help-23

[hidden steppe]

to write a formula

[lean ruin]

in terms of means "in this variable"

or using this variable only

[hidden steppe]

so write a formula for function h?

[lean ruin]

youve written a formula

YES

[hidden steppe]

for this variable v?

[lean ruin]

you have the answer there

YES

correct

[hidden steppe]

I still don't know what you mean with "variable v"

[lean ruin]

in that

in the formula, only V must be there

no X

no Y

no U

only V

[hidden steppe]

but what else could it be there?

[lean ruin]

U

or X

or Y

[hidden steppe]

U is the output

[lean ruin]

s

yes

so h(v) = u

that is correct

but its not in terms of V

its in terms of U

so we re-write it

[hidden steppe]

so what would it be if it said write a formula for h(v) in terms of x?

[lean ruin]

well how are the output and x connected?

lets say u = x2

so h(v) = u = x2

our answer would be h(v) = x2

youre overthinking this

[hidden steppe]

there is no x they are not connected

I just want to understand it

so I can solve similar problems

[lean ruin]

well its connected if i say it is

what is u or what is x outside of the relation?

noone knows

its arbitrary

because its not connected to the input

so its arbitrary

but because U and input are connected

its not arbitrary

its connected

[hidden steppe]

how is U and input connected?

[lean ruin]

u is output

input is input

[hidden steppe]

so the only connection is that they are both defined?

[lean ruin]

input and output are connected through function

[hidden steppe]

as input and output

[lean ruin]

yes

how are 1 and 2 connected?

[hidden steppe]

I wouldn't say they are it depends on the xoncetxt

they are both numbers

[lean ruin]

exactly

theyre both variables

depends on context

and the context question gives us the relation

[hidden steppe]

yes

[lean ruin]

hope this helps

goodnight

[hidden steppe]

well I think I understand it a little bit better atlaest

[hidden steppe]

goodnight thanks for the help

[lean ruin]

np

[rancid dagger]

https://cdn.discordapp.com/attachments/779496762406338603/1040386899929485422/caption.png

[lean ruin]

lmfao were u following

[rancid dagger]

Yes.

[lean ruin]

i dont give up easy eh

lmfao

[hidden steppe]

<@&286206848099549185> Could someone help me?

[lean ruin]

yea plz someone explain better than me. anyhow thanks for the convo bro bbye

[hidden steppe]

I think u explained well just having trouble understand the concept of this

[safe radish]

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[graceful urchin]

Hi I am having trouble on this trigonometry question asking for the area of triangle ABC with the given side lengths a=3, b=5, c=6. I assume they want me to use either law of cosine or sin but I'm not sure.

[lusty widget]

only side lengths given?

[graceful urchin]

yes

[lusty widget]

ok

pic of the qn

[graceful urchin]

not sure how

never used this before

one min

[lusty widget]

$\sqrt{s(s-a)(s-b)(s-c)}$

[flat frigate]

Springsskateboard

[lusty widget]

a b and c are ur side lengths

$s=\frac{a+b+c}{2}$

[flat frigate]

Springsskateboard

[graceful urchin]

how does that work?

[lusty widget]

it’s Heron’s formula

to find area of triangle with just the side lengths

[graceful urchin]

ahhh okay

we weren't taught that

[lusty widget]

ah

do u have a picture of the qn?

[graceful urchin]

so the area would be 7?

im on pc rn so idk if i can send a pic

[lusty widget]

,w sqrt(7(7-3)(7-5)(7-6))

[flat frigate]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Springsskateboard#8145

[graceful urchin]

lol figured it out

[lusty widget]

yeah it’s approx 7.48

unit squared

cm^2

ye the formula would work there

[graceful urchin]

i appreciate the help! thanks

[lusty widget]

np

[graceful urchin]

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[graceful urchin]

I need help explaining why I cannot use the law of cosines to solve this triangle with given ASA of 40 degrees, 20 degrees, and 13 cm

[thorn chasm]

Quite simply you have 2 angles and a side and the law of cosines requires 3 sides or 2 sides and a angle

[graceful urchin]

ahhh okay

makes sense

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[graceful urchin]

i am unsure my answer for this trig question is right so can you check it?

[pure agate]

Looks good to me.

[graceful urchin]

ok cool

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[devout palm]

Let P2(R) denote the subspace of F of all polynomials of degree two or less. That is P2(R)={ax2 +bx+c:a,b,c∈R}
(a) Find a basis for P2.

[devout palm]

hey guys

how would i put this in a matrix

plz

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[safe radish]

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[vivid dragon]

is that good?

the topic is optimization and modeling

it also asks for circumference and radius of a circle

i have (2pi) (x/2pi)^2

idk if that’s right

<@&286206848099549185>

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[lean otter]

Can someone please explain the working out for question g) i.

[lean otter]

Why did they sub d into it?

[peak estuary]

cause it works?

you get the sum of the evens on the LHS and the sum of the odds on the RHS

so those sums are each some number x

and then with a) you see that x+x=2^n

[lean otter]

What do you mean it works?

Why sub in d specifically?

[peak estuary]

well it gives you the answer

[lean otter]

Oh nah

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[peak estuary]

I'm not sure what kind of answer you want

there is no deep reason why we use d. it works and that's why we use it

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[sand crane]

I'm having a lot of trouble understanding how to solve for x in equations. Currently I am doing a problem set at university and reached this point but I'm not sure how to solve for X which is a part of the question.

Can anyone talk me through how to solve for X when doing algebra?

[tiny wraith]

the only x that appears is in the right-most denominator right?

then just move the terms not containing x to the left side and multiply by 1.1^2

[sand crane]

So would it look like: x = 0.06/1.1 + 0.786*1.1^2?

And yes it's only on the right denominator

[tiny wraith]

you have to multiply the 0.06 / 1.1 by 1.1^2 as well

[sand crane]

I'm confused

[tiny wraith]

$0.786-\frac{0.06}{1.1}=\frac{x}{1.1^{2}}$

[flat frigate]

Jelle

[tiny wraith]

then multiply both sides by 1.1^2

[sand crane]

When you say both sides do you mean add ^2 to the 1.1 that is the denominator?

[tiny wraith]

multiply by 1.1 and then by 1.1 again

[sand crane]

I'm really not following this right now

Do I multiply the 1.1 that is under the 0.06 as in make it 1.1^2?

[warm linden]

Take 1.1 to LHS
So you multiply 0.786 x 1.1 = 0.8646
Now in RHS you have 0.06 + x/1.1^2 so by squaring 1.1 you get 1.21
Next take that 1.21 to LHS and multiply with 0.8646 so you would get 1.04
Now take 0.06 to LHS and subtract it with 1.04 which will get you x = 0.986

The left side of the equal symbol is LHS and the right side is RHS

[sand crane]

I'm going to continue to practice this thanks for your guys' help maths is something that I can't seem to understand even at a basic level

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[eager turret]

What should be the height of fluid inserted in a horizontally placed symmetric cylinder of radius r and length l so that 1/4th of volume of cylinder is covered by the fluid? (assume fluid is water)

[sudden birch]

What is the formula for the volume of a cylinder? Divide that by 4, and you will have your answer

Hint: volume uses area of a circle and length

[warm linden]

Volume of cylinder = pi r^2 h

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[toxic pulsar]

how do i solve this?

[tight quest]

just substitute -6 to x

3/(-6)+4

[naive raven]

a soccer team has 3 possible outcomes when playing a game, win, loss or draw, chances of winning is 80%, a loss 15% and a draw 50%

anyone know how to do this

[stray socket]

Poor man got baited

[toxic pulsar]

oh

thats what it meant

-6 is x there

oHHHHH

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[olive rose]

I don't understand what I'm supposed to do

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[vestal hornet]

can i write 2y+x = 16 as my first inequality

[halcyon carbon]

Doesn’t look like an inequality to me

[vestal hornet]

jfajsd

i have no idea what to write

[halcyon carbon]

Well one is about the sum and x and y - what’s the maximum of x+y

The other is about the relationship of 2x and y

[vestal hornet]

x+y < 16?

[halcyon carbon]

Adjust that a bit it says at most

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[vestal hornet]

less than or equal to?

[halcyon carbon]

Yes

[vestal hornet]

so that's my first inequality

how bout the 2nd one

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[remote mist]

Is the sun of the degree different from handshaking lemma if so how? The articles I see online don’t seem to indicate very well or maybe I’m not searching the right thing

[drowsy moss]

gonna need some context here

[uneven fossil]

handshaking lemma is litteraraly the sum of degrees of vertices

[remote mist]

So this?!

Right? 1 sec for picture really slow internet

[uneven fossil]

i mean please give some context in case i would be wrong

[remote mist]

It’s for discrete math? Like it’s just a concept we should know but I do t understand it

Graph theory? I’m not sure what context I can give you

[uneven fossil]

well yea graph theory is part of discrete maths.

take any graph G with N vertices. you add up all of the degrees, and it gives you 2 times the number of edges

[remote mist]

Would this one be lemma or sum of degree

Like I don’t understand where one theorem ends lol

[uneven fossil]

the problem 1.3 is the theorem

i'm not sure i understand your question.

if you're asking what's the theorem, it just says sum of degrees (x_i) = 2 |E|

this is also called hanshaking theorem

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[stable hearth]

The solution says this

but for part c I got this

why are they different?

[final halo]

You used 3B not B

[stable hearth]

oh yeah

thanks

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[tropic canopy]

How do i turn this

Into the other one

[dire crypt]

reverse of distributive prop

[tropic canopy]

The soliution steps dont show it

[tropic canopy]

How would that look, bc idk the terms in english

[dire crypt]

google it

[somber torrent]

Notice that in the former equation (x-1) multiples with both x and -y, so we can use the distributive property to factor (x-1) out of the product.

[tropic canopy]

X-y is left?

[somber torrent]

The distributive property states that a(b + c) = ab + ac, so the reverse is true as well.

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[native pier]

What’s it asking you?

What does f(-2) mean

[obtuse harbor]

That’s the whole wuestion

[native pier]

It’s asking what is the function = to when x is -2

[obtuse harbor]

Yes yes

So

That would mean uhh

[native pier]

14 and -23

[obtuse harbor]

Yes thank you ur literally a god

Bless your heart bro

Wait one last thing

[native pier]

What’s up

[obtuse harbor]

I have one of the things right right but like I don’t get the other thing

[native pier]

0 is 1

[lean otter]

answer is 1

[obtuse harbor]

For a

Yes yes

Thanks y’all

🫡🫡🫡

[lean otter]

a is either -2 or 1

[obtuse harbor]

It wast 1

Thank you toyotomi and meep🫡🫡thank you

[lean otter]

toyota

[native pier]

Toyota

Toy yodami

[lean otter]

thats my new name

[obtuse harbor]

Y all I don’t mean to be stingy or Nything but like

[native pier]

What’s up

[obtuse harbor]

Yknow don’t mean to waste yaur time but like

Yknow I’ve been stuck on this

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[hasty fox]

i can't think of a recurrence

[lean otter]

suppose you had a pretty cool permutation for n=5. Before which numbers from 1 to 5 can 6 go to make a pretty cool permutation for n=6

[hasty fox]

5 and 4

and ik initial conditions are T1 = 1, T2 = 2

[lean otter]

yeah

[lean otter]

so for every permutation in n, there are three new permutations you can make in n+1

[hasty fox]

but isn't T3 = 6?

[lean otter]

eg 2 from before 5 and 4, and last one from putting it at the end

what is T3 then?

[hasty fox]

isn't it just 3P3

[lean otter]

3P3=6

[hasty fox]

since 1,2,3 are all within 2 of each other

[lean otter]

oh sorry misread

2*3=6

[hasty fox]

what are you suggesting the recurrence is?

[lean otter]

multiply by 3

[hasty fox]

T(N) = T(N-1) x 3?

[lean otter]

yeah, I think so

[hasty fox]

what about T2

[lean otter]

special case

[hasty fox]

(1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,2,1), (3,1,2)

in this case there's only two spots for 4 in each permutation

[lean otter]

yes

[hasty fox]

damn i have no idea what the recurrence is

wait you might be right

it can be before, n-1 or before n-2 or at the end if n-1, or n-2 is at the end

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[hasty fox]

no

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[worthy hemlock]

No

Depends on the function

[flat frigate]

Yousuf

[lean otter]

In this case yes

The domain is all numbers

[worthy hemlock]

Ask yourself, can x be a positive and a negative number?

[lean otter]

Because we can input every number in the function and we will get a real result

[worthy hemlock]

If yes, domain is all real numbers

[lean otter]

Hmm?

What about sqrt1

[worthy hemlock]

In the case of $f(x) = \sqrt{x}$, can you input positive and negative numbers

[flat frigate]

dldh06

[worthy hemlock]

So?

You're asking about domain

The corresponding y value is 0

[worthy hemlock]

.

$f(x) = \sqrt{x}$

[flat frigate]

dldh06

[worthy hemlock]

Can you input negative values?

And result in a real answer

[lean otter]

$f(x)=\frac{1}{x}$ is another example

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[flat frigate]

𝙹𝚒𝚗

[lean otter]

Yes

Yes

You cant divide by 0

Therefore 0 is not a possible input

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[vague willow]

Show that (273) to the base b can be the square of a prime number for no value of b

[hardy lion]

Consider 273 base 10

<@&268886789983436800>

[safe radish]

@vague willow Has your question been resolved?

[vague willow]

Is that it

I thought it was somewhere along yhe lines of how 2b^2 +7b + 3 isnt a square of a prime or smth

[hardy lion]

it should give you intuition for other bases

[vague willow]

Okie I will try it

Thamks

[hardy lion]

or try factoring that quadratic

[vague willow]

I've had no luck

[vague willow]

I've had no luck sadly

idk how to tackle the sum

[hardy lion]

One way you could factor 273 base 10 is 21×13

If you notice the quadratic can be factored into (2b+1)(b+3)

Since b is an integer greater than 7, we know that the factors are greater than 1 so the product is composite

The only way for it to be a square of a prime is if 2b+1=b+3
This implies b=2, but b needs to be greater than 7

[vague willow]

Tysm!

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[sonic sapphire]

forgot how to do this

XD

I guess FOIL has to go first?

[rocky zodiac]

u^2(1-u^2)(1-u^2)

[rocky zodiac]

yea

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[lavish compass]

Hey, I'm very stuck with this problem.

[lavish compass]

basically its asking for the derivative of s(t), which im having trouble getting

i've tried using the chain rule, but every time I do it i come up with (200*-2(t+1)^-3)(1), which isnt right

so now i think im stuck

[misty coral]

hmm

what is the form of your numerator when you bring your denom up

(200t)(t+1)^(-2)

@lavish compass

[lavish compass]

Wdym?

[misty coral]

what form does that match

what I wrote

[lavish compass]

Ohhh is that the product tule?

Rule*

[misty coral]

yes

you'll get it now

you can also just use the other rule

[lavish compass]

Ok sweet, that should be good enough thank you so much

[misty coral]

but whatever

floats

your boat

[lavish compass]

Lol

Thanks!

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@quartz tartan Has your question been resolved?

[plucky elk]

Generally no. You still have to plug in the new function composition into the differential equation and see if it's satisfied

[plucky elk]

Then check?

You just plug in your new function

You just plug g into your differential equation

Use chain rule

Why do you need to?

Use the fact f satisfies Laplace's eqn

Differential equations are true at all points in the domain

You can just call u, v the new variables if you want

[quartz tartan]

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[ebon yacht]

is there a way to do this question without making an example?

[acoustic wolf]

hey mate

ill be honest

i was about to say just use an example

do u need to find a way around or it?

or is it for ur own interest?

[ebon yacht]

for my own interest

[trim swan]

If the sphere has radius r, the cube has side length 2r

[acoustic wolf]

the sphere's surface area is 4πr^2

[ebon yacht]

aren't we using volume?

oh wait

mb

[ebon yacht]

alright ty

[acoustic wolf]

the cube's SA is 6r^2

[trim swan]

6(2r)^2

[acoustic wolf]

right

so is that 24r^2?

[trim swan]

yeah

[acoustic wolf]

bc exponents comes before multiplication

[ebon yacht]

ah i'm still a bit confused as to what to do from here

[acoustic wolf]

to quickly sum up what we have

[ebon yacht]

am i supposed to find what percentage of 24r^2 is 4pir^2?

[trim swan]

Yeah, exactly

[acoustic wolf]

the sphere's surface area is 4πr^2 and the cube's surface area is 24r^2

[ebon yacht]

alright

ty for the help guys

.close

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[lusty widget]

yo

[lusty widget]

bio qn

is D capillaries and E venules or nah

just making sure

[thorn chasm]

Bro this is a math server

[lusty widget]

I heard we’re allowed to post chem and bio stuff too tho

idk

[thorn chasm]

I mean I guess idk if anyone will help

[lusty widget]

yeah

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@lusty widget Has your question been resolved?

[plucky elk]

You were told wrong

#old-network for chem and bio servers

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[slow epoch]

can someone help me here?

[slow epoch]

I know how to solve it recursively but it does not use a memoization table

i have no idea how to solve this dynamically by storing stuff into a table

my approach is just to find the largest charge within S[1...n], disintegrate it, add it to the charge and then compute for S[1..n-1] (with the segment being disintegrated not here anymore)

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@slow epoch Has your question been resolved?

[buoyant shadow]

that sounds like the opposite of what i would do

[slow epoch]

yeah like i said this doesnt use a memoization table

[buoyant shadow]

like if I wanted to do it greedily like that I would go in ascending order

[slow epoch]

no clue how to do it dynamically

from what i know doing stuff dynamically is by reducing repetitive steps by storing them in a look up table of some sort

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@slow epoch Has your question been resolved?

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[astral wraith]

hi, i need some very basic probabilities help. To frame what i need help with, imagine the following situation:
let's say there's a bag with 26 cards in it, one for every letter of the alphabet. Then I randomly take 4 cards out.
I have to look at them, choose one, put it aside, and put the other 3 back in the bag. I get to do this 8 times in total. What are the odds that I find the 5 vowels?

[astral wraith]

To be clear, I don't necessarily need someone to solve this particular problem for me, i just want to know how I would go about calculating probabilities that way.
I understand for the first draw, each of the 4 cards I take out has a 5/26 chance of being a vowel. And that's pretty much all I know lol. Any help appreciated, maybe even some tutorial or something cause I guess this is pretty basic.

[grizzled fossil]

Find probability of doing it in 5 draws, in 6 draws (note this means 4 correct and 1 incorrect in 5 draws and then draw 6 correct),….
Prob of 1st draw having at least one vowel follows a hypergeometric distribution (easier to calculate prob of the complement (meaning no vowels))

And similar way you calculate the rest

[astral wraith]

i'd love to find that if i knew how lol

but like, what are the odds of finding a vowel in the first draw?

how would i get that?

you get 4 chances, 5/26 each (i think)

[grizzled fossil]

1-P(no vowels)

1-21/26 * 20/25 * 19/24 * 18/23

[astral wraith]

ohhhh

so that would give me the odds of not getting a vowel in the first draw?

[grizzled fossil]

P(at least one vowel)=1-P(no vowels)

So the prob you want

[astral wraith]

sweet, thank you!

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[ruby oxide]

How do I get the second equation from the first one?

[ruby oxide]

.close

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[primal mural]

how do i graph this

[arctic locust]

First put what's under the square in a canonical form so that you get half of a circle

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[primal mural]

oh

okay that helped

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[sharp cypress]

what did we do in the last step

how is (2m-1)! gone

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@sharp cypress Has your question been resolved?

[grizzled shoal]

ok

so

we have 2m(2m-1)!

think about what (2m-1)! is

lets assume m=5

2 * 5-1
2 * 5-2
2 * 5-3
...
2 * 5-9

[sharp cypress]

yes

[grizzled shoal]

now let's think about what 2m is

2m = 2 * 5-0

now think about what (2m)! looks like

2 * 5 - 0
2 * 5 - 1
2 * 5 - 2
...

[sharp cypress]

yeah

[grizzled shoal]

so in total, we notice that (2m)! is the same as (2m-1)!
just with the exception, that (2m)! has an extra term (2m)

therefore we get
(2m)!=(2m)(2m-1)!

[sharp cypress]

oh so

[grizzled shoal]

we used something similar for the denominator
m(m-1)!=m!

[sharp cypress]

so we didn't cancel terms out

we just write them in another way

[grizzled shoal]

exactly

👍

[sharp cypress]

Oh okay

i get it

thank you so much

[grizzled shoal]

^^

[sharp cypress]

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[tiny mist]

A little confused on this one
Im meant to find the limit of the function at the top left as X approaches infinity graphically

I assumed the answer would be positive infinity and even photomath’s answer was the same but the model answer on my worksheet is 0.
Am I missing something?

[fierce spire]

You're correct. Maybe there's a typo in the question?

If it was $x^4e^{-x}$ then your answer would be 0

[flat frigate]

FLORIDA MAN

[tiny mist]

Yeah I reckon there’s an error in the question

Thanks

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[signal granite]

For this limit, why do we choose x as 2i/n? i get that delta x can be 2/n

[frigid mason]

@kindred bridge

@kindred bridge

@teal flume

[final halo]

?

[signal granite]

To evaluate the limit i turn it into a riemann sum right? Im not sure what x to pick

Oh sorry i thought the ? was for me

So i know my riemann sum is suposed to be a product of a function value f(xi) and the width of the rectangle delta x_i-x_(i-1), when all intervals are equally spaced/the width of all the rectangles r the same it equals delta x. So we have riemandsum = sum f(xi)delta(x) for n to infinity with delta x = b-a/n. If i isolate a delta x from my sum im then left with the function f(xi), how do i choose an xi?

<@&286206848099549185>

[final halo]

f here is cos^2(3-x)

Notice that the 2i/n is the only bit that depends on i, so that's your xi

[signal granite]

Okey

it seems weird to have x depend on i and n for some reason, whats the 'intuition' behind that

[final halo]

It doesn't, x_i does

[signal granite]

hmmm

xi for every i therefor x does no?

[final halo]

x is unrelated to xi

x is just the variable, xi are the particular points in the riemann sum

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@signal granite Has your question been resolved?

[signal granite]

Oh okey thank you!

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[unique basalt]

is possible to find tan derivative intuitively?

[unique basalt]

or just memorize it to sec^2x?

[lean otter]

use the quotient rule

[unique basalt]

how

oh

sin/cos

[lean otter]

yeah

[stray socket]

Or be a Chad and memorize it as sec^2 anyways

[solemn barn]

Or invent calculus during the exam like a sigma

[stray socket]

On god

[unique basalt]

any diff between these 2?

[solemn barn]

nope

[merry pelican]

One of them is bad notation that should burn in Hell for eternity and beyond, the other one is pretty neat.

[solemn barn]

🤣

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[spring wasp]

i have no clue where to start

ive done part a only need to part b

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[spring wasp]

<@&286206848099549185>

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[frosty pecan]

I've got a question

[plucky elk]

[frosty pecan]

Ok so there is a question that goes: find area of triangle with vertices (2,4) (-3,1) and (3,-5)
The answers were given because it was an example and in the example it says to take 2 from each x value and take 4 from each y value.

Now there's a question that has (-2,2) (4,6) (3,0) and idk what to take from each

Do i still take from x and y

?

[final halo]

The point was to make the first coordinate (0,0), figure out what you need to do to all x values and to all y values in the new triangle to make the first coordinate (0,0)

[frosty pecan]

Plus 2 and - 2

[final halo]

Yeah

[frosty pecan]

So this applies to all triangles with 3 vertices that need the area to be found out ?

[final halo]

Well I mean it's something you can always do to help you, but not necessary

[frosty pecan]

Nah I think i have to do it

Also I hjave another question

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[lean otter]

is there another way to write sin(xy) like how sqrt(xy) = sqrt(x)*sqrt(y)

[stray bluff]

https://math.stackexchange.com/questions/1656407/is-there-a-formula-for-sinxy

[lean otter]

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[stray bluff]

x = 1 - 3y

plug into 2nd equation

and solve for y

[stray socket]

It's a lot easier to do elimination for 11

That'll automatically give you -2x = -14

Yeah

I don't need to solve on paper

I can just tell from looking at it x = 7 and y = -2

Oh I deal with bigger

No

,w NSolve[{x + 3y == 1, -3x - 3y = -15}, {x, y}]

[flat frigate]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by Umbraleviathan#3607

[stray socket]

Just checking if I did it right in my head

It's a mathematical program

But if you learned elimination, instead of doing x = 1-3y you can go straight to -2x = -14

Sure

if that implies (x, y) = (7, -2)

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[weak peak]

i’m pretty sure 3:15

[north dagger]

how would u go abt solving it>

[weak peak]

Might be 3

Because halfway through the trip is 2:00, then traffic slows him down to 40 per hour and then at 50 he calls

[delicate bobcat]

Yea this one is written in a way to try and trick you into trying to solve a more challenging problem

As russell said halfway through the trip is 2:00pm

[weak peak]

I’m 99% sure it is 3:00

[delicate bobcat]

Because the trip normally takes 10 hours

[north dagger]

yep

[delicate bobcat]

Halfway through would be 2pm

50 miles later at 40mph

Just figure out how much time that takes

[weak peak]

Try 3:00, lmk if it is correct

[delicate bobcat]

It's not 3

[weak peak]

Halfway is 2

[delicate bobcat]

Because it takes more than 1 hour before the call

Half is 2

[weak peak]

then 40 miles takes a hour

[delicate bobcat]

Then 50 miles at 40 mph

He travels 50 before calling

[weak peak]

3:12 or 3:15 maybe?

[delicate bobcat]

Figure out how much time it takes for 50 miles at 40 mph

50/40 = 1.2 hours

0.2 hours is 12 minutes

(1/5 of one hour)

[north dagger]

i got 3:15

as my final answer

[delicate bobcat]

Oh yea you did it right

I did bad math

50/40 is 1.25

Not 1.2

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[fresh widget]

how is the derivative on the left hand side $sin(x)(2y dy) + y^2(cos(x)dx)?$ thats dy not the derivative

[flat frigate]

LichBaw_GT

[fresh widget]

or am i confusing derivative with difference in y?

[outer coral]

It's not really a derivative but a differential

@fresh widget

For the most part you can quite simply "cross multiply" differentials in derivatives to get those equations

But yeah that's not entirely rigorous

[fresh widget]

oh

[fresh widget]

differential the difference in y right?

[outer coral]

dy is a differential in y yes

[fresh widget]

hmm i dont understand what taking differential in y is doing

because theres two variable

[outer coral]

Loosely speaking: "A teensy weensy small change in y"

[safe radish]

@fresh widget Has your question been resolved?

[fresh widget]

alr

how is dy/dt = -1?

[outer coral]

y decreases at the rate of 1 m/s

[fresh widget]

dy/dt is the rate at which y decreases over dt?

[outer coral]

"the rate" already indicates change wrt time usually but if you wanna be explicit you could say change in y wrt time

[outer coral]

And no not decreases but any change

Since it's decreasing in this case, the change is negative

[fresh widget]

what do you mean by wrt?

[outer coral]

"With respect to"

[fresh widget]

also dy is always proportional to dx right?

and finding the derivative is essentially finding the proportionality constant

[fresh widget]

isnt the rate at y changes is -1 if dt is 1?

but dt is approaching 0

[safe radish]

@fresh widget Has your question been resolved?

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[safe radish]

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[livid sparrow]

Could someone tell me if I am understanding this correctly?
I am learning A star pathfinding algorithm and I need to calculate the heuristic
I am using diagonal distance (8 way movement on a grid)

The formulas I'm using here are

    D = 10   (Cost for horizontal/vertical movement)
    D2 = 14  (Cost for diagonal movement)

    dx = abs(cell.x - targetCell.x)
    dy = abs(cell.y = targetCell.x)

    h = D * (dx + dy) + (D2 - 2 * D) * min(dx, dy)

But I am confused by one thing

Say the target is cell (3,7) on the grid

then when I do the calculations for these cells, the result of h is

    cell1 = (9,4) -->  h = 72
    cell2 = (8,2) -->  h = 70

I am confused because to me it looks like cell1 is closer to the target than cell2 is. But maybe I'm wrong. I'm hoping someone could clarify this and let me know if I'm on the right track here

These are the calculations

target = (3,7)

cell1 = (9,4)
dx = abs(9 - 3) = 6
dy = abs(4 - 7) = 3
h(cell1) = 10 * (6 + 3) + (14 - 2 * 10) * 3 = 72

cell2 = (8,2)
dx = abs(8 - 3) = 5
dy = abs(2 - 7) = 5
h(cell2) = 10 * (5 + 5) + (14 - 2 * 10) * 5 = 70

As you can see, according to the calculations cell1 is further away than cell2
But it just doesn't look like it on a grid to me
Have I done everything correctly here?
Which cell do you think is closer to the target?

[plucky elk]

CS server is in #old-network

[livid sparrow]

huh?

[plucky elk]

Computer science

[livid sparrow]

I am just wondering if I did the math correctly

and which cell is closer

it's not really a CS question

Forget the algorithm part I just want to know if the calculation for h is correct

What do you think? @plucky elk

[plucky elk]

Why did it not look right on a grid to you?

[livid sparrow]

It just looks like it is the closer one

[plucky elk]

Well that's not helpful

[livid sparrow]

Doesn't it to you?

Which one do you think is closer

[plucky elk]

Just use euclidean distances

[livid sparrow]

That's not really helpful. I am wanting to know if I have done this calculation correctly. I'm not looking for alternatives.

[livid sparrow]

I don't really know what you mean by this. There isn't really an answer. All I can say is that it just doesn't seem right. This is why I want to know if these calculation are correct for diagonal distance

[plucky elk]

Then why are you comparing the formula to your eyes' judgment

[plucky elk]

You're saying the calculations are wrong based on nothing

[livid sparrow]

I am not saying that they are wrong at all.

I am saying they could be wrong (because i am not a math genius and maybe did it incorrectly)
I am also saying they could be right (but I just want to confirm that they are)

It's one of the two.

I am just trying to make sure. Because I am only just learning

How is asking if I have done them correctly/incorrectly saying that the calculations are wrong?

[plucky elk]

.

[livid sparrow]

Yes this isn't me saying "The calculations are wrong"

This is just me saying "I'm unsure, someone more knowledgeable than me please clarify"

[plucky elk]

Yea that wasn't clear at all

[livid sparrow]

Read the first line of my question. I am asking if I understand this correctly

[plucky elk]

Euclidean distance is helpful because that's how your eyes judge distance

[livid sparrow]

Sure but i am wondering if I did this formula specifically correctly

[plucky elk]

Saying "it just looks closer" contradicts yourself

[livid sparrow]

How so?

[plucky elk]

That's pretty obvious

[livid sparrow]

How is it obvious?

It does look closer (to me) but I'm probably wrong. So this is why I'm asking for clarification

Refer to this line:
"I am confused because to me it looks like cell1 is closer to the target than cell2 is. But maybe I'm wrong. I'm hoping someone could clarify this and let me know if I'm on the right track here"

I'm literally just asking for clarification mate, nothing more. It's simple. I either did the math wrong or I didn't. I expected someone to answer something along the lines of "Calculations are good, that's the correct formula" or "You went wrong here" , not an argument about whatever it is you're trying to argue about

[livid sparrow]

I don't know why you are being so condescending

[plucky elk]

Jesus did you just go on a tirade and ask me for help again?

☮️

[livid sparrow]

I'm not asking you for anything, I would prefer if you didn't answer any questions from me because you're not very helpful and quite rude

I don't know why you bothered in the first place lol

[livid sparrow]

so no

[livid sparrow]

Thanks for derailing the question bro

.close

[safe radish]

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[lean otter]

One message removed from a suspended account.

[safe radish]

@lean otter Has your question been resolved?

[fierce ore]

i think c is true

[lean otter]

One message removed from a suspended account.

[fierce ore]

because you're on an interval

and it asks for a local extrema

i believe a global extrema is also a local extrema over the whole interval

you might wanna check to be sure

[lean otter]

By the extreme value theorem, you can discern if it would be global or not

I mean all global extrema are local to begin with

One message removed from a suspended account.

[lean otter]

One message removed from a suspended account.

I mean from what I know the first derivative would only break if there is some discontinuity at that point. So it seems to be a correct statement, though I'm not sure if this is some bad trick question your university is trying to ask you

[safe radish]

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[loud leaf]

Hi! I need to calculate the lenght of the following

[loud leaf]

I'm just a bit unsure how to tackle it

Do I simply use the arch lenght formula using x = f(y) = ln(...) - sqrt(1-y^2)?

Or do I need to solve for y first?

[fierce ore]

uh

first of all, the lenght of what

and why is there a random b in the inequality

[loud leaf]

I suppose they're asking for the lenght of the right-side expression in the equality

I missed last week's lecture so I'm not sure either why there is a b there

Full text is "Decide the lenght of the curve x = ..."

[fierce ore]

looks like it streches to infinity

maybe the area under the curve ?

[loud leaf]

I got this graph in Desmos

[fierce ore]

oh it's a 2

no it's a y

[loud leaf]

Nope, it specifically asks for the lenght of it

ohh

yeah my bad!

[fierce ore]

and there's an ln

[loud leaf]

What can I say... a morning without coffe is dead morning

[fierce ore]

yeah and it's 2 am for me + got an exam tmorrow so i'll have to go get some sleep

well i hope you can solve it

[loud leaf]

Good luck with your exam, Bolly!

[safe radish]

@loud leaf Has your question been resolved?

[safe radish]

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[grizzled lantern]

<@&286206848099549185>

[lean thorn]

!15m

[safe radish]

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.

[sonic sierra]

hello

do you still need help?

[safe radish]

@grizzled lantern Has your question been resolved?

[safe radish]

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[prime cobalt]

Hi

[prime cobalt]

how do I do this?

[lean otter]

"uuuuuuuuu" sure would know

(this is a hint)

[prime cobalt]

yeah

I did u=x+3

du=dx

sry forgot to mention

but idk how to continu

I got integral x(sqrt(u))du

and I’m lost

[lean otter]

when you make a substitution and you cannot eliminate the remaining x's with the derivative of u, write the remaining x's in terms of u

basically, solve for x in terms of u

[prime cobalt]

oh

so if I let u=x+3

then x=u-3

is that right?

[lean otter]

yeah

also

u can do IBP

[prime cobalt]

oh

[lean otter]

if u wanna

[prime cobalt]

what’s ibp

[lean otter]

thats also an option

integration by parts

[prime cobalt]

oh my question says by substitution

[lean otter]

ah okay, just do what i said

and then

expand the square root

[prime cobalt]

ok

brb

[lean otter]

tyt

[lean otter]

Also meant to say here in terms of u and solve for x. Had a brain freeze lol

[grizzled lantern]

yep

[sonic sierra]

hi pls make a new channel and post your q there

[safe radish]

@prime cobalt Has your question been resolved?

[safe radish]

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[acoustic wolf]

log base 4 of x^2 + log base 2 of x = 2

[acoustic wolf]

$\log_4(x^2) + \log_2(x) = 2$

[flat frigate]

WhyWouldYouKap

[acoustic wolf]

so I did the change of base ting

$\frac{\log_2(x^2)}{\log_2(4)} + \log_2(x) = 2$

[flat frigate]

WhyWouldYouKap

[acoustic wolf]

$\frac{\log_2(x^2)}{2} + \log_2(x) = 2$

[flat frigate]

WhyWouldYouKap

[acoustic wolf]

then I multiply every term by 2

i think

which is

[maiden jetty]

$x>0$, $\log_2 (x^2) = 2 \log_2 (x)$

[flat frigate]

秋水

[acoustic wolf]

yes ik i was getting there mate

thanks

$2 \log_2(x) + 2 \log_2(x) = 4$

what do I do here tho?

[flat frigate]

WhyWouldYouKap

[acoustic wolf]

bc of the plog law then its fine i think

[maiden jetty]

then you can get $\log_2(x)$

[flat frigate]

秋水

[acoustic wolf]

can I divide both sides by 2

to remove the 2s as coefficients and make the 4 a 2

[maiden jetty]

$2 \log_2(x) + 2 \log_2(x) =4\log_2(x)$

[flat frigate]

秋水

[acoustic wolf]

isnt it

$\log_2(16)$

[flat frigate]

WhyWouldYouKap

[acoustic wolf]

oh

[maiden jetty]

it is, but can be simpler

[acoustic wolf]

yeah i get u

so x is 2

$\log_2(x)=1$

[flat frigate]

WhyWouldYouKap

[maiden jetty]

yes, then by definition, x=2

[acoustic wolf]

ok great

.close

[safe radish]

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[lean otter]

can someone help me with this

[safe radish]

@lean otter Has your question been resolved?

[safe radish]

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[gusty glacier]

limx→∞f(x) = L
can first be done as follows: if someone gives us a margin of error ε > 0 around L and requires that
L −ε < f(x) < L + ε, so we can always find a sufficiently large number N so that the requirement is
fulfilled if x > N. That means: we can choose N so that f(x) does not deviate more than ε from
L as long as x > N.
Here we will study this for some functions that occur when studying swings
with possible damping, where the goal is for the function value to go towards 0 as x →∞.```

[gusty glacier]

h(x) = 1√x cos(x). If we now let ε be general, how can we choose N for
that h(x) should not deviate from 0 more than ε? Express N in terms of ε. Note that N does not
must be as small as possible, so set −ε < h(x) < ε n whenever x > N

[solar hazel]

is that 1/sqrt(x)?

[gusty glacier]

yes xd

i dont understand what they mean with epsilon being general

or i just dont understand the whole question

[solar hazel]

:c

it wants you to come up with, for any epsilon at all, an N that would make the conditions above hold

[gusty glacier]

so i am to find a N in a term of epsilon , so that when x > N it should be −ε < h(x) < ε for any given epsilon?

[solar hazel]

i’ll say yes but the “for any given epsilon” could be in the wrong place

it would sound better if it was said at the beginning

[gusty glacier]

can i not just give a really big value on N so that no matter what epsilon is picked its still in the intervall −ε < h(x) < ε

or is the tricky part, finding that big value of N

[solar hazel]

there isn’t one big value of N that will make it work for any epsilon

if that’s what you mean

[gusty glacier]

i see that now, but they said that i need to express the N as a term of epsilon, meaning like N = ε + "something" or N = ε - "something"

right?

[solar hazel]

not necessarily (and also no)

it could be like

N = (epsilon^4)/10

very random example

[gusty glacier]

oh, are you sure?, is that not a factor of epsilon and not a term, or is that just a figure of speech, to say "term" as in anything that can build up N out of epsilon?

[solar hazel]

second thing

[gusty glacier]

ok i see

i seem to have trouble finding a valid N, i guess im suppose to use the data from previous questions, where N = 100 when ε = 0,1 and N = 10000 when ε = 0,01. But how should i use this data, i tried N = ε * x where x is going to form a type of formula...yee im lost

[solar hazel]

an important thing is cos(x) lies between -1 and 1

for any x

so multiplying 1/sqrt(x) by cos(x) only brings 1/sqrt(x) closer to 0

which, even though you might not understand why yet, pretty much says you can ignore it for right now

[gusty glacier]

wait, now im confused, so i am to only consider the cos(x) part now, and come up with a N for that function instead?

[solar hazel]

no

but replace cos(x) with 1/sqrt(x) in what you just said and sure

[gusty glacier]

but in any case this will still give approximetly the same data as before, where N = 100 when ε = 0,1 and N = 10000 when ε = 0,01, but i dont really know how to obtain a formula on N so that the conditions are met

[solar hazel]

if i give you an epsilon, what’s an x large enough that 1/sqrt(x) < epsilon?

hint: algebra

[gusty glacier]

well is that not gonna depend on what you give me as epsilon?

[solar hazel]

ya but that’s the point lol

[gusty glacier]

https://tenor.com/view/cry-sad-gif-25488313

[solar hazel]

tell me what it would be for an any epsilon i could give you

[gusty glacier]

hmmm, ok so it cant be 1 since that is gonna give 1/1 = 1 and is not less then for example if epsilon = 0,1, so maybe when x = 0.00000000001

no

ok so x = 10/epsilon maybe?

[solar hazel]

is that a total guess?

how’d you get that?

[gusty glacier]

umm yes i think it was a guess, since i cant use anything to solve this, like i dont understand how this is algebra when there is nothing to solve, like i can make it so that 1 < sqrt(x) * epsilon by just multiplying sqrt(x), not this gives the same function in another format, but does not make it clearer, of how to find un x

oh wait

maybe (1/epsilon)^2 < x

is that something?

[solar hazel]

that’s something

[gusty glacier]

does something = the answer, or just a step towards the answer 🧐 ?

[solar hazel]

both?

[gusty glacier]

N = (1/epsilon)^2 is the answer

[solar hazel]

yes that will work

[gusty glacier]

you said that with a bad tone :(, is this not correct?