help-23

[lean otter]

$$ f(x) = x^2+x-4 $$
$$ \frac{d}{dx} y = \frac{d}{dx} ( x^2+x-4)$$

[flat frigate]

Brandon H

[sour abyss]

what is the integral with respect with

you didnt put dx or dy

anyone could just say 'whats the integral of f(x)' and then say its t*f(x) + c because it was with respect to t

[lean otter]

idk

[sour abyss]

then your question doesnt make sense

[lean otter]

my question was mainly about how to rewrite f(x,y)

f(x) can be rewritten as y in normal equations

so i was asking how that changes with two variable equations

[sour abyss]

usually z i guess but you can rewrite it as whatever you want calling f(x) y is convention because you have a y axis on graphs you could just say f(x) = b and then db/dx = f'(x)

i wouldnt get caught up in rewriting f(x) or f(x,y) or whatever as a variable it will probably make your understanding worse

[lean otter]

I need it to understand

anyways ty

You answered my quesion

.close

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[fickle abyss]

how would you do $\int 36sin2^2(x)cos(x)$ dx ?

[flat frigate]

yomiko

[left flower]

$\int 36\sin^2{2x}cos{x}dx$

[flat frigate]

jstN0body

[left flower]

I'm assuming this is what you mean?

[fickle abyss]

yh

[left flower]

So, have you done u substitution before?

[fickle abyss]

yh

[left flower]

oh wait hang on I'm thinking of this wrong

[fickle abyss]

chain rule?

[left flower]

sorry, for a second I was thinking it was just u substitution because I didn't realize the sin has 2x and the cos just has x

ok, what I would do is think of it like this

[pseudo scroll]

$144\int \sin^2 x \cos^3 x \dd x$

[flat frigate]

NEONPerseus

[left flower]

yeaah that

[pseudo scroll]

You can write cos^3 x as cos x(1 - sin^2 x) and then use trig identities

[fickle abyss]

how come theres 144?

[pseudo scroll]

$144 \int \sin^4 x \cos x \dd x - 144\int \sin^2 x \cos x \dd x$

[pseudo scroll]

Sin^2 2x is 4sin^2xcos^2x

That it multiplied with 36

[flat frigate]

NEONPerseus

[pseudo scroll]

Now you can just substitute sin x = u in both of the integrals

[safe radish]

@fickle abyss Has your question been resolved?

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[whole forge]

Need help understanding why the guess is x^2(ax+b)e^x, my understanding of the method of undetermined coefficients is just that the guess must be linearly independent from the homogeneous solutions. Since p(1)=0 and is of 2nd order, we know that (ax+b)e^x is a solution to the homogeneous equation, so we cannot use the guess (ax+b)e^x, however I dont see what’s stopping us from using x(ax+b)e^x as a guess and what makes it likely that x^2(ax+b)e^x is a better guess

[hot thistle]

the root shows up twice

and xe^x is already “in use” by the nonhomogeneity

[whole forge]

but x(ax+b)e^x would still be linearly independent from xe^x right

[hot thistle]

hm that’s a good point. given the solution, which makes sense, it should be ok to try x(Ax+B)e^x

[whole forge]

would it because this method is sort of just guessing so its possible for it to be wrong? So i will just move on to the next power of x if x^1 fails? There is an upperbound to the power of x here too so i am sort of guaranteed to get it within a reasonable number of tries

[hot thistle]

you can think of it that way

[whole forge]

okay sure, thank you for the help

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[whole forge]

ah actually now that i think about it, x(Ax+B)e^x will only have a singular simultaneous equation to work with which may not be enough since by superposition, the solution xBe^x will just give 0 when substituted into the differential equations. That’s why I have to bump it up by 1 more x so we have more simultaneous equations to work with. At worst, the coefficient of “A” just becomes 0 so its harmless.

[whole forge]

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[long mist]

can you please give me the first step in solving this question

[long mist]

(i am not very good with integrals)

[safe radish]

@long mist Has your question been resolved?

[whole forge]

This is really just practice to get them to the correct form, Im just going to be labelling the integrals to top bottom as A, B, C and D.

We start with B+A, now the f(x) term is of the correct form, but we have an extra g(x) term, do abit of manipulation on C and D to solve cancel it off. The correct manipulation turns out to be C+D so we have B+A-(C+D)

[long mist]

ohhh! that makes sense

do i need to use reimann sums in solving?

[whole forge]

no

the riemann sum involves something else entirely

B+A-(C+D) is the answer exactly which is 1+3-(-2+5)

make sure you expand this out and understand what your doing

[long mist]

i get it now!! thank you :)

[long mist]

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[lean otter]

im trying to learn discrete over the summer but im a little confused by this

[lean otter]

please ping me when responding

[sacred adder]

which part are you confused on

[lean otter]

im not sure where to start

[sacred adder]

do you know what the v symbol says?

@lean otter

[lean otter]

and?

[sacred adder]

or

[lean otter]

oh

[sacred adder]

do you know the truth value of the left side of the or statment

[lean otter]

no

[sacred adder]

its saying that -4 belongs to the natural numbers

[proper crypt]

p or q is true when at least one of p/q are true

p or q is false when both p and q are false

so try to think whether "-4 belongs to N" is true and whether "3 belongs in 2Z" is true

[safe radish]

@lean otter Has your question been resolved?

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[bright turtle]

how do i do this

[devout shale]

@bright turtle How old are you?

[bright turtle]

how do i do this

[devout shale]

Are you older than 13?

[bright turtle]

yes

[devout shale]

Okay, I am assuming you are trying to solve for "x" ?

This question is asking you, what number "x" when you subtract 7 from it is equal to 38

You should add 7 to both sides of the equation to solve for "x"

[bright turtle]

ok thanks

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[dim void]

Hi i was wondering if anyone can help me do this

Not 100% sure where to start

[narrow vault]

Do you know how many degrees pi is?

Pi is half a circle

So how many degrees is that?

[dim void]

180

so 180/2

=90

then what do i do about that 4?

[narrow vault]

Correct

Now you just have to remember the hand rule

[dim void]

what is that?

[dim void]

oh its basically like a unit circle on your hand

never have thought of it that way

[narrow vault]

This is how you can find sin cos and tan of every basic angle instantly

[dim void]

when it says top fingers

is that 90 and 60

or 60 and 45

[narrow vault]

The fingers

So

If you have cos 45, you have sqrt(2 fingers)/2

And cos 45 is pi/4

[dim void]

im watching a video on this

it sounds useful

bro

i see what you mean now

why have they never taught this neat lil trick haha

thank you

[narrow vault]

Best trick ever

[dim void]

so back to this

[narrow vault]

I learned it from a TikTok

[dim void]

tiktok is a lifesaver

how would i implement that trick to my question?

[narrow vault]

Okay so your second question is pi/2

So 90

How many fingers are over the 90 finger?

*thumb

[dim void]

0

omg

i see it now

[narrow vault]

Exactly

[dim void]

bro thank you

[narrow vault]

No

Np

[dim void]

:)

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[neat heart]

i have no idea on how to do this

[stray socket]

Distribute 5h^2

Simplify, collect like terms

Quadratic formula if you really need it

[neat heart]

i got it from a pre algebra book, no problem on doing quadractic formula

[tired ingot]

Solve the bracket

[neat heart]

but i think there is a way to do it without quadractic, right? since i didnt reach quadratic equation on the book

[tired ingot]

Yes

No need for that

Multiple 5h^2 into the bracket

[neat heart]

25h^2 - 15h^2
10h^2 = 150
am i doing it right

[tired ingot]

Noo??

5h^2 x 2/h = ??

[neat heart]

wait a sec

5h^2(2/h + 3) - 15h^2 = 150 -> 10h^2 + 15h^2 - 15h^2 = 150

[craggy pine]

no

what happened to the denominator h

[neat heart]

i thought we could consider it as 1

[craggy pine]

$\frac{5h^2 \cdot 2}{h} = ?$

[flat frigate]

gkn1

[craggy pine]

can you do this?

[neat heart]

im doing

wait a min

[craggy pine]

kk

[neat heart]

well

i cant

im not sure

[craggy pine]

it becomes $10h$

[neat heart]

i was afraid so

[craggy pine]

wtf

[flat frigate]

gkn1

[craggy pine]

i got that wrong

💀

it becomes 10h

[tired ingot]

Ok whats (5x5)/5=??@neat heart

[neat heart]

5

[craggy pine]

i think you should study cancelling with fractions

[tired ingot]

Exactly what happened with the H

[neat heart]

oooh

look at this

[craggy pine]

bro what

[neat heart]

nvm

this one

i treated e as 1 and got it right

[craggy pine]

i don't know how

[tired ingot]

That does not apply everywhere

[neat heart]

(3 * 5) - (3 * 1/e)
15e - 3/e

[neat heart]

i shouldnt do it anymore then

[tired ingot]

Yes

[neat heart]

about this

[jade gust]

Factoring 5h^2 should be the starting point here

[jade gust]

What?

???

[neat heart]

(3 * 5) - (3 * 1/e)
15e - 3/e

ignore this pic

[jade gust]

Me when 57=4

[neat heart]

e = 4

[neat heart]

do this equation treating e as 1

then you will find out that e = 4

but now i know i cant to this anymore

[jade gust]

No you can’t sub 1 to be e

I mean i dont even know where you’re going with that

e is a variable you’re solving for

[neat heart]

ye but what about that any variable starts = 1

i thought i could apply that

[jade gust]

?

What does that mean

[neat heart]

like x(4 + 3)
1(4 + 3)

[jade gust]

No

Unless x=1

I have no idea what you’re getting at

[neat heart]

im mostly confused

[jade gust]

x is x, x is 1 when x=1

Do you know what a ‘variable’ is?

[neat heart]

sure i do

wait a sec will get a thing

[green bane]

like x(4 + 3)
1x(4 + 3)

you mean this?

[neat heart]

this

like as if we could temporarily treat x as 1

but i think im just mistaken

[jade gust]

Why would you do that

[neat heart]

idk i remember reading somewhere i could do it

[neat heart]

and i got it right when i did it here

it seems its just a coincidence

look

now that i saw it right

x = x

not = 1 lol

sorry for the confusion

[jade gust]

What

[neat heart]

forget it

i was just mistaken

[jade gust]

The identity element of multiplication is 1

I mean what they’re tryna say there is

1 multiplied by a variable x, i.e, any number is itself

1*x=x

[neat heart]

i was just trying to reach this explanation

now i got it

[neat heart]

well its 10h

how should i proceed

[jade gust]

10h=150

Solve for h

[neat heart]

its funny because

look how i was doing
25h^2 - 15h^2
10h^2 = 150
h^2 = 150/10
h^2 = 15

i know i still had to do that h^2

but i still treated h as 1 and got the same result

not saying i would do that mistake again, its just funny

its solved thx yall

.close

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[tired ingot]

Wrong

[neat heart]

ikr

[safe radish]

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[lean otter]

how i can solve it ?

أ = ؟

<@&286206848099549185>

[neat mulch]

are you sure it's english?

[lean otter]

أ is

a

in english

but أ is a arabic letter

[tiny wraith]

And what does the symbol behind that mean?

plus?

[neat mulch]

the

° °

what is that

[lean otter]

a/a/a/a/a/a

for example : 2/2/2/2 = 1/4

[neat mulch]

oh okay

2 - i/i/i/i/i = 0

is that the equation?

[lean otter]

not "-" but its metrah

for example

[neat mulch]

okay, how does that work?

[tiny wraith]

Who made up these symbols?

[neat mulch]

arabs?

[lean otter]

: 2 metrah 4 = 2-2-2-2

[neat mulch]

they invented algebra as well lol

[lean otter]

2 metrah 3 = 2-2-2

[lean otter]

yes

[neat mulch]

hmm, okay

[tiny wraith]

Wouldn't the thing in brackets be 2? Because 2 - 2 = 0

[neat mulch]

a metrah b is just equal to a - (b-1)a

[tiny wraith]

2 metrah 2 = 0 right?

[lean otter]

yes

right

[neat mulch]

2(2 - 1/(i^3)) = 0

2 - 1/(i^3) = 0

2 = 1/(i^3)

[lean otter]

أ = ؟

means a = ?

[neat mulch]

by a, you mean the symbol that looks like "i" right?

the arabic letter

[lean otter]

yes

أ = a

[neat mulch]

2(a^3) = 1
a^3 = 1/2
a = (1/2)^(1/3) or 3rd-root of 1/2

[lean otter]

i think yes

[neat mulch]

i have a feeling you knew literally everything

lmao

[lean otter]

meksam

metrah

matroh

[neat mulch]

hm?

[lean otter]

meksam means a/a/a/a

metrah means a-a-a-a

matroh means 1-2-3-4-...

[neat mulch]

oh i see

[lean otter]

• ب أ - 2 أ

[neat mulch]

okay, but is your problem solved now?

[lean otter]

this is the role of metrah

[lean otter]

yes

but you know it before ?

we study it in egypt

[neat mulch]

i did not know this before

we don't use this in the west

[lean otter]

ok

[lean otter]

but why ?

this is important

to use it

very important

[neat mulch]

we can write it in other ways

[lean otter]

how

teach me

[neat mulch]

the first one is just equal to 1/(a^(b-2))

or a^(2 - b)

you can try it out

[lean otter]

yes

[neat mulch]

the second one is just a - (b - 1)a

or a(2 - b)

[lean otter]

yes

[neat mulch]

the third one is just 2 - (b^2 + b)/2

[lean otter]

yes

[neat mulch]

that's why we don't have symbol for those operations

also, they aren't very common

[lean otter]

yes

[neat mulch]

is there anything else i can help you with?

[lean otter]

no , thanks

[neat mulch]

np

[lean otter]

how can i close the channel ?

[neat mulch]

just do .close

[lean otter]

.close

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[lean otter]

ok

[safe radish]

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[frigid moth]

Let f be differentiable in the point a, I need to show that this holds

[frigid moth]

I've been thinking of Riemann sum but I can't see how that will give me my result

So Im not sure how to proceed

[safe radish]

@frigid moth Has your question been resolved?

[frigid moth]

<@&286206848099549185>

[neat mulch]

have you tried writing f'(a) as a limit

[frigid moth]

I tried, dont think thats the way unless I missed something

Writing it as lim x->a of whatever will not really help my case, since the limit of the LHS is to infty.

[lone arch]

This has been asked on Math StackExchange before:

https://math.stackexchange.com/questions/2773982/evaluate-lim-n-to-infty-big-fa1-n2fa2-n2-cdotsfan-n2-nf?noredirect=1

@frigid moth

[frigid moth]

Oh thanks very much

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[olive sorrel]

for finding the antiderivative of 1/f(x) how do I distinguish whether it is antiderivative of ln function or simply a function of negative power? Is it possible for derivative of ln to have a power in denominator?

[twilit spindle]

an antiderivative of 1/f(x) does not have a closed form but where to use the power rule or logarithms just consider for the power rule of antiderivatives it excludes the case n=-1

[olive sorrel]

like for example this one, because it is a square of x it can't be an ln x function or that's wrong?

[twilit spindle]

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

[flat frigate]

XxMrFancyu2xX

[olive sorrel]

yes, i know that

[twilit spindle]

n=-1 is the special case

(in the exponent)

this is n=-1/2

[olive sorrel]

okay, so only if it's n=-1 it's antiderivative of ln?

[twilit spindle]

A good rule of thumb but $\int\frac{c}{ax+b}\mathrm{d}x=\frac{c\ln(ax+b)}{a}+C$

[flat frigate]

XxMrFancyu2xX

[olive sorrel]

thanks

[twilit spindle]

Have a good day!

[olive sorrel]

u too

.close

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[kind dove]

Let T be the cheapest spanning tree of graph G. Then, for every pair of vertices s and t, it holds that the shortest path between them in T is also the shortest path between them in G.

[kind dove]

does it hold?

I don't think so. Spanning tree is tree, therefore between every two vertices is exactly one path. The path does have to necessary be the shortest one in graph G

[empty gyro]

You're not guaranteed to have a path between any two vertices, unless you mean it is fully connected. Just helpful to remember that

And you're right, it does not hold

Min tree minimizes TOTAL edge weight, not path between any two vertices

[quasi bison]

is there any cheap counterexample to this

feels like there should be

[empty gyro]

A ring of three or more vertices with s and t sharing an edge of weight 2. The remaining edges have weight 1

[kind dove]

in tree im guaranteed that between every two vertices exist path

hmm

[quasi bison]

the cheapest spanning tree is this graph minus edge AF

yet AF is the cheapest path from A to F

[kind dove]

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[lean otter]

.

[arctic sail]

how is the integral of sec^2 theta / 1 + tan^2 theta the answer that is given?

[final halo]

because $\sec^2(\theta) = 1 + \tan^2(\theta)$

[flat frigate]

ΣAC

[arctic sail]

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[eternal birch]

In a cartesian system there is a point with coordinates (2;3) and a straight line with the equation in the ss. What's the distance between them?

[proper crypt]

You mean parallel to the line you sent?

[safe radish]

@eternal birch Has your question been resolved?

[eternal birch]

it's not specified

I suppose they are talking about the shortest path

@proper crypt

[proper crypt]

No I mean what is your other line

Oh

Frick I misread it

Okay you want to find the shortest distance between the point and the line?

[eternal birch]

Well i think this is what they mean by 'distance'

[proper crypt]

I'm pretty sure there is a formula for that

[eternal birch]

but am not sure

[proper crypt]

Yeah it does

If you don't know a formula there's also another way to solve this

[eternal birch]

what way

[proper crypt]

You can let a general point on your line be (t, y(t))

Basically represent it with a single paramter.

Then, you want the value of t which makes the line from your 2 points perpendicular to the line you're given

the point (t, y(t)) can be anywhere on the line

but you want the value of t, which means it perpendicular

Then, you can just find the distance between the 2 points

[eternal birch]

how do I find t

@proper crypt

[proper crypt]

You find t by building an equation like this:

Find the slope of the line between A and (t, y(t))

and the slope of the given line

and you know that for them to be perpendicular, you need the slopes to multiply to -1

And that's your equation. then you solve for t

[eternal birch]

The slopes of the given line and the slope of the line that connect a and the given line, right?

@proper crypt

[proper crypt]

Yes

[eternal birch]

ty

Here's another one: There's a 4-sided regular prism ABCDA1B1C1D1 where the diagonals A1C and AC1 are perepndicular to each other. What's the measure of the acute angle between BD1 and B1C1

@proper crypt

[eternal birch]

<@&286206848099549185>

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[hazy totem]

hey out of curiosity why cant i differentiate a function that isnt continuous if i only am looking at the tangent lines in a region that is continuous

[hardy lion]

Yes

[hot thistle]

i assume you mean that you are looking in an open set where the function is differentiable

and if so, you can differentiate there

[hardy lion]

But be more specific please

[hazy totem]

im not sure what an open set is

[hot thistle]

(a,b)

an interval like that

instead of [a,b]

[hazy totem]

idk the difference

[hot thistle]

[a,b] includes a and b

(a,b) doesn't

e.g.
(0,1) is the numbers between 0 and 1

[0,1] is the numbers between 0 and 1, and also includes both 0 and 1

[hazy totem]

well i mean like the function f(x)=|x|, its not continous at 0, but can i differentiate at places that arent 0

[hot thistle]

it is continuous at 0

[hardy lion]

Yeah

[hazy totem]

ah ok

[hot thistle]

i think you are confusing differentiable and continuous

[hazy totem]

oh bad example lmao

[hot thistle]

i think you are asking why |x| isn't differentiable, since you can find the derivative at x = 10 or something other than x = 0

[hazy totem]

no i just gave a bad example thats not my question

[hot thistle]

ok

[hazy totem]

1/x

thats not continous at 0

[hot thistle]

right

[hazy totem]

so is it differentiable if we dont measure it at 0

[hot thistle]

the explanation is still pretty much the same

the function is not differentiable

differentiable means it is differentiable at every x

but it is differentiable for every x not equal to 0

[idle widget]

I mean you can define a different function that is differentiable if you exclude 0 from the domain

Which seems like what he’s saying

[hazy totem]

ah ok i think these explinations makes sense

ok cool that helps, thanks!

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[hot thistle]

well 0 is not included in the domain anyway

it is a terminology thing though

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[idle widget]

In that case this function is already differentiable isn’t it

[hot thistle]

depends on the definition you use

some would say differentiable means for all x in R

some say for all x in dom(f)

[idle widget]

Yeah that’s fair enough

[hot thistle]

that's why its a terminology thing

[idle widget]

It’s a pedantic distinction lol

Like math usually is

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[bright carbon]

Why can u remove all the logs and reduce the whole equation to just a quadratic?

[clear hound]

You're algebra is right, you just did a subtle error.

[rich tree]

You can remove logs because logs by definition are used to find the value of the power required to reach another number. As a result it is like saying an entire equation to the power of the same constant which means you can simply “remove the logs” as they have to be equal in the equation

[clear hound]

$\log (x(x + 2)) = \log(x^2 + 2x)$

[flat frigate]

M.

[rich tree]

This does not work if the logs are of different, so because they are all log 10 it is okay

[clear hound]

This was right. But you did: \
$\log(x^2 + 2x) = \log(x^2) + \log(2x)$

[flat frigate]

M.

[clear hound]

The log of a sum is not the sum of the logs.

You should end up with: \
$\log(x^2 + 2x) = \log(2^3)$

[flat frigate]

M.

[clear hound]

@bright carbon, make sense?

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@bright carbon Has your question been resolved?

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[odd shore]

Hey there, stuck at this question; I understand what is being asked, but how would you derive f(4x) in the numerator? Thanks

[pallid nymph]

Chain rule perhaps

[twilit spindle]

Let $u=4x$, then use $\frac{\mathrm{d}}{\mathrm{d}x}\left[f(g(x))\right]=\frac{\mathrm{d}}{\mathrm{d}u}\left[f(u)\right]\cdot\frac{\mathrm{d}}{\mathrm{d}x}\left[g(x)\right]$ then undo the substitution. The result should now be trivial and Bob's your Uncle!

[flat frigate]

XxMrFancyu2xX

[odd shore]

that makes sense. Thanks!

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[twilit spindle]

yw! :))

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[lean otter]

Hi, I need feedback if I have solved this properly + if I should format my working out in a different way.
(HSC Maths Standard 11th Grade Preliminary task)
Note this was done on pen+paper but I just typed it up so anyone can read it, cheers!

Abackyard = Afull - (Ahouse + Afront)

= (32.48 x 22.86) - ((14.1 x 14.2)+(6 x 22.86))
= 742.49 - (200.22 + 137.16)
= 742.49 - 337.38
= 405.11m^2 (2.d.p.)

[lean otter]

Forgot to mention! the question is asking for the area of the backyard to 2dp

[finite wasp]

I think there's a slight mistake here. 6m is the distance from the front of the house to the road. I think you want the distance from the fence to the road in that part of the calculation.

[lean otter]

Ooh thank you for pointing that out! I will go fix that

Is everything else okay? Like the working out and all ?

[finite wasp]

The rest looks fine to me.

[lean otter]

Okay, thank you so much for your help!

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[heady bobcat]

Help me to solve this

Anyone?

[mortal sandal]

That's not a problem

It's just an equation

[safe radish]

@heady bobcat Has your question been resolved?

[ripe crystal]

yes

hi

[heady bobcat]

Hi

[ripe crystal]

so

you need to find R

[heady bobcat]

No

[ripe crystal]

sorry write the equation in terms of r*

[heady bobcat]

It's algebraic

Formulae

[ripe crystal]

yeah

yes

but we need to write it in terms of R

r*

[heady bobcat]

Yh

[ripe crystal]

indicated by the brackets on the right

[heady bobcat]

But r is powered by4

I mean 3

It's confusing

[ripe crystal]

lets put pi r ^3 to the numerator

[heady bobcat]

Than?

[ripe crystal]

so v = (4 * x * r^3)/3

dont mind this, its so i dont need to scroll

[ripe crystal]

multiply 3 ith V

giving 3v = 4 x pi x r^3

then move 4 x pi to the left side

so 3v/4pi = r^3

and then take out the cube on the right by cube rooting the left

cubert(3v/4pi) = 4

ill write it down hold on

[heady bobcat]

Ok ty

[ripe crystal]

here

[heady bobcat]

Ooh

Ok

I understand now

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[sly nebula]

Can you please help me with the following question, I am a high school student (Year 9). I am confused on how to find the answer (distance).

A plane flies at a speed of 650km/h. It starts from point A and flies on a bearing of 120 degrees for 3 hours. At that time how far is it:
i) south of A?
ii) east of A?

[lean otter]

Best first step is definitely drawing it out I'd say

[sly nebula]

I done that.

[lean otter]

Show

[sly nebula]

Ok one sec.

Sorry it's a bad drawing, i done it on laptop.

Anyways so what we have to work out if x.

@lean otter

[grim plover]

This looks wrong

[sly nebula]

Why?

[grim plover]

Cus he starts with 120 degree rotation (bearing means rotation right?)

[sly nebula]

Yeah

The plane starts at point A, as displayed in the diagram

[grim plover]

But it turns some distance later

[sly nebula]

Then flies 120 degrees at a speed of 650km/h

[sly nebula]

It doesn't

<@&286206848099549185>

Can someone help me.

[grim plover]

Okay ig

[sly nebula]

Khaled — Today at 7:33 PM
Can you please help me with the following question, I am a high school student (Year 9). I am confused on how to find the answer (distance).

A plane flies at a speed of 650km/h. It starts from point A and flies on a bearing of 120 degrees for 3 hours. At that time how far is it:
i) south of A?
ii) east of A?

@lean otter

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[polar knot]

ok this is a stupud question but how does one go from ya = y/2(x-a) to x = 3a

[polar knot]

i jusy dont get why it is 3ay/2 instead of 3a3y/2

from here

ay + ay/2 = xy/2

y/2 * (x-a)

[pseudo scroll]

Divide y on both sides and multiply 2 on both sides

Then it's just moving stuff around

[polar knot]

i lnow but why is it

[polar knot]

^

[peak estuary]

dont use -> when you mean =

[polar knot]

oh

oh i see no

now* thanks

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[ashen epoch]

how is the derivative of $\frac{2}{x} = -\frac{2}{x^2}$ furthest I can get is $\frac{d}{dx}=2*\frac{1}{x^{-1}}$ but I don't see how that turns into $\frac{2}{x^2}$

[flat frigate]

budtard

[hazy elbow]

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

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

[flat frigate]

B-eard

[hazy elbow]

Bring down the power and subtract 1 from the power

[ashen epoch]

but how is that equal to $-\frac{2}{x^2}$ where does the $x^2$ come from?

[flat frigate]

budtard

[hazy elbow]

$\frac{d}{dx}2x^{-1}=\left(-1\right)2x^{-1-1}$

[flat frigate]

B-eard

[ashen epoch]

ok The extended power rule I forgor.

Thanks.

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[jovial sun]

are there any fun maths equations to turn a number that could be any number to an equivalent positive value and if it is already positive then doing nothing to it?

[brave wolf]

define "equivalent positive value"

[jovial sun]

-90 = 90 or -5 = 5

but dont worry just got it f(x) = sqrt(x^2)

thanks 🙂

[brave wolf]

this function is also called absolute value, denoted with f(x)=|x|

[jovial sun]

huh?

[lean otter]

|x| turns x positive or leaves it as it is if it is already positive

|-5| = 5
|2| = 2

[brave wolf]

yeah, it's the function that fits your definition. It's defined piecewisely, for x>=0 it just returns x, and for x<0 it returns -x

[jovial sun]

cool 🙂

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[wise iron]

how can i prove .999999999 is equal to 1

[tardy mango]

is that supposed to be a recurring decimal?

Source: https://math.stackexchange.com/questions/1963064/0-999-1-what-is-the-secret

[brave wolf]

simply but less rigorously:
x = 0.999...
10x = 9.999...
10x-x = 9.999... - 0.999...
9x = 9
x = 1

[wise iron]

that makes so much sense thank you

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[crude star]

Prove that $\forall x,y \in \mathbb{F}$ we have $(-x) \cdot y = -(x \cdot y)$

[crude star]

what I did so far is

[flat frigate]

Calc II Victim

[crude star]

$(-x) \cdot y + (x \cdot y)$ can be rewritten as $(-x + x) \cdot y$ using the distributive axiom.

And we know that $(-x + x) = 0$, Hence,
$ = 0 \cdot y$

So $(-x) \cdot y$ is an additive inverse for $x \cdot y$

[flat frigate]

Calc II Victim

[crude star]

but like idk how this proves what Im tryin to prove

Am I missing another step

[hot thistle]

how do you write an additive inverse

e.g. what is the expression for the additive inverse of 1

[queen ingot]

What is F?

[hot thistle]

presumably a field

[crude star]

the inverse of 1 is just 1 no?

1 * 1 = 1

[hot thistle]

that’s multiplicative

i’m asking about additive

[crude star]

oh

(-1) + 1 = 0

[hot thistle]

so the additive inverse is -1

[quasi bison]

formally you need to also prove 0*y = 0 or invoke this result as a lemma if youve proved it already

[hot thistle]

so what is the additive inverse of (x*y)?

how do we denote it

[crude star]

ah alr

[crude star]

-(x * y) + (x * y) = 0

[hot thistle]

so

i’m looking for something simpler

the additive inverse is in the equation you wrote

it’s one of the terms

[quasi bison]

maximo are you sure you arent overcomplicating

[hot thistle]

i think they are conflating the behavior of an additive inverse with the actual notation for it

they seem to have the rest of the proof down and couldn’t get that last step to
||additive inverse of xy = -(xy)||
so this seems like an important distinction to make

[quasi bison]

ah

yes that is an important point

i think this might be more of a wording issue?

[hot thistle]

possibly

want to give it a short

shot*?

[crude star]

wait i dont get it

[crude star]

did i not prove that

doe

[hot thistle]

prove what exactly

your proof looks good

[crude star]

(-x) * y is the additive inverse of (x*y)

[hot thistle]

you just need to see that the additive inverse of xy is -(xy)

[quasi bison]

ok let me try to explain how i see the situation

[cosmic grove]

F is a field ?

[quasi bison]

@crude star please confirm or deny that i understand the situation correctly:
you were able to prove

(-x) * y is the additive inverse of x * y

but you were unable to go from that to

(-x) * y = -(x * y)

[crude star]

yes

[crude star]

yes

[quasi bison]

right

[crude star]

idk how to prove that

[quasi bison]

well

what does the notation -(x*y) refer to, in words?

answer as a complete sentence: The notation -(x*y) refers to _______________.

[crude star]

we distribute the negative to (x*y) ?

[quasi bison]

❌

fill in the blank and answer with the full sentence:

The notation -(x*y) refers to _______________.

[crude star]

The notation -(x*y) refers to the negative value of two products which are x and y?

[quasi bison]

❌

[cosmic grove]

No

[quasi bison]

do not overthink it

also do not use the word "negative"

[cosmic grove]

^

[crude star]

oh the inverse of (x*y)?

[cosmic grove]

yea

[quasi bison]

fill in the blank and answer with the full sentence:

The notation -(x*y) refers to _______________.

[cosmic grove]

for addition

[quasi bison]

i want you to say it

[crude star]

The notation -(xy) refers to the additive inverse of (xy)

[quasi bison]

ok

great

so now,
you yourself have proved that:

(-x) * y is the additive inverse of x * y

and you now have said that:

The notation -(x * y) refers to the additive inverse of x * y

are you able to connect the dots

[crude star]

oooooo

tysm

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[dense cedar]

during substitution in integration, do you adjust the limits of the integral if you convert from u back to x before calculating?

[lean otter]

its more proper to adjust the limits

[hot thistle]

you should always adjust for the notation to make sense

[empty gyro]

If I understood your wording correctly, then yes

[hot thistle]

but if you prefer to not adjust, you must go back to x

[empty gyro]

Limits of integration always need to be accounted for when changing the integrating variable

[dense cedar]

so if i go to u and back to x before calculating

i keep the limits of x right?

[empty gyro]

I guess if you're going x -> u -> x, you might not need to, but I have no proof.

[hot thistle]

if you make a u sub and don't adjust your limits, you can't say the integrals are necessarily equal

[lean otter]

in that case you dont need to but it wont make sense in the middle of the process (you're integrating wrt u but bounds are still in terms of x)

[hot thistle]

but you can keep the x limits for convenience and use those at the end, yes

[dense cedar]

yeah im doing calculus after like 2 years and i just remembered i have to adjust after like 10 questions but my answers were all correct

[lean otter]

to you it may be fine but to others and in general it wont make sense

[dense cedar]

so i came to this conclusion

[dense cedar]

yeah so its wrong notation

i got it

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[still nymph]

How to calculate roots from f(x)=−1200x²+x−20 ?

[abstract dust]

quadratic equation

[still nymph]

explain

[abstract dust]

do you know what it is

[still nymph]

yes

[abstract dust]

ok so just

plug the numbers in

[still nymph]

no

[abstract dust]

ah

do you know about complex numbers yet

[still nymph]

i tried

was wrong

wait

[hot thistle]

@still nymph what methods to solve quadratic equations have you been taught?

[abstract dust]

good question

[hot thistle]

i'm going to name a few and you tell me if they sound familiar
quadratic equation
factoring
completing the square

[still nymph]

f(x) = -1/200x² + x-20 | / -1/200
x² - 200x+4000

x1 = --100/2 + root of (-100/200)² - 4000 = 100 +-4000= - 4000
x2 = --100/2 + root of (-100/200)² - 4000 = 100 --4000= 4100

thats what i tried

didnt worked

was wrong

[hot thistle]

i have no idea what you just did tbh

first of all do you know what a root of a function is?

[still nymph]

root is zero points or root

[hot thistle]

a root of a function f(x) is a value of x that gives us
f(x) = 0

[still nymph]

yes

but how to calculate the roots now the zero points

I tried how I showed you but that was wrong

[hot thistle]

i know

just follow along with me ok?

[still nymph]

ok

[hot thistle]

so we want to solve f(x) = 0

so
-1200x^2 + x - 20 = 0

[still nymph]

?

?

?

???

[hot thistle]

a single question mark would suffice

[still nymph]

why is there -1200

[hot thistle]

what's confusing you

[hot thistle]

.

[still nymph]

my was -1/200

[viral loom]

Because you said it

[still nymph]

ahh

sorry

i meant -1/200

[viral loom]

Print the question correctly

[hot thistle]

ok

so $-\frac{1}{200}x^2 + x - 20 = 0$

[flat frigate]

maximo

[still nymph]

what is the so?

[hot thistle]

an english word

don't worry about it

$-\frac{1}{200}x^2 + x - 20 = 0$

[still nymph]

ok

[flat frigate]

maximo

[still nymph]

what to do after that?

[hot thistle]

now we can do any of the methods of solving i mentioned above

which do you know?

can you name them?

[still nymph]

i know pq formula

thats the only one

i know

[hot thistle]

$x = -\frac{p}{2} \pm \sqrt{(\frac{p}{2})^2 - q}$?

[flat frigate]

maximo

[still nymph]

yesss

[hot thistle]

ok

[still nymph]

that

[hot thistle]

what is p and q for us?

[still nymph]

p is x and q is -20

[hot thistle]

no

to use this formula we need an equation like:
x^2 + px + q = 0

[still nymph]

we have one

[hot thistle]

no

[still nymph]

.

[hot thistle]

do you know what a coefficient is?

[still nymph]

no

ahh

do we need to | /-1/200 ?

[hot thistle]

i don't know what this means

[still nymph]

making this -1/200 away

so we only have x²

[hot thistle]

yes

we want to multiply by -200

[still nymph]

ok

[hot thistle]

can you do that and tell me what you get?

[still nymph]

I got x² - 200+4000

[viral loom]

now you can complete the square

[hot thistle]

x^2 - 200x + 4000 = 0

and yes, you can use complete the square, but why don't you use the pq formula now?

[still nymph]

i got for x1 = 177,46

[viral loom]

You don't need to do the sqrt

leave it like that

[still nymph]

i did already

[viral loom]

100 + 20sqrt(15) is the solution you want to leave

not 177,46

[still nymph]

no

i need number

[viral loom]

what i said is a number

[still nymph]

but good number

[viral loom]

or does the exercises tells u to do an approximation?

[still nymph]

wait

[viral loom]

numbers are not good or bad

numbers are numbers

[still nymph]

I need to calculate the distance of A and B

[viral loom]

if the exercises wants an approximation then 177,46 is a good solution

and in this case i think it's ok

[still nymph]

ok

[viral loom]

but if it's to get the root

the roots are 100 + 20sqrt(15) and 100 - 20sqrt(15)

[still nymph]

ok i got 154.92metres

thanks

.close

[safe radish]

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[fading mirage]

Created the equation b(b+2)=3 (mod11) from the equations given (expanding out the dot product). Dot product of two vectors in Z11 should also be mod11, right? b being in Z5 shouldn't impact that?
Ended up with b=1 being valid, but have a friend saying that b=3 should also be valid since b=8 also fulfills the b(b+2)=3 (mod11) equation, and 8mod5 is 3. But b=3 doesn't satisfy our dot product equation - so that can't be correct?
Having trouble explaining to him (and myself, I guess) why that shouldn't work, any insight would be appreciated

[safe radish]

@fading mirage Has your question been resolved?

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[wet yew]

hiiii i could use some help on calculating the smallest distance between a point and a function

[wet yew]

i have the function f(x)=3x+2 and the point P(3,1)
the assignment states that i have to use d(x) to find the optimal distance

[split ether]

What have you tried so far?

[wet yew]

so i think i understand it but theres one thing in the method that i dont understand how ure able to do it

[split ether]

What is it?

[wet yew]

why is it that i can do 20x+4=0 instead of the whole equation

[split ether]

Generally a fraction is equal to 0 if and only if the nominator is equal to 0

That's what it's saying

So a/b = 0 is the always same as a = 0 given b is nonzero

[wet yew]

so if a fraction is equal to zero, the nominator has to be equal to 0 too

okay i think i get it

[split ether]

Right

There are times you would also need to make sure that the denominator is not 0

[wet yew]

now its just calculating the y coordinate to this x coordinate and then using the distanceformula for two dots right?

[split ether]

Yes

[wet yew]

ty alot bro

🫶

.close

[safe radish]

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[wraith prism]

Why did he add two common parts and xy?

F(x,y) means i didn't understand it. It is something like a function of mutuality of x and y

<@&286206848099549185>

[calm prawn]

uh what do you need help with good sir

ill try my best to understand it

[wraith prism]

Do you understand Hindi?

I integrated separately in this question which is pretty close to that answer

But i didn't understand why they were adding it

[calm prawn]

uh no sorry

i dont understand hindi

[safe radish]

@wraith prism Has your question been resolved?

[wraith prism]

Did you understand my problem@calm prawn ?

[calm prawn]

no sorry

[safe radish]

@wraith prism Has your question been resolved?

[wraith prism]

@calm prawn

I integrated f with respect to x and y separately

I have to find fx,y)

[safe radish]

@wraith prism Has your question been resolved?

[safe radish]

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[safe radish]

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[worn sandal]

I thikn I am over thinking this

It looks simiple but for some reason I cant do this

[twilit spindle]

it's an isosceles triangle, what do you know about the legs of an isosceles triangle? :))

[worn sandal]

2 sides are the same

1 isnt the sae

wait

12+5x

bro

may I get help plz

[twilit spindle]

so 4x+1=x+4

[worn sandal]

y

o

bruh im sped

I was overthinking it

[twilit spindle]

dw happens to best of us :))

[worn sandal]

yup

anways I solved it

thank you

.close

[safe radish]

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[peak crane]

\

[peak crane]

how do you find the power dissipated

ik the formula

but its saying my answer is wrong

i got 0.12

[heady basin]

p=iv

right

or p=ir^"

2

[safe radish]

@peak crane Has your question been resolved?

[safe radish]

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[remote kernel]

Just a quick thing

[remote kernel]

what do you call the ratio of 100%A - 0%B?

Is it 1:0?

so its just 1?

well, for mroe context, its for a dihybrid cross

and all of the posible offsprings are the same

so i assumed its 100% - 0% or 1:0 right?

[hazy elbow]

Seems right