help-0

[hot bison]

thanks

[coarse hemlock]

np

[hot bison]

.close

[lone heart]

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[thick lynx]

Simplify $\frac{bx(a^2x^2 + 2a^2y^2 + b^2y^2) + ay(a^2x^2 + 2 b^2x^2 + b^2y^2)}{bx + ay}$

[ocean seal]

Kepe

[thick lynx]

Hints only please.

[ocean seal]

Kepe

[coarse hemlock]

have you tried to do all the calculations before?

[thick lynx]

multiplying it out completely?

[coarse hemlock]

yes

I'm not sure u will be able to semplify something

[thick lynx]

I thought about that but then again I didn't think that the author of this problem wants you to get into that complete mess

but I will try, alr

[coarse hemlock]

but what should you simplify with?

what topic/argument is it?

[thick lynx]

Special Factorizations, things like $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$

[ocean seal]

Kepe

[coarse hemlock]

ahh

alr

1 sec

[thick lynx]

$$\frac{ba^2x^3 + 2a^2y^2bx + b^3y^2x + a^3x^2y + 2ayb^2x^2 + ayb^2y^3}{bx + ay}$$

[ocean seal]

Kepe

[high rapids]

Have you thought about (bx+ay)

[thick lynx]

multiplied out

[thick lynx]

The parentheses are almost identical, yes, but the middle term isn't

[coarse hemlock]

ok so

Ive tried to do it but I'm not understanding. apparently I can not make anything

[high rapids]

Have you tried like expanding only the insides of the two parentheses and see what happens?

[thick lynx]

the original term is

It's already expanded?

Or do you mean multiplying out

[high rapids]

Oh ok

[coarse hemlock]

my brain is actually melting, i can not help

ah

[thick lynx]

The parentheses are interesting

they are almost identical except the middle term

[dense sleet]

$$(a^2x^2 + a^2y^2 + a^2y^2 + b^2y^2)$$
$$a^2(x^2 + y^2) + y^2(a^2 + b^2)$$

[ocean seal]

Pluton

[thick lynx]

also the bx and ay

[dense sleet]

Maybe helpful when added with other expression

[high rapids]

Now group all the bx terms and ay terms separate maybe?

[dense sleet]

Other parantheses factors like
$$x^2(a^2 + b^2) + b^2(x^2 + y^2)$$

[ocean seal]

Pluton

[thick lynx]

$$\frac{bx(a^2(x^2 + y^2) + y^2(a^2 + b^2)) + ay(x^2(a^2 + b^2) + b^2(x^2 + y^2))}{bx + ay}$$

[ocean seal]

Kepe

[high rapids]

No

Group the bx and ay terms separate in the numerator please

[thick lynx]

just

?

its already seperate?

[high rapids]

When you multiplied have you tried swapping the middle terms?

[thick lynx]

wait, let me try

[high rapids]

Like swap 2a^2y^2bx and 2ayb^2x^2 and then factor?

[dense sleet]

Now you can group
$$(a^2 + b^2)(ayx^2 +bxy^2) + (x^2 + y^2)(ayb^2 + bxa^2)$$
Maybe factor ab and xy
$$xy(a^2 + b^2)(ax + by) + ab(x^2 + y^2)(ax +by)$$
This is perfect

[ocean seal]

Pluton

[dense sleet]

Maybe

Not really but something could be factored again

$$(ax + by)(xy(a^2 + b^2) + ab(x^2 + y^2))$$

[ocean seal]

Pluton

[dense sleet]

This doesnt seem to help does it

[thick lynx]

Yesss I think this works, wait a sec

[thick lynx]

yes it worked, thank you

[thick lynx]

Swapping the terms seems to be how you solve this

thanks for your help too!

.close

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[gaunt eagle]

What is the best way to deal with questions like these without having to spend an hour on writing three pages?

I trying to prove that the derrivative of this function will be 0 but it becomes an algebraic nightmare really fast

[mortal trellis]

just use log properties

and then difference of squares

[gaunt eagle]

I used the chain rule

[mortal trellis]

you don't need to differentiate anything here

[gaunt eagle]

twice per term

[mortal trellis]

you can just combine the terms with log properties and then simplify

and then you are left with a constant

[gaunt eagle]

omg

it was literally that easy

how did I ot see that

[high rapids]

Yes

Happens

[gaunt eagle]

im nervous for an exam I will have soon, pretty sure I will make mistakes like these on it

and waste so much time on a wrong approach

[mortal trellis]

happens. but you should probably sooner try to find a different approach

sure suffering through the math can work. but especially in exams the questions are rarely like that

well at least in good exams

always try a bit of different stuff around before you tunnel vision one approach

[gaunt eagle]

yeah youre right

thanks!

[lone heart]

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[uneven isle]

i’m kinda dense and can’t do easy question

[uneven isle]

so i got up to

that y=x^2 - x - 6

which has gradient of 2x-1

[tawdry whale]

what does this say

[normal ingot]

Make those two equations equal to each other, then solve for x

[uneven isle]

just started learning calculus and was told to do it by differentiating and then equating something(teacher didn’t finish his sentence and zoom died)

but regardless

A(2, -4), B(-3, 6)

don’t really understand part B when it ask to find the vertical line through M meets the parabola

does it just mean it’s perpendicular to AB which M sits on? or just like a 90 degree line through M

[uneven isle]

,rotate

[uneven isle]

<@&286206848099549185>

[soft gazelle]

To find the midpoint, average the coordinates of A and B. (-0.5,1). Then it says it’s a vertical line through m so it must go through x=0.5

[uneven isle]

i’m up to that already

so then i just substitute x = -0.5

to find the value of y at T

[soft gazelle]

Into the equation of the parabola to find T

[uneven isle]

right , but then i’m confused about showing the tangent at T being parallel to AB

[soft gazelle]

So you can find the gradient of AB. Do you know how to differentiate?

[uneven isle]

yeah

gradient of AB is given already

of -2

gradient of parabola at any point is 2x-1

oh nvm i’m a brick wall

i see now

🤦‍♂️

[soft gazelle]

So differentiate equation of parabola and sub in value -0.5

[uneven isle]

so the equation of tangent is y=-2x+17/4

which has same gradient hence parallel

ty for the help

[soft gazelle]

Yeah, best not to waste time finding whole equation though just finding gradient is -2 is sufficient.

[uneven isle]

right fair enough

tysm

.close

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[toxic grail]

Can u plz plot this signal?

[toxic grail]

.close

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[scarlet heath]

is anyone able to walk me through this

[worn fox]

What have you tried?

[scarlet heath]

I actually have no idea where to start on this

do I need to use the division method or something to solve this?

[worn fox]

Have you expanded the left hand side of the ODE using the product rule?

[scarlet heath]

yes

or wait no I was wondering when I do that do i need to treat y' differently than a normal variable

[worn fox]

Uh no ig?

Product rule the LHS, then just plug and chug Y(x) and use the fact that y(x) is a solution

[scarlet heath]

right so I have this on the leftside right?

[worn fox]

What happened to the x^2 on your left term

[ocean seal]

ΣAC

[scarlet heath]

Mb I forgot to add that

Right but where do I plug in the Y(x) now

[lone heart]

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[frosty widget]

How does this happen like what are the more in depth steps

[frosty widget]

The way i tried to do it was by just getting rid of a^4

[chrome kite]

difference of two squares

[dense sleet]

They factored a^2

[chrome kite]

wait

[frosty widget]

Like Why couldnt i do this ?

[dense sleet]

No?

[chrome kite]

yeah factor out a^2

[dense sleet]

Better question. Why could you

[lime bobcat]

Jesus f. Christ

[frosty widget]

Arent divisions for algebra things like this where for the powers you can substract them

[dense sleet]

No

[frosty widget]

a^4/a^4 is a^0 so nothing ?

[dense sleet]

But this isnt that

And a^0 is 1 btw

$$\frac{3 + 1}{3 + 2}$$

[ocean seal]

Pluton

[dense sleet]

When we do this normally we get 4/5 which is 0.8

[frosty widget]

right

[dense sleet]

When we do the illegall thing of cancelling 3s we get 0.5

[frosty widget]

So then i need to factor out a^2 which means?

[dense sleet]

https://youtu.be/ctqviXu-mTE

[frosty widget]

Ok wait

So i do this then

[dense sleet]

Yes

[frosty widget]

And i can cancel out a^2 now because they are multiplying not an addition

[dense sleet]

Yes

[magic plank]

guys sorry butt....

Does anyone have a Chegg acc

Like I'm in urgent need for it rn

[dense sleet]

Why would you ask that in math help channel?

[frosty widget]

so say this problem came up i could also do this

[dense sleet]

Yes

[frosty widget]

Right alright

Well thank you very much

Ill close channel

.close

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[magic plank]

Because I'm exhausted from getting NOs from other servers

but I literally need help

Like fr fr

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[magic plank]

omfg no one believes me i have no idea why

[iron swallow]

What do you want

[rotund plank]

What are you talking about

‘Believes you’

No idea why someone could be in urgent need of a chegg account, you can’t just get help?

[magic plank]

I'm just tired of people saying no when they have an account and don't want to help because they think I'm gonna rob them or something lol

[magic plank]

Idk wanna help ?

[rotund plank]

Nobody’s obligated to give you their account

[magic plank]

I don't need the acc

[rotund plank]

Just post what you’re stuck with and people will help if they wish

[magic plank]

just want them to search for the question on Chegg

[rotund plank]

Either way they’re not obliged too

[magic plank]

dude srsly

[rotund plank]

It is still giving you access to it anyway

[alpine sable]

Post the question

Already

[magic plank]

It's a physics question btw 😔

I-

[alpine sable]

You know, if you want to get attentiont

There are better servers

[magic plank]

omfg

[alpine sable]

Like wayyyy better

You might even get empathy points who knows

[magic plank]

I'm not trying to get attention

omg no

I literally need a Chegg account, it doesn't matter if this is a math help server

but I apologize for seeking help ig lol

[alpine sable]

Could have posted the question

Could have gone to a physics server

A chegg server

But noooo

[magic plank]

Alright thx

[rotund plank]

Just post the question

If nobody can help immediately go to a physics server

[magic plank]

To perform calibration measurements, the researchers need to rotate the telescope by 90 degrees. For that, they fire the MRE-1 thrusters at the bottom edge of the primary mirror (see figure)
for 0.5 seconds with a thrust of 2.5 newtons.

This question is considered to be an advanced question

It's related to rotational motion and thrust force

[rotund plank]

Right well sounds like the figure’s important

And go to #old-network

There’s a physics server

[lone heart]

@magic plank Has your question been resolved?

[magic plank]

How long does it take for them to respond ?

[rotund plank]

Depends

[magic plank]

because it has been 15 minutes since I posted the question

[rotund plank]

On the question, time

[magic plank]

ok can't U solve the question ?

[rotund plank]

Also if you reference a figure you should post the figure

[magic plank]

oh my bad

[rotund plank]

You also haven’t actually asked any questions

You’ve just made statements, so nobody will really be able to solve anything

[magic plank]

omg

I just noticed dude

wtf is going on😢

[lone heart]

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[celest perch]

how do you do this

how can you even expand a surd?

[pseudo ice]

There's a formula for binomial expansion of powers which aren't positive integers (re. expanding surds):

(In this case, replace "x" with "3/x" everywhere, and set n=1/2)

[celest perch]

is it different to the normal binomial theoreM?

[pseudo ice]

If something like this one is the one you're used to, then yes: this pictured one only holds for natural powers but can be used to expand any value of a and b, the previous one can be used for any power of your choice but (unless n is natural) you have to restrict your choice of "x"

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@celest perch Has your question been resolved?

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[lone heart]

@wicked badger Has your question been resolved?

[lone heart]

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[wicked badger]

.reopen

[peak tiger]

someone pls help me

[gray ingot]

converting (cos2x + 1) into single angles would be the first thing you should do

use these

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[uncut depot]

why is the double derivative: $\frac{d^2y}{dx^2}$, is it just notation

[ocean seal]

azorfus

[uncut depot]

like, when you do this: $\frac{d}{dx} \frac{dy}{dx}$

[ocean seal]

azorfus

[uncut depot]

shouldn't it be$\frac{d^2}{d^2x^2} y$

[ocean seal]

azorfus

[wary stream]

It's just notation

[uncut depot]

Oh

nice

[wary stream]

https://math.stackexchange.com/questions/25102/why-is-the-2nd-derivative-written-as-frac-mathrm-d2y-mathrm-dx2

[uncut depot]

[wary stream]

It was just a link I found, but it's mostly notation

[uncut depot]

what is L

[uncut depot]

Nice, like how newton used dots over his stuff

[wary stream]

Sure

[uncut depot]

nice

btw, to study partial differential equations, how good should you be at "normal" calculus

[tacit arch]

There's no good way to answer this. Just as good as possible

[uncut depot]

so jumping over to PDE's just after starting calculus mustn't be a good idea

[tacit arch]

No way to know. Answer depends on you and your situation

[wary stream]

You definitely need a good grasp on differential calculus and integral calculus first before differential equations

[uncut depot]

oh

whats the difference between differential calculus and equations

stuff on google explaining this difference is confusing

[tacit arch]

An equation has an equal sign

Differential calculus has derivatives and equal signs

[uncut depot]

oh

uh, what

[tacit arch]

Like sin(pi)=-1 is an equation

[alpine sable]

Idk why but that was the same question i asked my teacher yesterday 🥲
But understood nothing

[tacit arch]

But it doesn't have a derivative

[uncut depot]

lol

[uncut depot]

oh

[tacit arch]

d/dx sin(x) = cos(x) is an equation AND had a derivative

[uncut depot]

so all differential calculus stuff with equations are differential equations

[uncut depot]

i see, "had"?

[wary stream]

Differential calculus is calc 1 or derivative calculus

[uncut depot]

oh

[wary stream]

It's just a naming scheme, where differential calculus is calc 1, integral calculus is calc 2, vector calculus is calc 3, and differential equations is calc 4

[tacit arch]

Real analysis calc 5-7

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[uncut depot]

oh

interesting

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[alpine sable]

in this example of a real world usage of square roots, what's the purpose of the -1 in the equation? like, why is it there, its not explained from what I can tell

[vale wigeon]

the equation is best rearranged as $V_2 = V_0(1+R)^2$

[ocean seal]

Ann

[vale wigeon]

(value at 2 years) = (starting value) * (1 + rate)^2

it is from this equation, with some algebra, that you get to $R = \sqrt{\frac{V_2}{V_0}} - 1$.

[ocean seal]

Ann

[vale wigeon]

@alpine sable does this make sense to you?

should i explain exactly what's going on algebra-wise?

[alpine sable]

yeah thatd be great

[vale wigeon]

ok well first off does the equation $V_2 = V_0(1+R)^2$ make sense to you?

[ocean seal]

Ann

[vale wigeon]

just to make sure that we're on the same page on that front

[alpine sable]

i dont see why its (value at 2 years) = (starting value) * (1 + rate)^2 instead of (value at 2 years) = (starting value) * (rate)^2
im unsure what the 1 signifies

[vale wigeon]

well let's try a concrete example shall we

let's say that you have an investment worth $1,000 that appreciates by 5% every year

can you tell me what its value will be after 2 years?

[alpine sable]

1100, right

[vale wigeon]

no

you're close but not quite

let's do it year by year

in the first year, the investment grows by 5% of its value. it goes from 1000 to 1000 + (1000 * 0.05), or 1000 * 1.05.

does that make sense to you?

[alpine sable]

yeah

[vale wigeon]

ok

so you see that an appreciation by 5% is actually a multiplicative increase rather than an additive one as might appear initially

and specifically it is a multiplication by 1.05

or (1+R) generally

you can think of the 1 as standing for the principal and R as standing for the interest (or appreciation or gain or whatever other term is more appropriate i guess)

[alpine sable]

yeah that does make sense

[vale wigeon]

in the second year it'll be the same thing, and the value will multiply by 1.05 again

thus getting us 1.05^2

,calc 1000 * 1.05^2

[ocean seal]

Result:

1102.5

[vale wigeon]

$1,102.50

of course, the $2.50 difference may seem small, but so was the initial investment (in finance terms anyway)

notice that if you had just multiplied by the rate squared, you'd get this:

,calc 1000 * 0.05^2

[ocean seal]

Result:

2.5

[vale wigeon]

and your thousand dollars would've devolved into chump change

@alpine sable does the formula $V_2 = V_0(1+R)^2$ make sense to you now?

[ocean seal]

Ann

[alpine sable]

im still thinking this through, but im think im getting it

[vale wigeon]

ping me when you're ready to move on to solving this equation for R

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

oh i think i get it

the interest is a percent of 100 (of course) and since 100% = 1, the 1 symbolizes the initial value of the investment
the sell value = the initial value * (the initial value + the gain) squared, which is 1 * whatever percentage

[alpine sable]

i think im on track

[vale wigeon]

okay yeah sorry for the delay on my part

was busy doing irl things

so now the algebra that i promised

[alpine sable]

no worries

[vale wigeon]

start with the equation: $$V_2 = V_0(1+R)^2$$ divide both sides by $V_0$ to get: $$\frac{V_2}{V_0} = (1+R)^2$$ square-root both sides to get: $$\sqrt{\frac{V_2}{V_0}} = 1 + R$$ and finally subtract 1 from both sides to get $$R = \sqrt{\frac{V_2}{V_0}} - 1$$

[ocean seal]

Ann

[alpine sable]

this makes perfect sense now

thanks a lot for your help, now i understand :]

[vale wigeon]

also while im at it

you can do similar things with periods other than 2 years

you would just take roots of other degrees (cube root, 4th root, etc.) depending on how long the time is

[alpine sable]

thanks, ill experiment with those rn, itd be a good way to retain this logic

.close

[lone heart]

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[ancient snow]

guys I forgot how to read as English (it's set theory)

[fluid basin]

the set of all x in D such that the predicate P holds for x

might reword the last bit depending on what P is

[ancient snow]

that was perfect answer!!!
I just couldn't remember 'such that'

[fluid basin]

sometimes also see "where P of x is true"

[ancient snow]

thank you!

[fluid basin]

yw

[raven rover]

If you’re done then .close 🙂

[ancient snow]

sure! one more question!
how to close? I confuse little bit 😄

[raven rover]

Just type .close

[ancient snow]

thank you!

.close

[lone heart]

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[umbral girder]

how do I differentiate this?
f(x) = 1 / (3x - 1)

[umbral girder]

gimme steps on how to do it

I dont know how to get the (3x - 1) to be differentiated

[native granite]

Do you know how to differentiate composition of functions $f \circ g (x)$ ?

[ocean seal]

Twenty

[umbral girder]

nope

I dont know what to do at this one (3x - 1)^-1

[native granite]

Okay so the formula is $(F \circ g)' = g' \times F' \circ g$

Well here we already have a f so

[ocean seal]

Twenty

[native granite]

Can you express f(x) = 1 / (3x - 1) as a composition of functions ?

[umbral girder]

no i guess

[swift mesa]

I think you might be overcomplicating it. Maybe they just know the power chain rule so far

[carmine oar]

right

or just quotient rule

[umbral girder]

what is that?

[carmine oar]

\frac{d y}{d x}=\frac{v \frac{d u}{d x}-u \frac{d v}{d x}}{v^{2}}

$$\frac{d y}{d x}=\frac{v \frac{d u}{d x}-u \frac{d v}{d x}}{v^{2}}$$

[ocean seal]

||𝓚𝓪𝓼𝓹𝓮𝓻||

[umbral girder]

I meant for this one

[molten pivot]

Fog

[umbral girder]

oops

[carmine oar]

what have you learnt

[umbral girder]

this one

[carmine oar]

like what do you know

[umbral girder]

whats that one

[carmine oar]

if you don't know it's fine

like what have u learnt recently

[umbral girder]

I dont get the composistion function

when you differentiate x^2, the power thing goes down

[carmine oar]

you are not required to use this tbh

[umbral girder]

this one

this one so far

[carmine oar]

like how about we start over @umbral girder

[umbral girder]

ok

[carmine oar]

cause I feel that you are confused

just delete your recent memory

f(x) = 1 / (3x - 1)

you try and find f'(x)

right?

[umbral girder]

yes

[carmine oar]

did you learn Quotient rule

[umbral girder]

Im not familier with the terms so probably nope

[carmine oar]

so what have you learnt recently

then

[umbral girder]

I learned derivative in general

[carmine oar]

right

[umbral girder]

how does the formula comes up

that one

I learned that only so far

[carmine oar]

this?

[umbral girder]

uhh

this one actually

https://www.mathsisfun.com/calculus/derivatives-introduction.html

the one here

[umbral girder]

I dont know most of the terms there

[carmine oar]

you don't

v and u are just random

[umbral girder]

owh ok then

[carmine oar]

yeah

[umbral girder]

those are variables?

[carmine oar]

yeah

[umbral girder]

what variebles to be precise tho?

[carmine oar]

,tex for $y=\frac{u}{v}$

[ocean seal]

||𝓚𝓪𝓼𝓹𝓮𝓻||

[carmine oar]

,tex then $\frac{dy}{dx} = \frac{\frac{du}{dx} v -\frac{dv}{dx}u}{v^2}$

[ocean seal]

||𝓚𝓪𝓼𝓹𝓮𝓻||

[carmine oar]

yeah

[umbral girder]

I see

ok

[carmine oar]

then try to work on your problem

try applying it

[umbral girder]

I was just confused with the formula since I never used it

[carmine oar]

right

try to use it

[umbral girder]

actually I should just give the whole question

[carmine oar]

yeah sure

[umbral girder]

for your info tho, I was never taught of the formula, I was just went by and do the differentiation directly without using any formula

[languid bolt]

$$f(x) = x^y$$
$$f'(x) = y(x)^{y-1}$$

[ocean seal]

MarveI

[languid bolt]

you only know this?

[umbral girder]

I was only taught of the rules of how does it work so yea I dont understand the formula thingy, but ye now I know

[umbral girder]

ye thats the formula in general

the problem was that on how to apply it on a fraction

[umbral girder]

right then, now I dont know how the function gets determined here

[carmine oar]

do you need calculus for this?
I mean like it is rigorous

but you can also solve it graphically

maybe try dividing into two parts
1/(3x+2) and x^2

[umbral girder]

btw is this true?
decresing = negative
increasing = positive

for the determining the function

[carmine oar]

and find it they are increasing/decreasing functions

[umbral girder]

welp I havent learned power chain rule

[umbral girder]

but I already solve for that

[carmine oar]

take this as example

looking this as interval as a whole

[umbral girder]

but this one

[carmine oar]

it is not increasing nor decreasing

[umbral girder]

this one true right?

[carmine oar]

maybe better way
when x increases, y increases -> increasing and vise versa

[umbral girder]

f(x) = 1 / (3x + 2) + x^2
f(x) = (3x + 2)^-1 + x^2
f'(x) = (-1)(3x + 2)^-2 (3) + 2x
f'(x) = [(-3) / (3x + 2)^2 ] + 2x

@carmine oar

[(-3) / (3 (-) + 2)^2 ] + 2 (-) --> (+) output + 2 (-), (+) + (-) = (-), so function is decreasing

this correct yes?

[lime bobcat]

$\left(\frac{f}{g}\right)'=\frac{f'g-fg'}{g^2}$

[ocean seal]

Categorist

[umbral girder]

whats this?

[median oar]

quotient rule

[umbral girder]

owh, welp thats just the same as this then

[lone heart]

@umbral girder Has your question been resolved?

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[alpine sable]

.reopen

ok

[languid bolt]

?

[lone heart]

@alpine sable Has your question been resolved?

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[stable night]

yo, can someone help me with this qn? ive defined the basis step but i have no clue how to even start on the inductive step

For all n, let P(n) denote if n can be written as a sum of distinct non-negative integer powers of 2.

Basis step:
P(1): 1 = 2^0
Hence, the basis step is true.

Inductive step:
Assume P(1)...P(k) is true
k + 1 would be either odd or even.
Case 1: k + 1 is odd
Then k is even
The representation of k would be 2^p + ..., where p ∈ ℕ.
This is because the inclusion of 2^0 would cause k to be odd.
So, we add 2^0 to k to obtain k + 1.
Case 2: k + 1 is even

[rotund plank]

I think you have your cases confused

[stable night]

oh wait

lemme change it

is it better now?

[rotund plank]

Yep

Gotta change case 2 to ‘k+1 is even’ though

[stable night]

oh right

okay done

problem is i have no idea how to get from k => k + 1 if k + 1 is even

[rotund plank]

Alright so you know that this is binary right?

[stable night]

yea

i actually didnt think about binary at all till u mentioned it lol

[rotund plank]

Oh really, alright so it could be a good idea just to experiment with that case using binary strings, which could give you an idea of how the transformation should take shape

[stable night]

i see, how do i "experiment" tho?

like do i just keep trying diff values and combinations?

[rotund plank]

Yeah just go from 1 to 2, 5 to 6, 31 to 32, 75 to 76 and so on

[stable night]

i see, then there should be a noticable pattern rite?

from there then ill come up with the proof

[stable night]

okay thanks alot sir

[rotund plank]

Yea sort of, it’s different from the odd case though

[rotund plank]

Yeah np

[stable night]

.close

[lone heart]

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[brisk thunder]

can someone explain to me why the -1 is still there in the expression even after being multiplied?

shouldn't it just go away since it's already been multiplied?

[gray isle]

wdym

[brisk thunder]

oh wait nvm

i was being stupid

.close

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[alpine sable]

<@&286206848099549185>

[lone heart]

@alpine sable Has your question been resolved?

[lone heart]

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[shy jackal]

The selector of the Serbian national football team made a list of 27 players for the World
Championship: 4 goalkeepers, 9 defensive players, 11 midfielders and 3 strikers.
(a) If the selector has decided that the goalkeeper will be Stojković, in how many ways can he choose
the other 10 players for the match against Switzerland (regardless of their position, but that they are not
goalkeepers)?
(b) In how many ways can he choose 1 goalkeeper, 4 defenders, 5 midfielders and 1
a striker who will play in the match against Brazil?

[shy jackal]

for the a

I did 23 choose 10

because it said their position didn't matter

and all players except goalkeepers is 23

is this right?

for the b

i don't understand whether it is permutation or combination

also sometimes when i do combinations i do them in different ways but they are both correct

if someone could just help me tell the difference i would greatly appreciate it

<@&286206848099549185>

[lone heart]

@shy jackal Has your question been resolved?

[languid bolt]

ok so

you still here?

@shy jackal

[shy jackal]

yes

[languid bolt]

how many ways can you pick 1 person out of 4 people (for goalkeeper)

[shy jackal]

4

[languid bolt]

how many ways can you pick 4 defenders out of 9 defenders?

[shy jackal]

9x8x7x6?

[languid bolt]

yes

how many ways can you pick 5 midfielders out of 11?

[shy jackal]

11x10x9x8x7

[languid bolt]

and then pick 1 striker out of 3 strikers

how many ways

[shy jackal]

3

but do we

[languid bolt]

multiply

[shy jackal]

but why it isn't it combination

for example

5 middlefielders out of 11

it says nowhere there is a difference between

left middlefielder and right

[languid bolt]

true

[shy jackal]

so it could be either way

[languid bolt]

does the order that you pick the players matter?

[shy jackal]

i don't know. Maybe yes because they are not all equal

like goalkeeper is different from striker

wait

can i ask another question

[languid bolt]

srry just got back

[languid bolt]

cuz if yes, i think it's just the product of how many ways can you pick players for each position

which is 4 x 9 x 8 x 7 x 6 x 11 x 10 x 9 x 8 x 7 x 3

[shy jackal]

yes i thought so too

but if the order of defender doesn't matter

it could be

4 choose 1 x 9 choose 4 ... and so on

[languid bolt]

ig so

[shy jackal]

wait let me send a pic

why is c

a permutation

if we picked

Couple1Person3

it would double count

Person3Couple1

or it wouldn't?

@languid bolt you here?

[languid bolt]

no

was eating

[shy jackal]

no problem

[languid bolt]

a) use combination formula
b) 5 choose 2 (women) * 5 choose 1 (men)
c) 5 choose 1 (choose 1 couple out of 5) * 8 choose 1 (random guy) * 3! (ways a couple and a person can be arranged)

@shy jackal

oh you did that already

anyways, it would double count

[shy jackal]

but it is a correct one

idk why tho

[languid bolt]

wdym

[shy jackal]

c) solution is 40

but it's permutation so it's double counting

or is it in this case?

since it's correct

[languid bolt]

wait...

CouplePerson1, Person3, CouplePerson2 should be counted too no?

should be * 3!

[languid bolt]

is this the correct solution btw

[shy jackal]

yes

[languid bolt]

or is it your answer

[shy jackal]

correct solution

[languid bolt]

240 is my answer

OHH

i understand

order they're picked arent counted

yes

it shouldnt double count

[shy jackal]

what do you mean

order they are picked not counted

[languid bolt]

oh i mean like..

person 1, person 2, person 3
person 2, person 3, person 1
person3 , person 2, person 1

this counts as 1

the order arent counted

it's a N choose K scenario

[shy jackal]

shouldn't it be then combination

since the order doesn't count

[languid bolt]

yeah

it's combination

tbh combination and n choose k both have the same formula, why are the names different nvm they're the same

[shy jackal]

wait

then we could just do

(10x1x8)/2!

like we can choose 10 people

then there is only one option left

x 8 remain people

/2! duplicates

[languid bolt]

why not choose 1 out of 5 people

cuz there are 5 couples

you choose 1

[shy jackal]

true

ok i see

then x 8

[languid bolt]

yes

8 choose 1

8C1

[shy jackal]

yeah

ah i see

but ok

[languid bolt]

i c 2

[shy jackal]

but then

i have one example

so

There is a registration plate

7 symbols

2 alphabet (26 options)

[languid bolt]

permutations

[shy jackal]

5 digits (10 options)

yes

but

they can mix together

so it can be

a12345a

or 12345aa

it doesn't matter

[languid bolt]

multiply by 7!

wait... but what about identical numbers...

12245aa
12245aa

will be counted as 2

[shy jackal]

i did it somehow correctly

but i don't understand how i did it

sending a pic

[languid bolt]

kk

[shy jackal]

this was a correct answer

i did basic combinations

like up

26x26 is permutation

then divided by 2!

to account for duplicates so it doesn't double count

and then same for digits

and then x 7!

[languid bolt]

oh ok

[shy jackal]

what i don't understand

is why I had to multiply by x 7! to get the correct solution

[languid bolt]

cuz 7! is ways you can arrange 7 symbols

[shy jackal]

true

but then in our couple example

shoudn't i also multiply by 3!

since you can also arrange 3 members of committeee in 3 ways

[languid bolt]

i think no

[shy jackal]

why

[languid bolt]

you cant differentiate the people

so how many ways you can arrange the committee doesnt matter

[shy jackal]

ah i see

[languid bolt]

if you do, it's called racism btw

😄

[shy jackal]

lol

but wait

if it was monkeys and humans

then we would multiply

because we could differniate

?

[languid bolt]

i dont think so

how do i explain this

[shy jackal]

even with basic

there are men and woman

[languid bolt]

they all have the same position*

[shy jackal]

you can tell the difference

[languid bolt]

i understand the concept but i dont know how to explain it

just think of it as distributing 3 "identical" positions to 10 people

[shy jackal]

but why does the order in licence plate suddenly matter

when they are also identical

[languid bolt]

wait

[languid bolt]

anyways....

idk

how to explain

need helper

[shy jackal]

like i sort of get it but not quite

like i want to know so i don't make a mistake somewhere else

tho i doubt they will help

[languid bolt]

they usually take a while

[languid bolt]

or they just dont help

[shy jackal]

im gonna write it all on paper just to make it easier

[languid bolt]

wait..

[languid bolt]

they're not identical

their "position" is different

nvm i still dont know how to explain

[shy jackal]

like there was then under b)

and it said

0 cannot be in the first place

so

i did

(26 x 26)/2! x (10x10x10x10)/4! all of that x 6!

since there is like 6 positions left

and that was correct

and that 5th 10

became 1

since only 1 option

[languid bolt]

i dont rlly understand now

lets just wait until someone come
_ _

context: there are 5 couples (10 people) that are forming a committee of 3 people.
c) there has to be a couple inside the committee

why does the order that they're pick doesnt matter

oh i have an idea

.close this help channel and open a new one

[shy jackal]

wait

[languid bolt]

10 people will check the help channel then

[shy jackal]

idk

but maybe the way my prof did it could help you

<@&286206848099549185>

Why is like this?

7! mistake

@languid bolt thank you regardless

[languid bolt]

np

[lone heart]

@shy jackal Has your question been resolved?

[lone heart]

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[keen solstice]

Hello! I seek help in my maths pie chart homework. Could someone please help?

[languid bolt]

[keen solstice]

May you please help me with this:

[languid bolt]

$\frac{\text{Frequency}}{\text{Total Frequency}} * 360\text{°}$

[ocean seal]

MarveI

[keen solstice]

alr

thanks

[languid bolt]

np

[shy jackal]

.reopen

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@keen solstice Has your question been resolved?

[lone heart]

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[errant zinc]

Need help with part B

[alpine sable]

to find a minimum, we need to use calculus

ie, find the critical points (F'=0, end points and undefined points) and then use the first/second derivative tests

[errant zinc]

but it doesnt show any use of diffrentiation in the mark scheme

nvm

i get it now

thanks

.close

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[alpine sable]

if you know the max of cos(x) is at 0, then you could probably skip the diff

[errant zinc]

yh it was 25

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[grave verge]

A whole number will be upon what? Ex. 6 upon 7, 5 upon 9 but what about whole number

[alpine sable]

upon 1 (or any number that the numerator is divisible by:

[vale wigeon]

are you asking how to write a whole number as a fraction?

[alpine sable]

2=4/2=2/1

[grave verge]

Yea

[vale wigeon]

then toby said it

n = n/1

[grave verge]

Oh alr thanks

.close

[lone heart]

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[patent swallow]

struggling to understand how these are solved

[patent swallow]

I know you have to have a same base everywhere

[ocean seal]

Chuti

[patent swallow]

and it gives an irrational number so :/

dont really know how to do this

[gray ingot]

are they 3 times 2^x+2 or (3.2)^x+2

cause normally this is how it should look like $3 \cdot 2$ and not like $3.2$

[ocean seal]

Swas.py

[patent swallow]

I suppose its $2^x+2$ since there are no ()

[gray ingot]

$$3 \cdot 2^{x+2} - 2^{x+3} - 4 \cdot 2^{x-1} = 1$$
$$3 \cdot 2^{x+2} - 2^{x+3} - 2^2 \cdot 2^{x-1} = 1$$
$$3 \cdot 2^{x+2} - 2^{x+3} - 2^{x+1} = 1$$
Then factor $2^{x+1}$ and use exponent laws for that
$$2^{x+1}(3 \cdot 2^{1} - 2^{2} - 1) = 1$$

[ocean seal]

Swas.py

[gray ingot]

$$2^{x+1}(6 - 4 - 1) = 1$$
$$2^{x}\cdot 2 = 1$$
$$2^{x} = \frac{1}{2}$$
Now you know that $2^{-1} is \frac{1}{2}$ so x = -1

[ocean seal]

Swas.py

[patent swallow]

tysm @gray ingot

[lone heart]

@patent swallow Has your question been resolved?

[patent swallow]

Wait why this?

$1 is 1^1$

[ocean seal]

Chuti

[patent swallow]

so when you apply that woulld get 2^2+2

instead of 2^x+1

[gray ingot]

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

[lone heart]

@patent swallow Has your question been resolved?

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[languid bolt]

a wire that is 44cm is shaped like a rectangle, is it possible to find the area?

[dry ridge]

Let x be one side of the rectangle, how would you express the other side?

[vale wigeon]

no, unless you mean the maximum possible area across all such rectangles

[dry ridge]

nvm.

[languid bolt]

yeah

mb

i mean maximum possible area

[median oar]

it's still yes

you can find the area in terms of the side lengths

it'd be some function that you can find a maximum point for

[keen pasture]

A quadratic

[languid bolt]

a quadratic function?

[keen pasture]

Yeah

[median oar]

it could be a quadratic, idk haven't thought that far

[weary wyvern]

.

[tall hearth]

assuming length and breath is x and y
x + y = 22
and you need max value of xy

[languid bolt]

yes that's what im trying to find

and another question, the area of a square is larger than a rectangle right?

[median oar]

no

[tall hearth]

not necessarily

[median oar]

squares are rectangles

[tall hearth]

yeah it would be easier if you tried somehow connecting the two eq

[median oar]

well ok you want the area in terms of some variable

so you can differentiate it and set it to 0 to find maximum

you know that x + y = 22

what else do you know about the side lengths?

(remember you are trying to find area here)

[languid bolt]

length x width = area?

[median oar]

yea xy = A

so now you have 2 equations

A = xy, x + y = 22

[tall hearth]

or ... if you dont wanna use calculus you could try forming a quadratic

[keen pasture]

In this case conpleting the square might give a better unserstanding of the problem

[median oar]

using these 2 equations can you realise that if f(x) or f(y) = A, you can find the derivative?

[dry ridge]

Hmm I don't think you need all that. Let x be one side of the recentagle, the other side is 44 - 2x = 2y, (44-2x)/2 = y. Hence the area is x(44-2x)/2.

[median oar]

well ok that's true, if you aren't up to calculus you might be better off doing completing the square

[languid bolt]

yeah, but i need the values

[tall hearth]

not really

[languid bolt]

22-x = y btw

[tall hearth]

you need to find the highest x(22 - x) can go@languid bolt from these 2 eq

[odd geyser]

can u guys tell me the question in order to help?

[median oar]

there's enough people helping already, thanks for offering to help though

[odd geyser]

ok

[languid bolt]

ok ima try

[median oar]

do you understand where x(22 - x) comes from

[tall hearth]

if you ever wanna find the original ques... you could check pinned messages

[median oar]

because that is very important

[languid bolt]

yeah

side = x

other side = 22-x

[odd geyser]

well guys the problem asks wether it is possible to find the area

[languid bolt]

wait...

[odd geyser]

so due to lack of information it is not possible

[languid bolt]

we're trying to find the maximum value

for the area

[odd geyser]

ohhhh

[tall hearth]

please read the entire thread for better context

[odd geyser]

i didnt know

[languid bolt]

btw, the closer a rectangle is to a square, the higher the area right?

[median oar]

yes

although i would use the word greater

[languid bolt]

ok

max value = 121 if a square is considered as a rectangle

else, it's 12 * 10

[tall hearth]

there are infinite other measures

[median oar]

what are you saying

[languid bolt]

for integers*

[median oar]

lol

[tall hearth]

youre still missing many others

[languid bolt]

what do you mean?

highest possible value is 121

[tall hearth]

x = 1 and y = 21 for ex
area = 21 * 1

[languid bolt]

,w plot y= x(22-x)

[tall hearth]

yeah

[ocean seal]

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[languid bolt]

ok ty

.close

[lone heart]

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[proud basin]

you couldve done x + y > 2sqrtxy but seems like you guys like the hard way

[lone heart]

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[alpine sable]

K

[alpine sable]

Expression:

My answer

The supposed answer (number 15)

My problem is that I do not know how did i get the incorrect answer

[tall hearth]

√(1/4) = 1/2

[alpine sable]

How 2 doesn't go into 1

[tall hearth]

hmm?

$\sqrt{\frac{1}{4}} = \frac{1}{2}$ since $\newline \bigg(\frac{1}{2}\bigg)^{2} = \frac{1}{4}$

[ocean seal]

kinglacto

[alpine sable]

We can just add an exponent when we want?

[tall hearth]

what?

[alpine sable]

The exponent is negative

So we have to flip the 1/3

That becomes 9, 9-5 is 4

There is no exponent next to the 4

Oh yeah, this is order or operations btw

[tall hearth]

the square root symbol applies for the entire fraction

[alpine sable]

Okg

Omg

I see my mistake

I didn't square root the 4 or the 1

[tall hearth]

ngl i thought you were trolling

[tall hearth]

yea

[alpine sable]

My brain was malfunctioning my bad

[tall hearth]

np

[alpine sable]

I was like "Wait a minute 🤨"

But yeah thanks

.close

[lone heart]

Channel closed

Closed by @dusty isle

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[torn isle]

May I know how to solve this?

[torn isle]

This is my working and after I do integration I got 0 for the final answer

Not sure which steps I did wrongly

[lone heart]

@torn isle Has your question been resolved?

[torn isle]

<@&286206848099549185>

[alpine sable]

hm

,w dot product [sin²t, sin t, 3 sin t], [cos t, 3 cos t, 2 sin t cos t]

[ocean seal]

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[alpine sable]

...

,w int 7(sin²t)(cos t) + 3(sin t)(cos t), t = 0..2pi

[ocean seal]

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[alpine sable]

i dont think you did that incorrectly. youre right that F • dr is 7sin²tcost + 3 sint cost

[torn isle]

Yea, but there’s a answer for it

[alpine sable]

which is zero

[torn isle]

Hmm… what if the F is in [x,y,z] order?

[torn isle]

Given answer us 23/6

[alpine sable]

idk how that happened