is actually an interesting question

I will try and solve it

[faint nest]

Tysm

[harsh nimbus]

What’s the questions asking is it just simplify

[faint nest]

Yep

[stuck jolt]

Its interesting to find the derivative

[harsh nimbus]

Oh derivative sure

[stuck jolt]

$\frac{\frac{d}{dx}\left(\left(e^x+e^{-x}\right)^2-\left(e^x-e^{-x}\right)^2\right)\left(e^x-e^{-x}\right)^2-\frac{d}{dx}\left(\left(e^x-e^{-x}\right)^2\right)\left(\left(e^x+e^{-x}\right)^2-\left(e^x-e^{-x}\right)^2\right)}{\left(\left(e^x-e^{-x}\right)^2\right)^2}$

[ocean seal]

Captain_Mat01

[stuck jolt]

lol, I love eulers constant

[harsh nimbus]

What’s is Euler constant I am not smart

[faint nest]

Pretty sure it’s just 4/(e^x-e^-x)^2

[stuck jolt]

Nah

Derivative it is not

Denominator will prolly have a power of 3

And a negative sign at the end

[faint nest]

O Idrk what derivative is lol

[stuck jolt]

Ah, lmao

[harsh nimbus]

Instantaneous slope

That’s basically what it is

[topaz scaffold]

e

[harsh nimbus]

I see

Isn’t it 2.7

Something like that

[topaz scaffold]

The number with the nice property that $\dv{x}e^x = e^x$

[ocean seal]

RipeOrange

[topaz scaffold]

Around that

[stuck jolt]

Yeah, because the roc of e is e

That is why finding the derivative of the other question was fun

[harsh nimbus]

Wait that’s interesting

[topaz scaffold]

Yeah

You can also see it as continuously compounded interest

[safe roost]

could i make the generalisation that a function has to be injective to be invertible?

[alpine sable]

I'm in high school and I just want a explanation for 5(y-2z-2) - (3y-2z+1)

[topaz scaffold]

I think so

[vivid fulcrum]

i think i found out, you just substitute the numbers given

and do the log

[harsh nimbus]

Do you want to just simplify it using distributive property

[alpine sable]

I want to simplify it yes

do remember I am only 15 and have not unlocked this Interesting vocabulary

[harsh nimbus]

It’s similar to how you did the last problem
I will send my work in a second

[alpine sable]

thanks

it's just a bit more variety and I'm just not sure

I want an explanation for it so I will know in the future

[harsh nimbus]

5(y-2z-2)-(3y-2z+1)
First part of the equation:
5y-10z-10
Second part of the question:
-3y+2z-1
Merge them together:
5y-10z-10-3y+2z-1
Next you can just combine same variables
5y-3y-10z+2z-10-1
2y-8z-11

[alpine sable]

thank you very much

[urban lily]

can someone pls tell me whats the (angle of static friction between the block and the plane)

[alpine sable]

and say for example,+ 2 (4y2 - 3) 4y is cubed, does the 2 turn into 3 squared

[alpine sable]

1/x^2 is the same is x^-1?

[undone dock]

No

$x^{-1} = \frac{1}{x}$

[alpine sable]

so

[ocean seal]

K.

[alpine sable]

ok 1sec

so

(x)^1/2

how do i find dy/dx here

[harsh nimbus]

Can’t you use the power rule

[alpine sable]

idk

I know how to do the square root of x but i cant do the 1/x^2

[wet path]

1/x^2

is just x^-2