help-27

[devout snow]

@restive river Has your question been resolved?

[north plaza]

It's pretty straightforward if you think about it.
They've given the cross section of a bowl, they're asking you to find the depth i.e. the distance from the deepest point on the bowl to the highest point. Now they've given an equation which represents the bowl. Try thinking about it now. Also what do you not understand specifically?

Also have you done differentiation?

[devout snow]

@restive river Has your question been resolved?

[restive river]

no

i dont understand the question at all idk what is meant by cross section

maybe i should just leave the question

[spare kernel]

what was the last topic they've been teaching you in class??

[restive river]

algebraic fractions💀

[spare kernel]

um

this might be a bit tricky to attempt through algebraic fractions

through differentiation: you just differentiate to find the rate of change, then use simple quadratics using that information to find the turning point (where rate of change = 0, AKA lowest point), and then with the knowledge of the X value of lowest point, substitute it into the equation to find the height.

[devout snow]

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[spare kernel]

but if u don't know differentiation, ur options are to either learn it now or just skip the question lol

[devout snow]

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[devout spruce]

Need help pls

<@&286206848099549185>

??

[devout snow]

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[devout spruce]

. Close

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[coarse agate]

is there a general solution for a non-homogenous linear discrete dynamic system of form $x(0) = k$, $x(t+1) = ax(t) + b$. What I get is $x(t) = a^tk + b(\sum_{i=0}^{t-1} a^i)$ but idk if thats right

[woven radish]

Ann

[supple knot]

how is x(t) defined for 0 < t < 1?

if you're working on a problem, it's best to just show the entire context

[coarse agate]

$t \in \mathbb{N}$

[woven radish]

Ann

[coarse agate]

this is the entire context

[supple knot]

then this is just a recursive sequence

what makes it a dynamic system?

[coarse agate]

okay

my bad

it is a recursive sequence

no it's not the other Ann

dw

i regularly get pinged instead of her lmao

yeahhh

i for one do both !

[empty flame]

Sorry for the interruption

[coarse agate]

no worries

[supple knot]

you should be able to prove this is true by induction. use n instead of t

check small n=1,2,3 as well

[coarse agate]

i did the math for n = 2,3

[coarse agate]

hmm ok makes sense

im not sure how to prove it by induction... i can definitely prove it works for low n [ex. n= 1,2,3] but idk how that implies it works for n+1

[supple knot]

try simplifying x(n) first. use the formula for geometric progression

again, with n instead of t here. then show that x(n+1) = a x(n) + b = the formula here but with n+1 instead of n

[coarse agate]

$x(n) = a^nk + b(\frac{a^n - 1}{a-1})$

wait im confusing myself

[woven radish]

Ann

[coarse agate]

okay i got this from here

.close

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[restive river]

why do i feel like this long division is so much harder than the standard ones?

what is the difference?

what is the trick?

it is multi variable

right

[devout snow]

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[devout snow]

@restive river Has your question been resolved?

[devout snow]

@restive river Has your question been resolved?

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[finite stream]

did I do this right?

[nimble atlas]

can someone help me with this please

[devout snow]

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).

[thin tapir]

No, the correct formula is $\left(f^{-1}\right)'(x) = \dfrac{1}{f'\left(f^{-1}(x)\right)}$

[woven radish]

d

[finite stream]

o

[finite stream]

inverse function is just 1/f(x) right?

o wait no, I should find derivative(1/f(x))

I think idk

[thin tapir]

The inverse of f is usually another function g such that f(g(x)) = x and g(f(x)) = x, but maybe in this context it is what you have said

[finite stream]

idk, the only function given was f(x)

[thin tapir]

But do you know what the inverse function is in this context?

[finite stream]

i don't think so?

idk

[thin tapir]

The concept of inverse function is a bit ambiguous and its meaning in this question might be different than the usual meaning

[finite stream]

so in this case would it just be 1/(f(x))?

[thin tapir]

I don't know

[finite stream]

oh

[thin tapir]

It depends on what it says in the book you are studying

[finite stream]

my teacher says to use calculator

there's no book

[thin tapir]

Then how did yout teacher define the concept of inverse function?

[finite stream]

idk

the ones we did for inverse had a table

then find the points of f and g

then slope and just put the slope of f as 1/f'(x) = g which was inverse of f

[thin tapir]

Then I think they are using this definition

[thin tapir]

Just to be sure, could you send one of these examples?

[finite stream]

yea let me find

basically reciprocal

[thin tapir]

Ok, so in this example f and g are the inverse of each other

That does not mean that g = 1/f, but rather, that g(f(x)) = x for all x

For example, since f(-4) = 12, g(12) = -4

[thin tapir]

To find the derivative you have to use this formula

[thin tapir]

It is similar to what you did here, but not exactly the same

[finite stream]

so if x is -4,
g(f(-4)) = g(12) = -4

[thin tapir]

Yes

[finite stream]

do I do chainrule then to find derivative

g'(f(x))f'(x)

wait there's no g

nvm

🗿

[thin tapir]

$g$ is just $f^{-1}$

[woven radish]

d

[thin tapir]

Since g(f(x)) = x, you do chain rule and obtain g'(f(x))f'(x) = 1

Or even better, since f(g(x)) = x, f'(g(x))g'(x) = 1 and then g'(x) = 1/f'(g(x))

Which is the formula I sent before

[finite stream]

hmmmmm

gimme a bit to think abt it

so for this problem

it would be inverse f(x^3-3x^2-2x+1)?

[thin tapir]

Not exactly
The inverse (in this case it is called f^-1 instead of g) satisfies the equation f^-1 (x^3-3x^2-2x+1) = x

[finite stream]

uhhhh

but if inverse of f is the x value

wait

so f^-1(x^3-3x^2-2x+1) = 2 then right?

[devout snow]

@finite stream Has your question been resolved?

[devout snow]

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[rapid socket]

I meant divided by 8 but it's still wrong

wait no i was right

oh damn i distributed wrong

704 damn

.close

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[dense walrus]

Can someone PLEASE just tell me what is the correct equation to complete this transformation ASAP, I’ve been stuck on this for like an hour:

[devout snow]

@dense walrus Has your question been resolved?

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@dense walrus Has your question been resolved?

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[floral surge]

how can i find the point of intersection

[boreal karma]

You can write two equations, one for each company, to start

[floral surge]

done

y=0.35x+5 and y=0.5x+3.5

[boreal karma]

Okay so we know they need to charge the same so what does that tell us about the two equations

[pseudo basin]

do you know in general how to find the intersection point of two lines?

[floral surge]

yes, but im not sure how to solve it without graphing using y=mx+b style

could i move the x onto the other side in one of the equations

[pseudo basin]

... you might be overthinking it? you don't need to graph.

[floral surge]

not trying to graph

[pseudo basin]

you just need to solve the equation 0.35x + 5 = 0.5x + 3.5

that is it

[boreal karma]

Because they charge the same we can set the equations equal to eachother

Then it’s just algebra to find x as Ann said (:

[floral surge]

wait what

im sorry i think im too tired for this

can you walk me through how id solve it

[boreal karma]

Where’d you get stuck

[floral surge]

as soon as i wrote the equations

[boreal karma]

Okay so in your equations y is cost and x is distance

[floral surge]

yes

[boreal karma]

You’d agree with that right?

Okay so we want the cost to be the same and we solve for distance

So we can say .35x +5 = y = .5x +3.5

You good with that?

[floral surge]

no

[boreal karma]

We’re looking for when y will be the same in both equations

[floral surge]

mhm

[boreal karma]

That means both equations are equal to one another because they’re providing the same y

[floral surge]

yeah

[boreal karma]

1+3= 4 = 2+2 for example

[floral surge]

im trying to solve this using substitution by the way

i probably shouldve mentioned that

[boreal karma]

There’s no substitution here involved

I guess you can rewrite an equation

[floral surge]

ill try that

[boreal karma]

It makes the problem far more complicated, is it necessary to use substitution?

[floral surge]

i have to use either that or elimination, thats what we're learning

[boreal karma]

Basically you rewrite y=.35x +5 in terms of x

If you can do that

Then plug that value of x into the other equation

That’s substitution

Elimination I don’t think can work here

[floral surge]

thats why im trying substitution

[boreal karma]

I mean you can force it again but it’s messy

Both methods are messy

[floral surge]

i think im figuring it out

ah shit i did it wrong

i plugged it into x instead of y

[boreal karma]

You’re supposed to do that

What did you get x=?

[floral surge]

not done yet

[boreal karma]

And actually I think elimination isn’t too bad I just was thinking about x

[floral surge]

yeah i could see it working

[boreal karma]

You can change y=.35x+5 by multiplying both sides by -1

Then eliminate y to solve for x

[floral surge]

yeah

i got x=10

[boreal karma]

Yeah that’s what I got as well

[floral surge]

great so i do know what im doing

now the relieving part, just got to plug it back into one of the equations to find y

[boreal karma]

If you need to find the cost yes

10 is your distance in km

[floral surge]

i got 8.5

is that correct

[boreal karma]

For the cost?

Should be correct yes

[floral surge]

alright thank you for the help

have a nice night

.close

[devout snow]

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[mild umbra]

I've already asked but one one replied

[mild umbra]

can i please get help w this hw quesiton I have

the second part

[restive river]

What grade level is this b

[mild umbra]

abt finding the x values

[restive river]

*?

[mild umbra]

this is first year uni

discrete math

1028

[restive river]

Have you tried it yourself?

What are you stuck on?

[mild umbra]

I don't even know where to start tbh w u

I figured out the proof that it's injective

but idk how to go about finding the x values

This was never covered in my lectures

[restive river]

Do you have a friend you could ask?

Chegg maybe?

[mild umbra]

I have one friend and all he said was "inverse" and went offline

[restive river]

Lol I’m sorry I’m like 0 help in a senior in hs lmafo

[mild umbra]

the chegg question isn't going through on homeworkify 😭

[restive river]

Im*

[mild umbra]

its so doomed

[restive river]

LOL I love homeworkify

wait is this calc 1

[mild umbra]

am i allowed to ping ppl

this is discrete math

[restive river]

Ping people on ? Probably

Is ur name actually phresh?

[mild umbra]

yes its my government name my parents hated me

[restive river]

I was gonna ask my question till u got here faster🤨

[mild umbra]

@icy otter could u be of any assistance 🙏

[graceful cosmos]

Have you been able to show this is injective?

[mild umbra]

inshallah

[mild umbra]

yes I have

[restive river]

Omg ur a fellow muzzie!

Can |x| <_ -4 be represented using a number line?

Can someone answer this too

[mild umbra]

I did the whole f(x) = f(y) x = y thing

[graceful cosmos]

If g is injective, there's only one x value that can be mapped to 0

[mild umbra]

omg

i did not think about that

bro i need some SLEEP

[restive river]

Kaynex

Can |x| <_ -4 be represented using a number line?

[graceful cosmos]

And, I'm guessing it's not too bad to find by algebraing

[mild umbra]

wait

but

the function given is

g(g(x)) + 2g(x) = 2x

and its asking me for g(g(x)

how do i isolate it

[graceful cosmos]

It's not asking you for that, as far as I can see

Just any value such that g(g(x)) = 0

[mild umbra]

it says values where g(g(x)) = 0

but what would I plug it into I only have the equation that also has the 2g(x)

or wait

0 + 2g(x) = 2x ... ?

[graceful cosmos]

If we assume that g(0) = 0, then the equation is satisfied

So x = 0 is the solution

[mild umbra]

can i assume that?

[graceful cosmos]

It ends up satisfying the equation, which is the definition of g

Btw I don't know why your friend said "inverse", and I doubt g even has an inverse. They might have done it wrong

[mild umbra]

i think he just skimmed the question

okay i will take ur answer and ask my TA at the next tutorial to run me through a similar problem.

oh also

can ulook at my proof for it being injective and lmk if it checks out

one sec

my answer for the second part is there too if u can take a look at that :3 @graceful cosmos

ignore the gog

[restive river]

Looks pretty solid

[mild umbra]

do u mean <=?

[restive river]

Yesss

[mild umbra]

uhhh

[restive river]

is this too easy for ur complex math homework

[restive river]

No it can’t bro

That’s wrong

[mild umbra]

i forget if its paranthesis or brackets for including

thats how you'd solve |x|<=-4 unless I am mistaken

I mean

it cant be less than -4

[restive river]

Nah it’s saying u can’t do it on a number line but idk why

That’s my problem

[mild umbra]

cus its an absolute value

they have to be positive

mb

yea u cant put it on a number line

[restive river]

Yeah so if it’s |-5| it’ll turn into a 5

[mild umbra]

it will

[river gorge]

yeah and 5 not less than -4

[mild umbra]

and the inequality will be wrong

oopsies

[restive river]

Yessss

Okay I get it now

[mild umbra]

i will retreat into my hole of shame sorry

[restive river]

Pls do.

You’re doing first year math and can’t even answer a grade 12 level calc question

Be ashamed

Lol jk

[mild umbra]

teehee

computer engineers 😍

[restive river]

omg are u brown

Why is every single brown person taking comp eng or comp sci

[mild umbra]

i am not at liberty to answer that (white man)

[restive river]

Ur white?

U said inshallah I don’t believe you

[mild umbra]

mygf is a muzzie :3

[restive river]

if ur not Muslim don’t say muzzie

[mild umbra]

teehee

i have revealed too much

i must retreat into my hole

[restive river]

so ur white? I was gonna say smth but nah

[mild umbra]

cracker... lets not get racist in the mathematics discord server !

[graceful cosmos]

You've proven that g(g(x)) + 2g(x) is injective. You want to prove that g(x) is injective.

[restive river]

Bro said cracker and told me not@to be racist! Okay!

[mild umbra]

oops idk if cusses r allowed here

[graceful cosmos]

That is, g(x) = g(y) implies that x = y

[mild umbra]

shitake

christ

okay

[graceful cosmos]

Applying g to both sides is fine though:
g(g(x)) = g(g(y))

[mild umbra]

but how would ik that g(x) = x?

[graceful cosmos]

It isn't

[mild umbra]

but this

[graceful cosmos]

Let's say g(x) = x³
Because x³ = y³ implies that x = y, g would be injective

Even though g(x) ≠ x

[mild umbra]

but g(x) is not given

only the equation w the extra stuff

[graceful cosmos]

Just showing that g(x) doesn't need to be x

Hint: applying g to both sides is fine.
g(g(x)) = g(g(y))

[mild umbra]

but where do u go from there

[devout snow]

@mild umbra Has your question been resolved?

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[red fulcrum]

Is this the correct derivative?

[worthy smelt]

check your quotient rule, not quite

[river gorge]

express f(x) as $25(x^2 + 25)^{-1/2}$

[woven radish]

nalin

[red fulcrum]

ah okay

so it’s possible to do it this way? (By rewriting instead of quotient rule)

[bleak fossil]

yea the 25 is just a constant so you dont have to use quotient rule

[red fulcrum]

Like this?

I forgot the x in the nominator

Ignore that

@river gorge

[bleak fossil]

yea, i would leave it in the ^3/2 form

[red fulcrum]

Thank you

Do you know how i can set this derivative equal to 0 easily?

[river gorge]

correct

[red fulcrum]

Can i just take the nominator and set it equal to zero?

[river gorge]

yep

so

x=0

[red fulcrum]

How is it 0?

Oh nvm

I see

Thanks guys

.close

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[smoky gyro]

Can anyone let me know if I’m wrong so far and if I’m not what do I do from here?

I’m trying to evaluate the limit

[smoky gyro]

oh wait

I wrote the question wrong

The upper limit is just x

Not x^2 💀

Anyways what do I do here

Oops

Should be x^2 in the sinx for last line

Ignore that

so

if i pull out a 1/3

snatch it from the limit

i get 1/3*lim x->0 (sin(x^2))/x^2

but what do i do then

herm

[supple knot]

use sin(t)/t goes to 1 as t goes to 0

If you haven't learned that, use a substitution and then l'hopital again

[smoky gyro]

like differentiating the top and bottom of sin(x^2)/2x?

but doesnt that mean im taking the second derivative? is that allowed when evaluating limits? it doesnt change the answer?

[supple knot]

No

The order matters. Do a substitution

[smoky gyro]

how do you mean?

[river gorge]

h'(x) is wrong, it's sin(x^2) not sin(x)

[river gorge]

ah you've written sin(x^2) here, alright

[smoky gyro]

yeah i adressed the mistake earlier

any ideas
?

[river gorge]

let x^2 = t

then you'll have 1/3 lim sint/t

lim t->0 sint/t is a standard limit

=1

so the answer is 1/3

[smoky gyro]

ohhhhhh

okay

i see

thanks

i was looking at a solution on symbolab and it got that but it applied L hop twice technically and still got the same answer. I say technically because i didnt write the actual function with the integral and everything because symbolab cant compute that so i just asked it sin(x^2)/3x^2

[river gorge]

yeah there's no need of doing that

[devout snow]

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[devout snow]

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[restive river]

Can someone guide me on how to do number 1

[long pasture]

do you know tip-to-tail method?

[devout snow]

@restive river Has your question been resolved?

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[wanton pecan]

I'm curious about the effect of simplification in the uncertainty of an indirect measurement. Say I want to measure the ratio of 2 voltages through an amplifier with gain A_d with an uncertainty of 0.05%. When calculating the ratio A_d will cancel out, is that really sane? I'll end up with only the uncertainty of the original voltages only, how could the amplifier not contribute at all?

[wanton pecan]

I can give a more concrete question but I fear it'll just scare away math people

What is the guarantee that A_d is the same A_d when I measure again?

[pine rock]

amplified v1 is v1 * a_d * (1+-0.05%)?

[wanton pecan]

v1 also has an uncertainty of it's own, +-10mV

I want to calculate v1/v2, but can only measure a_d * v_1 and a_d * v_2

[pine rock]

so ((v1+-10mV) * a_d * (1+-0.05%))/(v2+-10mV) * a_d * (1+-0.05%)?

[wanton pecan]

Yeah, I think that looks right

[pine rock]

well, you add relative uncertainty when multiplying/dividing

but uve got absolute one with v1 and v2

[wanton pecan]

I know the nominal value of a_d so we can have an absolute one for that too a_d = 2 +- 0.05%

I've read through GUM but I don't quite see how one would handle a case where simplification of B type uncertain quantities happen

[pine rock]

dunno about gum but to add/subtract u need absolute uncertainty, to multiply/divide you need relative one

i mean you can add/subtract absolute and multiply/divide relative

so after adding absolute ones in the eq above you will need to somehow convert to relative to divide

nvm, its multiplying so you will need all to be relative

[devout snow]

@wanton pecan Has your question been resolved?

[pine rock]

so if you can convert +-10mV to relative you can just add relative of .ultiplying and subtract if dividing

[wanton pecan]

Say it were relative, how would you keep going?

[pine rock]

(v1 +- relv%) * (a_d +- rela%) = v1*a_d +- (relv+rela)%

[wanton pecan]

I see, I'd also love to hear from someone that knows about how GUM treats standard uncertainties

[devout snow]

@wanton pecan Has your question been resolved?

[devout snow]

@wanton pecan Has your question been resolved?

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[slim token]

Hey, just learned about derivatives and r.o.c, i have been trying to substitute cube(x) into (a), and getting results with either 1, or a numerator of 0

Unless I am doing it wrong, I was conjugating the numerator to make the denominator not equal to 0, but then I end up with the numerator of 0 instead.

What other approach can I take for this question?

[slim token]

.close

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[marsh bluff]

HII so rn I’m working on dialation and I kinda sorta don’t understand because the question isn’t visible and just in words, help please!

[marsh bluff]

<@&286206848099549185> 🙇‍♀️🙇‍♀️

[quiet sail]

@marsh bluff Can you explain what dilation does to a line segment?

[marsh bluff]

Makes it bigger

I think

Projects it so it’s larger

[quiet sail]

Exactly! And how much bigger does it make things for a factor of 5?

[marsh bluff]

Times 5?

[quiet sail]

PRecisely

[marsh bluff]

okay so

15

[quiet sail]

So about dilation images you should remember that the distance between two points in the image is always a factor f, times their original distance.

[quiet sail]

I believe so.

[marsh bluff]

Not her question

Another’s *

Another*

[quiet sail]

Go ahead.

[quiet sail]

This asks you to recall another important property of dilation images.

Do you know any others, or perhaps you can deduce it from what I have told you earlier.

[marsh bluff]

Emm

Could I say it’s not true because c is farther down in b’c’d’

[quiet sail]

Yeah that is a pretty good intuition, dilations preserve shapes.

So in this context the shape of an object will always be the same after a dilation image, which it is clearly not!

[marsh bluff]

i have so many questions hopefully you dont mind

[quiet sail]

Put in other words, since the distances are blown up by the same factor for every point, one cannot suddenly be relatively further away.

[marsh bluff]

i missed school a bit so i missed two homework segments of eight

[quiet sail]

I see, I dont mind explaining some things, maybe with this new info you can have a better shot at the next one.,

[marsh bluff]

thank you so much!!

[marsh bluff]

see the problem is with these thingys our teacher kinda needs to like teach us for teh homework or else it doesnt make sense

[quiet sail]

Yeah makes sense, I also had to look it up real quick.

[marsh bluff]

okay wait

i think i understand it

so

it measure twelve

ik that their similar number is like 4

so maybe a scale factor of three

[quiet sail]

A scale factor of three would blow ABC up to have a largest side of length 36, do you see why?

[marsh bluff]

12 x 3

humm

[quiet sail]

Yeah, but we would like that longest side to be 8 instead, not 36 right?

[marsh bluff]

yes

[quiet sail]

Do you have any ideas?

[marsh bluff]

not exactly 😭

because 8 is less then 12

[quiet sail]

That is fine, lets work through it.

So we've already seen that the result of our scale factor, lets give it a name, f, is 12*f

So if we take a scale factor of f = 2 we get a longest side of 12 * f = 12 * 2 = 24

Do you see that?

[marsh bluff]

yeah bc 12 x 2 is 24

[quiet sail]

Okay cool, now we have the question, what f do we need to pick such that 12 * f = 8

Have you ever dealt with such algebraic expressions?

[marsh bluff]

probably but last year i failed math

[quiet sail]

Oh that sucks!

[marsh bluff]

hg DID NOT do her work

[quiet sail]

We have a trick to deal with these, to figure out what f should be, we can do the same things on both sides of the equals sign.

In this case we will divide both signs by 12

12 * f / 12 = 8/12
f = 8/12 = 2/3

[marsh bluff]

OH

so is teh scale factor 2/3?

[quiet sail]

Which works out, since if we try our f we see that
12 * 8/12 = 12*8/12

Which is equal to 8

[quiet sail]

It is, but do you see why?

And would you be able to replicate how we got there?

[marsh bluff]

no way

im better at word language then math language

[quiet sail]

Then we'll try a more wordy approach.

If we we want to calculate the scale factor we want to know how much it has grown right?

[marsh bluff]

yes

[quiet sail]

So we take how large it is, divided by how large it used to be

So we have the new length, divided by the old length, it is like percentages, which you might have had

Does that make more sense?

[marsh bluff]

ok so it was 12 before and now its 8 so 8/12

and 8/12 is 2/3?

[quiet sail]

Yeah that is it!

It seems like that was a better explanation.

[marsh bluff]

is there a way to simplify 2/3 i seriously forgot 😭

[quiet sail]

There is not hahaha

[marsh bluff]

what goes on top again og or copy?

[quiet sail]

Read carefully

[marsh bluff]

i think ik how to get scale factor

wait lemme find my notes

ok so copy over og

but

okok

i only have a example of triangles 💀

[quiet sail]

Well this is very similar to what you just did, see if you can so the same again?

[marsh bluff]

12/8

[quiet sail]

Yeah you got it

[marsh bluff]

okok

it just sounded wrong in my head since i didnt have a line segment inm y notes

[devout snow]

@marsh bluff Has your question been resolved?

[marsh bluff]

<@&286206848099549185>

[devout snow]

@marsh bluff Has your question been resolved?

[marsh bluff]

<@&286206848099549185>

.close

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[eternal pecan]

Hello, I'm struggling to understand this. Where did the 2 come from? I dont know what to search to find out what formula was used

[eternal pecan]

totally understood the right side ofc

[woven radish]

NEON

[eternal pecan]

thank you!

.close

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[thin fern]

With each cut, the most you can do is double each piece you have so wouldn't it just be doubling each time?

[scenic surge]

right but

if thats the case

then wont it be 2^x

so if I cut it three times I will have 8 pieces 2^3

but then

for 100 pieces

[thin fern]

Yeah you'd just round up to the next power of 2

[scenic surge]

it would be 6.64 cuts

i put it in a calculator

[thin fern]

Because 6 cuts won't be enough since 2^6 gets you a maximum of 64

so you'd need at least 7

[scenic surge]

right

[thin fern]

so the expression is just round up to next power of 2

[scenic surge]

but is that right

to say

[thin fern]

and take the exponent

[scenic surge]

I would need atleast 7

[thin fern]

Yes

[scenic surge]

like would that be the "minimum value" then

is that what they meant

[thin fern]

Yes because you can't do 6

[scenic surge]

right

so the formula would be

wait a min acc

what would the recursion formula even be

[thin fern]

$m(n) = \lceil \log_2{n}\rceil$

[woven radish]

Ari

[thin fern]

o that worked

[scenic surge]

WTHHHHH

how did u even

come up with that

[thin fern]

have you learned logs

[scenic surge]

reminds me of

binary

algo

[scenic surge]

yes in hs havent worked with them since like calc 1/2

[thin fern]

what math class are you in rn?

[scenic surge]

its not even math

its computer science

cs theory

[thin fern]

oh

[scenic surge]

but isnt that similiar to

binary searcj

log_2 n

where u keep dividing in half

[thin fern]

Idk what that is

but do you know the ceiling function (the thing I put around the log_2 n)

[scenic surge]

oh nvm

never seen that before

dont think it would be fair to use it either because I have never seen that

[thin fern]

I'm not sure there's a better way to write it without using log or ceiling

at least not in math expressions

[scenic surge]

acc

il ask my prof but

could u explain it

what it does

the thing u put around

[thin fern]

Ceiling function is the least integer greater than or equal to

[scenic surge]

isnt ceil similiar to rounding

we had it in cs too

[thin fern]

or like basically you just round up to the next integer (unless it's already an integer, which it won't change)

so like ceiling(pi) = 4

[scenic surge]

right it just rounds up

i remember ceil my bad

never knew it had a notation for it in math

but

would that rlly be the recursive formula?

how is that recursive

[thin fern]

it's not

I'm not sure how'd you use a recursive function here

[scenic surge]

instead that would be a closed form expression right

[thin fern]

yes

[scenic surge]

m(n - 1) + 1

wait

lets say

i had a odd number n

wont it have the same minimum cuts as n + 1

so like 7 unit and 8 unit

will have the minimum cuts

2^3

so 3

so recursion formula would be

if n = 1 then 0
if n odd then m((n+1)/2) + 1
if n is even then m(n/2) + 1

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[crystal gazelle]

Hi guys. I feel extremely stupid but how do you end up with 17,4 when doing long division on 122/7? I forgot most of it and get only 17,3. Uni student here 💀

[wooden veldt]

Show your work

[topaz axle]

i can't remember anyone explaining long division here

maybe i missed it

butmostly people just say google it

[crystal gazelle]

I never did math in my life and now in uni im struggling with it

[restive river]

Math trick! $\frac{122}{7} = \frac{122 + 18}{7} - \frac{18}{7} = \frac{140}{7} - \frac{14}{7} - \frac{4}{7}$ $$ = 20 - 2 - \frac{4}{7}$$

[woven radish]

What should I do: Physics

[crystal gazelle]

Answer gotta be 17,4 without calculator. Can you get there?

I mean right answer is in decimals, 17.4. How can I get that number without calculator?

[restive river]

use the trick i just showed up

simply the fraction so the top is is a multiple of the bottom

keep doing that untill you can't anymore

then it's just basic addition / subtraction

all you have left to do is division of $\frac{4}{7}$

[woven radish]

What should I do: Physics

[devout snow]

@crystal gazelle Has your question been resolved?

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[barren garden]

Hello

[barren garden]

how is this wrong?

[devout snow]

@barren garden Has your question been resolved?

[graceful cosmos]

ye

[barren garden]

huh?

im asking why is it wrong

[graceful cosmos]

Oh it is? It looks right to me. Hmm.

Oh whoops yep, the second one shouldn't be checked

Some elementary row operations change the determinant in predictable ways

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@barren garden Has your question been resolved?

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[still dawn]

if i find tbe derivative and it’s a constant, is that the slope of the entire function? or does the derivative change?

[tame palm]

That depends. If you found f'(x) = c for all x, then yes.

It's typically only linear functions that will have a constant derivative for all x.

[devout snow]

@still dawn Has your question been resolved?

[still dawn]

ty

why is it F(y) ?

this is soln

why didnt the power rule apply for 2nd line

they had y^-2

shouldnt it be -2y^-3?

oh nvm they did

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[stark shuttle]

Hello

[stark shuttle]

I'm not sure about this

[steep marten]

no

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[limber wraith]

How do i derive the formula d = vit + 1/2 at^2 to get the formula for time

d = displacement
vi = initial displacement
a= accelleration
and t = time

[still dawn]

I don’t think you can for that unless your given more info

[restive river]

do you mean rearrange?

$$\Delta x = v_0 t + \frac{1}{2}at^2$$

[woven radish]

What should I do: Physics

[restive river]

$\frac{1}{2}at^2 + v_0t - \Delta x = 0$

[woven radish]

What should I do: Physics

[restive river]

Quadratic equation, solve for t

[devout snow]

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[devout snow]

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[twilit estuary]

,rotate 270

[twilit estuary]

hows x=0 discontinous

[robust dust]

are you asking about 11 or 12

because the variable for 12 is p, and the function isn't even defined for p=0, so it doesn't really make sense to say whether it is continuous or discontinuous there

or, I guess if you define D(0) to be any particular value, then it'd still be discontinuous because the right-hand limit of D tends to infinity as p tends to zero

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[calm kayak]

Hey anyone available for help

[calm kayak]

?

[main gull]

Just post your question

[calm kayak]

Need help reviewing for a test

[kindred mantle]

this question is weird

you can use quadratic equation if you like

[calm kayak]

Where do I start, kind of lost ? Do I factor it down ?

[kindred mantle]

well do you know factor by grouping

it makes this shit hella easy

excuse my homework but i did this rq for you

do you understand the process of factor by grouping?

you can separate 13 into two parts technically

-3 and 16

because if you add -3+16 you get 13

[calm kayak]

Yes, thank you so much, okay group factoring it

[kindred mantle]

the answer is on the right

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[midnight radish]

Hi I'm not sure what it means or the difference of reflect over x and y axis. This is parent functions and I gotta turn the statement to an equation which is in a form of y=a |x-h| + k

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[slim token]

Because it has a open circle

oh you deleted it

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[restive river]

Why are they doing 1/2* 1 mil *3500

shouldnt it be 1/2 * 1 mil * 5000

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@restive river Has your question been resolved?

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[restive river]

it’s not a function right

i just need some confirmation

[solid spire]

Since x=4 has 2 solutions it can't be a function

[restive river]

You are correct

.close

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[stray nova]

Is my A U B correct?

[eager lodge]

no

[pale bolt]

note that there are real numbers below 2 that aren't 0, 1, and 2

[stray nova]

oh you are right

(-negative infinity, 2] U (2, positive infinity)?

[pale bolt]

this was not what I meant at all

B is a set of integers

for example, the real A union B does NOT contain 1.5, but your definition would

[stray nova]

so we interpret B as a single entity?

[pale bolt]

B is basically the list of numbers 0, 1, 2

so what do you get when you combine 3 integer numbers with the set of all reals greater than 2

[devout snow]

@stray nova Has your question been resolved?

[stray nova]

Oh I get what you mean now

[devout snow]

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[mild basin]

i know that dy/dx is not a fraction
but it feels like I am almost multiplying dx to both sides of the equation here

what is a better way to interpret it?

S dx are like brackets for the integrand

but why isn't it dy =?
we have removed "with respect to x" from the left side of the equation
so now it's just y=

I think I am almost getting it but not quite. the notation is still rather confusing to me

[tall knoll]

The left side is $\int \dd y$ which is just y

[woven radish]

Steakanator

[tall knoll]

(We ignore +c for now)

[mild basin]

OH, so we did multiply both sides by dx?

we also multiplied both sides by S?

[tall knoll]

I've always thought of it as multiplying by dx and I've yet to have it bite me

We aren't multiplying by it, we're integrating both sides

[mild basin]

huh.. even though dy/dx is not a fraction

it feels so weird

[stone stump]

this is basically abuse of notation but chain rule says that it works

[mild basin]

yeah, so in a way we are just doing basic algebra to get to the next step?

[stone stump]

you are integrating both sides with respect to x

so on both sides you have int (stuff) dx

[mild basin]

what's a better way to think about it, to avoid abuse of notation?

[stone stump]

where the left side is int dy/dx dx

[mild basin]

if I don't multiply both sides by dx I would ______ think of it this way instead

[stone stump]

aka you are integrating the derivative of y

which just gives y back

[stone stump]

.

[tall knoll]

Which step

[mild basin]

second line

wait maybe I misunderstood

you said you think of it this way and it is yet to bite you

[tall knoll]

Again I don't like saying "multiplied by S"

[mild basin]

with multiplying LHS and RHS by dx

[tall knoll]

As mentioned it's an abuse of notation

[mild basin]

lol

Yeah, it doesn't even make sense

S dx belong together like ( ) belong together

I'm not multiplying both sides by ( on the left and ) on the right

I'm just surrounding the expression in paranthesis

so the same is true for S dx

alright lemme think about it

this is really what's going on here?

[stone stump]

yes

[mild basin]

but why do I get this when I try to calculate the integral of dy/dx?

so it's still treating it like a fraction

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[brisk raft]

Why are these two not equal?

[brittle burrow]

$\sqrt{9(\frac73\sec x)^2-49}$

[woven radish]

chlamydia

[brittle burrow]

on numerator

[brisk raft]

Still no match

oh

nvm

No match still

Got it

thanks

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[hard valve]

When doing long division when do I stop when the degree of the remainder is less than the divisor or less than or equal

[pine rock]

if its equal you can divide some more

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[simple basin]

can someone please help me with this?

[simple basin]

it’s about transformations

[narrow lagoon]

inverse u mean $1/f(x)$ or $f^{-1}(x)$?

[woven radish]

Gigrise

[simple basin]

the second one

f^-1 (x)

[narrow lagoon]

Aint that part of definition? The inverse is a **function **such that blabla?

[simple basin]

not sure.. that’s what i assumed too lol

[narrow lagoon]

thats why its probably ment multiplicative inverse 1/f(x)

cause that fails to be a function sometimes

Do u have definition of an inverse?

[pale bolt]

the inverse of a function is not always a function

[orchid sierra]

Hi, @simple basin

You only need one example of each

Having said that, I'm pretty sure that an inverse function must be a function? 🤔

Ok, so the mapping we find which is an inverse may not be a function, but we are used to defining the original function on a domain such that its inverse will be a function

Classic example: f(x) = x^2

This is a function

Its inverse though:

x = y^2
y = +-sqrt(x)
f^-1(x) = +-sqrt(x)

Is not a function

But if we define f(x) only on x>=0, then the inverse function will only be the upper branch of f^-1(x), so it will also be a function

[simple basin]

oh i see!

i sort of figured it out but that confirmed it for me thank you!

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[spare stratus]

hey

[spare stratus]

couting by 1000 seconds every 5 seconds how long will it take to get from 765000 to 50000000

Wait I got it it's 2 61/72 days

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[barren garden]

Hello

[barren garden]

I have a more of a physics related question

what do these binding posts do?

Also what have I done wrong here in finding i1 and i2

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[barren garden]

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[prisma frost]

How on earth do I answer 4?

[narrow lagoon]

most likely by observing b)

[prisma frost]

How does b help me?

[narrow lagoon]

I suppose u will have explicit formula for A and then could estimate A(t)<4 or smthn like that

[devout snow]

@prisma frost Has your question been resolved?

[delicate fox]

just calculate the area A by pi*r^2 and take the derivative lol

for b) you integrate

then see what happens to the answer in b) for values of A past 4 in c

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[fickle canyon]

how did they substitute the value in -4x^2y^2

[fickle canyon]

in the second last line

im confused due to the signs

[dense jay]

(x^2+y^2)^2=x^4+2x^2y^2+y^4
(x^2-y^2)^2=x^4-2x^2y^2+y^4

the second line is the first line -4x^2y^2

hence (x^2+y^2)^2-4x^2y^2=(x^2-y^2)^2

then add across to get the line shown

(x^2+y^2)^2=(x^2-y^2)^2+4x^2y^2

[fickle canyon]

$(x^2+y^2)^2=x^4+2x^2y^2+y^4$

[woven radish]

xiskzwajinsaju

[fickle canyon]

$(x^2-y^2)^2=x^4-2x^2y^2+y^4$

[woven radish]

xiskzwajinsaju

[fickle canyon]

$(x^2+y^2)^2-4x^2y^2$=$(x^2-y^2)^2$

[woven radish]

xiskzwajinsaju

[fickle canyon]

alr i understood what u mean but how did they subsitute ad-bc bracket in place of +4x^2y^2

i dont get that sadly

[dense jay]

(-2xy)^2=4x^2y^2

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[hard valve]

Where did the e^x in the numerator go?

[brisk raft]

u=e^x
du=e^xdx

The e^x in the numerator become du

[hard valve]

Ohhh

So I just replace e^x dx by du

[brisk raft]

Yeah

[hard valve]

But we let u= e^x of the numerator right

[brisk raft]

You substitute u into the denominator

When you do u-sub you must have everything with respect to u

so you have to get rid of the x's somehow. And you also have to make sure du substitutes in

[hard valve]

Got it

Thank you !

[brisk raft]

np

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[quasi wasp]

How would i begin this question?

[hybrid snow]

Change the cubic to x^3 + kx^2 + (1-k)x^2 - x + k, divide by x-l, then manipulate the second-to-highest order again

[quasi wasp]

How would I change the cubic to that?

@hybrid snow

[hybrid snow]

You just do

Replace it

Divide by x-k

It's equivalent

All@im doing is breaking down ferms

Terms

[quasi wasp]

Im sorry I just dont see why we have changed the cubic to the other equation?

[hybrid snow]

Split the fraction

And my bad it should be x^3 - kx^2 + (1+k)x^2 - x + k

If you divide by x - k, and split fractions:

(x^3 - kx^2)/(x-k) + ( (1+k)x^2 - x + k)/(x-k)

The leftmost fraction becomes x^2

[quasi wasp]

Ok so to get it to the form of x^3 - kx^2 + (1+k)x^2 - x + k initially what do I times it by

[hybrid snow]

Wdym times it by