help-33

[worthy obsidian]

no

you did 0-x right?

[ember saffron]

Because -52.244 m is the height

a we are referring to sea level that would be 0

this would mean the bird is starting underwater and diving further down'

[worthy obsidian]

32^2=2 (-9.8) x (0-x) (-9.8 multiply -x) =9.8 x

[ember saffron]

Okok let me step back and do it again

1024m^2/s^2 / 2(-9.8m/s) = -x

1024m^2/s^2/-19.6m/s = -x

Oh I see

its positive 52.224 m

[worthy obsidian]

ok this is one way to think about it

you measured all the things from the river

[ember saffron]

Did I do the problem correctly?

[worthy obsidian]

yes

[ember saffron]

Okok

[worthy obsidian]

but i am explaining a imp concept

if you want to know

[ember saffron]

Yes I would like to know

[worthy obsidian]

have you been told that gravity is always to be taken with a negative sign

[ember saffron]

not gravity

acceleration due to gravity

gravity itself is 9.8

[worthy obsidian]

but that is not always the case

lets say you were measuring things from the point where the seagull was jumping from

[ember saffron]

ok

[worthy obsidian]

what would you write the equation as?

[ember saffron]

is this a rhetorical question?

[worthy obsidian]

no it has answer

[ember saffron]

Okok

[worthy obsidian]

basically what i am trying to say is if you measure along the direction of gravity you take g to be possitive

[ember saffron]

Wdym by the position of where the seagull was diving

[worthy obsidian]

lets say i am standing on a building and measuring from top to bottom then i would take g=+ve but if i am measuiring from bottom to top then g=-ve

[ember saffron]

Like a clif?

cliff*

[ember saffron]

Wouldn't it be the other way around?

[worthy obsidian]

no

you can understand it by the seagull example

write the equation from both perspective

first from bottom to top which we did

then from top to bottom

[ember saffron]

Right but wouldn't the direction from the bottom to top be negative acceleration?

[worthy obsidian]

yes

[ember saffron]

Since we are moving the the negative altitude

Right so then wouldn't gravtiy be -9.8 m/s because its weighting the seagull down -9.8 m/s and not lifting it up 9.8 m/s

[ember saffron]

Also are you open to help me with another problem? I'm confused on how to find the correct equations to use

[ember saffron]

Ahhh I see

We top to bottom is we are talking about the relation from the ground

[worthy obsidian]

yes

[ember saffron]

not from the position of the falling object

[worthy obsidian]

you assume ground to be initial position

but from top to bottom you take the objects falling positon to be initial positon

[ember saffron]

This problem I just need the correct equation and then I could figure it out

but the next problem I need a lot of help on

55. has a lot of steps

[worthy obsidian]

why is it given in inches and ft lets convert it to m

1.7272

meter

[ember saffron]

For this is got Y initial = 0m, Y final = 1.1m, Time = ?, Acceleration = -9.8m/s

Does the guys height matter in this problem?

[worthy obsidian]

well his height doesnt matter

[ember saffron]

Okok

[worthy obsidian]

we will consider only his legs

consider his legs to be a point which goes up by 1.1 m

[ember saffron]

Right so his legs go up 1.1 m

I got the variables down

but idk which equation fits

because they all use velocity

which is not given

[worthy obsidian]

no one of them uses displacement

[ember saffron]

or are we assuming velcity to be 0?

velocity*

[worthy obsidian]

yes

initial velocity

[ember saffron]

then whats final velocity?

[worthy obsidian]

not needed

[ember saffron]

?

Ohhh

I think I know which equation to use

[worthy obsidian]

have you memeorized all of the equations or need to refer to them

[ember saffron]

but it still doesn't make sense to me

[ember saffron]

I have a physics sheet I'm allowed to use for tests and the ap exam

so I don't need to memorize them

[worthy obsidian]

when intial and final velocity along with time and accelaration is given or asked use the first equation
when intial velocity displacement time and accelaration is given use second equation
when intital velocity final velocity accelaration and displacement is given use third equation

in this question you have intial velocity displacement and accelration and asked time

[ember saffron]

Ok let me try to work through this this

Our equation is

X final = X initial + Velocity Initial x time + 1/2 x Acceleration x time squared

So to rewrite it

[worthy obsidian]

yes

[ember saffron]

1.1m = 0m + 0m/s x ? +1/2 x -9.8m/s squared x ? squared

[worthy obsidian]

yes

[ember saffron]

1.1m = 1/2 times - 9.8m/s squared x ? squared

[worthy obsidian]

nope

[ember saffron]

Oh

Ok what did I do wrong?

[worthy obsidian]

rmember the signs

[ember saffron]

ye

0 x ? = 0

[worthy obsidian]

this concept

[ember saffron]

??

[worthy obsidian]

before solving a kinematics question choose where you will measure things from

[ember saffron]

ok

Ohhhh

its positive 9,8

9.8

since its relation to the ground

not to the person?

[worthy obsidian]

where have you decided to measure from?

[ember saffron]

his airtime

so for low long he will stay in the air until he hits the ground

[worthy obsidian]

are you measuring from the ground?

[ember saffron]

Yes

[worthy obsidian]

so g would be negative

as g direction is from top to bottom

[ember saffron]

Okok

[ember saffron]

So what is wrong here?

[worthy obsidian]

since you are measuring height from ground it will be 0-1.1 = -1.1

[ember saffron]

Why -1.1?

I'm lost

don't u jump up 1.1 m and not down -1.1m

Oh wait

but 1.1 m is our ending

not our intial

so he is coming down at 1.1m

so its negative

[worthy obsidian]

yes

ok i have to go solve the equation for x and that is the time

[ember saffron]

Ok

Thank you for your help

I will probably ask someone else for problem 55 because that one is difficult af

[worthy obsidian]

try yourself now

you are ready for solving any question

all concepts you have need to think

[ember saffron]

Okok

thank you

before you go

My ending result if (-4.9m/s) -1.1m = time cubed

[worthy obsidian]

time squared write

[ember saffron]

no cubed

I had

-1.1m = t + (-4.9m/s) x t squared

[worthy obsidian]

2.2/9.8=x^2

[worthy obsidian]

whats t?

where you get te from

[ember saffron]

in the equation there is two t's

[worthy obsidian]

the eqaution is 1.1=1/2(9.8)xt^2

[worthy obsidian]

what is v intial value

[ember saffron]

0

Oh wait wait

@worthy obsidian so its the initial time also 0?

it confused me because it didn't state it was the initial time

there is no symbol

[marsh citrus]

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[lyric kelp]

how can i show something this obvious

[lyric kelp]

.close

[marsh citrus]

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[turbid galleon]

Can someone pls explain how to do B

[turbid galleon]

When I substitute y = 0, why does it not work

[red nimbus]

You are basically looking for the roots

You can use the zero product theorem

[turbid galleon]

So I should sub y = 0 and solve the quadratic equation

[red nimbus]

x+3=0
-x+2=0

Yea

[turbid galleon]

Thanks I got the answer

[turbid galleon]

B is 2 and c is -3 is that correct??

[red nimbus]

Yup

[turbid galleon]

But how do I find the line of symmetry

[turbid galleon]

Usually for these questions it's on a graph

But this does not have a graph so I can't just see the values

[red nimbus]

It is in the middle between the two roots

[turbid galleon]

Is it (2 + (-3) ) /2

[red nimbus]

yes!

[turbid galleon]

Tysm

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[red nimbus]

x = (2+(-3))/2 *

[marsh citrus]

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[stark trail]

What you try bro

[fallen ice]

well it was originally csc2x/cotx

thats as far as i got and then i got stuck

[stark trail]

Bro do you know double angle formula

For sine

[fallen ice]

oh i forgot

[stark trail]

sin(2x)=2cos(x)sin(x)

[stark trail]

Is okay, we all forget things sometimes

Earlier I forgot for 10 minutes anything about the whole entire yesterday. Thought I was losing it

My fish oil must not be working

[fallen ice]

would i also use the double angle formula here?

[stark trail]

Do it here

The next step, we don’t need it

[fallen ice]

oh ok i got that one

but the 2nd one i also had trouble with

[fallen ice]

can someone help me with this one?

[late geode]

you can apply the same thing

or alternatively do something like express x^2 in the form
k * (2x)^2
or do a sub like u = 2x

[fallen ice]

so would it be 2sin^2 x cos^2 x/x^2

how would i simplify it further though

[late geode]

it'd be 4 *,

[worthy obsidian]

limx--->0 sinx/x =1

[late geode]

the 2 gets squared too

[fallen ice]

oh so

[late geode]

same identity as you would've applied above

[fallen ice]

OH i see

tysm

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[cunning oak]

how do i do this?

[cunning oak]

i have to find the constants a,b

i got that a = b/sqrt(2)

[mellow crag]

if ur allowed to, i think l'hopital's just works

[cunning oak]

im not allowed to

[mellow crag]

ok

are you allowed calculus in any way?

[cunning oak]

no

the examples tell me to make the fraction 0/0 so asqrt(2) - b = 0 then manipulate what i got to find a and b

[red nimbus]

Maybe we can use a linear approximation

[mellow crag]

oh right

so if we can find the limit as x->1 of

(sqrt(x+1)-sqrt(2))/(x-1)

[cunning oak]

er i got a = 4 and b = 4sqrt(2)

[mellow crag]

then we'd be done (then just find the appropriate factor in front for a)

[cunning oak]

is this right

[mellow crag]

yeah

[mellow crag]

you can then simplify this fraction to get

[cunning oak]

oh dang

[mellow crag]

1/(sqrt(x+1)+sqrt(2))

[cunning oak]

ah

then use x = 1?

[mellow crag]

i feel like a linear approximation is still too 'calculus'-y?

[mellow crag]

yeah

[cunning oak]

can i ask another question?

[mellow crag]

sure

[red nimbus]

I just saw this method today lol so I proposed, especially because the term (x-1) appears

[mellow crag]

yh fair

but like in order to get the linear approximation the normal way to do it is to just differentiate

there are probably some obscure ways where you can get a linear approximation without differentiating

(or without like analysis)

[cunning oak]

i cant find an answer to this

[mellow crag]

yeah so the same method we did up there works for this one

realise that we can take the factor of a out so it's sufficient to find the limit as x->2 of $\frac{\sqrt{x-1}-1}{x-2}$

[elfin berry]

LY

[mellow crag]

then stare at the fraction for long enough to realise it simplifies

(if we're avoiding calculus at like all costs, and we haven't done like analysis basics, it's generally quite hard to do limits)

(so a lot of the time it does end up being that the fraction we have simplifies and we get something nice)

[cunning oak]

hmm

oh dang i looked at the question wrong mb

.close

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[cerulean drift]

hi so ik the formula

i got the intersection = 0.125

but i don’t how to get pr of B which is probability of at least one head

[still temple]

is the formula you are using

[elfin berry]

jl7up~

[cerulean drift]

yea

[still temple]

ah k

you first calculate P(A)
than you calculate P(B)

afterwards you calculate

,, P (A \cap B)

[elfin berry]

jl7up~

[still temple]

afterwards you substitute the values into this formula and youll get the answer

just the hint that the answer is a decimal (i would call it endless)

[solid fiber]

nice friends

[still temple]

huh

dorian can you continue to help the guy

i gtg

[marsh citrus]

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[marsh citrus]

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[brave spire]

if a divides b-x then does a+x divide b?

[dusky viper]

i dont think so

let a=2,b=8,x=4

[knotty trellis]

What makes you think it would

[still temple]

i dont think any addition or subtraction is divisible

[marsh citrus]

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[open seal]

the equation is D(q) = -q^2 -2q +517

Im just not sure what the q axis is?

Oh nvm I got it, it was 21.759, never heard it as q axis, always as x axis

.close

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[oblique void]

Why I integrate from pi to 2pi and the answer is opposite

[marsh citrus]

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[near elbow]

Guys, what does they mean? Isn’t b the same as letter A?

[main idol]

A and b are different letters

[royal flicker]

no it means intersection of the tangents

Like if u extend the tangents they will meet

[near elbow]

ohhhhh

so basically the intersection of the tangents with the points A and B that was previously answered in the first questionn?

[royal flicker]

Ya

[marsh citrus]

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[near elbow]

Thankyouuu

[near elbow]

Thank youuu

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[whole tapir]

Hi, I'm wondering what is the most efficient technique to solve this system of equations.

[velvet cedar]

Elimination should work fine

[royal flicker]

ur teacher is toxic for giving those numbers

[red nimbus]

I dont know about most efficient way but the cleanest would be to work with an augmented matrix imo

Observe the denominators

[whole tapir]

Does Elimination work on every system of equations?

[red nimbus]

Notice how you can multiply by 5, 61 and 221 to get rid of the fractions

[whole tapir]

you got a point

let me try

Now it looks easier

I think I need to learn how to work with an augmented matrix

I see people using that all the time

[red nimbus]

it's just this without a, b and c

just the coefficients

so you only focus on the numbers or have a better overview

[whole tapir]

So an augmented matrix is nothing but a cleaner format of the original matrix ?

I see

[red nimbus]

ye

[whole tapir]

because the augmented matrix allows us to do the Gaussian thing

I think

[velvet cedar]

You could do gaussian elimination with the equations as is. Row operations <-> combining equations in the system

[whole tapir]

Ok, what do we need an augmented matrix for ?

[velvet cedar]

But you definitely wouldn't want to write x y z out for every set of row operations

[whole tapir]

Ok I see

[unique basin]

Augmented matrix is used to write full linear equations in matrix forms

[whole tapir]

what about the non-linear ones ?

[unique basin]

The augmenting part lets you include the stuff on the other side of the equals sign

In general you dont use linear algebra techniques for non linear equations

Systems of non linear equations can require many different kinds of approaches

[whole tapir]

just like this, am I correct ?

[whole tapir]

really ?

[velvet cedar]

looks good

[whole tapir]

I'll continue on my own from this point onward. Thank you guys ! ❤️

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[dull sable]

Sort of a dumb question but can an integral equal a complex number? The real part of this complex number is the value of the integral I want

[main idol]

the left side is absolutely a real number with 0 imaginary part

the right side is not

so i don't know where you get "=" from

,w int 0 to inf 1/(x^3 + 1)

[elfin berry]

Results provided by WolframAlpha

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Requested by rie.mann

[main idol]

yea that looks like the real part of the right side

[dull sable]

I put it in quotation mark because I don’t know if it equals that

I just want to know if it’s okay to say the integral equals the left side and “omit” the right side

If not, must’ve done something wrong in the calculation

[royal flicker]

id assume integrals cant be complex as long as the integrand is real

cause the def is the area under the curve, which cant be complex

[dull sable]

Can it be possible to take the real part on both sides

[royal flicker]

wdym both sides

[dull sable]

Something like this

[royal flicker]

ya thats true

[royal flicker]

im just saying that the integral on the left shouldnt have a complex part

[dull sable]

Let’s say I is a convergent integral that equals some real number so can I say Re(I) =I

[marsh citrus]

@dull sable Has your question been resolved?

[marsh citrus]

@dull sable Has your question been resolved?

[main idol]

what's your question ?

[dull sable]

What do you mean by question,I already asked the question

[main idol]

oh it's the same I

yes Re(x) = x for all real values x

[dull sable]

So if that’s true, would this be allowed

[still temple]

Do you wanna know how to evaluate this integral

The equation itself is meaningless

[dull sable]

Well In evaluating the integral I got that equation

[still temple]

Then you did it wrong

i can tell you how to evaluate it the right way

[dull sable]

I just wanted to verify if the real part can equal the integral, if not that's fine but want to be 100% sure

[still temple]

no dude it makes no sense a real number cannot be equal toa complex number

i can surely use complex numbers to maks computations if there is no fucking up in domains any ranges of my functions but i do not get a complex number as a "result"

suppose you had to integrate sinx

you can write it as( e^ix - e^(-ix))/2i

because that doesn't affect the overall function it will be the same

[dull sable]

Maybe I messed up somewhere here

[still temple]

use partial fractions to evalute this

factorise it as (x+1)(x^2 -x + 1)

[dull sable]

I'm aware of doing it that way but here I tried using contour integration

This was the setup, but I’m still a beginner to these concepts

[dull sable]

.close

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[marsh citrus]

Please don't occupy multiple help channels.

[stark field]

guys

why denominator not change +/-

but it stayed the same

[stoic slate]

Why should?

You gotta know what |ab| is and what |a/b| is @stark field

[marsh citrus]

@stark field Has your question been resolved?

[proud basin]

easiest way to know if it works or not is just to plug in some random value p

[marsh citrus]

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[lean falcon]

pretty sure i am right with C

just wanted to confirm

<@&286206848099549185>

[dry prawn]

!15m

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Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[dry prawn]

but yes c is correct

[lean falcon]

got it my bad

[lean falcon]

thank you so mch

.close

[marsh citrus]

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[celest folio]

how do i get the derivative

is it (1/2)((x+1)/(x)

or (1/2) * the quotient rule

[limber hearth]

1/2quotient rule((x+1)/x)^-1/2

[still temple]

alternatively, do it implicitly

[tight furnace]

the square root of something is not 1/2 times that thing

or you're doing chain rule

[celest folio]

the latter

[tight furnace]

you have to use power rule on the outside

f(x) = sqrt(x), what's f'(x)

[celest folio]

1/2sqrtx

[tight furnace]

so g'(x) * 1/2sqrt(g(x))

g'(x) * f'(g(x)) ^

[celest folio]

is sqrt(x+1)/(x) the same as sqrt(x+1)/sqrt(x)

if so can i do just quotient rule here

[devout mauve]

might be easier to just write the fraction as 1+1/x

[celest folio]

ok this is a lot 😭

i hate algebra

[celest folio]

wdym

[devout mauve]

(x+1)/x is the same as 1+1/x

the second one is much easier to deal with

no quotient rule

[celest folio]

can you show me how

[devout mauve]

how what

[celest folio]

how do i apply this

[devout mauve]

well you differentiate sqrt(1+1/x) instead

[celest folio]

so sqrt2/sqrtx

[devout mauve]

what

thats not how fractions in text work

$1+\frac1x$

[elfin berry]

Denascite

[marsh citrus]

@celest folio Has your question been resolved?

[marsh citrus]

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[dreamy hull]

Hi, good afternoon, someone help me with this exercise pls?
Ex.4) State V or F (justifying): If R and S are relations of order in A, then:
(d) If R⊂S ∧ S is total order -> R is total order.

[marsh citrus]

@dreamy hull Has your question been resolved?

[craggy wolf]

The difference between a partial and total order is the strongly connected axiom, so does the subrelation necessarily satisfy this?

[marsh citrus]

@dreamy hull Has your question been resolved?

[dreamy hull]

not necessarily?

[marsh citrus]

@dreamy hull Has your question been resolved?

[delicate prairie]

if you think so then you should find an explicit counterexample

[marsh citrus]

@dreamy hull Has your question been resolved?

[marsh citrus]

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[bleak obsidian]

quick question, does 2n! mean (2n)! or 2(n!)

[upper gust]

$2n!$ would be $2 \cdot n!$

[elfin berry]

tobi

[digital robin]

wat

[bleak obsidian]

uh

[stark trail]

Tobi is correct

[digital robin]

well dang mb

[upper gust]

factorial only binds to the object directly after that

[stark trail]

recall FPEMDAS

factorial parenthesis exponent multiplication division addition subtraction

[slender socket]

Err, how would you apply factorial before parentheses? That would mean the factorial applied to just the ), which makes no sense

[gentle sierra]

idk tbh some people might say the parentheses are implied and 2n! is clearly meant to mean (2n)!

[digital robin]

thats what i thought

[bleak obsidian]

i mean the context is this if that helps

[upper gust]

no, you always use brackets

[gentle sierra]

it is ambiguous though

[slender socket]

I challenge you to find a calculator that does this

[gentle sierra]

a calculator would never do that, but often people writing math leave the parentheses unwritten

in lots of cases

my point is that it's ambiguous so you should be clear

[slender socket]

I can't say I've ever seen that

[gentle sierra]

in this case it is 2(n!)

im pretty sure

[bleak obsidian]

ok tysm

[gentle sierra]

hey some people write $\ln x$ instead of $\ln(x)$. $\ln x^2$ is therefore ambiguous

[elfin berry]

i can tea lore

[gentle sierra]

i think it's a perfectly valid question for @bleak obsidian to ask. it's not obvious imo, and seriously worth clarifying.

personally, i would write 2(n!) rather than 2n!

[slender socket]

I agree that no one should write ln x, but that's a different thing that people actually do in practice

[gentle sierra]

2n! is just awful. at least add a \, so it's 2 n! or something

[gentle sierra]

never said that. i do it all the time

[bleak obsidian]

i mean i would write ln x instead of ln(x), but writing lnx^2 is just bad

[slender socket]

(sin²(x) is also dumb notation while I'm at it)

[upper gust]

(good notation)

[gentle sierra]

yeah and that's kind of my point. if you write ln x, then you should be very careful when potentially ambiguous situations arise.
notation can be ambiguous when parentheses aren't clear. so the answer isn't always obvious. and parentheses can clutter things and they take time to write, so it's not as simple as write parentheses around everything like you're typing it into one of those tiny calculators.

[bleak obsidian]

https://tenor.com/view/sentiments-regrets-gif-10058350

[gentle sierra]

writing 2((x)^2)+3(x)-3 is dumb

[gentle sierra]

anyway, im glad you asked about this rather than try to prove an incorrect statement. good luck proving it

[bleak obsidian]

tyty 🙏

.close

[marsh citrus]

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[vague raven]

What's the value of sin∅.cos∅ if tan is equal to root 2 minus one

[slender socket]

How are tan, sin, and cos defined?

[vague raven]

?

[slender socket]

The 3 functions that you're taking about, what are they?

How would you write down an equation for each of them?

[vague raven]

If tan∅= √(2) -1 then find value of sin∅.cos∅

[slender socket]

If you answer my question then you'll work out how to solve that pretty quickly

[vague raven]

I know tan∅ is written as sin∅/cos∅

[sudden stirrup]

Maybe find theta first

If you want a hint, trigonometric functions are just illusions of each other

[slender socket]

That's probably the less direct way to do it, but it works

[sudden stirrup]

I mean idk how to proceed after doing $\frac{\sin\theta}{\cos\theta}=\sqrt{2}-1$

[elfin berry]

0_א

[eager tinsel]

we know tan

so making a triangle and finding other trig ratios is not difficult at all

[slender socket]

I was thinking tan = opposite/adjacent rather than tan=sin/cos

[wise musk]

i got an answer can someone crosscheck it

1/(2root2)

thought so

[eager tinsel]

oh lol

it is correct

mb

[wise musk]

oh nice

[wise musk]

no prob

[late geode]

how are you getting that?

[wise musk]

use sin theta = root(1 - cos^2theta)

[late geode]

what else are you applying

[sudden stirrup]

Wait is he finding the product of sin and cosine?

[wise musk]

i think thats abt it

[wise musk]

yes

[late geode]

oh

thought you wanted both sin(t) and cos(t)

[sudden stirrup]

I didn't notice the dot

[late geode]

read that as a comma

then yeh, its fine

[wise musk]

ohh

[marsh citrus]

@vague raven Has your question been resolved?

[sudden stirrup]

But how

[sudden stirrup]

And how would u find opposite and adjacent

[wise musk]

do you know about the pythagorean identities in trigonometry?

like sin^2theta + cos^2theta = 1

[sudden stirrup]

Yes

[marsh citrus]

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[native iron]

Confused what is happening here

why did the y sec^2 y suddenly turn into (y-1)

[sinful thistle]

it... didn't?

y sec^2 (y) - sec^2 (y) = (y-1)sec^2 (y)

[native iron]

why is there a y-1

oh is it just doing some weird way of showing that they cancel since it equals 0 when you plug in 1

.close

[marsh citrus]

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[quaint sentinel]

guys how do i do this>

[late geode]

apply the property concerning the angles of an isosceles triangles
to set up an equation

[dapper escarp]

6x-15=2x+29

4x=44

x=11

[quaint sentinel]

thank u

[dapper escarp]

mhmm

[dapper escarp]

u got what i did?

[quaint sentinel]

yea

[dapper escarp]

since opposite sides of isosceles triangle is equal

[quaint sentinel]

the first equation then do the thingamabob

[dapper escarp]

both equations should be equal since opposite angles are equal in isosceles triangles

[quaint sentinel]

alr

[dapper escarp]

@quaint sentinel

[quaint sentinel]

tanks

[dapper escarp]

no worries!

[marsh citrus]

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[quaint sentinel]

.close

[marsh citrus]

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[topaz rock]

how to solve this problem:

[topaz rock]

given that 1 is approaching from the left, meaning that its gif if 0. then i substitute it

it becomes 0/(0-1)+0 = 0

is this correct?

<@&286206848099549185>

[still temple]

calculate lhl and rhl differently

oh wait they asked only 1-

i assume [x] is integer part of x

right answer but wrong method

[topaz rock]

yea

[topaz rock]

whats the proper method?

[eager tinsel]

didn't saw that 1- too☠️

[still temple]

answer is 0 no?

exact 0

There is a lemma saying that $\lim_{x\to a-} = \lim_{x\to a-\text{ and }|x-a|<\epsilon}$

[elfin berry]

uop

[still temple]

choose a small enough epsilon, then you simplify the expression inside

numerator exactly equals 0 so...

its exact 0/0 approaching

thats 0 exactly

[still temple]

yes, and the denominator is not 0, but it only works when x is close to a, hence the lemma

[still temple]

if numerator exaclty equals 0 then theres no other question arised

???

0/0.0000000000001=0

[eager tinsel]

you can't say the whole limit is zero unless, denominator is non-0

[still temple]

what?

numerator is exactly 0

and denominator approaches 0

so thats 0/0.00000000000000000000000000000000000000000000001

[eager tinsel]

it does not

[still temple]

which is 0

[still temple]

in this case it really doesn't matter, because the numerator is a zero constant

[topaz rock]

i dont understand

[still temple]

wdym it does not

[odd dagger]

hi

how do I do logrithms?

[still temple]

denominator is -1exact +1 approaching, which is 0.00001

but you may send the wrong message that the same argument works with something like x/x

something

[still temple]

whats your doubt

logarithm is whole vast topic

so, what you can say instead is $\frac{[x]}{[x-1]+x} = 0$ when $x$ is close to $1$ from the left, and it really has nothing to do with the denominator, as long as the denominator is not exactly 0, i.e. the expression is well-defined.

[elfin berry]

uop

[still temple]

thats what i said, literally homie 😭

thats what i said, that since the numerator is exaclty 0, and denominotr is a number that is NOT zero

so the overall limit is 0

@topaz rock did youunderstand?

[topaz rock]

if u guys mean that 0/1 = 0, then yeah lol

limits is so confusing man

i just dont understand whats the "proper" method

[still temple]

0(exact)/any number which is APPROACHING zero=0

this is not an indertiminant form

but 0 approaching/0 approaching

is an indeterminant form, and then u have to use methods to solve the limit

[odd dagger]

idk much about logrithms rules

[topaz rock]

ahh i see

[still temple]

take a clas

[topaz rock]

is the numerator 0 exactly?

[still temple]

yes

[odd dagger]

isn't this server where u can learn maths? 💀

[still temple]

1- means like 0.9999999999999999999

and gif of 0.9999999999 is 0 exactly , correct?

[topaz rock]

yup

[still temple]

well, we cant explain a whole ass vast topic like that, can help you with questions

logarithm has a whole world to itself

[odd dagger]

I see

[still temple]

i suggest, search up a lecture for logarithm in youtube

since logs are very important

[topaz rock]

thanks @still temple imma leave now

[still temple]

youre welcome

[topaz rock]

.close

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[fathom jay]

I'm doing a physics report where I measure the magnetic field strength and its effect on the time it takes for a simple electromagnetic train to complete a set distance. I need to derive a formula that can compare the directly this effect, but I am currently facing several problems, such as how to correctly calculate the work done by the magnets. Any help is appracited thanks!

[marsh citrus]

@fathom jay Has your question been resolved?

[marsh citrus]

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[fathom jay]

I'm doing a physics report where I measure the magnetic field strength and its effect on the time it takes for a simple electromagnetic train to complete a set distance. I need to derive a formula that can compare the directly this effect, but I am currently facing several problems, such as how to correctly calculate the work done by the magnets. Any help is appreciated thanks!
I'm doing a physics report where I measure the magnetic field strength and its effect on the time it takes for a simple electromagnetic train to complete a set distance. I need to derive a formula that can compare the directly this effect, but I am currently facing several problems, such as how to correctly calculate the work done by the magnets. Any help is appracited thanks!

[marsh citrus]

@fathom jay Has your question been resolved?

[fathom jay]

close

.clsoe

.close

[marsh citrus]

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[marsh citrus]

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[delicate smelt]

can someone help me find the area of fbgk and explain it

[delicate smelt]

can someone help me find the area of fbgk and explain it

[lucid turret]

bro what

[hidden dawn]

can u atleast describe

[proud basin]

!xy

[marsh citrus]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[lucid turret]

bro uses ms paint for making diagrams

[delicate smelt]

this is the diagram

[proud basin]

bro is tryinf to summin a demon

[lucid turret]

much better lol

[proud basin]

i cant type :(

[hidden dawn]

tryst me, FBGK was nkthing like what u drew

[lucid turret]

lol

[raw hawk]

Translate

Aaaaaaaa

[raw hawk]

There's no point E

[proud basin]

could you translate? google translate is kinda dum dum

[delicate smelt]

yes

abcd is a recangle, ak=ae, ef=fg=gc

i just need the forth

ak=kd=ae=4

ad=8=bc

[marsh citrus]

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[stark field]

Guys is this not homogenous f(x,y) ?

[marsh citrus]

@stark field Has your question been resolved?

[marsh citrus]

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[tawdry summit]

can someone explain to me how you do this question, pls?

[tawdry summit]

This is the answer, but i dont understand it

why is it PR instead of PQ? and wut is unit vector j

[void elm]

a unit vector is just a vector with length 1

the unit vector pointing from south to north is often called j

I'm not sure about the PR thing

that might be a typo?

I think it is a mistake yes

but you can do the same thing with PQ

[marsh citrus]

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[night lion]

cant solve

[night lion]

as book showed that the n<gif expression<n+1

how

[unreal geode]

I don't understand [bla] notation

[night lion]

[] it is gif functiob

floor function

[-0.5]=-1, [1.2]=1 e.t.c.

[marsh citrus]

@night lion Has your question been resolved?

[knotty trellis]

This looks wrong

oh wait

[night lion]

im cooked 😭

[knotty trellis]

does gif expression mean the expression inside of the gif?

not including gif?

[night lion]

yeah

yea

[knotty trellis]

ah alright then

so we only need to prove that

[night lion]

lemme write it n< sqrt(n^2+n+1) <n+1

[knotty trellis]

n^2 < n^2 + n + 1 < (n+1)^2

[night lion]

how did u square

[knotty trellis]

this is wrong. It has to be without []

[night lion]

the inside term

[night lion]

yeah without

mb

[knotty trellis]

i squared everything in the inequality

[night lion]

ohhh

[knotty trellis]

i squared n and n+1 too

[night lion]

fuck i am so dumb

https://tenor.com/i4DmDUnFKwy.gif

yea i am cooked

i got it

what u did

i just didnt think of it

i should have

...

[sqrt(n^2+n+1)] =n right

@knotty trellis why tho?

there isnt writte n that n is integer

[knotty trellis]

This is usually assumed when they use the symbol n

in context of limits

if n could be any real, then the limit wouldnt even exist

[night lion]

got it

btw

@knotty trellis

i solved it

but i have a question about it

i used the fact that since f(e^a) is gonna be meeting that point its value its 0

i replaced limit with x->0 and f(x) with x

and then i expanded the taylor series

took common x and got my ans

they used some weird derivative stuff here in the book

[knotty trellis]

I think your approach works

[night lion]

yeah

it did give me right answer

but im wondering

what does it mean when they did that

[knotty trellis]

idk what they did

[night lion]

wait lemme show

[knotty trellis]

there are some special cases though. E.g. f(x) = 0. In that case the whole thing wouldnt even be defined

[night lion]

what do you mean?

[knotty trellis]

I mean that if f(x) = 0, then the problem doesnt have an answer

or better, the answer is that the limit doesnt exist

[night lion]

yeah

this

then they simply removed the derivate f?

are they using the definition of derivative here?

[knotty trellis]

Holy

they applied l hopitals rule

:bending_skull:

[knotty trellis]

they assumed it's non-zero

factored it out

and canceled

[night lion]

oh

so they didnt used

anything about that statement

[knotty trellis]

yeah

[night lion]

dang

then i guess

i am smort

using that

[knotty trellis]

your approach is definitely less of an overkill

this is just ugly

[night lion]

pretty shady to do that tho what they did

[knotty trellis]

the only thing they used is that there is a tangent line, meaning f'(x) exists at that point

and around it

[night lion]

hmm got it

they used the fact that a tangent is there then it must be differentiable

thanks

.close

[marsh citrus]

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[main idol]

Stop advertising everywhere

[marsh citrus]

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[deft jewel]

hi

[deft jewel]

how do I simplify

this?

[desert dirge]

factorise!

[lone heart]

I don't think that's factorable

[marsh citrus]

@deft jewel Has your question been resolved?

[deft jewel]

OH shoot

not yet

i don't know how to factor it tho

thats my issue

<@&286206848099549185>

[echo karma]

pls again?

[deft jewel]

it says "solve"

[winged cove]

You have to find the value of y?

[deft jewel]

so how do i solve this

[raw hawk]

Complete the square

[deft jewel]

yes

[raw hawk]

Or use quadratic formula

[echo karma]

what can I help?

[winged cove]

This or quadratic formula

[deft jewel]

so, im going to be a sophomore in hs going into honors alg 2

my last math teacher did not teach the quadratic formula

in fact, on the final i couldnt answer nearly half the questions and got a 94% bc of the massive curve

so how do i.. figure this out, for lack of better words

[night lion]

what do u know

so far

in math

[deft jewel]

polynomials mainly

and also i briefly learned about simplifying with square roots

[night lion]

know how exponents work?

[deft jewel]

yes

[raw hawk]

Have you learned quadratic formula

[night lion]

for quadratic function

learn how to factorise

complete the square

quadratic formula

[deft jewel]

i'm sorry, i dont quite understand what you mean by complete the square?

[deft jewel]

i think this can't bef actored any further

[night lion]

google to learn more duh

[deft jewel]

sorry

it's just ive tried using resources and have been left confused 😭😭

.close

[marsh citrus]

Channel closed

Closed by @deft jewel

Use .reopen if this was a mistake.

[night lion]

https://www.khanacademy.org/math/in-in-grade-10-ncert/x573d8ce20721c073:quadratic-equations

@deft jewel

[deft jewel]

k

[still temple]

@deft jewel use the quadratic formula when yo8 can't factorise

[still temple]

Over here a is 1 <the number infront of y^2, b is 8 the no infront of y and -10 is c

[still temple]

This is the formula like they said

[deft jewel]

i see

[still temple]

It's in the form ax^2 +bx + c

Also u can use your calculator it Solves for you

Remember if B^2 -4ac is less than zero then there is no real answer and the root is imaginary

If u see the formula you'll understand why as you cannot square root a negative number

[deft jewel]

thank you

[still temple]

If b^2 -4ac is 0 that means there's only one value for x and if more than zero that means 2 values for x

[still temple]

You're welcome

[marsh citrus]

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[marsh citrus]

@magic jewel Has your question been resolved?

[ember siren]

Ai

[still temple]

just put the integral symbol, dont try to solve the integral out

unless you couldn't put the integral symbol....

[slim surge]

have you considered the axis of rotation y=4 and the fact that f(x) is sec(x) translated up by 4?

yeah you would have to translate the line y=6 too to y=2 and rotate around 0

[marsh citrus]

Channel closed

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[lunar jungle]

no

[lunar jungle]

oh shoot

I didn't know this was open

.close

[marsh citrus]

Channel closed

Closed by @lunar jungle

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[drifting musk]

32. A car moved from one city to another and turns back by using another way. First way is 48km and the second way is 8km shorter than the first way. In the return way, the speed of the car is increased by 4km/h. trip in the second way took Ih less time. Find speed of the car in first way.

[drifting musk]

<@&286206848099549185>

Nvm done it

.close

[marsh citrus]

Channel closed

Closed by @drifting musk

Use .reopen if this was a mistake.

[marsh citrus]

Available help channel!

Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[lean falcon]

so i need to factor this polynomial: x^2 - 3x - 28

[lean falcon]

would it be (x + 28)(x + 3) or (x + 4)(x - 7)

[hazy lion]

what have you tried

i mean, do you know how to check?

[lean falcon]

isn't it just the opposite

i used a calculator

[hazy lion]

the opposite?

a calculator is good

so is graphing

you could use wolfram here

in #bots

,w (x+4)(x-7) = x^2 - 3x - 28

[elfin berry]

Results provided by WolframAlpha

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Requested by janniku

[hazy lion]

[lean falcon]

ohhh okayy

[hazy lion]

or, just distribute

by hand

[lean falcon]

i get it thank you

[hazy lion]

np

[lean falcon]

i have another question if ur still here

so i have to divide these two

and (x + 4) cancels out right

does that mean theres a hole in the graph

[mellow kraken]

so long as x doesn't equal -4 (otherwise x+4=0 and you can't cancel zero

[mellow kraken]

yes, there's a hole in the plot at x=-4

[lean falcon]

okay got it thank you so much

[lean falcon]

wait where would the vertical asymptote be

<@&286206848099549185>

[broken zealot]

Yes @lean falcon

[lean falcon]

for this equation here would the vertical asymptote be x + 7

[broken zealot]

I'll figure it out

To find the vertical asymptotes, we need to look at the denominator. Vertical asymptotes occur at values of x that make the denominator zero, but not the numerator.

In this case, the denominator is (x + 4)(x - 7). Setting each factor equal to zero gives us:

x + 4 = 0 --> x = -4
x - 7 = 0 --> x = 7

However, we notice that (x + 4) is also present in the numerator. This means that x = -4 is a hole in the graph, not a vertical asymptote.

Therefore, the only vertical asymptote is at x = 7.

Let me know if you have any further questions!

@lean falcon does that help

[lean falcon]

is that chatgpt

[broken zealot]

Kinda

[lean falcon]

it's because sometimes its wrong so i can't go off that

[broken zealot]

I checked it

[lean falcon]

okay

@cunning fiber what do u think

[cunning fiber]

!nogpt

[marsh citrus]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[cunning fiber]

That’s what I think

But it’s right this time

[lean falcon]

thats why i said that

[cunning fiber]

Good I don’t need to pull up my host of examples lol

[lean falcon]

thank you man

[lean falcon]

lmaoo

[lean falcon]

sorry to bother again bro i'm trying to find the coordinate of the hole which is x = -4 in this case

i cant seem to find it

[cunning fiber]

,w x^3-21x^2+130x+600, x=-4

[elfin berry]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by civil_service_pigeon

[cunning fiber]

Is this the original

[cunning fiber]

Cause if so, the numerator is wrong

[lean falcon]

thats after i factored the polynomial

here's everything i did

disregard the wording stuff the work is the most important

the wording is just for me to understand better

[cunning fiber]

,w factor x^3-21x^2+130x+600

[elfin berry]

Results provided by WolframAlpha

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Requested by civil_service_pigeon

[cunning fiber]

,w true or false (x+4)(x-10)(x-15)=x^3-21x^2+130x+600

[elfin berry]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by civil_service_pigeon

[cunning fiber]

Take that as you will

[lean falcon]

wait i factored wrong?

[cunning fiber]

Yeah

[lean falcon]

damn bro

so that changes everything right

[cunning fiber]

Yeah

[lean falcon]

can you help me with this factoring here

i'm confused now

can you see everything

[cunning fiber]

,w x^3-21x^2+130x+600=0

[elfin berry]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by civil_service_pigeon

[cunning fiber]

Yeah uh

Have fun

Are you sure there isn’t a typo?

[lean falcon]

there has to be no way everything is just wrong

but where

like

hold on