help-0

[alpine sable]

But it isn't a standard circle

If you shift origin it might have other terms too

But iirc it lacks xy

So I am asking similarly for ellipse

[small bear]

Correct, shifting wont introduce the xy term in a circle

and another thing to note, a circle is an ellipse

so does that answer the question?

[alpine sable]

Nope. Does ellipse have all of those terms?

.

Xy too

[small bear]

An ellipse written as x^2 + y^2 = r^2 doesn't have all of those terms

[alpine sable]

A standard one mate

[small bear]

You would take cases then, since when a^2=b^2 what I said was true

[jaunty phoenix]

Yoow I got 96/100 in my exam thx to u guys

[alpine sable]

Congratulations. What level was the exam at?

[jaunty phoenix]

wdym level?

[alpine sable]

Like which standard or year

[jaunty phoenix]

do you mean like 8th grade or 9th grade

or something

[alpine sable]

Yes

[jaunty phoenix]

8th Grades topic is Sets

[alpine sable]

@small bear did you get the question now?

[small bear]

Sadly I can't answer that, perhaps re-post it or post in an adequate channel since it seems like a harder problem

[compact meadow]

The function has a minimum x value ?

I think it does

[alpine sable]

It only requires knowledge of the equation of standard forms of ellipses

I got a bit lost on the internet

[north lynx]

7th grade honors is funky can someone help me with this one please?

[alpine sable]

Was it a complete function? Or only the part that is visible is the function?

[alpine sable]

Is it 470-530? 😆

[north lynx]

YES!! thank you

[alpine sable]

@small bear I got it. Thanks for your help.

[vagrant rover]

Does (infinity, 2/3) mean that the set of number would be anything less that 2/3?

Please ping

[compact lynx]

that doesn't mean anything to me

that set would include nothing

from my undersatnding

@vagrant rover

[glass lichen]

that's a degenerate interval as written

if you meant (-inf,2/3), then yes, it'd be x<2/3

[vagrant rover]

But would 1/3, for example (which isn't negative) be included in the set?

@glass lichen

Oh sorry for ping, idk if that's okay or not.

[glass lichen]

answer the more pressing question... what is the interval suppose to be

[vagrant rover]

It is supposed to be x<2/3

[glass lichen]

ok so $(-\infty, \frac{2}{3})$

[ocean seal]

Mosh

[glass lichen]

yes, since 1/3 < 2/3

[vagrant rover]

I see. Really what I'm asking is if 1/3 is included in -infinity

Because I thought it was all negative number

s

[rapid spear]

I’m trying to figure out some stuff about relation ~ on Z where x~y is x^3 = y^3 mod 4

But I’m trying to find the number of equivalence classes and describe each one which I am having trouble with

Any ideas?

[robust flax]

i was wondering how these questions are different . i am thinking it should be d/dt[gamma(t)] = F(gamma(t), t) for both but if someone could offer some insight that would be great

[tight locust]

with streamline you keep t fixed

with pathline t is allowed to vary

[low topaz]

Are cats and dogs the same topologicaly speaking

[sharp barn]

if f(x)=1-2x^2 whats its inverse function

inversefunction

can anyone help pls my device dying

[spring kiln]

f(x) - 1 = -2x^2

so f(x)/2 - (1/2) = x^2

so x = (f(x)/2 - (1/2))^(1/2)

[thick shard]

why is this false?

[sharp barn]

is the answer this?

[spring kiln]

yes I missed a negative sign

[thorn kindle]

Is ln(x+2)=ln(x)+2 ?

[sharp barn]

alright thank you

[thick shard]

oh right

[spring kiln]

Yes. Only technicality I could think of is the two nasal passages/sinuses connecting in one but not the other.

[vast cypress]

hi, i'm doing my homework rn and i'm not sure how to do this one

i've found the value of dy/dx and taken the point (a, b)

dy/dx has to be equal to (y-b)/(x-a)

but now i dont know how to find the x and y intercepts

$$\frac{dy}{dx}=-\frac{\sqrt{y}}{\sqrt{x}}$$

[ocean seal]

Arat

[thorn kindle]

$(y-y_0) = (y'(x_0))(x-x_0)$

[ocean seal]

AMD

[thorn kindle]

[vast cypress]

what does that mean?

im kinda stupid

wait

is the rhs = y-intercepts?

[glass lichen]

it's the equation of the tangent line

in general terms

[vast cypress]

ohhhh

[thorn kindle]

Point slope form is easiest

[vast cypress]

so y intercept would be slope * x-x0?

[glass lichen]

no

y intercept is when x=0.

[alpine sable]

hey ! i have a question saying "write the following expression without using indices: x^-0.5
can i write this in log form?? or how do i write this in a form other than indices

[vast cypress]

so do i just

multiply out? i'm still not sure

[robust flax]

so for formally describing streamline do we say "let t be fixed. then you let the inputs of gamma(x) vary freely?

what is the reason for this keeping t fied?

[thorn kindle]

$(y-b) = (-\frac{\sqrt{b}}{\sqrt{a}})(x-a)$

[ocean seal]

AMD

[thorn kindle]

@vast cypress

[vast cypress]

so y-intercept would be

$$\frac{a\sqrt{b}}{\sqrt{a}}+b$$

[ocean seal]

Arat

[thorn kindle]

The y int is when x=0

[compact lynx]

whoops sry

[vast cypress]

yeah

[thorn kindle]

Now simplify

What is a/sqrta

[vast cypress]

sqrta

[thorn kindle]

So then you have sqrt(ab)+b as the y int

[vast cypress]

$$\sqrt{a}\sqrt{b}+b$$

[ocean seal]

Arat

[vast cypress]

ohhh

yea

[thorn kindle]

You should simplify further

[vast cypress]

yeah

$\sqrt{ab}+b$

[ocean seal]

Arat

[thorn kindle]

Good. Now find the x int

[delicate goblet]

Without using a calculator determine the square roots of the irrational numbers to two decimal places. (Hint: Start with your answers to question 4, then apply Heron's Methoid)
a) √75

4. answer for √75 is 8.7 and I am really confused on what to do.

[compact lynx]

yo you literally

posted this question

in like 5 chats

[delicate goblet]

well

apparently

no one helps

sooooooo

[thorn kindle]

Do you even know what Heron's method is

[delicate goblet]

yeah but its confusing

[vast cypress]

$$-\frac{x\sqrt{b}}{\sqrt{a}} + \frac{a\sqrt{b}}{\sqrt{a}} + b$$

[ocean seal]

Arat

[delicate goblet]

???

i thought joining this server would help me..

[glass lichen]

Be patient.

[vast cypress]

#❓how-to-get-help

[glass lichen]

No one is entitled to help you, everyone contributes voluntarily. Also yeah, you spammed your question which makes people (at least me) less inclined to help

[thorn kindle]

You should not have an x

[winter rock]

Can someone help me with my calculator?

It's telling me syntax error

[vast cypress]

huh? why?

[thorn kindle]

The y intercept is when you set x = 0

[winter rock]

When I try to do cos‐¹(-1) it tells me syntax error

[vast cypress]

yeah but now im trying to find the x-intercepts

we arleady found the y-ints

[thorn kindle]

And the x intercept is when you set y=0

So when you find the x intercept is should be something in the form x = something

You forgot to solve for x

[vast cypress]

ohh

true

idk if i did this right but

$$x = \frac{a\sqrt{b}+b\sqrt{a}}{\sqrt{b}}$$

[ocean seal]

Arat

[thorn kindle]

x = sqrt(ab) + a

Good job

[vast cypress]

yeah if i simplify it further that'd be the value of x

okay so now i just add them and that'd be it right

[thorn kindle]

Sure lets do that

You're not quite done with the proof though

[vast cypress]

wdym?

i've found the x and y intercepts, now should i add them and set them equal to c?

[thorn kindle]

What is the sum

[vast cypress]

$$a+b+2(\sqrt{ab})$$

[ocean seal]

Arat

[vast cypress]

and that's the initial equation squared

[thorn kindle]

Yeah now set it equal and arrive at an identity

[vast cypress]

how? would it be

[thorn kindle]

How do you know that it is equal to the original equation squared?

[vast cypress]

$$x+y+2\sqrt{xy} = a + b + 2\sqrt{ab}$$

[ocean seal]

Arat

[vast cypress]

because a and b are points in the function

[thorn kindle]

yeah that works

nicely done

[vast cypress]

thank you!

[winter rock]

@thorn kindle hi

Can I ask u a question pls bro

[thorn kindle]

ok

[winter rock]

50 = 5sqrt2 + 5sqrt3 + cosBCD

Is it equal to 10=sqrt2+sqrt3+cosBCD/5?

@thorn kindle

[thorn kindle]

yeah

[carmine geode]

just need the equation

[thorn kindle]

what shape is the dorm room?

[carmine geode]

it doesn’t say anything

it’s a poorly worded question and it’s giving me a headache

[glass lichen]

well yeah, it's incomplete if it doesnt give the shape of the room

ok... then what's the other side

[thorn kindle]

assuming it's a rectangle (which is fair) you have enough information to solve

i guess you are also to assume that each of the adjacent sides are the same length?

[carmine geode]

i’ll try

[solemn dirge]

Can someone explain this to me

[thorn kindle]

let us represent the identity by this equation:

$\frac{a-b}{b-a} = x$

[ocean seal]

AMD

[thorn kindle]

what is x?

can we solve for it?

[solemn dirge]

Idk I don’t rlly get anything abt it:’)

[thorn kindle]

ok, let's try manipulating the equation a bit

$(a-b) = x(b-a)$

[ocean seal]

AMD

[thorn kindle]

now what?

[haughty falcon]

One message removed from a suspended account.

[ocean seal]

HenHen

[solemn dirge]

Idrk can you pls explain everything fully?

[alpine sable]

@everyone please help me with my math question

if johnny ate 10x apples then spits 7 x 10 apples he will receive 18 apples back. How many apples will he grow in a matter of weeks

[wary stream]

Factor

Show your work

[glass lichen]

find the roots then do sign curve/interval chart.

[alpine sable]

Bro why is there formulas for inequalities

I don’t understand like do I even need to know them

Cuz I can answer inequalities just fine without it

[winter rock]

Hi

I have to do

60 / 2sqrt14 × 3sqrt10 = cosO

But idk how to do it

Like it's 60/6sqrt140?

Idk

Got no idea

[kindred warren]

like this? $\frac{60}{2\sqrt(14)} * 3\sqrt(10) = cosO$

[ocean seal]

Tra-Guy

[kindred warren]

or is the 3root10 at the bottom of the fraction

[kindred warren]

oh

ok then

[winter rock]

@kindred warren at the bottom

[kindred warren]

ok so you have $cos(O) = \frac{60}{6\sqrt(140)}$

[winter rock]

Yup!

[kindred warren]

oh it didnt work

[ocean seal]

Tra-Guy

[kindred warren]

there we go

[winter rock]

60/ 2sqrt14 × 3sqrt10

It is the same as 6sqrt140?

[kindred warren]

depends

is the 3sqrt10 on the denominator?

[kindred warren]

is it 60/(2sqrt14 * 3sqrt10)

[proud anchor]

Can someone help me with this

[winter rock]

@kindred warren yup

[kindred warren]

ok

so you can just simplify the fraction

6root140

how can you simplfy that

[proud anchor]

nvm i got it

[thorn kindle]

(a-b) = -1*(b-a)

a-b = -b + a

lmao

[alpine sable]

<@&286206848099549185> anyone?

[wary stream]

Add the two expressions and set it equal to 110

Find x

Then plug that x back into each segment

[thick flame]

I need to confirm that I'm not crazy, is sec^2(x) equal to tan^2(x) + 1?

Oh wait, it's an identity XD

Nvm XD

[thorn kindle]

Take sin2 + cos2 = 1

Then divide through by either sin2 or cos2

[alpine sable]

X would be 7.14 right?

[wary stream]

How did you get that?

[wispy olive]

Is not is -
5x + 50 + 2x - 10 = 110.

Solve this equation.

7x = 70.

x = 10.

Now at least solve for each of the equations as per given, the length equations.

[wary stream]

Why did you give the full work to them?

[wispy olive]

They were not replying, I was bored and wanted to see them solving it but since they did not reply my boredom solved it.

And this is arithmetic come on man.

[wary stream]

Well, don't solve it for them

[wispy olive]

I can not even study Math now since I have to listen to the online classes.

[wispy olive]

Oh okay.

[wary stream]

This was sufficient info

[wispy olive]

I think I can do HS Geometry.
But I want to do Algebra 1.

[wary stream]

That doesn't mean doing people's work for them

[wispy olive]

Yes.

Sorry.

And thank you.

[alpine sable]

is chess and math related? like will chess help me with math

[thin osprey]

<@&286206848099549185>

[quartz osprey]

how do i tackle this problem im ont eh first derivitive

and i cant factor it

12x^3-54x^2+1

i cant really do much :/

[wary stream]

Isn't concavity the second derivative?

[quartz osprey]

yea but i think it wants an like exact point

and by getting that you get the zeros of the first derivitive or osmething

or am i tripping

i am tripping my god

the way i just said was to find the minimum and maxima

i set the second derivitive to 0 and got like x=0 and x=3

then i did my sin chart i got + 0 - 3 -

concave down is -infinity to 0

[undone dock]

i believe the 0's of the second derivitve give inflection points and you can then find out intervals where it is concave upwards and downwards

[quartz osprey]

im kinda wrong tho so idk how to go about this problem

[quartz osprey]

ok thanks

[undone dock]

the coefficient for x^4 is positive which means it is overall going to be concave up on the far left and right

[quartz osprey]

dude i dont even know anymore i did teh chart and uhh i duno

i did the approximations and idk how to go about it tnow

[undone dock]

finding the 0's of the second derivitive will only give you where the graph changes concavity, but you can use the fact that it is upwards on (-inf,a) which means it will be down on (a,b) and up on (b,inf) where a and b are the 0's of f''(x)

[quartz osprey]

to find inflection do i plug back into the original ?

where it changes gotcha but like i then do the chart where i approximate like how it would act

by pluggin in numbers

and that tells me + or - where its concabe up and down

[undone dock]

no, what did you get for the 0's?

[quartz osprey]

0 and 3

so i would plug -1 1 and 4 into like

the main equation?

[rigid wind]

zero out the second derivative ?

[quartz osprey]

or like the first or second derivitive

[rigid wind]

what ..

[quartz osprey]

yea

[undone dock]

that doesnt seem to line up with the graph i made on desmos, let me try to work it out

[quartz osprey]

wait no here let me give the derivitive

so i got

36x^2-108x

as second derivitive

36x(x-3)

oh

x=0 x=3

[rigid wind]

equate first derivative to 0 to find all extrema, at each local minimum or maximum, plug that input into second derivative to test whether it’s a minimum (concave down) or maximum (concave up)

[quartz osprey]

bruhhhhhh

alright

how do i solve the 0s for the first derivitive lol

its 12x^3-54x^2+1

i thought i could just approximate it

by making a chart

• infinity to 0 0 to 3 and 3 to infinty

and i plug in the numbers

and plug those nubmers into the first or second or original equation

idk which one to choose between the 3

[alpine sable]

Is there any site for download college/University mathematics books for algebra?

[quartz osprey]

nvm solved it

[quartz osprey]

google

[alpine sable]

Fuck off

[quartz osprey]

havent tried?

what makes you think you would get an answer here without you helping yourself first

people here dont just give answers

they help you to the answer

fucking dumbass

[alpine sable]

Get lost dickhead

You have been roasted already

[wary stream]

Using Google to look up sites to download books

[digital zephyr]

Is there some rule with r^2 for part d?

[alpine sable]

I'm asking for suggestions here

Not for fucking kid type answer

[wary stream]

You wanted an answer to your question, that's your answer, Google

[digital zephyr]

is this it?

[thick shard]

how is this wrong?

is there a further way to simplify this?

[lilac nest]

25x²+10x+5x+2 --> (5x+1)(5x+2)?

[flat vale]

i mean it's clearly wrong

[lilac nest]

Idk how (fg)(X) works though

[flat vale]

that's a product function

the result must be a cubic

[thick shard]

is it not f(g(x))

how would you write that

[flat vale]

that's composite

this is product function

[thick shard]

ah alright

thanks man 😁

[flat vale]

composite fn can be written as f∘g(x) so ye i get where you are coming from

f*g(x) this is product

[tame sorrel]

so you multiply (5x+2)(5x^2+3x)

?

[flat vale]

just multiply two fn together

yes

[tame sorrel]

can you help with this btw?

f(x)=x+5/2x-1 show that ff(x)=x, x is not equal to 1/2

[flat vale]

also remember that deg(f*g) = deg(f) + deg(g)

[flat vale]

what's ff(x)

[elfin fiber]

Can someone help with question 10 pls

[flat vale]

i'm not familiar with that notation

[flat vale]

what's "two and a half" * 3?

[tame sorrel]

it's supposed to be composite

[flat vale]

ah okay

[tame sorrel]

that's how it's written in my book anyway

[flat vale]

ur textbook should be f∘f(x)

[tame sorrel]

7.5 laps

[tame sorrel]

should but it's not

[flat vale]

then the textbook should be wrong

or i'm just not aware of the alternate notation

anyway what's f(f(x))

don't simplify

[tame sorrel]

maybe, it's a levels

[elfin fiber]

How do I show the work

[tame sorrel]

let me get my phone and send a pic

[flat vale]

👍

[tame sorrel]

2.5 laps = 1 km therefore, 3km = 3*2.5 laps i.e 7.5 laps?

[flat vale]

well anyway

if u solve for f(f(x))

u will find that the denominator is 2x-1

but denominator can't equal to 0

hence x can't be 1/2

[tame sorrel]

well no we're supposed to show f(f(x))=x

the x is not equal to 1/2 is just a parameter

[flat vale]

ah

than just do f(f(x))

[flat vale]

it's really straight forward

is there a higher quality pic

i can't see ur writing

[devout sigil]

the denominator will be 0 if x=1/2 right?

[elfin fiber]

It’s like multiplying fraction?

[flat vale]

What happened here

you can’t just work from f(f(x))=x

with show that q, you can’t use the answer

you are trying to derive the answer

[tame sorrel]

right right

hold on

[flat vale]

Also this is where u made ur mistake

should be
f(f(x)) = (11x/2x-1)*(2x-1)/11)

instead

[devout sigil]

oh ye ur denominator is simplified incorrectly

[tame sorrel]

?

[flat vale]

looks good to me 👍

maybe just add "as shown" or "as required" at the end

[tame sorrel]

thanks man this is what saved the answer

[flat vale]

or QED

[tame sorrel]

what's that mean

[flat vale]

it's a latin word for hence demonstrated iirc

just remember as quite easily done :)

[flat vale]

abbreviation*

[keen elm]

what level of math is this

[flat vale]

any

[keen elm]

i understand the function part cause we studied that two classes ago

[flat vale]

ah like the previous q?

[keen elm]

modulus, inverse and composite functions

[flat vale]

hmm maybe yr9?

that's when i learnt composite func

you need to ask him tho

[keen elm]

yeah but whenever i look at the type of questions people post here for help on discord, they seem extremely hard

[tame sorrel]

a level maths

[keen elm]

even though i'm in year 12 lol

[keen elm]

ahh

[tame sorrel]

like junior year equivalent? in the US?

[keen elm]

maybe i'm just a dumb student

nope i think this is like final year hs

[flat vale]

depends on where you live

[tame sorrel]

the question i posted?

[keen elm]

yes

[tame sorrel]

year 12 is junior year or senior year?

[keen elm]

the uae

[tame sorrel]

like final year of highschool or second last?

[keen elm]

for us year 12 is the senior year and then we move on the university

[tame sorrel]

yeah the question i posted is from year 11 then

second last

[keen elm]

oh nice

what subjects do you guys couple with math

[tame sorrel]

Is this justification right?

[tame sorrel]

Business, accounting and economics

[quartz osprey]

🤣 @silent marten google is a great resource just to let you know

oh hes gone

😭

[keen elm]

nice

[tame sorrel]

it says find the least value of k for which the function is one-one

and it's clearly -1 but how to justify/show the work?

[keen elm]

graphing inverse functions was a bit confusing

[flat vale]

👍

[tame sorrel]

what'd he do

[quartz osprey]

be a dumbass

reee

im actually sutkc on finding the zeros of the second derivitive

😭

oh wait i dont need it do i

[elfin fiber]

Helppp

[tame sorrel]

what?

[raw shard]

@elfin fiber you didn’t specify what you need help with

[quartz osprey]

bruh dont you just multiply left to right

[raw shard]

for multiplication it doesn’t matter @quartz osprey

[quartz osprey]

well yea but like you know what i mean

[raw shard]

yeah

[quartz osprey]

☠️

im so smart

[raw shard]

big brain stuff

[quartz osprey]

thats what im saying

ayo save me on my problem 😭

do i plug the second drivitive to 0

well yea thats waht i do but how do i do that lmao

wait was it undefined or 0

i cant rememeber anymore 😭

[raw shard]

oof i don’t know if i’ve learned that just yet

[crisp grove]

@quartz osprey what does y''> 0 tells you?

[quartz osprey]

if its bigger than 0 then it is concave up U shape

so a min,

and the oother is n shaped with a max

[torn heart]

Help plz

I got most wrong

[crisp grove]

@quartz osprey check the question and see they have asked you to find

remember y''>0 means concave up and <0 means down

@torn heart share SS, also channel is busy

[torn heart]

Ok

[limpid flicker]

I need help for 11b

[quartz osprey]

alrght

[limpid flicker]

I know the answer but i don't know how to get it

if that makes sense

[quartz osprey]

determine where so it wants an exact location right ?

[crisp grove]

no exact location, in interval to be specific

also remember that x^2 is always non-negative

[surreal radish]

what would the complement of A be

confused with this

can anyone pls help me

[limpid flicker]

sorry for poor shading but it's that

explaination: since a is this

the compliment of a is everything that is not a

so it would be this

[kindred nymph]

can someone please help me with my homework ive been struggling for a while

variations

[undone agate]

I know I can solve this using the other defintion of derivative

But why does this not work?

According to this form, the limit diverges but clearly it should not...

I cant solve it using the other definition either

[gray isle]

try factorising the numerator as a difference of two squares,
and factorising the denominator as a sum of two cubes

[alpine sable]

The area of the rectangle is (16m2+4m) square feet,If the width is 4m feet,find the length

Can anyone help me with this?

[undone agate]

Is this it? Then take lim from right and left?

Can we just plug in -8 since it is continuous there. The top and bottom are both continuous functions on R

[still ocean]

I'll give a try but is it 16 m² + 4m?

@alpine sable

[alpine sable]

Yeah

Idk how do i type an exponent so i just placed 2

[still ocean]

Ok

m is a var right?

[raw shard]

probably not

[still ocean]

Then?

[raw shard]

wait idk actually because if it’s meters why is it only squared once

[still ocean]

There is feet too

@alpine sable is m a var?

[alpine sable]

Yeah

[still ocean]

If so 16m² + 4m is the area

[alpine sable]

Ft is the measurement

[still ocean]

Now divide( 16m²+4m)/4m?

[raw shard]

odd for m to be a variable when the measurement is feet lol

[alpine sable]

Idk

They didnt really give examples

[still ocean]

Can u take 4 out of (16m²+4m)?

Like writing (8x+12x) as 4(2x+3x)?

@alpine sable

[alpine sable]

Yes

[raw shard]

you can take 4m out if you need

4m(4m+1)

actually that’s the answer isn’t it

[still ocean]

Now there is 4m in the denominator?

[raw shard]

should be lol

@alpine sable i got the answer, it’s 4m+1

[still ocean]

(16m²+4m)/4m =4(4m²+m)/4m
4m²+m/m =4m²/m + m/m =4m+1

Ok

[raw shard]

that was a lot of unnecessary work just so you know

you could have just went and factored out a 4m and been done

[alpine sable]

Thanks

[still ocean]

Yeh ok

[raw shard]

although that’s what you did anyways so i guess it doesn’t matter

[marble sparrow]

is this channel free?

[raw shard]

yes

[marble sparrow]

I'm a little confused about the combinatorial proof here

[still ocean]

It's the same I did right

[raw shard]

yes

[hexed yoke]

@quaint narwhal

[raw shard]

same answer at least

[still ocean]

Ok

[marble sparrow]

why do we have (n-1 k-1) in the first bullet point?

[quaint narwhal]

@hexed yoke

[alpine sable]

I have one question

In my diff. calc in one variable notes there's something called the "density property" that states the following:

For any interval $I$ in $\mathbb{R}$, we have that:

$I\cap\mathbb{Q} = \varnothing$ and $I\cap(\mathbb{R}\setminus\mathbb{Q})$

I don't understand why this shows that in several variables we have that $([0,1]\times[0,1]) \cap\mathbb{Q}^2 = \varnothing$

[ocean seal]

xd nope

[stray estuary]

was there anything else you had written about it?

[alpine sable]

The following: "This shows that we can approximate any real number by a rational or by a irrational"

[stray estuary]

first of all do you understand what they mean by the density property and the “denseness” of the rationals?

[alpine sable]

Not much

[stray estuary]

okay then did you write anything else when you wrote the intersection between I and (R\Q)?

[alpine sable]

No

[stray estuary]

ok well the denseness of the rationals is interpreted by the fact that we can always have a rational in between two rational numbers

[alpine sable]

I just have that $\mathbb{Q}$ is numerable and $\mathbb{R}\setminus\mathbb{Q})$ isn't numerable

[ocean seal]

xd nope

[alpine sable]

Oh, okay

[stray estuary]

alright cool

numerability refers to its “countability”

so you can agree with me that we can count the number of whole numbers right?

its infinite in size but its countable

Q is still a countable set as well

but R is uncountable

too many numbers compared to N and Q

[alpine sable]

yes

[alpine sable]

Okay

[stray estuary]

okay so

if we have a set in R

which is our interval I

so I is a subset of R

I would also be uncountably infinite right?

if we take the intersection of I with the set rational numbers where I contains no rational numbers

then it would be empty right?

[alpine sable]

Yes

[alpine sable]

yeah

[stray estuary]

if we have two intervals (simulating two variable functions) then their intersections with the set of rationals would be 0 given that there are no rationals in the interval

[alpine sable]

Oooooooh, I see

[latent dawn]

Hey guys, can u help me with (b)?

[formal solar]

<@&286206848099549185>

:(

[rough python]

I need help with the underlined part of the question.

[placid zinc]

Well, expand the left. You'll need binomial theorem

[rough python]

I did that but I get this result not the one asking in the question to prove.

[vale wigeon]

are we to assume p is prime

@rough python

i.e. not zero

if p=2 then -b = b, if p>2 then p is odd and (-b)^p = -(b^p)

[rough python]

Got it now, so the equation can only be proved if p>2?

[vale wigeon]

no

it holds for p=2 too

[alpine sable]

how do i do this ?

[vale wigeon]

@alpine sable channel busy please move

@rough python in characteristic two there is no such thing as negatives

every element is its own additive inverse

[rough python]

Oh, got it now, thanks.

[winged walrus]

Please give me a real life application for rational function

[vale wigeon]

is this for your own curiosity or did you get assigned a problem that asks you for it

[winged walrus]

im just curious because i only know real life examples of piecewise function

i just want to know the difference

[wispy olive]

Find all x such that x^5 = -x^3.

This is the given solution. Why is 0 an answer? Should not is just be i and -i?

Question 12.22.

[wispy olive]

Hello Ann.

[winged walrus]

[wispy olive]

<@&286206848099549185> .

[simple wraith]

is it appropriate to ask a question about machine learning here?, there's a problem i've been stuck on

[wispy olive]

#computing-software .

[simple wraith]

ok thanks

[crude hamlet]

Can someone explain how to find the C in a quadratic function? There's no specific problem that I need help on. My teacher explained how to find the C today in class but I don't understand

[wispy olive]

$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

[ocean seal]

Senku Ishigami

[wispy olive]

The form of the equation -

ax^2 + bx + c = 0.

$ax^2 + bx + c = 0$

[ocean seal]

Senku Ishigami

[wispy olive]

You have the a,b and x?

[crude hamlet]

Yes

Ohhh sorry I thought you were asking a question 😭

So u just substitute x into the formula and solve then?

[vernal dragon]

what is this?

it it diff equations

can sonemone send me link to this kinds of math? want to get a better understanding

[wispy olive]

Yeah.

We just play with the equations.

Following the laws.

[crude hamlet]

Oh okay thanks!!

[slender root]

Hi

[wispy olive]

Yo.

[slender root]

Ya

Im me

[buoyant stream]

Hi! can someone help me please, it's trigonometry the question is
Looking at the triangle, what are the sine, cosine, and tangent values ​​of the alpha angle?

please

[vague coral]

do you know the formula of sin, cos and tan ?

[buoyant stream]

I don't know anything, I don't know how to do this exercise, and I need the result,
I can't do it please help me

[vague coral]

I wont do it for you

lets that be clear

[buoyant stream]

hm

[vague coral]

try it yourself, im telling you to use sin, cos and tan formula

[alpine sable]

yo

can anyone help me with Direct and inverse Proportion

[buoyant stream]

I don't have much time, please I need the result of this

[alpine sable]

A and B can do a piece of work in 12 days, B and C in 15 days and C and A in 20
days. How much time will A alone take to finish the job

this is my second sum

[vague coral]

I dont care for real.

[alpine sable]

how do it solve it

i dont understand

[buoyant stream]

😖

[vague coral]

All I tell you, is to use the formula, that you can find on google

[buoyant stream]

but I don't understand how to do it, and as I said, I don't have much time, please

[vague coral]

how dont you know how to apply a formula ?

[buoyant stream]

because I don't know anything about trigonometry

[vague coral]

have fun

[buoyant stream]

please, I don't understand

[vague coral]

I don't know how to be more clear than that

[buoyant stream]

ok

is that I'm really stressed and I'm not able to think straight,
because of the time, and I don't have much

let me calm down

[vague coral]

is it a test or something

[buoyant stream]

ok

[buoyant stream]

yes

[alpine sable]

if you are done can yo help me pls

[vague coral]

the exercise you sent is a test ?

[buoyant stream]

yes is a test for me

[vague coral]

????

[alpine sable]

he means he is testing himself

[buoyant stream]

ok, for me to find the sine

[vague coral]

then why are you stressing

[buoyant stream]

because I have time to do it

[alpine sable]

try having a cold shower

[buoyant stream]

I dont have tive

[alpine sable]

oo

[vague coral]

then its a real test, or a homework

[buoyant stream]

I do 13 x 5?

[buoyant stream]

real test

[alpine sable]

given from school?

[vague coral]

your teacher gave you this test to do in class ?

if so, you are cheating and i wont help you

[buoyant stream]

no i'm at home

[vague coral]

no cap ?

[buoyant stream]

I arrived at a new school, and very close to the exams, and I don't understand much

[alpine sable]

ah i understand that thing

[vague coral]

You have a test in one hour or what ?

[alpine sable]

my exams coming soon too

[buoyant stream]

I have to deliver in 50 minutes

[vague coral]

._.

just apply the formula I sent you

[alpine sable]

[buoyant stream]

srry my poor english, i still learning

[vague coral]

i wont do your homework, i'll just say what you have to do

find it yourself, its not even that complicated

[buoyant stream]

my time is running out, i have 15 minutes, and I don't know how to do it, please help me

[vague coral]

You are not even listening to me, you just want the result

good luck bro, I tried all I can to help you

[alpine sable]

if ya done can you help me ;-;

#help-1

[buoyant stream]

I calmed down and tried to understand what you were talking about, thanks for trying to help me, I've already taken my test, I don't know if I did well, but thanks anyway

[ruby sluice]

i'm so confused

[alpine sable]

Hello guys, I really need someones help
Actually there is key answer but I still confused especially number 2. I answered 1/27 but the key answer is 7/24.
can someone give me explanation?

[ruby sluice]

how do i do this algebritaclly

[waxen schooner]

1=c(x+2)+d(x-3), how can I get c and d?

[alpine sable]

someone help

is there any good programs for shaping your own graph? i need a formula to make something like this green line instead of plane linear line.

[verbal ermine]

desmos.com

[alpine sable]

Thanks, but don't find it super intuitive actually. - Now i decided to just draw the points and then make a regression model for it, that works. But preferable i would like to easily drag the points etc. - actually it's pretty ok, maybe im just bad

[amber tartan]

Can someone help me with this questuon?

Thanks!

[alpine sable]

can some one help me wit hthis

[amber tartan]

Is that a simultaneous equation to solve?

[alpine sable]

wdym

[amber tartan]

Are those two equations were you have to fibd x and y

Find*

[alpine sable]

yes

when i try do get the same x i get the same y at the same time

[amber tartan]

So basically fr this q u can make x the subject by rearranging the equation

Then substitute that equation that is equal to x into teh second equation

So you only have one variable - y

[alpine sable]

i did that but the i get the same y

[amber tartan]

Wdym you get the same y

Ohhhh

[alpine sable]

like i multiplay the first by the number of x in the second and the same for the second if you get it

[amber tartan]

I get it

Wait

Have u tried graphingg it

And find point of intersect

[alpine sable]

wdym

[amber tartan]

Wait nvm

I got it

Minus the bottom equation from the top

Den make x the subject

Den sub in

[alpine sable]

can you help me in a vc its gona be more helpfole for me

[abstract fractal]

Not all lines intersect

[alpine sable]

?

ohh true

[amber tartan]

Wait

This q

Is impossible

[abstract fractal]

Multiply the top by 3, you get 3x + 6y = 15 and 3x + 6y = 10

[alpine sable]

realy

[abstract fractal]

The lines are parallel

[alpine sable]

ohh then what do i type

[amber tartan]

This q is impossible

Ahhahaua

Idk

[abstract fractal]

"No solution" is a good answer

[alpine sable]

my techaer gave it to me

k

[abstract fractal]

It's not impossible, it just has no solutions

[alpine sable]

k

ty

[lapis stream]

I guess this is done

[alpine sable]

ya

[amber tartan]

Wair

Can someone help with my prev w

Q

Thanks

[gleaming tree]

hi how do i check the answer as proof that the answer provided was correct? thanks in advance

[elder glacier]

you can just check boundaries of the interval [3,infinity)

[lapis stream]

Three people in a row wow

[elder glacier]

@gleaming tree or you can do mathematical induction where you test for x=3, then sub x=n, then prove true for x=n+1

[gleaming tree]

ohhokk thanks

[elder glacier]

@lapis stream just write 59-68/38-32 as a decimal aswell as 48-32/59-68

and have (59-68/38-32)*x=48-32/59-68

and solve for x

[lapis stream]

I just want a quick way to flip the fraction

What was the magical number dammit

That’s a middle school thing probably

[elder glacier]

@lapis stream hit answer

press enter sorry

then do 1/ans

[lapis stream]

Yeah that worked

Thanks wonderful human

[elder glacier]

@lapis stream x is a variable in this case, not multiplication

[alpine sable]

If the length of diagonals of a quadrilateral is 16 cm and 22 cm, then the number of possible integral values of perimeter of the quadrilateral is . please help me with ths

[vagrant rover]

I don't get it, what am I doing wrong here???

I know it's 9

But I just don't understand where I'm messing up

[elder glacier]

@vagrant rover its your fourth line.

can you see what you did wrong

[vagrant rover]

@elder glacier This fourth line?

[elder glacier]

yes

you cannot times a fractions by both sides

[vagrant rover]

You can't?

Really?

[elder glacier]

times the dominator on both sides

then divide both sides by the numerator

[vagrant rover]

Hm, sec lkemme try

[elder glacier]

aka you should times ur rhs by the reciprocal of the fraction

[vagrant rover]

OHHHHHHH

Ohhhhhh

[tame sorrel]

@vagrant rover

[vagrant rover]

Okayyyyy, now I see it

[vagrant rover]

Oh thank you!

[elder glacier]

@vagrant rover you assyrian by any chance

[tame sorrel]

Ohy god bad quality

[vagrant rover]

I'm arab

I'm from Baghdad

So technically that would make me a descendent of the assyrians, right?

[vagrant rover]

I think that's how it works lol

[tame sorrel]

Help me understand how we get the value of k please

[tame sorrel]

.

@elder glacier can you help?

[golden nymph]

I know this font from miles

[golden nymph]

CAIE A level Mathematics paper 1 oxford university press book

[golden nymph]

Gottem

[elder glacier]

do u guys have terry lee textbooks over there

[tame sorrel]

Haha

[golden nymph]

Or is that the cambridge university book

Yeah not the oxford

[elder glacier]

hardest textbooks where im from.

[golden nymph]

#book-recommendations

So what’s bothering you

[tame sorrel]

@golden nymph tired of smashing my head against a brick wall I don't understand how we find the value of k

[golden nymph]

You know the horizontal line test?

[tame sorrel]

To see if it's one one or many one?

[vagrant rover]

@elder glacier\

[golden nymph]

Yes

Do you know when’s a function is one to one?

[vagrant rover]

How come I can't multiply both sides by the reciprocal at the very beginning?

[tame sorrel]

See how many times it intercepts y axis iirc?

[tame sorrel]

When one input leads to only one output

[golden nymph]

And this is satisfied when it is monotonously increasing or monotonously decreasing

[crisp grove]

No

[elder glacier]

@vagrant rover you can, and it just cancels ur coeficent of b on ur lhs

[tame sorrel]

Right?

[golden nymph]

(Accroding to the syllabus that’s correct)

This channel is very distracting

Can you send your question somewhere peaceful?

And ping me

[crisp grove]

one value always gives one output, take x²

[tame sorrel]

Questions-3

[vagrant rover]

b=15-b(3/2) @elder glacier Can I add b to both sides here?

[crisp grove]

that's well definedness not one-one

[vagrant rover]

So I would get 2b=15(3/2)

I feel like this is wrong

[elder glacier]

no if u times by reprical from line 1 you get -b+(3/2)(5)=(3/2)(20)-b(3/2)

so theres no point

just always collect like terms

[vagrant rover]

Like this? @elder glacier

[elder glacier]

no

you have to times every product

[vagrant rover]

OHHHHHHH

I see it

I see it now

[elder glacier]

here, -2/3b+5=20-b

[vagrant rover]

Alrighjt alright

[elder glacier]

u got it?

[vagrant rover]

Yeah yeah, I'm only multiplying by the fraction on the left side and not everything else on bopth sides

Yeah

I got it

ALriught tysm

❤️

[stable plume]

hello

[severe beacon]

1+1

Pls help

[stable plume]

How I can calculate this using center method?

[tame sorrel]

11

[severe beacon]

YAY I GOT IT CORRRECT

[severe beacon]

89 Is the answer

[brave garnet]

I have to prove that the two things I drew rectangles around are equal

[stable plume]

can you please delete yourself

[severe beacon]

No?

[jaunty root]

Is transitivity property same as substituting?
let's say a=b, b>c, then a>c?

[brave garnet]

That's really funny m8, excellent joke

[fast mantle]

Given that the positive integers x and y satisfy the equation 2547x + 69y = 2823. The value of (3x + 4y) is

how do i get started on this?

[brave garnet]

I dont think you should compare those two things

I think substitution helps you show transitivity

but really when thinking of it, just keep the definition in mind

[severe beacon]

Thanks

[glass lichen]

transitivity is that if $aRb$ and $bRc$, then $aRc$

[ocean seal]

Mosh

[brave garnet]

that

[brave garnet]

isolate x, isolate y, then develop (3x + 4y), see where it leads you I suppose

because you cant really factor them

[jaunty root]

Well how can find contradiction on a>b, b=c, a<c?

[glass lichen]

cause $a>b =c\implies a>c$ which contradicts by order of $\mathbb{R}$

[ocean seal]

Mosh

[fast mantle]

didn't lead me anywhere :/

[jaunty root]

Yes i am thinking of that but what axiom of real number is that?

[glass lichen]

Order

or just how inequality works

[brave garnet]

well you can factor both sides by 3

but that wont help you much either

[fast mantle]

mhm

didnt

i took lcm and tried to eliminate one variable but that just ended up as a mess

[brave garnet]

well as far as I know, you have two variables and one equation, so all youll be able to find is a literal expression

do you really think they expect a specific value for (3x+4y)

[fast mantle]

yup

i ended up with 19 once but i dont think it's correct-

[brave garnet]

did you just plug it in

oh wait

theyre integers

[fast mantle]

yeah they are 👀

[cerulean wolf]

why is the answer C

[gray isle]

19 looks fine

[fast mantle]

hmm

[gray isle]

did you remember what you did when you got 19

[fast mantle]

i was just eliminating

[gray isle]

be more specific

[fast mantle]

i dont really know tbh

was just manipulating the equations so that i'd end up with something

[gray isle]

positive integers x and y satisfy the equation 2547x + 69y = 2823.
note that under that condition neither 2547x nor 69y can exceed 2823

consider that to deduce the value of x

[plain canopy]

yo my homework is due in 20 minutes can someone help me with some kinematics

[gray isle]

and subsequently determine y based on that

[plain canopy]

wait ill go to another one

[fast mantle]

oh okay got it

x=1
y=4

plugging them in 3x+4y gives 19

thank youu

[severe beacon]

Help

[alpine sable]

<@&286206848099549185>

Can someone help me with my home work it’s due in like 30min I only have 12 left that I don’t know

[boreal isle]

do you know what parellel means?

[alpine sable]

Like the same

[boreal isle]

no

it means they'll never intersect if they go on to infinity

and they'll stay the same distance apart

so if you draw a vertical line on a piece of paper, then you draw another vertical line next to it, no matter how far those lines go on for, they'll always be the same distance apart

[alpine sable]

Ooh is it c

[boreal isle]

yes

[alpine sable]

Is this d

[boreal isle]

yup

[alpine sable]

👍

B

Is it b

[boreal isle]

is this for homework? Is it graded for accuracy?

[alpine sable]

Both

[boreal isle]

ugh i hate when teachers grade homework for accuracy

[alpine sable]

Because homework is like 30% of my grade

[boreal isle]

DAMN that's rough

idk why teachers even do that, it's just a take home quiz at that point

[boreal isle]

yup B

tho i dont think we're supposed to just endlessly check work for accuracy in this server

[alpine sable]

Idk this

I forgot

[alpine sable]

Really

[fast mantle]

option 1

[alpine sable]

How did u get that

[fast mantle]

wdym?

it's just a thing

what grade are you in? 👀

not to be rude-

[alpine sable]

11

[fast mantle]

how do you not know alt interior angles then

[alpine sable]

I never took geometry

[fast mantle]

oh-