help-23

[lean otter]

ok so in here, 32 students represents the elements of the universal set right?

😰

abhe yaar

calm down

araaaaam se

[lean otter]

yar do they represent or not

[lean otter]

ok yar

[tight void]

tell me why you think 32 students represents the elements of the universal set

[lean otter]

hanji

[lean otter]

cause 32 represents the total elements of the sets and all of the sets are subsets of that big set , representing everything here

[tight void]

why 32 tho?

[lean otter]

cause the question said 32 students in class

😭 ?

[lean otter]

does it represent it or not

[lean otter]

pura question kidr he

[lean otter]

pic

@lean otter

pic pe 32 nehi likha hua

pic pe aur koi information nehi he?

OMG WRONG PIC

OMGOGMOGM

BRIB

lmaooo

[lean otter]

@tight void

now answer

[tight void]

yes 💀

lmao

[lean otter]

is 32 the unversal set

ty

[tight void]

the universal set is the 32 students

[lean otter]

ily bro

[lean otter]

tumhe samaj agyei he?

universal sets ke bare me

ok so, from this we can conclude that, universal set is always the biggest set and all sets are subsets of the U set and it can have finite or infinite elements and so, here, its finite and G and S are its subsets and so now.. IMAGINE.. imagine there was this same but empty ven diagram, the S/U set was = {1,2,3,4,5,6,7,8,9,10} , A set was {1,2,4,5} NOW, NOSQLDB, you said B could be anything right? like, B={} or {1,2,4,5} or {1,5} etc... so if B was{3}, this element could be in the B set and SINCE THERE ARE 6,7,8,9,10 AS LEFT OVER, WE would then put them in the ``dont belong to either sets` part aka the area outside the circles in the rectangle right?*** cause those left over elements *must *be represented right?***like, if this wasnt a ven diagram, those left over elements could be ignored but not in a ven diagram right? (THIS WAS MY QUESTION SO YEA 😄 D; ) @tight void

[tight void]

Sounds about right

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

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[whole gale]

Is the answer all 3 of them?

can someone check my answer

<@&286206848099549185>

????

<@&286206848099549185>

why

@lean otter

ok

.close

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[whole gale]

.reopen

[safe radish]

✅

[whole gale]

Can someone help me

[past hare]

the 2nd one

[whole gale]

you sure I can choose multiple answers

it can be all of them or two of them

I personally think its all

[past hare]

why do you think its all?

[whole gale]

because since its straight it will have a upward facing parabola on the left and a straight line on the right and all of them have that

[past hare]

Yes but the first one doesn't have a hole at x=0 right?

The third one could work though because the derivative of 0 is just 0

So probably 2 and 3 then

[whole gale]

idk what to put 2 people told me all of them now you say this

these are my choices

[past hare]

Yeah nevermind go with all 3 cuz the derivative fails to exist at x=0 but not because of a hole but rather because of a corner

So it could be 1 as well

So all 3

[lean otter]

@whole gale

[safe radish]

@whole gale Has your question been resolved?

[safe radish]

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[modest jasper]

Can someone help me solving this?

[safe radish]

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[icy lance]

assume two inputs give the same output, then prove said inputs must be equal

[violet mango]

x = x_1

so i+j = i_1 + j_1

idk how to solve

[icy lance]

assume f(a,b)=c and f(x,y)=c
(a+b, a-b)=c=(x+y,x-y)
(a+b,a-b)=(x+y,x-y)

show a=x, b=y

then youve proven one-to-one

[violet mango]

so first im trying to prove i = i_1 which is that equation ^

idk what to do next

[icy lance]

im not sure what you mean by this and the line below

[violet mango]

in the problem i have to show, i+j = i_1 + j_1, to prove i = i_1

but how do i solve that

or in your equation its a+b = x+y

[icy lance]

oh right

well if vector a=vector b then the corresponding entries must be equal right?

[violet mango]

didnt learn vectors

function?

[icy lance]

elements of Z^2 are 2 dimensional vectors

(a,b) where a and b are integers

if (a,b)=(c,d) then a=c and b=d

[icy lance]

a+b=x+y, a-b=x-y

[violet mango]

i get this

[violet mango]

and this

[icy lance]

if you add the two equations to eachother

then 2a=2x

a=x

[violet mango]

how

[icy lance]

how what

[violet mango]

does the two equations equal 2a=2x

[icy lance]

if a=b and c=d then a-c=b-d and a+c=b+d

(a+b)+(a-b)=(x+y)+(x-y)

2a=2x

[violet mango]

how did you order the equation like that

[icy lance]

what do you mean

i just added them

[violet mango]

but can you do that with order pairs

[icy lance]

this applies to anything, it doesnt matter what you have

[violet mango]

if its like (a+b, a-b) = (x+y, x-y)

you can just add them?

[icy lance]

no because thats two elements, theres nothing to add

however

you could subtract one from each side

(a+b,a-b)-(x+y,x-y)=0

(a+b-x-y, a-b -x+y)=0

0 is the 0 vector (0,0) btw

then a+b-x-y=0

and a-b-x+y=0

a+b=x+y, a-b=x-y

doesnt really get you anywhere, just to where i started

[icy lance]

its just this

[violet mango]

i get that but the function arent equal to each other

and how do i show a = c

[icy lance]

who said a=c

i just said if you put the pairs into f you get the same thing, c

[violet mango]

thats what we are supposed to prove

in the problem i+j = i' +j'

[icy lance]

im showing a=x

not a=c

which ive already done

[icy lance]

here

you can do something similar to prove b=y

[violet mango]

i dont really get this proof

[icy lance]

f(a,b)=f(x,y)
(a+b,a-b)=(x+y,x-y)
a+b=x+y and a-b=x-y

thats literally what im doing

what do you think this is

[icy lance]

add the left and right equations
(a+b)+(a-b)=(x+y)+(x-y)
2a=2x

thats the work up to that point compressed

a=x

[violet mango]

howd you get this(a+b)+(a-b)=(x+y)+(x-y)

[icy lance]

i told you
if a=b and c=d then a+c=b+d

im just adding the same value to each side, thats not an issue

[violet mango]

this is for every one to one?

[icy lance]

no, this for anything ever

doesnt matter what thing a,b,c and d are

if a=b and c=d then a+c=b+d

[violet mango]

so how does a = b correlate here because its different operations

or is it just by definition

[icy lance]

my man

[violet mango]

im sorry bro

[icy lance]

this is just general

its like saying 2=2 and 3=3 so 2+3=2+3

[violet mango]

oh my

lmfao okay i get it

[icy lance]

phew damn

[violet mango]

soundded so overcomplicated in my head idkl

in the problem you cant add a + c @icy lance

or is it i+j + i-j

[icy lance]

oh dear

[violet mango]

i thought i got it ngl

[icy lance]

do you agree with this my man

[violet mango]

yes i get that

[icy lance]

alright, im just adding the left equation and the right equation

[icy lance]

exactly in the same way i did here

a+b=x+y and a-b=x-y
so (a+b)+(a-b)=(x+y)+(x-y)

[violet mango]

in this case if a =x, b = y

[icy lance]

thats what youre trying to prove yes

the a and b when im explaining stuff are not the same a and b im using in your problem, ik that might be confusing

[violet mango]

ok now this proves a = x

i got it

[icy lance]

it does

you can subtract them to get b=y

[violet mango]

a-b = x-y, if x = a, b = y

the variables confusing but i think i got it

[icy lance]

you cant say that no

7-2=25-20

7 isnt 25 and 2 isnt 20

i mean (a+b)-(a-b)=(x+y)-(x-y)

[icy lance]

well the way youve written it isnt wrong
but you cant say x=a and b=y because a-b=x-y

you can say a-b=x-y because x=a and b=y

but you dont know that

[safe radish]

@violet mango Has your question been resolved?

[violet mango]

other way around, ty @icy lance

.close

[safe radish]

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[unreal river]

If anyone wouldnt mind helping me with these 2 problems

That would be great

[tight void]

I’ll help you with this question

[unreal river]

Y e s

T h a n k

Im so lost

[tight void]

Draw a graph what does it look like

[unreal river]

A circle

[tight void]

To find the area let’s find the area of one half and double it?

[unreal river]

So

pi*r^2/2

[tight void]

We wanna use integration

[unreal river]

Im honestly confused

[tight void]

Draw the circle out

[unreal river]

I have

[tight void]

And solve for y in terms of x

[unreal river]

So you mean

y = sqrt(9-x^2)

[tight void]

Mhm

But this only positive part

[unreal river]

Right

[tight void]

So multiply by 2

[unreal river]

I meant its just 2sqrt(9-x^2)

[tight void]

Mhm

Now integrate that from -3 to 3

[unreal river]

How did you get the bounds

By setting sqrt(9-x^2) to -sqrt(9-x^2)?

[tight void]

The circle goes from -3 to 3 in the direction

If you drew it out

[unreal river]

What

Yeah

I was gonna say

[tight void]

Did you draw it out?

[unreal river]

Isnt it -3 to 3

Yes

[tight void]

Be honest with me

[unreal river]

?

Yes

[tight void]

Aight okay

Now integrate with trig sub

[unreal river]

Thats why I was confused when you said -1 to 1

Bc its -3 to 3

So

Cant I just do from 3 to 0

And integrate sqrt(9-x^2)

.close

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[safe radish]

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[devout shale]

I have a doubt about this substitution

should it not become sin(z+kpi)

which will be -sin(z)

is that why the absolute value goes away and it becomes just sin(z)

[left gyro]

|sin(x)| = |sin(z + kπ)| = |sin(z)| = [if 0 ≤ z ≤ π] sin(z)

[left gyro]

is it assumed that k is odd? sin(z + kπ) should be (-1)^k sin(z) for integer k

[devout shale]

it is not

[devout shale]

I see

thank you

.close

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[solar hazel]

lmfao

[safe radish]

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[dense wadi]

how do we u sub this equation

[keen sequoia]

x^3+1 = u

[dense wadi]

and then its 2x

waht do i do with the x^4 left

[keen sequoia]

it isn't 2x?

it's 3x^2

[dense wadi]

oh yes mb

glasses problems

but even if its 3x^2 what do i do with the rest of x

[keen sequoia]

just give it a try , you'll figure out

[dense wadi]

and im left with 3sqrt(u) x^3

[keen sequoia]

yes

x^3+1=u , x^3= u-1

[keen sequoia]

it isn't sqrt

its u^(1/3)

cube root

[dense wadi]

ah yes

cube root

[dense wadi]

oh

wait

ill try that

so it ends up being

3 cbrt(u)(u-1)

[keen sequoia]

yes

throw the 3 out of that integral

it's a constant

u^(1/3)(u-1) = u^(4/3) - u^(1/3)

now easy to integrate?

[dense wadi]

ahh

i never thought of that wtf

okay ty!

.close

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[hollow silo]

Please I have a simple question about how to make a perfect square with any 2 numbers example iny case 11^2 + 7^2 ?

[potent seal]

,calc 121+49

[flat frigate]

Result:

170

[hollow silo]

I mean x time x gives exactly 170

[potent seal]

x won't be an integer then

[hollow silo]

Yes o course

In this example how can I find the value of x ?

[umbral swan]

hm could you rephrase your question? don't quite get what you seek

[hollow silo]

Ok

In 11^2 + 7^2 which equal to 170

I wanna make a perfect square that x*x = 170

[umbral swan]

then your answer is x = sqrt(170)

[hollow silo]

Exactly

[umbral swan]

which you can determine via a calculator

[hollow silo]

I found a perfect square but in 13^2

But remain 1

[umbral swan]

ys, for instance take x*x = 226

[thin bridge]

still not sure what you're trying to do

[umbral swan]

you can also have 25*25 = 225 + 1

but you can't find an integer with x*x = 226

only for certain values there is an integer solution

[umbral swan]

you can't get "closer" to 170 than 13² with remainder 1 with an integer value for x

[thin bridge]

the positive solution to x^2 = k
is sqrt(k)
whether that can be simplified further, whether sqrt(k) is an integer is a different issue

[hollow silo]

Alright this is my question, make a perfect square with any 2 numbers and then find out the one side Wich multipled by himself gives back total of a^2+ b2

Without calculator

[thin bridge]

the value for the above example is just sqrt(170)

and the value can be left as that

certain square roots can be simplified if they have perfect square factors
if you're trying to get decimal approximations of square roots, there are tedious algorithms for that

[hollow silo]

Exactly you understand me now

[thin bridge]

that's what we inferred before

[hollow silo]

Trying to get decimal

[thin bridge]

ok

that's a different issue from what you were trying to present

[hollow silo]

Oh yes sorry

Anyway you got it

[thin bridge]

https://brilliant.org/wiki/approximation-of-square-roots/

[hollow silo]

Oh yes that's awesome

I was frustrating to don't be able to find it

Thank you so much for your help appreciate it

Now I'm going to check that

Have a great day

Almost found it 🤩

[safe radish]

@hollow silo Has your question been resolved?

[safe radish]

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[lean otter]

I want to convert this to degrees

It was measured in radians

So

LHS x 180 = degree

RHS, (4Pi - 0.643 ) x180?

[versed wave]

multiply each side by 180/pi

[lean otter]

Or 4Pi = 720 - (0.643 x 180)

How do u convert 4pi to raidans

[versed wave]

multiply by pi/180

[lean otter]

ah ok

isee

ty

@versed wave im confused

is RHS

683

Or 604

Does the stuff prior effect the answer?

Im still confused what 4Pi - 0.643 is in degrees lol

[safe radish]

@lean otter Has your question been resolved?

[still raven]

why don't you use a calculator

A level Edexcel allows you to have a calculator

[timid scroll]

I am

But I don’t know what it is

[still raven]

why do you want to use degrees

[timid scroll]

Cause I always convert to degrees

And then draw it

[still raven]

oh

chapter 3 should tell you how radian and degrees relate

you should know the formulas by heart

have a look

[timid scroll]

Ik them

Pi/180

180/Pi

But I’m confused with the 4Pi

[still raven]

what's the problem then xd

pi is equal to 180 degrees, 4pi is just 180*4

[timid scroll]

Ok

[still raven]

is that all?

[timid scroll]

No

Why is it that you do not convert 1/2 Pi, 5/2 Pi

Into radiants

Before adding +0.6435

[still raven]

they are in radians already tho

this is the radians form

[timid scroll]

Ok then according to that logic

4Pi -0.6435

Converted to degrees

Is just x 180

No?

Which gives you 2146 degrees

See what I mean

What the flip

[still raven]

mmh

does that not sound right

I mean effectively we're solving for a value of x

[timid scroll]

Yeah ok

That could make sense

[still raven]

I'm not too sure to how you would want to sketch that 4pi anyway ngl

[timid scroll]

It’s just the range

[still raven]

but why would you want to sketch that

as in

[timid scroll]

So I can see what angles lie inside the range

[still raven]

oh

[timid scroll]

[still raven]

[timid scroll]

I don’t know I think I’m going to redo all the questions I did the last 4hrs

[still raven]

that chapter

[timid scroll]

Because I’ve somehow never got anything wrong

[still raven]

is quite funny at first

[timid scroll]

To why am I getting everything wrong

[still raven]

I remember learning it

exactly a year ago

lol

[timid scroll]

Haha 😂

Congrats for graduating

[still raven]

thanks, get those A*s 👀

[timid scroll]

Oh wow

How do the math exams look like

For pure

Is it all just trig

And circles

[still raven]

personally

[still raven]

lol no

[timid scroll]

Or how did you revise

[still raven]

I think the most difficult topic for most people is differential equations but it's the very last chapter so you probably haven't covered it yet

[timid scroll]

Yea im far behind

I haven’t done any statistics

[still raven]

oh shit

[timid scroll]

And I’m ch7 for math

[still raven]

ngl stats is the reason why I didn't get A*

pure was good

mechanics also good

stats I got like 50% 😭

[timid scroll]

😂

I just hate stats

[still raven]

me too

revise that Large data set

do not undermine it

😵

pretty sure we had like 4 marks worth of large data set

[timid scroll]

Oh ok

[still raven]

and watch some Bicen maths on Youtube

he's the goat

[timid scroll]

Okok interesting

I’ve only been doing book questions till now

[still raven]

ngl exam questions are harder than the book

[timid scroll]

Oh

I thought book is tough

[still raven]

when you're done with the book you should really grind the past papers

[timid scroll]

Sometimes

[still raven]

the modelling question you just sent

[timid scroll]

Did your school also do these predicted A level papers

From a certain website

[still raven]

is more or less a typical exam question

[timid scroll]

Oh ok

[still raven]

I think they're hidden to students lol

I do have a script from last year if you want tho

[timid scroll]

Na like people make them

[timid scroll]

YES PLEASE?

[still raven]

yea sure

[timid scroll]

I’m doing online school

Lol

[still raven]

I'll dm it to you

ohh

[timid scroll]

A bit tough

:/

[still raven]

sounds hard

[timid scroll]

It’s like you learn through book method

But the book answer simplify it

And then when you reach the end of the chapter you get everything wrong

Because the actual full method is shown

[still raven]

yea

[timid scroll]

Meaning you’ve been just using the simplified method

This far which works most of the times

[still raven]

use the blue boxes at the end of each chapter to refresh your memory

[timid scroll]

But not when they change the question

[lean otter]

:0

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

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[tardy wolf]

From what should I start and what should I rely on?

[crystal palm]

we only sum up to k

sin and cos are bounded

the bottom however diverges to infinity, so the whole fraction should converge to 0

not a proof, just my thoughts

[tardy wolf]

Yeah I also thought about this at first but the problem is that there ain’t cos(n+N), but cos (ylog(N+n))

So it’s looks kinda like this

[crystal palm]

yeah, but it would still always be in [-1,1]

whereas the (N+n)^0.5 would diverge to infinity

[tardy wolf]

I've come to this point now, too, and I understand it, but now need to prove it by definition

And the problem also is that this is sum and we need to prove that this graph is symmetrical cuz sum is 0

[safe radish]

@tardy wolf Has your question been resolved?

[safe radish]

@tardy wolf Has your question been resolved?

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[oak violet]

did i do good

[plucky elk]

explain how you got your answer

[oak violet]

plugged in x^3+1 and 2xy-1

oh wait

i did that totally wrong

yeah idk can someone walk me thru it

<@&286206848099549185>

[lean otter]

it should indeed by (x^3+1)*(2xy-1)

whats the problem?

[lean otter]

Is this the question? I think you’re supposed to multiply (x^3 + 1) w (2xy - 1)

[lean otter]

Oh yes

[lean otter]

But the first option is wrong yeah? What r the other options?

[oak violet]

i fgd it ou

[lean otter]

Oh phew that’s great!

[oak violet]

yipeee

ty ty

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[lean otter]

https://tenor.com/view/catshakira-cat-dance-catdance-catdancing-gif-22503034

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[sinful grove]

How many angarams of the word 'ALGORITHM' have no consecutive vowels?

First thing first, there are three vowels viz. A,I,O and six consonants namely L,G,R,T,H,M. Now the six consonants can be permuted in 6! ways, and the three vowels can be arranged in 3! ways, how do I count all cases when no vowels occur consecutively? one conf can be CVCVCVCCC, another CVCVCCVCC etc. each corresponding to 6!×3! distinct ways, but is there any way to count all these different configurations which satisfy the constraint that no vowels occur together?

[buoyant shadow]

7 choose 3

[sinful grove]

How you got that?

[buoyant shadow]

a vowel goes where the dots are
.C.C.C.C.C.C.

[sinful grove]

hmm yeah that makes sense

Thanks

So the solution should be (7 choose 3) times 6!×3!?

[buoyant shadow]

yeah that should work

[sinful grove]

Thanks

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[haughty ruin]

Since there are 2 solutions, how do I find them?

I know it's 2

x=2

But how do I get the other solution by making it negative

do I make the 10 negative, the 8 negative, or the 2 negative?

[severe pond]

well when u take the square root

there r two solutions a positive and negative

think of the graph of x^2

[umbral swan]

(x+8)² = 100 <----> x+8 = +-sqrt(100) = +-10

[haughty ruin]

Oh you make the sqrt negative

alright

So it would be

x=2

and

-2

[severe pond]

no

[umbral swan]

nono:

[severe pond]

u can’t just negate the other solution

[haughty ruin]

I didnt

I make 10 negative

[severe pond]

u did

[umbral swan]

@haughty ruin are these steps clear?

[severe pond]

but x+8=-10

how’d u get -2

[haughty ruin]

oh i was in the middle of a game idk why I thought to add 10

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@haughty ruin Has your question been resolved?

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@haughty ruin Has your question been resolved?

[umbral swan]

still unresolved?

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[patent vault]

how would i do this? im kind of confused

[patent vault]

probably pigeonhole? but im not sure how to set it up

[abstract crown]

not entirely sure but i think you can consider the worst case and prove it will work

id consider one row, on day one, the row with the most amount of people

to minimise this, say each row has the same number of people

7

7*7=49, so one row has 8 people

so on day 1, there is at least one row with at least 8 people

now, on day two, we can pigeonhole and say, as there are 8 people, but only seven rows, two people must share a row

[abstract crown]

i think thats the pigeonhole?

[patent vault]

oh yeah

this is pigeonhole

thank you!

[abstract crown]

awesome, no worries.
would you mind sharing the origin of this question?

[patent vault]

a math program i do on saturday

[abstract crown]

very cool

do send any more interesting ones if they come up

[patent vault]

sure will

[patent vault]

wait doesnt each row hold 10

[abstract crown]

up to 10 i think

[patent vault]

yeah

[abstract crown]

there will be 20 empty seats scattered

[patent vault]

you want to use each row though?

yeah

[abstract crown]

wdym

[patent vault]

oh wait the minimum in each row?

[abstract crown]

well, the smallest maximum

[patent vault]

yeah

thank you for your help!

@abstract crown

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[frail beacon]

What is 1^2?

[frail beacon]

My teacher said -1

But google say 1

Both are correct I guess

[light shoal]

you have almost certainly misunderstood your teacher

[frail beacon]

Why

Isn’t -1 times -1 = 1

[light shoal]

because 1^2 is certainly not -1

[frail beacon]

Oh ok

[light shoal]

sure, but that's not what you asked

1^2 is 1 times 1

[frail beacon]

Ohhhh ok

I see now

[frail beacon]

Yes. What my teacher had was -1^2

And it was 1

Oh same thing

[light shoal]

ah yes that's correct

well assuming you mean (-1)^2

[frail beacon]

Yes

[light shoal]

-1^2 is parsed as minus (one squared)
not (minus one) squared

[frail beacon]

Oh okay

So I should add parenthesis ?

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[lean otter]

help me with this question https://shattereddisk.github.io/rickroll/rickroll.mp4

[plucky elk]

!ss

[safe radish]

Please post images (such as PNGs or JPGs) of the question rather than other filetypes such as PDFs which have to be downloaded. Non-image downloads can potentially contain viruses or other security risks.

[plucky elk]

<@&268886789983436800> Rick roll lmao

[lean otter]

just playt the video

.solved

haha

[safe radish]

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[plucky elk]

It's in the name

Couldn't be more obvious

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[rapid summit]

how do i do 10b?

[thin bridge]

do you know what the graph of f(x) looks like

[rapid summit]

yes

[thin bridge]

cut off a chunk so that it passes the horizontal line test

[rapid summit]

then what do i do after that?

[thin bridge]

identify the new domain

[rapid summit]

can u tell me how?

[thin bridge]

try doing this on paper,
draw what you have after cutting off a chunk

[rapid summit]

alr

[rapid summit]

then what do i do in order to find the domain of the remaining chunk?

[thin bridge]

defintion of domain, reading the graph

in your new graph, what are the values of x that have corresponding y value

[rapid summit]

nvm i get it

i accidentally plotted the wrong equation

ty

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[rapid summit]

.reopen

[safe radish]

✅

[rapid summit]

wait the answer for this is x >=0.5

what if i cut off the right chunk?

into this

wouldnt it be x <= 0.5?

[thin bridge]

both would be acceptable

[rapid summit]

oh so if im taking the igcse exam would it be possible if i just wrote both >= 0.5 and <=0.5?

[thin bridge]

or, not and

usually the right side is taken

[rapid summit]

alr ty

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[sage terrace]

help

[sage terrace]

please

please helppppp

[terse lichen]

what do you think your variables should represent

[sage terrace]

idk

[terse lichen]

the question asks you to find the number of onion rings and chicken wings

so?

[sage terrace]

okay

dude you gotta explain this to me rn I'm more tired than than a kid on nyquil

[terse lichen]

question asks for num of onion rings and chicken wings

so thats what your variables should represent

[sage terrace]

okay

[terse lichen]

now they say that the total number of chicken wings and onion rings is 19

so whats the equation for that

[sage terrace]

idk

[terse lichen]

you should have two things added together

which equals to 19

[chilly atlas]

chicken wings + onion rings = 19

[sage terrace]

okay thank you

now what

[chilly atlas]

That's one equation, but you need one more relating the amount of chicken wings/onion rings, and calories

[sage terrace]

okay

[chilly atlas]

we know that chicken wings are 75 calories, and onion rings are 40 calories. An unknown combination of chicken wings and onion wings should give 970 calories.

[sage terrace]

okay

[devout shale]

Represent that using an equation

[chilly atlas]

So try and set up a new equation, bearing in mind the fact that the amount of chicken wings and onion rings are unknown

You should be using letter variables, like 'r' for onion rings (as an example)

Notice how it says "let ___ = something"

I think it wants you to choose variables, and say what they represent

you could use 'o' and 'w', or 'r' and 'c', or even 'x' and 'y' to represent chicken wings and onion rings

but you should get in the habit of using symbols to represent quantities

[sage terrace]

970 divided by x+y

[chilly atlas]

I'm pretty sure it wants you two find a system of two linear equations

[devout shale]

this isn't an equation

[chilly atlas]

970 over 'x + y' doesn't properly represent the relationship given

[sage terrace]

okay

[chilly atlas]

A proper equation needs an equals sign

[sage terrace]

okay

im lost

[chilly atlas]

Here's a hint: If 1 onion ring has 40 calories, then how many calories does 2 onion rings have?

[devout shale]

What have you tried?

[sage terrace]

80

[chilly atlas]

Exactly

How did you get that number?

[sage terrace]

multiplying it

[chilly atlas]

so you multiplied the calories by the amount of onion rings

[sage terrace]

yes

[chilly atlas]

so now do the same thing, except pretend that you dont know the amount

use a symbol to represent an unknown amount

[sage terrace]

okay so 970-xy=

[devout shale]

what is x?

what is y?

what is it equal to?

why are they being multiplied?

[sage terrace]

chicken and onions rings

god i want some sonic now

[chilly atlas]

But you have to choose which variable, x or y, represents chicken or onion rings

[sage terrace]

x chicken y onion

[chilly atlas]

That works

They have different calories, so they should have different coefficients

Chicken has 75 calories, so one of your terms should be 75x

[chilly atlas]

Remember how you solved this? Its the same principle

An onion ring is 'y', and onion rings have 40 calories.
You essentially did 40 times y, substituting 2 for y

y is the quantity of onion rings

Now the key here is that adding "onion rings times 40 calories" and "chicken wings times 75 calories" should give you 970 calories

So set up an equation representing that

using the variables 'x' and 'y', as you defined them

[sage terrace]

x+y=970?

[chilly atlas]

This equation is essentially saying "the amount of chicken wings plus the amount of onion rings equals 970 calories"

does that make sense?

[sage terrace]

yes

[chilly atlas]

No no...

If you had 3 chicken wings and 2 onion rings, would it be correct to say that you have 5 calories total?

I don't think it would be

You have to use the calories for each food item within the equation

When you told me 2 onion rings at 40 calories each would equal 80 calories total, you were on the right track

Just apply that same logic to this equation

[chilly atlas]

This is very close, you're just missing the calories for chicken wings and onion rings

[sage terrace]

i gotta be honest idk

[chilly atlas]

75x + 40y = 970

does that make sense to you

By adding in the 40 and 75, we are now operating within the realm of calories

x and y represent the quantities of chicken wings and onion rings (eg, 1 onion ring, 2 onion rings, etc.)

75 and 40 represent the calories of each

[sage terrace]

yeah some what

[chilly atlas]

You seem like you might be a little confused on what a variable represents

[sage terrace]

no im just tierd i need rest badly

[chilly atlas]

'x' and 'y' are variables, and they represent any possible number (in this case, quantity of food)

If you remember, you told me that 40 calories times 2 onion rings equals 80 calories

But what if we didnt know how many onion rings?

You would use something like "40y = total calories"

When you plug in 2 for 'y', you get 80

'y' can vary depending on how many onion rings you want to calculate the calories for

2 onion rings? 80 calories. 3 onion rings? 120 calories. and so on...

[sage terrace]

okay i got it

i gtg now thank you

verymuch

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[rapid summit]

can anyone help explain 7ii, the answer for 7i is a = 6, b = 2

[terse lichen]

long division

[rapid summit]

oh wait i thought they meant diffrintiation when they wrote dx

mb

🤦‍♂️

anyways ty

[vapid cypress]

lol

[rapid summit]

.close

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[steep spindle]

Whyd it become (u-2)² and not (u-2)³

[cunning shard]

can you identify u?

@steep spindle

[steep spindle]

u=e^x + 2

[cunning shard]

right, so $u-2=e^x$

[steep spindle]

Ahh nvm

[flat frigate]

.doc

[steep spindle]

An e^x was cancelled

[cunning shard]

now it should be evident

[steep spindle]

Thanks

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[brazen parrot]

excuse me

[brazen parrot]

why isnt it letting me graph

i have x^2+x-12

[frozen marlin]

@brazen parrot

why ru using that

use desmos

[brazen parrot]

bc i can use it in my test

[frozen marlin]

also yes hello

[brazen parrot]

on the calculator section

[frozen marlin]

oh then i have no idea

i've never used a manual graphing calc

[brazen parrot]

wth is there an automatic one

[brazen parrot]

wthhh its compulsory in year 9

[frozen marlin]

idk

my school never allowed calcs

[brazen parrot]

how did u do like cosine law and sine law

[frozen marlin]

manually?

they would give values

xD

[brazen parrot]

lol

r u old just asking?

[frozen marlin]

??

wdym "r u old"

[brazen parrot]

liek 30

[frozen marlin]

no bruh 😭

[brazen parrot]

oh

[frozen marlin]

my role is undergrad for chr7st's sake

[brazen parrot]

oh...

[frozen marlin]

xD

[brazen parrot]

wth

so u didnt even use this

[frozen marlin]

lmfao

[frozen marlin]

i mean i have

but not very often, no

only w/o internet access when i was a child

or when i was attempting problems from books

which required calculators

(i did maths at home for fun, so yea)

[brazen parrot]

no way...

[frozen marlin]

yea

i love maths

[brazen parrot]

how come my values are so diff

is theirs right or mine

[frozen marlin]

?

[brazen parrot]

for xmin i got -11

but they got -10

[frozen marlin]

i have no idea what ur saying

[safe radish]

@brazen parrot Has your question been resolved?

[safe radish]

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[clear crest]

Is |a|÷|b| = |a÷b|?

[lime dust]

Make you these two questions

Are both the same ratio?

Are both possitive?

[clear crest]

Guess they are the same then

[lime dust]

Yes

[clear crest]

Ight thanks

.close

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[primal gazelle]

hey, I want to clarify something if a continous function has two roots on an interval (a,b) then it must have a local extremum at that interval is that correct?

[hard crest]

as long as it's not constant 0 between the roots, yes

[primal gazelle]

alright thanks a lot

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[wild cape]

.reopen

[safe radish]

✅

[mossy raptor]

hello?

...i'm new um.....

[wild cape]

@hard crest @primal gazelle hmm i think constant 0 is fine

[shadow glade]

check out #❓how-to-get-help

[mossy raptor]

thx

[primal gazelle]

how so

[hard crest]

depends on what you mean by local extremum

also I love the energy of just kicking in the door with "AND ANOTHER THING"

[wild cape]

cant have the channel locked!

[wild cape]

i imagine there arent many defs of this?

[shadow glade]

btw this question is a good illustration of the mean value theorem

[wild cape]

0 is a local max (and min) of the constant function 0

[shadow glade]

(although thats limited to differentiable functions) if you connect two points on the graph of a continuous differentiable function (the orange segment), at some point in between youll be guaranteed to have a tangent with that same slope

[hard crest]

yeah ok the definition I've seen is that f(x) has a local extremum at x if f(x) is the maximum value on some neighborhood (a,b) of x

[primal gazelle]

oh thats cool Ive never heard of that

[hard crest]

so ye in that case ⁰(x) has local maxima and minima everywhere

[wild cape]

0(x)

[shadow glade]

yes, it's one of the most important theorems in calculus, so in your case, the slope between x = a and x = b would be 0 since they are both roots, so a differentiable function will have a local max\min with slope of 0 somewhere in between

[primal gazelle]

oooh

[shadow glade]

a good analogy for this is: you can imagine a plane taking off (it's pointing at an angle up) and when it's landing it is pointing at an angle down...but somewhere in between we can imagine it would have to be perfectly flat because it is transitioning in a continuous way between the angles (it can't be pointing up one moment) then suddenly teleport to pointing down without moving through every angle in between.

the plane's direction is basically like the direction of the tangent, it's always pointing exactly in the direction the plane (or graph) is moving in....and just like your original question, the position of the plane starts and ends at ground level (y = 0 ). somewhere during flight it must be going horizontal to the ground (ok we're ignoring curvature and earth and whatnot but you get the gist)

[primal gazelle]

yeah

I get it

[shadow glade]

mean value theorem is a good thing to have the intuition for cause it's used in like half of calculus proofs 😄

for the various theorems that come later and whatnot

[primal gazelle]

Ill prob learn it in uni so it will be useful for sure

thank you

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[eternal heath]

Hi

[eternal heath]

Can anyone make me understand this

@fiery merlin

<@&286206848099549185>

.close

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[dense wadi]

Why is this DNE

[safe radish]

@dense wadi Has your question been resolved?

[lime dust]

Show your work

[dense wadi]

I figured it’s cuz both of them don’t reach 0 ever

But ty

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[unkempt thorn]

I need a convex and continuous functin h:[a,b]->R such that the expression in the the picture is strictly negative

[left gyro]

h(x) = (x - a)(x - b) - 1 is an immediate idea

[unkempt thorn]

this is true for all m, n, right?

@left gyro

[left gyro]

h(a) = (a - a)(a - b) - 1 = -1 < 0
h(b) = (b - a)(b - b) - 1 = -1 < 0
h(x), as a parabola that opens up, is a conex and continuous function

[left gyro]

Trust me™

[unkempt thorn]

ok thanks

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[still ether]

how to calculate this:

[abstract crown]

3root3 -2root3 is just root3

Then you can group roots

[severe pond]

it’s root 2

[abstract crown]

Oh yeah oops

Then probably manually expand brackets

Unless there's a smarter way

[velvet escarp]

u can write 5 as 2 + 3
maybe now u can try

hint: complete the square

[abstract crown]

Oo smart

[still ether]

thanks i solved the second part with the root but still cant solve the first one:(

nevermind i did it thank you for the help:)

.close

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[urban breach]

Claim: If (p) is a prime number and (p \mid (a - b)), then (p \mid \frac{{a^p - b^p}}{{a - b}}).

[urban breach]

Claim: If $(p)$ is a prime number and $(p \mid (a - b)), then (p \mid \frac{{a^p - b^p}}{{a - b}})$.

[flat frigate]

Abir

[vast obsidian]

Hint: Show that if p | (a-b) then a^p mod p = b^p mod p

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[cobalt estuary]

I am having some trouble plotting a point on the circumference of a circle. (my math is in the comments below)

<svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 110 110">
    <circle cx="55" cy="55" r="50.55" stroke="black" fill-opacity="0" />
    <path d="M 55 55 L 55 5 A 50 50 0 0 1 105 55 Z" fill="red" />
    <path d="M 55 55 L 105 55 A 50 50 0 0 1 55 105 Z" fill="green" />
    <!--
        1.25 * pi = 3.926990817 (should be 180 + 45 degrees I think)
        cx = 55
        cy = 55
        r = 50
        (105 * cos(1.25pi), 105 * sin(1.25pi))
        (104.7534733966, 7.190953438) ?!
    -->
    <path d="M 55 55 L 55 105 A 50 50 0 0 1 104.7534733966 7.190953438" fill="blue" />
</svg>

[cunning patio]

Looks like it treats the input to cos and sin as degrees.

Instead of radians.

[cobalt estuary]

why would anything be doing that

weird calculator

[cunning patio]

No idea. What package did you get the cos and sin functions from?

[cobalt estuary]

im using my phone calculator

[cunning patio]

It might have a rad/deg setting somewhere, unless it's just weird.

[cobalt estuary]

but once i get the math right, i plan on using the Math library from .NET

[cunning patio]

That should definitely use radians as default.

[cobalt estuary]

not sure how to change samsung's calculator to rad

[cunning patio]

Might not be possible then. Weird default behavior though.

You can pop in the degrees then. Or use Wolfram Alpha.

,w (105cos(1.25pi), 105cos(1.25pi degrees))

[flat frigate]

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[cunning patio]

Ok, not the exact output I had hoped for, but we can still see the values. The first one, -74.2, is the right one, and the second one, 104, is when interpreting the input as degrees.

[cobalt estuary]

yeah, that one looks a little better but its in reverse

no floating point precision

[cunning patio]

Right

,w 105cos(1.25pi) with 8 decimals

[flat frigate]

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[cunning patio]

,w 105sin(1.25pi) with 8 decimals

[flat frigate]

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[cobalt estuary]

I think my math is off for the 105 part

[cunning patio]

The 105 should be the radius of that circle.

[cobalt estuary]

the radius is 50 while the circle is at (55, 55)

[cunning patio]

Then I imagine something like (50cos(angle) + 55, 50sin(angle) + 55)