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[summer dirge]

sure, you can always open a new one afterwards for parts 2 to 4

[robust light]

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[robust light]

if you are still here

when proving for multiplication with a scalar, should/could that scalar also be complex?

I.e. uT(v) = T(uv), u member of C?

[summer dirge]

yes

the scalar should be from the underlying field

[robust light]

okay thanks! 🙂

Okay so here is my answer for i)
If we let u=ax^2+bx+c and v= dx^22+ex+f, a,b,c,d,e,f in ℂ
We get that:
T(u+v)=((c+f),(b+e))
We can see that this is the same as for: T(u)+T(v).

If we check for sT(w)=T(sw) where w=ax2+bx+c, a,b,c,s in ℂ
We get that: T(sw)=((sc),(sb))
Which is the same as for: sT(w)=s((c),(b)).

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[robust light]

hopefully clear enough?

[robust light]

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[red pelican]

am i buggin

[red pelican]

easy math problem but i think i am buggin:
work out the value of (27 to the power of 4/3) - (16 to the power of 3/2)

i got 17 but idk the right answer i dont have a mark scheme

[alpine sable]

thats right!

[red pelican]

much thanks

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[clever wren]

I dont understand solving systems with substitution can anybody help me?

[robust light]

I think it would help if you had a more detailed question / example.

[clever wren]

oh alr I got one

3x+5y=13
2x+y=4
how do I get y?

[winter light]

From the second equation you can get y = ...

[robust light]

if you have 2 equations, and 2 variables

you can subtitute one of the variables in one equation with the information from the other

You have
3x+5y=13
2x+y=4

Rearrange the seconds one a bit:
3x+5y=13
y=4-2x

now you take the y in the second and "subsitute" the y in the first with that info, you then get:

3x+5(4-2x)=13

You now have an equation with only 1 unknown variable, so you can solve and get x = ?

after you found x, "subsitute" the value for x in any of the original equations to find y the same way.

[clever wren]

I think I get it thank you

[robust light]

3x+5(4-2x)=13
3x+20-10x=13
-7x+20=13
7x=20-13
x=7/7
x=1

[clever wren]

Do I close this now or?

.close

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[hollow blade]

Hello I have a question

[gloomy kettle]

what is it

[hollow blade]

2x+2 turn into 2(x+1)

why does it happen

or how can it happen

[gloomy kettle]

in (2x + 2) you can factor out the common factor 2

2x + 2 = 2(x + 1).

if you redistribute the 2 back you get 2x+2

[hollow blade]

okay I understan

Thank you!

[gloomy kettle]

You're welcome

[clear mantle]

Which linear inequality graphs the solution set shown? A y > 3/2x + 3 B. y ≥ 3/2x + 3 Cy<2/3x+ 3 D y ≤ 3/2x + 3

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[light ivy]

Is there a way to solve this without graphing? A shortcut like how:

• If the Line of Reflection = x-axis, just change the sign of the Point's y-value
• If the Line of Reflection = y-axis, just change the sign of the Point's x-value

I feel like there is, I have a strong feeling that there is, I just can't figure it out rn

[light ivy]

It isn't a super important question since I can graph it out or do it in my head, but it would take more time and effort

[maiden glen]

reflecting across y=-1 is the same as adding 1 to y-value, reflecting across x-axis, then subtracting 1 from y-value

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[light ivy]

wait huh, if i did that w/R(-3,-5) i'd just get R'(-3, -4)?

[light ivy]

.reopen

[maiden glen]

(-3,3)

(-3,-5) -> (-3,-4) -> (-3,4) -> (-3,3)

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[light ivy]

I see, thanks

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[hot trail]

Well since acceleration is the change in velocity over the change in time

then I would assume that $ a = \frac{\Delta v}{\Delta t}$

[ a = \frac{\Delta v}{\Delta t} ]

[ocean seal]

hamr

[hot trail]

So therefore 34*0.1=3.4, but thats not an option

[red reef]

then the correct value is not given

[hot trail]

Ok

[red reef]

the time

its the time in between c2 and c3 correct?

[hot trail]

Id assume so: 0.1 s

[red reef]

then for the given acceleration the final velocity is 3.4 ms^-1

[hot trail]

yes:
C3: 3.4
C4: 6.4
C5: 9
C6: 11.4

[red reef]

yes

exactly

[hot trail]

ok

[red reef]

wait

[hot trail]

Or do I do c3: (3.4+2.6)(1/2)(0.1)

And do trapezoid riemans sum

[red reef]

i don't think you have to do all that

[hot trail]

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[plush heron]

can someone please help me solve this

[median oar]

Looks like some trig identities

1 + sin2x looks like you can change it

To another form

[plush heron]

sin 2x = 2 sinx cosx

how does this help

[median oar]

Hmm

Interesting thing to note

Log_a(x) is positive on (0,1) if 0<a<=1

And negative on (1,inf)

[plush heron]

so does this mean that the we can get out of the absolute values

[median oar]

We also know that sin(2x) is bounded by -1 to 1

I’d probably try to

I don’t know exactly how to solve this but that’s what I would try

It doesn’t look particularly like triangle inequality so I wouldn’t try that first

[plush heron]

idk maybe check cases

[median oar]

Ooh this function on the left is an odd function

That could be useful

[plush heron]

solving this without the absolute values seems much easier

we would have

(1+sin 2x)(1-sin 2x)=0

if 0<= 1+sin 2x, 1-sin 2x <= 1

<@&286206848099549185>

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[last rampart]

how do I identify local min/max given of a function f with a constraint given the countour map

why are p and q minimums but R is neither

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[languid tapir]

i dont know what to do

[tacit arch]

Expand the denominator

[languid tapir]

does that mean multiply x+2 and x-4?

[tacit arch]

Yes

Then use the first limit equation

[languid tapir]

@tacit arch so it becomes ax^2+bx-24/x^2-2x-8 so a = 2?

[tacit arch]

Yes

[languid tapir]

k and then how would i solve for b

cause plugging in 4 make denominator 0

[winter light]

Exactly, if the numerator was not 0 you'd get number/0 which is ∞, but that's not your case since the limit is 7/3

Therefore you have to make 4 being a root of the numerator as well

[languid tapir]

im confused on what this means

oh wait does that mean I need to get an (x-4) in the numerator so they cancel out?

if so how should I do that

[tacit arch]

Factor the numerator or use polynomial division

Or work backwards from the limit being 7/3

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@languid tapir Has your question been resolved?

[languid tapir]

ty I got it right @tacit arch I got 1 more question tho, I'm confused why this is wrong

isnt theres no VA at -2 and 3 cuz of the black circle

or is some of the things I checked wrong

[tacit arch]

?

[languid tapir]

I had to select the vertical and horizontal asmptotes but my current answer is wrong

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[vernal kite]

This is my teachers solution for trinomial factoring by grouping but instead of 2 and -12 I did -4 + -6. My answer came out wrong

[vernal kite]

So is 2 and -12 the only right answer

Or factor thing

[jagged cobalt]

you cant do -4 and -6

since their product is 24, not -24

[royal meadow]

yeah there's only ever one way to factorise things like this

[vernal kite]

Oh ok

Thx

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[rustic rivet]

Is this correct so far

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[keen oasis]

how do i solve this, cant seem to figure it out i know the midpoint formula and others but i didnt learn how to deal with 7/10th of a point

[foggy copper]

have you worked out the length of the line QS yet?

[keen oasis]

nope but on the teachers answer key she didnt need to find QS

but qs is 448.07

[foggy copper]

hm

oh wait

yeah you odn't need QS

you know the horizontal distance from Q to S

so the horizontal position of V will be 7/10 of that

[keen oasis]

horizontal distance is 350 right?

[foggy copper]

and likewise the vertical change

ye

[keen oasis]

ohh ok got it

it was such a simple question

🤦

[foggy copper]

don't feel too back

*bad

i started by rambling abt something irrelevant

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[long umbra]

where do you get the 5 from?

[long umbra]

the highlighted

[limber flint]

how do you know these are equal with work?

[charred jewel]

trig identities

your goal is to manipulate one side until its the same with the other side

[long umbra]

.CLOSE

.close

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[charred jewel]

oh wait its not even his channel lmao

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Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[long umbra]

.close

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[alpine sable]

something I'm noticing is that these 2 points actually represent a y=mx+b eqn

or a slant

^^ problem is I'm not sure if those points are included?

how do you tell

and I am getting the wrong answer doing that

like looking at it graphically

y/x

[oak chasm]

mx + b is a polynomial.

Polynomials are continuous functions.

The limit of a continuous function is just the value with what x is going to filled in.

[alpine sable]

wait a minute do you take the rise over run of the two points and find m then?

[oak chasm]

No.

[alpine sable]

by taking average ^^

of the two

somehow getting the answer

that way

-2/1 + 4/-1 divided by 2

[oak chasm]

[\lim_{x \to 1} f(x) = -2]
[\lim_{x \to 1} mx + b = -2]
[m(1) + b = -2]

[ocean seal]

Chai T. Rex

[oak chasm]

Do you see how I filled in x with what it's going to in the limit?

With a continuous function, you can just do that to get the limit.

[alpine sable]

so you know that x=1

hence why you subbed it in

[oak chasm]

No, not exactly.

[alpine sable]

wait kinda confused

actually no just keep talking that'll probably clarify

[oak chasm]

f is a continuous function.

With continuous functions, you can do this:[\lim_{x \to a} f(x) = f(a)]

[ocean seal]

Chai T. Rex

[oak chasm]

You just fill substitute what x is going to for x.

[alpine sable]

because that's what it goes to

[oak chasm]

It's a way of solving limits.

[alpine sable]

okay

[oak chasm]

Yes, but this only works for continuous functions.

[alpine sable]

okay then so now we have our

y=m(1)+b

what next

or actually

-2=m(1)+b

-2=m+b

[oak chasm]

[\lim_{x \to 1} f(x) = -2]
[f(1) = -2]
[m(1) + b = -2]

[ocean seal]

Chai T. Rex

[alpine sable]

wait a mintue are you doing it for the other one

[oak chasm]

You're right.

[alpine sable]

and adding it up

actually thats kind asmart

lemme try that

4=-m+b

-2=m+b

adding gives

2=b

[oak chasm]

Almost.

4 - 2 = 0m + 2b

[alpine sable]

ohh ok

[oak chasm]

If you add the equations together.

[alpine sable]

2=2b

b=1

[oak chasm]

Right.

[alpine sable]

-2=m+1

-3=m

ahhhh okay

this approach makes more sense

than whatever i was doing before

lol

thanks

[oak chasm]

You're welcome.

[alpine sable]

.close

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[mossy raptor]

So apparently the answer's 9pi/2 and I got 9pi

Where did I go wrong in this?

[mossy raptor]

^Start

[alpine sable]

seems like fun math lmao

[mossy raptor]

lmaoo welcome to calc 2

[alpine sable]

in calc 1 rn

lol

[mossy raptor]

ayyyyy

Imma be honest
Calc 1 doesn't prepare u at all for calc 2

[alpine sable]

idk like it seems not enough to make a math course

but maybe that's because I've just started

[mossy raptor]

Yehh calc 1 overall has less stuff
And then calc 2 they combine rotating volumes, sequences/series, a bunch of other stuff that looks hard etc

[alpine sable]

looks beautiful honestly, looking forward to it

[mossy raptor]

Yo pro tip btw, while u still got time
Memorize trig formulas
Like if u look up trig formulas you need to know for calc, like double angle, half angle etc
It'll make your life wayyyy easier in this class

[alpine sable]

oh yeah no I got that down in a different math class

basically know it like my name

[mossy raptor]

Ok thats good thats good
You'll prob do well then yee

[alpine sable]

hopefully lol, gl with it

[mossy raptor]

Thankthankkk
Gl with calc 1 as well ye ^^

[alpine sable]

thx : )

[mossy raptor]

:]

[mossy raptor]

Anyways yehh looked thru this again guys, and I honestly have no idea where I oculd be missing a 1/2

Like legitimately no idea

[ionic lava]

how did you get from the 2nd to last step to the last step here

[mossy raptor]

pi/2 - (-pi/2) = pi/2 + pi/2 = pi

Owait that one?

[ionic lava]

cuz its 1/sqrt(1-x^2) isn't it

[mossy raptor]

I mean arcsin(1) is pi/2 and arcsin(-1) is -pi/2 no?

[ionic lava]

yeah no I mean the other one

[mossy raptor]

Yeah thats the formula for arcsine integrals I thoguht

[neat grove]

It's not just sin inv

[ionic lava]

yeah it seems like you went from sqrt(1-u^2) to arcsin

even though arcsin is 1/(sqrt(1-u^2))

[neat grove]

Use this

It's int of √(a²-x²)
The general formula

[mossy raptor]

Ohhhhh I see I see

[mossy raptor]

Imma be honest, theres no way I can remember that lmao

Apparently the solutions use an entirely diffeent method as well

WIth the circle formula and whatnot

I just wanted to see if my path would work as well bc I got 9pi which looked close

[neat grove]

Yeah this is way easier

[ionic lava]

that's actually really clever

[neat grove]

And way better method😂

[ionic lava]

i would not have thought of that

[mossy raptor]

Yehhhhh Lool

Guess we learned smth today ye

Anyways Imma keep studying for my midterms

Thanks for helping ye🙏

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[amber isle]

confused on how to do this

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[zealous ingot]

Complete the square first

[amber isle]

.close

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[unreal sierra]

Complex nums. i thought it would be 1/13 which is 0.0769. Am i trippin or is mcgraw hill just wrong?

[unreal sierra]

<@&286206848099549185>

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[humble oak]

can someone explain one this one

[humble oak]

Im just stuck on the part after and so

[tight locust]

Which part do you not understand

@humble oak

[humble oak]

they justr multiplied by c'

right

[mortal trellis]

yes

[humble oak]

and mc' is just some integer

right

we can say x?

[mortal trellis]

yes

[humble oak]

ah i see

ok thanks

[tight locust]

So we've shown existence but not uniqueness

[mortal trellis]

well the solutions arent even close to unique

[tight locust]

It's a biconditional though, we still have to show that there exists a solution only if gcd(a,b) divides c

[mortal trellis]

well ok but that has nothing to do with uniqueness

[tight locust]

Yeah wrong word there

So suppose gcd(a,b) does not divide c. Then?

[mortal trellis]

a direct proof is better here

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[grizzled zephyr]

can someone help

i do not understand 2nd FTC at all

how the deriviative of antiderivative is f(x)

that doesn't make a single sense

this

[pseudo ice]

First part is saying “if you integrate then differentiate you get your original function back”, so like integration and differentiation are opposites

Second part is combining the first part with chain rule

If that helps? Or is it more applying it?

[grizzled zephyr]

when i find the derivative of an "antiderivative"

i get the f'(x)

right?

[pseudo ice]

Well you get f(x) if the original function was f

[grizzled zephyr]

can you show me how you solve 1 please

i do not understnad it at all

[grizzled zephyr]

they neglect the lowr bound

always

[pseudo ice]

Yep as it doesn’t really matter much what it is, as long as it’s constant

[pseudo ice]

For that you just need to identify what your function f(x) is and check the upper limit is just x, then you can happily say “it’s that function”

[grizzled zephyr]

i meant like can you show me the rules we apply

we first find the anti derivative of 3t^2 +4t

right?

then what

then what is "F'(x)

isnt F(X) anti derivative

[pseudo ice]

I’ll give you a slightly different example I’ll make up: the derivative with respect to $x$ of
[
\int_5^x{\color{green} \cos(t) }\dd t
]
Here you can identify that ${\color{green} f(x) = \cos(x)}$ so you know that $\dv{x} \int_5^x{\color{green} \cos(t) }\dd t = {\color{green} f(x) = \cos(x)}$

[ocean seal]

@pseudo ice

[pseudo ice]

Replace the green with any other function and it’s the same idea does that help?

[grizzled zephyr]

if i apply FTC 1

we should do anti derivative of cos then F(x) - F(5)

[grizzled zephyr]

bo 😭

no

[pseudo ice]

The whole point of the FTC is that you don’t need to do them explicitly (and many of these questions will deliberately give you integrals that are hard, if not virtually impossible, to actually find)

[tidal summit]

does this help

[pseudo ice]

Actually finding the antiderivative isn’t really applying the FTC as they want you to

[tidal summit]

F(a) is just a constant so it just vanishes

[grizzled zephyr]

so basically whenever i have a variable in the upper bound

i just replace that variable inside X

f(x)*

thats the 2nd FTC?

[tidal summit]

do you see the logic here tho

[grizzled zephyr]

yes

i took the derivative of F(X) and f(A)

derivative of F(x) gave me f(x) ( which doesnt make sense but ill memmorize it )

[tidal summit]

why not?

the derivative of the antiderivative of a function is the function

[grizzled zephyr]

antiderivative gives me f(X)

what is the anti derivative of f'(x)

f(x)

[tidal summit]

yes

[grizzled zephyr]

so how does the derivative of anti derivative give you f(x) lol

[tidal summit]

here f'(x) is the function

we are taking f'(x) 's antiderivative

which is f(x)

hence the derivative of the anti derivative (derivative of f(x)) is the function itself f'(x)

how do you define an antiderivative

[grizzled zephyr]

f(x) is f'(x)?

[grizzled zephyr]

idk the opposite of derivative?

lol

[tidal summit]

no

[grizzled zephyr]

am self studying calculus

so sorry 😅

[tidal summit]

the antiderivative of f'(x) is f(x)

[grizzled zephyr]

yes

[tidal summit]

the derivative of an antiderivative of SOME function is the function itself right

[grizzled zephyr]

yes accoridng to 2nd frcxc

ftc

[tidal summit]

the derivative of f(x) is f'(x)

think of it like this

the antiderivative of cos(x) is sin(x)

that means that

the derivative of sin(x) is cos(x)

F(x) is just notation we use to say the antiderivative of f(x)

F'(x) = f(x)

[grizzled zephyr]

kk thanks

i got it

ill go solve practice problems now

[tidal summit]

do you know why the FTC is true btw?

[grizzled zephyr]

if you ask me i do not know what is FTC

i only memorize

[tidal summit]

i suggest watching a proof of it

ill link a good one i saw

[grizzled zephyr]

mhm thanks alot

[tidal summit]

https://www.youtube.com/watch?v=mhb0epc6aFk

this one helped me understand why we even need antiderivatives lol

[grizzled zephyr]

thanks alot

i think i need a proof for limits too

and everything i learned so far

cuz i only memorized

barely understand any term

like what means differentiable?

[tidal summit]

been there

you can ask me questions in dms if you want

[grizzled zephyr]

i would appreciate that alot

can I friend you?

[tidal summit]

sure

[grizzled zephyr]

thanks alot man!

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[thick sigil]

how to solve this further

[modern skiff]

you find any common terms in this?

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[slow root]

Can you guys guide me towards learning techniques involved in 3d plotting ( to understand the surfaces ), also what we can do regarding n-dimensional ones?

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@slow root Has your question been resolved?

[hearty quartz]

Did you want to use a computer programming language

For n-dimensional there is high dimensional visualisation that can be use

[slow root]

I am more concerned about understand those surfaces mathematically.
for example: I have got some lead that in order to understand an n dim surface we learn about its different prooerties eg extremas , gradients etc

[mystic swallow]

i think linear algebra is the way to go

not sure since ive just started it

but i think it might help

and definitely multivariable calculus

[slow root]

I have just restarted on linear Algebra as well. Though till now haven't found anything bugger than 3d. Have worked on level curves now

[mystic swallow]

hmm

okay

try multivariable

[slow root]

I'll check
Thankyou

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[modest aurora]

How am I supposed to do this?

well I know to find a, it's just the amplitude

so 110/2=55

but the markscheme says it is -55

[alpine sable]

i would probably find b first

[next elbow]

Bcs you start at the bottom

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[limpid abyss]

I don't understand number 5, is ABC can't change order of itself like BAC or ACB or it could change ?

[jovial radish]

in permutation order matters

[limpid abyss]

So the "ABC" part, order matters too?

[jovial radish]

yes

[limpid abyss]

Ohh Thank You

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[shrewd violet]

Hi guys, require assistance with this equation:
This has been all my progress on it so far and I've been stumped by this weird looking integral.

[shrewd violet]

I've also thought of using u substitution but I'm not sure how that'd work with y(x) as 1 of the terms inside of u

[mortal magnet]

try d/dxing both sides

[shrewd violet]

ok I've gotten to
a y^2(x) = b y(x) + c

there's no way quadratic is allowed in this situation right

wait

it is just quadratic isnt it

[mortal magnet]

it could in fact just be quadratic

I dont think y(x) is any more than one of two constants here

[shrewd violet]

nvm

I'm dumb

I took the derivate of -1/y(x) with respect to y

when it should've been with respect to x

Im going to head to sleep now, I'll ask again if things go to hell again

thanks for the inspiration

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[mortal magnet]

np

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[clear tendon]

Hi I I just need help with the 1sr question not the entire sheet pls just so I can understand the concept

<@&286206848099549185>

[mystic swallow]

!15m

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[clear tendon]

Can I ping someone now

[mystic swallow]

i mean, sure?

[clear tendon]

Can u help me pls

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[gentle willow]

can someone help

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[deft girder]

1+1

[cursive tide]

Can someone with knowledge on dynamical systems please explain why the fixed point a/2 has a velocity function given by the above (would expect the velocity function to be 2x-a) ?

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[spring stirrup]

do you help with calculus and computational methods?

[limpid turret]

Calculus most people can help. Computation, some maybe.

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[frozen pilot]

how do i derive x√sinx

[frozen pilot]

its the xth root not x times 2nd root

[maiden glen]

like this?
\begin{equation*}
\frac{d}{dx}\sqrt[x]{\sin(x)}
\end{equation*}

[ocean seal]

Desync

[frozen pilot]

yeah

is that sinx^1/x ?

[maiden glen]

sure, I guess

that notation isn't super clear though so I'd use brackets on paper

but yeah, it's just chain rule

[frozen pilot]

okay so how do i solve sin(x)^1/x

derive

[placid zinc]

Problem with this function is that the chain rule isn't very clear here

What's the outer function?

[frozen pilot]

bro idk whats the chain rule or outer function

[placid zinc]

You haven't been taught the chain rule? Wait, are you looking for a derivative?

[frozen pilot]

yes

idk the english names of mathemathical operations

or i do rather but not all of them

like the rules

[limpid turret]

Try $a^b=e^{\ln(a^b)}$

[ocean seal]

SWR

[frozen pilot]

oke so i get

e^ln(sin(x)^1/x)

what do i do with that

[maiden glen]

you can move the 1/x out of the log

[frozen pilot]

so use up the ln to move 1/x

in front of sin(x)

so i get

e^1/x sin(x)

[maiden glen]

the ln is still there

e^{1/x ln(sin(x))}

[frozen pilot]

okay so what now?

[maiden glen]

now you're just looking for the derivative of an exponential

d/dx e^(f(x)) = e^(f(x)) * f'(x)

[frozen pilot]

what i got the solution from my professor, can you explain this to me

looks like she ln's the full function

[maiden glen]

yeah, then just take derivatives of both sides

either way works

[frozen pilot]

okay thx

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[peak path]

anyone able to help me with this?

[fresh sand]

well have you tried anything?

[peak path]

idk

[fresh sand]

what part is not clear?

do you know how to graph a function?

[peak path]

not rlly

[fresh sand]

well, I suppose you should look at some materials before trying to graph them.

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[vapid steppe]

is there a way to use $\frac{1}{1-x}=1+x+x^2+x^3+...+x^n+...$

[ocean seal]

Jash

[vapid steppe]

.close

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[trail summit]

For the person helping me please help until the end because people just leave

[trail summit]

I need help doing these not sure what to do

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@trail summit Has your question been resolved?

[short fulcrum]

Which one do you want to start with

[trail summit]

c

[short fulcrum]

Well (f*g)(x) would be the same as f(x) multiplied by g(x)

I hope this helps

[trail summit]

hey if you donbt mind

can u do f

i got very similar to light purple

i think she made a mistake

can you tell me what you get

[short fulcrum]

Well, while I don't think we can give answers on this server, I will say that you should square (X+2)^2 into a quadratic and then multiply it by 2x+9

[trail summit]

please i can show you my work

its so weir di think she mest ti up

[short fulcrum]

Ok you can show your work. All I'm saying is that I can't show you the real answer and work

[short fulcrum]

does that say 44 or 94

[trail summit]

44

[short fulcrum]

Oh in that case, your answer is correct, good job 🙂

[trail summit]

can you help me find (f times g)(-1)

[short fulcrum]

Sure, which letter is that?

[trail summit]

f

[short fulcrum]

Oh well all you need to do is plug in -1 for x, since you already have the equation for (f times g)(x)

so that will be

2(-1)^3+17(-1)^2+44(-1)+36

[trail summit]

7

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[trail summit]

.reopen

[lone heart]

✅

[trail summit]

ios it correct?

[short fulcrum]

Yes it’s correct

[trail summit]

are you sure

no offence\

its cuz its a project grade

i need help with c

the second part

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[short fulcrum]

Yes the question is right

[trail summit]

can you check my answers for all of them?

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[spare crane]

wut happened here

[spare crane]

a just got squared out of nowhere?

[jagged cobalt]

(ab)^2=a^2 b^2 is all that happened

they removed a bracket if you look closely

[spare crane]

ohh i see ty!

thought they just added that by some weird rule

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[patent estuary]

Calc 2 improper integrals

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[patent estuary]

What

.reopen

I think I broke it

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[shadow verge]

https://en.m.wikipedia.org/wiki/Lanchester's_laws hi, could anyone help me out? I want to know what math topics I should study to learn about the lanchester laws for a project

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@shadow verge Has your question been resolved?

[twin nimbus]

@shadow verge do you have a background in mathematics, specifically differential equations? If not, what is the highest level of math you have attained?

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[willow cliff]

Is there a closed form solution for this?

[willow cliff]

expectation of log Gamma(x) for log-normal distribution

[tacit arch]

Did you plug it into Wolfram

[willow cliff]

yeah

ran out of time

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[brisk leaf]

can i simplify (-3x+4a)/a into (-3x/a) + 4

[fossil laurel]

$\frac{-3x+4a}{a}=\frac{-3x}{a}+4$

[ocean seal]

DerTheo

[tight locust]

Only if a is not zero

[fossil laurel]

yeah you can

[fossil laurel]

yeah

[tight locust]

If a is zero then you have some problems

[fossil laurel]

$\frac{-3x+4a}{a}=\frac{-3x}{a}+\frac{4a}{a}=\frac{-3x}{a}+4$

[ocean seal]

DerTheo

[brisk leaf]

ok ok thank you

[fossil laurel]

you can use .close now

[brisk leaf]

.close

[tight locust]

Your welcome

[lone heart]

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[storm gale]

Alvaro is 26 years younger than Hanita. 2 years ago, Hanita's age was 2 times Alvaro's age. How old is Alvaro now?

[storm gale]

I don't think my algebra is wrong. Maybe I'm misinterpreting the question?

[left isle]

almost

A=x-26 is good. your second equation, 2(x-2)=x-28 is not

2 years ago, they were both two years younger then they are now

but at that time, one was double the age of the other

i see what you did now hold on

did you plug in A-2 on the right and substitued?

[storm gale]

Yeah.

[left isle]

i think you might have them switched

hanita's age is 2 times alvaro's, so H=2A

but then add in the part that it's two years ago, so
H-2=2(A-2)

[tulip bone]

love ur name

btw

[storm gale]

Thanks lol

[tulip bone]

HAHAH

[tulip bone]

yes

[left isle]

yeah. now substitute in your first equation

[tulip bone]

why put now in italic

bro was like

focus up.

HAHAH

[left isle]

gotta lock in for maths

[tulip bone]

love it

HAHAHAH

[left isle]

adds some pizzazz

idk

[storm gale]

Ohhh I got it

Thanks haha

.close

[lone heart]

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[lone heart]

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[near umbra]

how to solve average velocity if the given is D=852km T= 1hr and 30 mins?

[split mantle]

What unit is velocity?

[near umbra]

wdym

[split mantle]

Unit for distance is km, time is s.

[near umbra]

A plane regularly takes off from Manila at 5:30 am and
expected to land in Zamboanga, 852 km south of Manila, at
exactly 7:00 am. What should the average velocity of the
plane be if it is to land in Zamboanga City on time?

thats the question

[split mantle]

Yes, are there any formulas that comes up in mind?

[near umbra]

the triangle one

for displacement,velocity, and time

[split mantle]

Use that.

[near umbra]

do I convert the time to seconds?

[split mantle]

Keep it as h.

[near umbra]

then its gonna be 1.30 because of the mins?

[split mantle]

What do you mean?

[real parrot]

1.5 since 30 mins = 0.5 hours

[near umbra]

oohhh yeahhh

sorry

so its gonna be 852 divided by 1.5

[real parrot]

yes

[near umbra]

the answer is 0.568

[real parrot]

hm so you have to change the units then

[near umbra]

what do I change

both of them?

[lone heart]

@near umbra Has your question been resolved?

[lone heart]

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[upbeat eagle]

Im struggling a bit on Ranges and Domains for Inverse Functions

[upbeat eagle]

Someone talked about, how the range of the f(x) is not equal to 1

How did they get that?

I understand its its asymptote

[snow cobalt]

because if you put a 1 in place of x you get a 0 in the denominator which makes the function undefined

[upbeat eagle]

Right

Then how would I calcualte the range of it?
Of f(x)
which is f(x)^-1 domain

[snow cobalt]

range of f(x) right?

[lone heart]

@upbeat eagle Has your question been resolved?

[lone heart]

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[real parrot]

!status

[lone heart]

What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[clear tendon]

2

[real parrot]

what have you tried?

[clear tendon]

finding fmax

Mu x N

So 2 x 9.8 to find N which is 19.6

[real parrot]

alright

[clear tendon]

Then 19.6 x 0.5 which fixes 9.8

But I’m not sure that’s correct

[real parrot]

absolutely

that is the static friction, since they've not mentioned coefficient of kinetic friction, $\mu_s = \mu_k$

[ocean seal]

Wither

[clear tendon]

I’m just confused now I have my 9.8 for Fmax how I continue to get the final answer

[tight locust]

Mu

[real parrot]

you need to counter friction

F - f = ma

[clear tendon]

Would friction be the same value then

Or something

Since friction only acts as much as the net force

[real parrot]

same value

cos no kinetic friction coefficient is mentioned

[clear tendon]

F - 9.8 : 2 x 5?

[real parrot]

yes

[clear tendon]

Sorry if this is a dumb question but how do I know whether it’s 9.8 - F or F-9.8?

It’s the direction right

[real parrot]

yes

so you need the acceleration right?

a = +5

[clear tendon]

Yea

[real parrot]

and

the acceleration is not due to the friction

[clear tendon]

Ah ok so positive acceleration so in the positive direction

[real parrot]

since it opposes relative motion

[real parrot]

yes

[clear tendon]

Thank u this is clear

[real parrot]

no probs

[clear tendon]

Can I ask u for some guidance on another question please this one’s quite wordy and I’m not too sure how to start it

[real parrot]

yeah sure

[real parrot]

alright

[clear tendon]

I think I would need to find Fmax first since I’m given the coefficient

[real parrot]

you need to use equations of motion here

[real parrot]

yes

[clear tendon]

Suvat

For the equations of motion

[real parrot]

yes

[clear tendon]

So it would be 1 x 9.8 = 9.8 then 0.25 x 9.8

[real parrot]

yes

[clear tendon]

Which gives 2.45

[real parrot]

ys

[clear tendon]

So is this the Fmax value

So the largest value the friction can be

Now I’m a bit stuck on how to go after this step

[upbeat eagle]

Yes- can we continue in dm?

[lone heart]

@clear tendon Has your question been resolved?

[clear tendon]

nvm it has.

.close

[lone heart]

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[stable warren]

I have studied the head to tail rule to add vectors...

Here my teacher mentions that rule... but I dont understand how he concluded that the result of the Head to tail rule will be an even longer vector...

Like; let me just draw it..

[hearty quartz]

It is not guranteed. It possible for two vectors to cancel out and result in a zero vector.

[stable warren]

Yes absolutely.

Only if they are unlike and parallel forces

[lone heart]

@stable warren Has your question been resolved?

[lone heart]

@stable warren Has your question been resolved?

[lone heart]

@stable warren Has your question been resolved?

[stable warren]

uh

[shadow verge]

Algebra, Geometry,

[shadow verge]

I can watch some YouTube videos on differential equations

[twin nimbus]

!occupied please open a new help thread and ping me there

[lone heart]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[stable warren]

hehe

[lone heart]

@stable warren Has your question been resolved?

[lone heart]

@stable warren Has your question been resolved?

[lone heart]

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[bleak pumice]

Help solve this?

[kindred cave]

x is 2.00582

[hushed locust]

!nosols

[lone heart]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[bleak pumice]

thats wrong?

also this question goes with it I guess

[chilly pike]

what have u tried

[bleak pumice]

I think its D, as I am doing trial and error and this is the only one that can be correct

[chilly pike]

i mean D is right

but trial and error shouldnt be your go to method

try setting up some trig ratios

with respect to theta

[bleak pumice]

Like?

Academic comeback is not happening 💀

[chilly pike]

if you want to find the angle measure theta

you need to find the angle measure of that whole angle

[bleak pumice]

sure

[chilly pike]

minus the angle measure of the small shaded part

if you refer to the whole angle as angle theta

then tan theta = 14/x

[bleak pumice]

yea

[chilly pike]

and then looking at the small white triangle

if you refer to that angle as theta

[bleak pumice]

oh yeah I see

[chilly pike]

tan theta = 2/x

so then your desired angle measure

[bleak pumice]

okay so that gets the first question

[chilly pike]

is arctan 14/x - arctan 2/x

and you can use that to solve for x

[bleak pumice]

call me stupid but

I got -7.25

[chilly pike]

x cant be a negative value

[bleak pumice]

ofc

but I put it in the calculator as it is on paper and thats what I got.

[chilly pike]

whatd you plug in the calculator

[ocean whale]

That's because you had a value stored in x

[bleak pumice]

well I cant NOT have an x value either I just found out

[ocean whale]

You don't need a calculator for that question, as it's a symbolic solution

You can plug in random values of x and calculate that

[bleak pumice]

Okay so I have no idea what im doing still

[chilly pike]

crossbit

do you know how to do optimization problems

[bleak pumice]

i dont even know what an optimization problem is

i have bullshitted math my entire high school career

and have somehow maintained a high B the whole time

explain?

[lone heart]

@bleak pumice Has your question been resolved?

[bleak pumice]

Can I just get the answer

[bleak pumice]

...

https://tenor.com/view/ace-ventura-looking-searching-find-jim-carrey-gif-20785150

[lone heart]

@bleak pumice Has your question been resolved?

[lone heart]

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[lone heart]

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[fervent quarry]

.reopen

[fervent quarry]

need help guys i suck at factoring 😅 im clueless and idk where to start, i need tips as well in dealing with factoring questions like these

[tidal summit]

mcqs r easy

clearly one of the factors must have +2y

cuz there is 2xy

and clearly 4y and 6 are in different factors

either -4y and - 6

or 4y and 6

to multiply to form 24y

so use process of elimination

[fervent quarry]

do you have any tips for me to get on this level of thinking

[tidal summit]

see how the things multiply

[fervent quarry]

its like foil sorta right but its 3 numbers right

[tidal summit]

also 24 y part uhhh aint it

4y and 6

and 2y and 3 play a role

like they all have to add up to 24y

so in that case

4y and 3 are in different factors

and

2y and 6 are in different factors

so that they multiply to form 12 y each

which add up to 24 y

[fervent quarry]

ok i konda get it

thank you

ill just pracrixe

[sonic salmon]

Yo do u still need help?

[lone heart]

@fervent quarry Has your question been resolved?

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[ancient hedge]

.reopen

[ancient hedge]

Im completely confused with solving integrals

The professor that taught it to us was really confusing and none of us got the lesson

[static fractal]

reverse power rule

[mystic swallow]

@ancient hedge keep in mind that the derivative of $cx^{n+1}$ is $cx^{n}(n+1)$

[ocean seal]

ren

[mystic swallow]

and the fact that the derivative of $c\frac{x^{n+1}}{n+1}$ is $cx^{n}$

[ocean seal]

ren

[mystic swallow]

hope this helps

[upbeat eagle]

Is it not just simple integration

and then add +c

......

[mystic swallow]

@upbeat eagle it is, but im assuming they don't how how to integrate

its mentioned

[ancient hedge]

Yeah our teacher really doesnt teach the class well and expects us to do homework😔😔

[mystic swallow]

it's fine

you'll learn

[ancient hedge]

Are there any possible videos that would help on this topic?

[mystic swallow]

watch 3blue1brown