help-10

[tardy epoch]

That's not how trig functions work at all

[long hedge]

$sec^2x sec^2y(y+x\frac{dy}{dx})$

[tardy epoch]

sec^2(xy) ia one term

[warm shale]

putridplanet

[tardy epoch]

Absolutely not

sec(xy) doesn't equal sec(x)sec(y)

[long hedge]

bruhhhhhhh

i se

$ysec^2(xy)+xsec^2(xy)\frac{dy}{dx}$

[tardy epoch]

...

sec(x)y does not equal sec(xy)

[warm shale]

putridplanet

[long hedge]

.

[tardy epoch]

Right

A+Bz=z. Solve for z

[long hedge]

$\frac{dy}{dx}=\frac{-ysec^2(xy)}{xsec^2(xy)-1}$

[warm shale]

putridplanet

[long hedge]

$\frac{dy}{dx}=\frac{ysec^2(xy)}{1-xsec^2(xy)}$

[warm shale]

putridplanet

[long hedge]

@tardy epoch

[obtuse pebble]

@long hedge Has your question been resolved?

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[slim cove]

.close

[obtuse pebble]

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[obtuse pebble]

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[timid silo]

A Ball is shot above the horizontal at an angle of 38.9. The height of the ball is above 10m after 1.2s. What are the two velocities at these times and what are these two times?

[timid silo]

Anyone have any idea on how I’d start this

I got velocity for 1.2s, is this right

got it

again to double check my work

the y velocity goes on top and x velocity goes on bottom right?

and they should add to that angle

this means im right... right..?

since i now have the x and y velocities

would i do a^2+b^2 = c^2 to get my velocity at that angle?

not at that angle

at that specific time of 1.2s

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[hard citrus]

can someone help with question e?

[plain stag]

fear not Austin

[fathom flicker]

if your symmetric interval

contains only .7286 percent of the data

then outside of your interval

must contain how much?

for understanding this value we shal prevail

if we divide by 2

we shall understand how much data is to the left of our interval, some would say inferiorly to -a

and if we know this value we can find -a itself

hiding in the shadows

waiting to be revealed

do you concur @plain stag ?

[hard citrus]

whoawhoawhoa foot on the brakes there buster

[plain stag]

idk if this is getting into !nosols territory but I don't disagree with any of that

[hard citrus]

1- 0.7286

[fathom flicker]

the 9 has inserted itself unambiguously into your text message

however it is false

[hard citrus]

oops

oh

[fathom flicker]

Indeed this is the total value outside so if we were to ponder on how much value is just to the left or just to the right it would be most logical steakanator that half of is on either side of the aisle

[hard citrus]

so divide it by 2

and look on the thing

lemme do taht

[fathom flicker]

else we might be teetering into a tyranny of non-normal distribution

[hard citrus]

i got 1.1

I think I did it wrong

[fathom flicker]

quite the interesting result. We can compare this to our knowledge of the empires distribution

if the result was 1 then how much data would fall between -1 and 1

[hard citrus]

68

%

[fathom flicker]

might it then be the case that adding an extra .1 to each side of our interval would add approximately 4% of data to our interval

perchance

perhaps not

[hard citrus]

mayhaps

[fathom flicker]

perform the calculation again and be surefooted in each of your moves

strike only with precision

and you will be certain in your result

[hard citrus]

aight lemme do it step by step

1- 0.7286 = 0.2714

0.2714 / 2 = 0.1357

I don't think there is such a value on the table

[fathom flicker]

we must ascertain whether it is true or not that such a value or one closely approximating it could lie hidden in the vast uncharted depths of our table

[hard citrus]

do I do 1 - 0.1357?

[fathom flicker]

for that would give you the right hand side which we duly note would also satisfy our ambitions for this solution

[hard citrus]

hmm

don't you still need to account for the 0.1357 on the right side though

since its on both ends

[fathom flicker]

my kind sir

if 1-0.1357 percent of the data

is to the left our particular goblin value hiding in the caves

then how much is to the right?

[hard citrus]

0.1357

[fathom flicker]

perchance it is exactly the 0.1357 percent that we are searching for

proceed fastidiously

[hard citrus]

however the 0.1357 does not appear to be located on the table kind sir

[fathom flicker]

with haste

for we do not seek 0.1357 we seek its stronger and much superior brethen

that which will produce its values to the right hand side of our table

[hard citrus]

ah

[fathom flicker]

recall forthrightly 1 subtract 0.1357

[hard citrus]

right away good sire

I have located it on the table to be 1.1 good sire

[fathom flicker]

don't be doctrinaire, if this culprit 1.1 seems to present himself when we search our problem from all directions, backwards and fowards, in reverse and from beneath

prechance it is truly our one true solution

[hard citrus]

blud is schooling me in english and maths

but does the 1 - 0.1357 not contain both (-a < Z < a) and the extra/2

[fathom flicker]

for a well rounded mind will allow one to approach your problems from a vast multitude more directions. if we could find a solution before in reverse, and now we proceed in a sphere like fashion, for what might you be able to ascertain when your mind has ascended our mortal dimensions? What new directions can you consider when searching for answers to the questions this universe presents you?

[hard citrus]

auuUUUUUGGgggh

[fathom flicker]

the value cooresponding to the 1-0.1357 is such a value that it contains .1357 percent of the data values to its right. perchance this means its negative counterpart contains .1357 percent of the data to its left. if you interpret left and right to be negative opposites, this seems to be the only duly noted solution.

perchance

[hard citrus]

right

let me take a couple hours to process that

[fathom flicker]

Indubitably you will 🧺 as we do with all new information no matter how trivial

[hard citrus]

so when we refer to the table using the 1 - 0.135 what value are we trying to find

[fathom flicker]

Perchance it will reveal itself to you forthrightly in a dream

[hard citrus]

mm

[fathom flicker]

Indeed we are

[hard citrus]

Indeed we are trying to locate which particular value?

[fathom flicker]

A value in particular yes this is what we seek

What are our options?

Optimally this value we find will be one which aids us in our journey to our solution

[hard citrus]

A, or the space outside A

[fathom flicker]

Consider these the most important options

[hard citrus]

or -a < z < a

[fathom flicker]

Indeed

[hard citrus]

holup lemme draw the thing

coz i have a question which idk how to word

[fathom flicker]

Lead my brethren on a wild goose choose would not I

[hard citrus]

If you do 1 - 0.1357 are you not also counting the x/2

[fathom flicker]

For the most wild goose cannot be caught

[hard citrus]

I swear this a legit question

[fathom flicker]

And this is my most legitimate reply

For if you find a

The value with has x/2 to the right

Indeed -a has x/2 to the left

This most logically infers that inside of -a to a we contain 1-x of the data

Perchance this is what we sought from the very beginning

Do not get caught chasing goose when the golden egg is what you are truly after

[hard citrus]

yes

my dearest dearest apologies sire but my brain cannot grasp this confuddling brain-muddling concept that is evading my greatest efforts

ok so

[fathom flicker]

Good sir what if I asked of you to find the values which contain within them 68% of the data?

Would not your strategy be the same?

32% must lie outside

[hard citrus]

yes

[fathom flicker]

We forget the empire

16% on either side

[hard citrus]

yep

[fathom flicker]

For which value contains 16% to its left?

This will be -a

Or indeed we can find a instead

Perchance our table does not contain -a

It is not an exhaustive list

What percent of the data has 16% to its right?

Indeed 84% perchance

[hard citrus]

1 - a

[fathom flicker]

So if we find the value with 84 to its left

We have indeed found the value with 16 to its right

Congratulations

Indeed this is the golden egg we seek

[hard citrus]

1 is the closest value on the table

oh so that's one of the a

[fathom flicker]

1 is the exact value

[hard citrus]

OH MY DAYS

[fathom flicker]

Now

Forget not that this was merely an example

A piece of chicken for you to sink your teeth into

For understanding and supporting values

You have now tasted goose

Go find your golden egg

[hard citrus]

thank you so much 🙏🏿🙏🏿🙏🏿🙏🏿🙏🏿🙏🏿🙏🏿🙏🏿🙏🏿

[fathom flicker]

Apply the same traditions and techniques to a question regarding not 68% but 72. Whatever

Indeed you will prevail

Perchance

[hard citrus]

One day I aspire to have a fraction of your unlimited wells of patience

[fathom flicker]

Have it then you will

[elfin burrow]

the greatest help channel of all time

[fathom flicker]

For it should be I who aspires

After all it is you who helped me!

[ruby path]

the hell is happening

[hard citrus]

in what way have I helped you?

[hard citrus]

play along wit it

[fathom flicker]

You have grown my heart and my ambitions. I am more fulfilled knowing you are closer to your golden egg

[ruby path]

as was prophesized

[fathom flicker]

Is man not to be judged by how others judge man?

How else might I judge myself

Perchance

[hard citrus]

well it has come my time to say farewell good sire

[fathom flicker]

Farewell it is not

Simply it is a see you in another time

Indeed

.close

[obtuse pebble]

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[stuck herald]

how to approch this

please help

are 0.21 is same as 34% 16% etc are on normal distribution like i mean is it probability?

<@&286206848099549185>

[zenith spade]

Yes it is probability

[unique nebula]

Read a textbook

[stuck herald]

oh i got it

.close

[obtuse pebble]

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[royal basin]

!occupied

[obtuse pebble]

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).

[shadow wolf]

What do I do ? I can't draw it if I multiply by 200

[royal basin]

yeah ngl it's strange what they're asking of you lol

[shadow wolf]

What about this one

[obtuse pebble]

@shadow wolf Has your question been resolved?

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[scenic sand]

Is this a question

[tiny topaz]

yeah im really stuck

[scenic sand]

N mean natural number right

[tiny topaz]

yes

would it be A - {1,2,3,4,5,7,8} and B - {1,2,3,4,5,7,8}?

[scenic sand]

Hell naw

See we have two possible value of set A which is {1,2,3,4,5,6,7,8} and {1,2,3,4,5} so what's common here {1,2,3,4,5} so, A={1,2,3,4,5}

BUT IN B THERE IS OR SO

you need to fill all

[tiny topaz]

ohhhh

i dont know why i blanked on the "and" and "or"

makes sense

[scenic sand]

You need to understand why and , or are used

And means having same element in both

Or common elements

or mean all element of condition

[tiny topaz]

could you also help me out with another problem? I don't understand what some of the symbols mean

[scenic sand]

So A={1 to 5} and B={1 to 8}

[scenic sand]

Ok

Just remember in short
and :-represnts common
Or:- represents all

[tiny topaz]

I don't understand why K is part of the key when it is in AnC

[scenic sand]

Hmm

Anc mean common

And (Anc)' other element excluding common element

[tiny topaz]

but a common element of a and c is k right?

[scenic sand]

Yes

Lemme see

yeah But k is not common inB AND A

THATS WHY

@tiny topaz

[tiny topaz]

so i have to consider only the ones that are common elements in a c while also a b?

if its only in anc then its a correct element?

[scenic sand]

Question have asked (Anc)'U(BnA)' not (Anc)' only

Where U mean "or"

[tiny topaz]

ohhh okay I understand

I really appreciate all the help

[obtuse pebble]

@tiny topaz Has your question been resolved?

[obtuse pebble]

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[drifting merlin]

Hi

[drifting merlin]

I need some help understanding this

Can someone explain what they're trying to say here?

Idk why they suddenly said "the second premise would no longer be needed".

[obtuse pebble]

@drifting merlin Has your question been resolved?

[plain charm]

Can you provide the full worksheet

[obtuse pebble]

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[void dust]

Hello

[void dust]

Can someone tell me if this is correct

**

[wet flint]

yes its correct

[polar fossil]

what is Z*?

[wet flint]

all integers except 0

[void dust]

yea, what he said

:)

[void dust]

Thank you, have a great day!

.close

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[bitter bloom]

how would I find the constant c in this question?

[fossil crag]

What's the condition for P_N to be a PMF ?

[bitter bloom]

this is all we were given

[obtuse pebble]

@bitter bloom Has your question been resolved?

[unique nebula]

Read up on what makes a valid PMF

[obtuse pebble]

@bitter bloom Has your question been resolved?

[obtuse pebble]

@bitter bloom Has your question been resolved?

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[rancid leaf]

Hello good morning, I have to do the following exercise but I don't know how to proceed, could you please help me?

[rancid leaf]

Let (X, d) be a metric space and {X_n} be a Cauchy sequence in X. Suppose that there exists {C_n} C R such that:

(i) d(X_n, Yn) < C_n, ∀n ∈ N.
(ii) lim n→∞ C_n = 0.

Prove that {Y_n} is also a Cauchy sequence.

That's what I have done, I don't know if it's right.

[obtuse pebble]

@rancid leaf Has your question been resolved?

[rancid leaf]

.close

[obtuse pebble]

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[silver plover]

shouldn't the solution be Ke^at?

not, aKe^at

[ruby path]

I think they're just verifying that the solution satisfies the DE

[silver plover]

oh i see ok

thx

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[lime garnet]

question is determine whether the function is odd /even/neither

confused on how to determine on inverse functions

[ruby path]

Same thing, check if f(-x) = f(x) or f(-x) = -f(x)

[lime garnet]

what is cos^-1(-x) = to

cos^-1(x)?

cause cos(x)=cos(-x)

[warm shale]

jan Nejon

[lime garnet]

am i just meant to know this?

[ruby path]

well

you'd be told it generally speaking

you can still check if its even or odd even if you don't know this

You can check if $\cos^{-1}(0.5) = \cos^{-1}(-0.5)$

[warm shale]

jan Nejon

[lime garnet]

oh fair enough

thank you

.close

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[exotic swan]

Hey I’m having difficulty in what I should do first for question 3

Any help would be appreciated thanks !

[obtuse pebble]

@exotic swan Has your question been resolved?

[exotic swan]

hmm..

wait are the critical numbers just

5pi/4 and 7pi/4 since thats when the derivative is =0

but does anyone know what the second derivative test is?

[sonic spire]

yeah

[sonic spire]

if f''(x) > 0, and f'(x) = 0, then x is minima
if f''(x) < 0, and f'(x) = 0, then x is maxima

[exotic swan]

OHHH

so i do like the line thing for the second derivativee again

and see which one is postive and negative?

using the criticcal numbers above?

[sonic spire]

you are already given f'' function

just put the points in there

to see if its > 0 or < 0

[exotic swan]

5pi/4 and 7pi/4 correct?

[obtuse pebble]

@exotic swan Has your question been resolved?

[obtuse pebble]

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[cinder pendant]

what does it mean by sign varation? b)

[cinder pendant]

do i just see if its negative or positive?

theres no extreme points right?

[obtuse pebble]

@cinder pendant Has your question been resolved?

[cinder pendant]

.close

[obtuse pebble]

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[novel forum]

Hi guys

[novel forum]

Is this right?

[tepid mountain]

Can you write the question in a better form
Is it like this ?

$$2x+i(x+2i)$$

[warm shale]

Sherif Player

[novel forum]

Find x,y €R

[tepid mountain]

Yeah is the left hand side is this

[novel forum]

Yes

(7)

[tepid mountain]

It is different than the one there I think

[novel forum]

Oh sorry

My bad

[tepid mountain]

And if you are more comfortable talking in Arabic I can speak Arabic

أنا مصري أساسا

[novel forum]

اها

تمام

رقم 3

(3)

[tepid mountain]

اه تمام كدة حلو

[novel forum]

الحل صح او خطأ؟

[tepid mountain]

بشوفه

صح

@novel forum

[novel forum]

يسعد دينك

شكراً على المساعدة؟

[tepid mountain]

العفو

[novel forum]

،

كيف اسكر الروم

.clode

[obtuse pebble]

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[ember spade]

how solve: square root(x-4) not equal 0 ?

[tepid mountain]

You can solve it like equality but instead of the equal sign just a not equal sign

[ember spade]

i dont need say under square root is > than 0

i just need not equal

?

[tepid mountain]

Do you know how to solve it if it was like this
$$\sqrt{x-4} = 0$$

[warm shale]

Sherif Player

[ember spade]

ik

not equal same ok

agree

[tepid mountain]

If you can then solve it like this but the equal sing will be not equal

It is just the same

[ember spade]

ok thanks

.close

[obtuse pebble]

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[shell hill]

I got the answer for this, (2.236,2) but the answer key wrote it as (√5,2) (-√5,2) why did they not put decimals instead?

[shell hill]

how i got the answer

<@&286206848099549185>

[tepid quest]

you have to divide by two the two expressions

and then do the Inverse function

which is on a calculator ^-1

[obtuse pebble]

@shell hill Has your question been resolved?

[high lily]

exact values are preferred

[obtuse pebble]

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[obtuse pebble]

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[uneven igloo]

apparently these angles are wrong

[uneven igloo]

@abstract beacon

these are meant to be the angles

[abstract beacon]

those r right

theta is indeed 10, 110, 130

x=30 is also right, and x=360-30 too, but NOT: x=180-30, 180+30

@uneven igloo

[uneven igloo]

wait what

ur saying the person who did it was wrong

[abstract beacon]

yes

[uneven igloo]

how did u get that last one

[abstract beacon]

x=360+30

[uneven igloo]

how yk that

[abstract beacon]

bc cos has the same value every 360 degrees

so if x=30 solves then x=360+30 also solves

[uneven igloo]

i thought cos was only + in the 1st and 4th

[abstract beacon]

Take a guess where 360+30 is

[uneven igloo]

4th?

[abstract beacon]

think about it

[uneven igloo]

idk where to think

[abstract beacon]

Okay

point at 30 degrees

now add 360 degrees

how many degrees are in a full turn

what is 360 degrees' significance

[uneven igloo]

2pi

[abstract beacon]

R u trolling, thats not degrees

[uneven igloo]

yk what i mean

can u explain this using CAST

[abstract beacon]

Nothing i explain will make sense if u dont know what 360 degrees is

[uneven igloo]

yea ok 360 and what

[abstract beacon]

its a full turn my guy

[uneven igloo]

yeye

[abstract beacon]

nothing ever changes when you add 360 degrees

360+30 is the same angle as 30

[uneven igloo]

ohhh

[abstract beacon]

which is why they solve the same

[uneven igloo]

right

360 and 0 are the same

smartass

thanks

[abstract beacon]

Happy to help 👍

[uneven igloo]

my man

the other dude confused me

[abstract beacon]

not a man

[uneven igloo]

.close

[obtuse pebble]

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[shell arrow]

I'm still doing something wrong here and I don't know what

[shell arrow]

Exercise 9, minimum distance between P(4, 2) and the line y=2x+3 using Lagrange multipliers

[obtuse pebble]

@shell arrow Has your question been resolved?

[shell arrow]

I think the problem is the constraint. Idk if what I'm doing is correct

I tried many approaches but I can't get it right

[obtuse pebble]

@shell arrow Has your question been resolved?

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[wooden axle]

Hey guys sorry for the bother, I'm just really stuck e), I used chatgpt to double check my answers but it's changing up everytime and when I ask for explaination of how chatgpt got his different answers it just keeps changing up the answer, so I got for TanTheta = -12/5 and for CosTheta I got 5/-13 and chat gpt says it's 5/13 but I don't understand how it got positive 13 if we're in quadrant 3 which both x and y is negative

[eager niche]

For c I would interpret that to mean you only need one answer, the cos(theta) = 12/13 and sin(theta)<0 so you would only get one line going out

[wooden axle]

I'm still using CosTheta = 12/13?

I thought it ended at a) and that from b) on we're usiing sine of angle so SinTheta=-12/13 or -12/-13

[eager niche]

Also sohcahtoa is an acronym, you wouldn’t write that in an equation

I interpreted ‘the condition in b’ to mean there is one angle A that has a cos(a)=12/13 and sin(a)<0

[wooden axle]

Will I get in trouble if I write it down? it just helps me remember if o/a or a/h

[eager niche]

No, you can write it down, but don’t write it like that

[wooden axle]

so for b) it doesn't transfer the CosA=12/13 to the Sin and that I'm starting a new angle SinA-?

[eager niche]

No reread b)

[wooden axle]

Sine of the angle is negative

I would think of SinA=-12/13

[eager niche]

There’s two angles with a cos(A)=12/13 but only one angle that has cos(A)=12/13 and sin(A)<0 (between 0 and 2pi)

[wooden axle]

two angles with CosA which are in quad 4 and 1 and Quad 1 is both pos for sin and cos

but sin is negative tho

[eager niche]

Yes

Your logic for A and B is good

[wooden axle]

I wrote C for the same thing as I wrote in B

[eager niche]

But if angle A is either in 1 or 4, and in either 3 or 4, then where is it?

[wooden axle]

1...

WAIT

hu

oh 4

[eager niche]

Yeah

[wooden axle]

so I resolve using quad 4 instead of quad 3 so that 13 is positive?

so SinA=-12/+13

12 is negative and 13 is positive?

[eager niche]

Yeah

[wooden axle]

when there's a negative in a fraction how would i tell if one is negative and one is positive in the future?

because I thought if there was a negative sign on top then that means both denomination and numerator were negative

[eager niche]

You know the hypotenuse length from cah and soh,

[wooden axle]

I had 5 from last time

but I'm gonna resolve

[eager niche]

For d you know 13^2=12^2+b^2 from the Pythagorean theorem

[wooden axle]

yeahhh

and for b^2 i got 25

[eager niche]

Then I think it’s actually looking for soh and Toa in e

[eager niche]

Yep

[eager niche]

And yes this is why you get two possible angles from sin(a) and cos(a)

[wooden axle]

so for the cordinates can i use cos 12/13 so that 12 is A/X and H is r/hyponeous or do I have to use Sin=12/13 so that 12=O and 13 =h

[wooden axle]

but sin's angle is negative and cos is positive so it would only work in cos's quad

[eager niche]

CAH means cos(theta)=adjacent/hypotenuse

[wooden axle]

so it would be positive 12 over negative 13 since quad 4 is +x,-y?

[eager niche]

Yes so that’s how you’d do it in the future

[wooden axle]

so I can use that for E?

and D?

As you said CAH = A/H so CosTheta = 12/13

so 12 is A

and H is 13

but we're in quad 4 so -12/+13

[eager niche]

Yep then you know it’s a right triangle so Pythagoras

[eager niche]

No

[wooden axle]

huh 😭

[eager niche]

The cosine is positive 12/13 as given in A

[wooden axle]

yos

[eager niche]

So the only thing you don’t know is O

[wooden axle]

now my answers are both positive 😭

[eager niche]

Which would be -5 from sqrt(25)=+/-5 but we need a negative sin(A) =O/H

So what is soh and toa?

[wooden axle]

wait so we don't solve for Cos/Cah?

I thought we were still using sin

wait a min

[eager niche]

Cah, cos(theta)=adjacent/hypotenuse is given

[wooden axle]

but we switched to sin after b no?

or as that just one to help us

identify which quad it's in

[eager niche]

This

An angle always has a sine and cosine component

[wooden axle]

uhmm this is what i have now 😭

[wooden axle]

OMG SO

[wooden axle]

since they're opposite of each other ?

omg I'm gonna try again

[eager niche]

Your adjacent and opposite values are switched a=12

[eager niche]

You can think of cos(theta) as the x and sin(theta) as the y of a point

[wooden axle]

okay so I just solved it again

and I used Cos

instead of Sin

this time

so Cah = a/h

so 12 is a

and 13 is h and this time I was figuring out O

instead of figuring out A

and for Tan I got 5/12 and Sin was 5/13

but that's still diff from what Chatgpt said 😭

[eager niche]

Yep that’s right

Also chatgpt is kinda trash at math

[wooden axle]

There's no other ai for math thooo

[wooden axle]

THIS WAS SO HELPFUL

THANK YOU OMGGG

[eager niche]

So is that everything?

[wooden axle]

yes sir

Thank you so much

🙏

[eager niche]

Have a good night

[wooden axle]

you too

take care

.close

[obtuse pebble]

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[narrow badger]

Let 𝑓(𝑥)=5−𝑥^2,𝑐=−1,𝐿=4,
and 𝜀=0.35
.

Find a value 𝛿>0
such that 0<|𝑥−𝑐|<𝛿⇒|𝑓(𝑥)−𝐿|<𝜀

[obtuse pebble]

@narrow badger Has your question been resolved?

[narrow badger]

<@&286206848099549185>

[sacred barn]

!show

[obtuse pebble]

Show your work, and if possible, explain where you are stuck.

[narrow badger]

idk the question

[narrow badger]

don't hv any work

<@&286206848099549185>

[sacred barn]

You have to try something, anything

[narrow badger]

chatgpt is tripping and i genuinely got no clue

[sacred barn]

If you're so lost that you don't know where to start, you should start by reading your textbook or watching some videos on limits

Chatgpt is not going to help you with this

[obtuse pebble]

@narrow badger Has your question been resolved?

[obtuse pebble]

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[solar quest]

How do I do this?

[wispy wadi]

area of a triangle is base*height/2

so do a change of variable

either it's still a triangle or you can draw the new shape

also, you can use that x²-1 and f are even, so f(x²-1) is even

[solar quest]

Yeah I thought about this

But how would I calculate it?

[solar quest]

What do you mean change of variable?

[wispy wadi]

you need a change of variable to get the x²-1 out

you set like y = x²-1

and you get something*f(y) dy

the something is what's changing the shape

but it should be calculable from here

[solar quest]

After you do the change of variable what do you do?

I’m confused

[wispy wadi]

you draw the something*f(y)

but wait

[solar quest]

How are you supposed to draw it if you don’t have the full function?

[wispy wadi]

because you would have to draw it only in an interval where you would know what f would look like

f(x²-1) even so your integral is 2int f(x²-1)dx between 0 and 1
and it's kinda assumed that f(x) = -x+1 on [0, 1]
so that f(x²-1) = -x²+2 on [0, 1]

,w integral of -x²+2 from x = 0 to x = 1

[warm shale]

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[wispy wadi]

hmm where did I do dumb things

[solar quest]

Lol I did this

Then multiplied by 2

But it was wrong

[wispy wadi]

yeah that doesn't work

f(x) = x+1 on [-1, 0]
so f(x²-1) = x² on [-1, 0]

,w integral of x² from x = -1 to x = 0

[warm shale]

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Upgrade to WolframAlpha Pro!

Requested by not_melo

[wispy wadi]

1/3+5/3 = 2

must be that

[solar quest]

Oooo

Why do you have to do them seperately?

[wispy wadi]

the "f(x²-1) is even" part had something dumb inside it

without us realising

[solar quest]

Ohhhh

So it’s secretly odd

[wispy wadi]

no

it's def not odd either

[solar quest]

Then why can’t you multiply the 5/3 by 2?

[wispy wadi]

because it's not even

the reasoning f(x²-1) is even because both are even it's dumb, we were not taking into account that the x²-1 changes the interval

so we get different parts on each side and we don't have the same 0

x²-1 on [-1, 1] has value only in [-1, 0]

we're not "feeding" the same thing to f

[solar quest]

Oh ok

Thank you

[obtuse pebble]

@solar quest Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[dawn thunder]

partial fractions

what the heck happened?

did they just factor out and combine?

nvm i see it now

.close

[obtuse pebble]

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[echo swift]

Alright, i'ma use this ch to study up on 2nd order homogeneous differential equations. MY CHANNEL (I don't need any help, just studying on my own)

[mild bay]

alr

[echo swift]

So I'll just pretend I'm studying on my own

[forest sinew]

hey channels are a hot commodity here

sometimes we run out

you shouldnt take a channel if you don't need help

[echo swift]

oh but there are open ones ya?

[forest sinew]

for now

we run out almost every day

[mild bay]

@echo swift this is exactly why i was skeptical off the bat 😭

[echo swift]

well I'll take my leave when I see that there are no free ones

cool?

[forest sinew]

what is the purpose of taking a channel when you dont need help

this isnt a study server

[mild bay]

where does it say that

[echo swift]

just to study up. it's nice to just be able to bounce and see ideas and stuff out loud

[wind oar]

you can create a brand new server on your own using discord as like a study note server

• you can organize them too if you feel like

[echo swift]

I don't want any issues though. I just saw this ch open but if you guys want me to leave, that's fine. are yall pinged everytime someone opens a new ch?

hello?

[mild bay]

anyways let's study diff eqssss (i have yet to take calc 1 but ill try my hardest to follow along)

[echo swift]

aight lol I'll let you follow along then.

So I remember in class we talked about second order homogeneous DEs. We did $y''+3y'+2y=0$ and said let $y=e^{rx}$. I'ma try to work this out again

[warm shale]

JayRoc (The Hurricane Panda)

[forest sinew]

no

[wooden cipher]

I appreciate the sentiment of wanting to have a channel, but its also highly unlikely that most channels below the top 10 tend to get a new question answered

[echo swift]

well I asked because there's a number of students who are in chs who come to discussion

and in math discussion saying they've been waiting in chs without any help

(ofc idk how long, or if there pings, I was just curious)

So continuing. This almost looks like a polynomial I can factor. I'ma see if I can make it this way again

$y'=re^{rx}$ and $y''=r^2e^{rx}$

[warm shale]

JayRoc (The Hurricane Panda)

[echo swift]

Plugging it into my equation

$y''+3y'+2y=r^2 e^{rx} +3r e^{rx} + 2e^{rx}=0$

[warm shale]

JayRoc (The Hurricane Panda)

[echo swift]

Oh, then I can factor out the e^(rx)

$e^{rx} (r^2 +3r+2)=0$

[warm shale]

JayRoc (The Hurricane Panda)

[echo swift]

I know $e^{rx}=0$ can't happen. so now I'm left with $r^2+3r+2=0$ oh and that's the characteristic equation we talked about in class

[warm shale]

JayRoc (The Hurricane Panda)

[echo swift]

So if I factor this:

I get $(r+2)(r+1)=0 \rightarrow r=-2,-1$

[warm shale]

JayRoc (The Hurricane Panda)

[echo swift]

By superposition $y=c_1 e^{-2x} + c_2 e^{-x}$

[warm shale]

JayRoc (The Hurricane Panda)

[echo swift]

Anyway, that's the idea here

first time I was tagged by helpers tho so maybe not a good idea lol

[slim cove]

@echo swift if you want, I can just open a thread for you in #odes-and-pdes instead

I don't think opening a help channel for this makes sense

[echo swift]

oh no i'm ok, I was just kinda throwing ideas to ryu on a possible way to study

(i do sometimes go in my own server and do this tho)

[slim cove]

This channel is probably not the place to do it

[echo swift]

yeh i see

XD

[slim cove]

I made #1162230448223698944

.close

[obtuse pebble]

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[heavy citrus]

can anyone help me with this exercise? I just started statistics and I'm having trouble figuring out independence of events and how I should go about solving these types of exercises in general

[obtuse pebble]

@heavy citrus Has your question been resolved?

[heavy citrus]

<@&286206848099549185>

.close

[obtuse pebble]

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[shell ermine]

Can someone tell my what I'm doing wrong here, I turned the symmetric equations into parametric equations, then plugged them back into the plane equation and I get 0 = 2 which isn't a valid answer

[lavish patio]

everything

[shell ermine]

oh

[daring rock]

that's completely unhelpful. why even bother saying that?

[daring rock]

your method sounds good, can you show your work?

[shell ermine]

sorry if its a little messy i was writing with a mouse

[daring rock]

watch your x

x = -4 + 2t

you dropped the 2 when you substituted

[shell ermine]

ohhh

thank you!

[daring rock]

no problem 👍

[shell ermine]

.close

[obtuse pebble]

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[daring rock]

also it looks like your constant terms disappeared from the right side

[daring rock]

the -4 and the 6 in the next step

[shell ermine]

i just added 4 and subtracted 6 from the right side

to get 2

[daring rock]

oh right i didn't see you changed the rhs too

nvm 👍

.close

[obtuse pebble]

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[timid silo]

How would i go about solving the following equation?

[honest sail]

log

[timid silo]

So far, i've tried turning it into an equation of logarithms like this:

yeah

then you bring out the exponents

so it'll be 3x(log2) = (x-1)(log5)

but i'm not sure where to go from there

[brave bramble]

Don't let the logs throw you off. This is just a linear equation now

• Distribute fully
• Bring everything with an x to one side, everything without x to the other
• factor out x
• Divide the term on x

[timid silo]

ohh

i see

thanks!

.close

[obtuse pebble]

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[cloud shadow]

hey

whats up?

[timid silo]

Hi

[cloud shadow]

ok may I ask

what are you tring to find here

f'(x)?

[timid silo]

I was wondering whether this would be the correct approach or not

[cloud shadow]

let me see

[timid silo]

Yep. it's a multi step question but this is the first

[cloud shadow]

so i can see

you are trying to approach it with chain rule and product rule together

[timid silo]

Yeah

[cloud shadow]

so you want to find the derivative of (x+1)^2

[timid silo]

Of the whole thing

[cloud shadow]

so suppose (x+1)^2 = u

find u'

then let x-2 = v

then you can use product rule

[timid silo]

So (x+1)^2 * (x-2)

Hmm

I can't use the binomial formula here can I?

[cloud shadow]

i dont think so

[timid silo]

Any reason as to why?

@cloud shadow how's this?

[cloud shadow]

hey

let me have a look

yup thats perfect!

[timid silo]

When I do the 2(x+1) I keep the parenthesis right?

[obtuse pebble]

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[timid silo]

<@&286206848099549185>

if i could get some help 😦

[obtuse pebble]

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[timid silo]

<@&286206848099549185>

[obtuse pebble]

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[vernal shore]

Im writin out a matrix in overleaf with latex, and one of the rows is too long and wraps back around. how do i rewrite it so this doesnt happen (i expect by making all the numbers smaller in some way)?

[vernal shore]

this is the code

[kind hawk]

you could change the font size. or you could not write down D= in front of it

or instead write down \hat D which is defined as D*Deltax.

btw #latex-help

[obtuse pebble]

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[vernal shore]

missed that channel somehow

[obtuse pebble]

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[dapper venture]

The part of the solution I am confused about

is why they take out the -1/3

That would clearly affect whether the gradient was decreasing or increasing

.close

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[obtuse pebble]

@daring olive Has your question been resolved?

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[silent ibex]

what is the distance between (-3,2) and (5,8)

[timid silo]

d=√((x2 – x1)² + (y2 – y1)²)

[warm shale]

Modus

[silent ibex]

so i do √(-3-2)² +(5-8)²

[timid silo]

No, read the equation carefully

It says "x2-x1", not "y1-x1"

[silent ibex]

so i swap em?

[timid silo]

Yeah

Let's see if you're gonna swap them correctly though

x1 = -3 x2 = 5 y1 = 2 y2= 8

[silent ibex]

so i do √(-3-5)² +(2-8)²?

[timid silo]

Yep

no

[timid silo]

wdym yep???

Huh?

[lean wyvern]

Haha

[timid silo]

(-3,2) is x1,y1

(5,8) is x2,y2

What's the problem?

ok whatever works

The formula should be remembered as sqrt((difference in x)^2+(difference in y)^2) anyways

@silent ibex By the way this is literally just the Pythagorean theorem

[silent ibex]

I actually just cant understand maths

[timid silo]

Most people who think they're bad at math are mostly just disinterested

Kinda easier to understand a subject when you don't have to put effort in to focus on learning because you actually enjoy it in the first place

im sorry @timid silo i wasnt able to see it correctly. yes it's interchangeable

whatever works

[silent ibex]

I have failed all my maths tests i honestly try i just cant do maths

[timid silo]

:/

[silent ibex]

fr

[timid silo]

This certainly isn't the first time I've tried to convince someone that being bad at math isn't a thing

Like there's no gene for it or anything

It's a complicated mix of your current psychology, how you view math, your interest in math, what your education is like, etc...

[silent ibex]

it honestly doesnt click, it has to be spelled out at a primary school level for anyhting to go in

[timid silo]

What's wrong with that?

I always thought of this as the default way for math to be taught

[silent ibex]

it just moves way too fast for me, but im killin it with probability rn

[timid silo]

I'm gonna resist ranting about the education system again, I've done that so many times it has become an unhealthy habit

Don't forget to .close unless you have any more questions

[silent ibex]

.close

[obtuse pebble]

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[mellow remnant]

What are these called so I can look them up?

[obtuse pebble]

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@mellow remnant Has your question been resolved?

[void dawn]

i dont think there is a specfic name for this type of exercise

you are simplifying an expression

try googling 'simplification of expressions exercises'

[timid silo]

Factorisation?

[mellow remnant]

Okay, thanks guys!

[obtuse pebble]

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[modern sierra]

Not really sure what to do with this one

[obtuse pebble]

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[modern sierra]

<@&286206848099549185>

.close

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[runic seal]

I'm trying to understand slope, I know the formula is y2-y1/x2-x1 but in this example it doesnt follow that rule, but I feel as if it's correct, could someone help? I expect it to be -7-5/-4-2

[frail peak]

-7-5/-4-2 is an alternative way to put it

-7-5/-4-2 = -12/-6

as both the numerator and denominator is negative the term is positive

you can see it as 12 * -1 / 6 * -1 and you cancel away the -1

my asterisk disappeard

[runic seal]

Oh really? I didn't think about that, would you have an idea on why the example was backwads? Or was it intentional to not make it negative?

oh yeah sadly on discord asteriks are for making texts bold, idk how to actually put them to show

[frail peak]

it dosent order of points dont matter

people just like seeing positive numbers instead of negative ones

[floral pawn]

guys someone explain the formula for the area of the parallelogram with three given st. Lines

[runic seal]

Ahh I see, thank you for clearing that up!

[frail peak]

np

[runic seal]

.close

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[shadow lava]

i was hoping the u sub would cancel x

any suggestions?

[frail peak]

maybe integration by parts?

[royal basin]

i mean you could complete the substitution and end up with $\int u^2 e^{2u} \dd{u}$ but yeah integration by parts is the way to go here

[warm shale]

Ann

[royal basin]

whether you do the sub or not

(i think it's less headache-y to not do the sub)

[obtuse pebble]

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[rose iris]

I've tried solving 8 by using the method in 7

but I can't seem to be able to get anywhere

I think I'm doing the same thing

but the answer is supposed to be (- 1/7, -5/7)

[obtuse pebble]

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[rose iris]

.close

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[timid silo]

What does (⬜,0) say about x and y?

[honest flicker]

Uhhg

Y is 0

I think

[timid silo]

Indeed

So you can substitute that in

Replace all y's with 0's

[honest flicker]

2x=5x

[timid silo]

Yep

Now solve for x

[honest flicker]

.

Uhh

x=2.5x

💀

That sounds illegal

[timid silo]

It is legal

[honest flicker]

Oh

[timid silo]

But it's useless

Got any other ideas?

[honest flicker]

Wat if it's like

0

[timid silo]

Yep, that's the idea

[honest flicker]

OK

Is the answer just 0 then

[timid silo]

By the way if you said 2x=5x => 2=5 I was gonna point something out that might be useful later

If you divide an equation by something and then realise it has no solutions anymore that likely means that that something was 0

So it was illegal to divide by it in the first place

Another way to look at it is that each time you divide by something you have to split it into 2 cases: either it's not 0 and you can divide by it or it's 0 and you can just substitute

[honest flicker]

So cool

[timid silo]

The last method would give:
x is 0: 2(0)=5(0) => 0=0, this is a valid solution
x isn't 0: 2x=5x => 2=5, no solutions exist

So yeah long story short the answer is (0,0)

@honest flicker Unless you have any more questions, you can .close

[honest flicker]

MY CONNECTION NOOO

So is one of the points 3,4

Then 6,8

Idk

[timid silo]

It could be that, or it could be (-3,-4), or (6,8), or something else

[honest flicker]

Wat is the unit fate

4/3

[timid silo]

Yeah, it's as simple as that

I recommend you use the points (0,0) and (3,4)

[honest flicker]

Easy

Too late

I used 6,8 frfr

[timid silo]

By the way it looks like they're trying to give intuition for "speed" as "rate of change of distance"

d means "distance" and t means "time"

So you get v=d/t=4/3