help-23

[humble grove]

no i dont think so

<@&286206848099549185> its been more than 15 mins

im in desperate need

for help

exam in a fwe days

and i barely understand this topic

[hexed dune]

If it is proportional to the square of the initial speed

That means

When you double your speed

Your minimum braking distance will quadruple

[humble grove]

okay

makes sense

[wintry condor]

isn't that what i said here?

[humble grove]

ah

[hexed dune]

Yh you did say that

[humble grove]

i misunderstood

my bad

but its asking

wait

so i would choose one point

then quadruple it

?

[hexed dune]

@humble grove pick a speed

[humble grove]

20

[hexed dune]

Find the minimum braking distance that corresponds to that speed

[humble grove]

so id quadruple it?

im really confused rn

[hexed dune]

Then pick a speed that is double the speed you already took

[humble grove]

sorry

[humble grove]

how do i find this

[hexed dune]

The graph

[humble grove]

ohhh

60?

20,60

[humble grove]

yes

[hexed dune]

Yh

[humble grove]

and do the same?

[hexed dune]

Yh

[humble grove]

40,240

so is that it?

[hexed dune]

Then see if the minimum braking distance is quadruple the other one

Yg

Yh

[humble grove]

60x4

OH MY GOD

BRO UR SAVING MY FUCKING LIFE

HOLY SHIT

bro i literally

last quarter

studied

at least 80 hours in 1 week

before the exam

and got a 9/30

[hexed dune]

Ooof

[humble grove]

can u please help me on another question

[hexed dune]

Sure

[humble grove]

wait i did the same thing in the exam

she marked it was wrong

is it bc of the messed up shit that i wrote around it

[hexed dune]

Yh

That's an absolute mess

[humble grove]

"Explain why, if the braking force is constant, you would expect theoretically the braking distance to depend on the square of the speed."

[humble grove]

BRO I DIDNT

KNOW WHAT TO

DO

ISTG

[hexed dune]

You literally already did it lmao

It was even circled

[humble grove]

no i dont think i did that purposely, i think i just picked 2 random points istg

she circled it

not me

[hexed dune]

Yh

As in

You were right

Even though you didn't know

[humble grove]

yup

bro how old r u

uni?

[hexed dune]

Yh

[humble grove]

nicee

[humble grove]

If the braking force is constant, the braking distance will depend on the square of the speed because when you double the speed, the minimum braking distance will quadruple?

[hexed dune]

Do you know your Suvat equations

[humble grove]

yes

[hexed dune]

@humble grove do you know the one that relates acceleration distance and speed

[humble grove]

yes

[hexed dune]

Which is it

[humble grove]

v^2=u^2 +2as

i think

[hexed dune]

Yh that's right

[humble grove]

yes

[hexed dune]

So now just say u² = 0

[humble grove]

2as

uh

wait listen man

wait wait

@hexed dune

[hexed dune]

https://media.tenor.com/3N71OTe0__cAAAAM/frank-castle-wait.gif

[humble grove]

How much for you to tutor me for 1 hour everyday

or 30 minutes

whatevers food enough to u

physics

[hexed dune]

i can do physics and maths. Don't ask me about chemistry though

[humble grove]

nah i dont take chem

but pls dont charge too much

im still a teen u get me

paying w my own money

[hexed dune]

Well at this point we are past the scope of this server

So just dm me

[trim dune]

lol

[safe radish]

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[ornate beacon]

can u solve this?

[safe radish]

Please don't occupy multiple help channels.

[tardy mango]

#help-9

.close

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[unique citrus]

How on earth would one calculate the nth digit of Pi with code? I'm seeing all of these super confusing formulas and Idk what they mean or how to implement them. I'm a programmer not a mathematician ;-;

[brave wolf]

If that formula works, you can just rewrite this into code

If there is some symbol you don't understand I will explain it

The only thing I don't understand is B_2n

lemme search it...

[unique citrus]

I don't understand much of it, the context is confusing

And yeah the B_2n I don't get

Are the (1 - something^-n) terms exact, or do you add more of them to increase precision?

It looks like some sort of series to me but idk how it works

[brave wolf]

It looks kinda like this, but there are only 4 terms, and no dots

So I suppose it's not meant to be infinite product

or it's just wrongly written

What's the source of your formula? I cannot find anything similar

[unique citrus]

https://mathworld.wolfram.com/Digit-ExtractionAlgorithm.html

I need to calculate pi to n base-10 digits

[brave wolf]

If you just need to calculate pi, you can just do 1-1/3+1/5-1/7+1/9..... and multiply by 4

[plucky elk]

what's the point of the formula? there are expansions of pi you can just download

[unique citrus]

That's the Leibniz series

It only converges on pi, you can't trust the results to be precise for any given n

[plucky elk]

that's what the remainder theorem is for

[unique citrus]

I have an implementation of it but it takes a crap ton of n to even get a few digits

// Gets the first n digits of pi using the Leibniz formula
fn digits_of_pi(n: u32) -> f64 {
    let mut pi = 4.0;
    // Start with subtraction for the first term
    let mut parity = false;

    for i in 0..n {
        let term = 4.0 / (i * 2 + 3) as f64;

        match parity {
            true => pi += term,
            false => pi -= term,
        }

        parity = !parity;
    }

    pi
}

[unique citrus]

I've not heard of that

[plucky elk]

https://en.wikipedia.org/wiki/Chudnovsky_algorithm

[brave wolf]

B_n is bernoulli number

[plucky elk]

if your n is less than $10^{10^{12}}$, then just download a file

https://pi2e.ch/blog/2017/03/10/pi-digits-download/#download

[flat frigate]

riemann

[unique citrus]

It's for an assignment I don't think that my prof would like that

[unique citrus]

Pi is actually a rational number

[brave wolf]

really?

I mean srrsly?

[unique citrus]

I really don't have any idea where to start with this

All I know is that I would need a for loop for the summation

I have a factorial function

[brave wolf]

So what's the problem

[unique citrus]

Well what are the first two fractions? What do they represent? It looks like just a ton of arbitrary numbers to me

[brave wolf]

I am not sure about this, but I think that you compute the infinite sum to some precision, and then you look back

[plucky elk]

no

[plucky elk]

they meant all with respect to the world record

[unique citrus]

Also, I assume q has to do with the precision, but how do I convert an n (as in the nth base-10 digit) to a q

[plucky elk]

q is just the dummy index

more typical dummy indices are i, k, n

[brave wolf]

Once you find the infinite sum You use this and compute the fraction on the last line to get pi

S is the infinite sum

Is it correct @plucky elk ? I am not sure if it's how the algorithm is meant to be implemented

[plucky elk]

lots of different public implementations online

e.g. just on github https://github.com/topics/chudnovsky-algorithm

no and don't interrupt people's help channels

[safe radish]

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[jaunty echo]

im just starting this kind of math can someone help me understand this

[sand minnow]

$(3x-4y)-(4x-3y)=3x-4y-4x-(-3y)=3x-4y-4x+3y=-x-y$

[flat frigate]

Duh Hello

[jaunty echo]

?

[sand minnow]

the only real step here is that the 2nd parenthesis has a - in front of it that you need to distribute, so $$-(4x-3y)=-4x+3y$$

[flat frigate]

Duh Hello

[jaunty echo]

oh ok

[sand minnow]

so you get $$3x-4y-4x+3y$$from here you can just subtract the ones which have same variables

[flat frigate]

Duh Hello

[sand minnow]

can you see how the answer comes from there?

[safe radish]

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[spiral pine]

Can someone explain this question?

[potent bay]

u know the difference between the 2 given intervals(the "universes")?

[spiral pine]

yea

first one is without 0 and 1

second is with 0 and 1

[potent bay]

a) says for ALL x there EXISTS such y, that x>y

[spiral pine]

would the correct answer be true, true?

oh so y can only be between 0 and 1

aka the answer is false for both

[potent bay]

x too

[potent bay]

no

[spiral pine]

dangit

for (0, 1) i can always pick a y closer to 1 or 0

so that must not be in the universe?

[potent bay]

hm? the question in which universe is the given statement true

[spiral pine]

think im dumb dude

[potent bay]

and yeah, in an open interval, u can always find a smaller number, for example 1/n is all in the universe and it gets smaller than any given number from the universe after a while

[potent bay]

no, but so that must not be in the universe? made no sense for me here

[spiral pine]

okay so, (0, 1) is true but [0, 1] is false

@potent bay how about this one tho

on the [0, 1]

[safe radish]

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[idle cave]

How do I convert an if then statement in discrete math to a representation that uses AND or OR

[idle cave]

I already claimed this channel

Sorry

[river snow]

Yeah, sorry!

[idle cave]

If p then q

How do I represent that without the arrow

I know it’s possible but I can’t find any resource on it on google

[trim swan]

(not p) or q

@idle cave

[idle cave]

Thank you

[trim swan]

no problem

[spare walrus]

@idle cave remember to .close

[idle cave]

Thank you baro

.close

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[rose tapir]

sorry i know thisll be a real long explanation and i keep asking questions ksjdksjd, but i have no clue how to do this because the 2nd image is the only thing in our notes and i dont get how they started (like how they knew to divide by x+2) so if someone could walk me thru the steps or even just knows the keywords i could search for something on yt thatd be

[plucky elk]

https://www.cuemath.com/calculus/asymptotes/

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@rose tapir Has your question been resolved?

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[inner shoal]

how do i find the horizontal asymptote for x-5/x+4

[plucky elk]

scroll up

[inner shoal]

thanks

.close

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[gleaming juniper]

just part 2 please

[gleaming juniper]

What I have so far

[safe radish]

@gleaming juniper Has your question been resolved?

[spark geyser]

When is that going to be real

[gleaming juniper]

when it equals zero?

[spark geyser]

When what equals 0

[gleaming juniper]

the solution 🥹

[spark geyser]

When the imaginary part equals 0, the whole complex number is real

So you want to find the value of n where isin(n theta) = 0i

There is 75 so just find the lowest value of n for sin(75n) = 0

[gleaming juniper]

mmm

ahh

so sin-1(0)/75

[spark geyser]

Basically find the LCM of 75 and 360

Then do that divided by 75 to get n

[gleaming juniper]

oop

[spark geyser]

If you don’t understand why I can try to explain

[gleaming juniper]

please do

it would help

[spark geyser]

You American?

I’m just wondering which course you’re doing

[gleaming juniper]

no

im irish

[spark geyser]

Oh well I’m English and I’m doing further maths a level so maybe it’s similar

Anyway

[gleaming juniper]

leaving certificate higher level

maybe

[spark geyser]

Basically when you have a complex number what sets that apart from a real number?

[gleaming juniper]

the i

[spark geyser]

Exactly

So a complex number is real when it has 0i

[gleaming juniper]

mhm

[spark geyser]

So with your example of r^n(cos(75n)+isin(75n) you want to make the imaginary component 0

[gleaming juniper]

yeah

so youd separate it

[spark geyser]

So to do that you can ignore the rest of the question and just focus on isin(75n) = 0i

So then we get sin(75n) = 0

We know that sin = 0 in multiples of 360

So if n can only be a natural number (positive integers >= 1) we need to find the lowest number where 75 and 360 meet in their multiples

You will find that 1800 is the lowest point where that happens

So then do 1800/75 to get 24

You can then check that by doing sin(75 * 24) = 0

So does that make sense?

[gleaming juniper]

i get what youre saying, its just ive never seen this bit before

😭

[spark geyser]

Oh

Just imagine a sin graph

[gleaming juniper]

if i could just understand that id say i have it

[spark geyser]

Oh wait I might have made a mistake

It should be in multiples of 280

180*

Tho k of your sin graph

It touches 0 at every 180 degrees

[gleaming juniper]

yes

[spark geyser]

Which means if you have 75 theta you want that to be equal to a multiple of 180

You with me so far?

[gleaming juniper]

yeah i think

no yeah id o

[spark geyser]

Ok so if 75 theta is a multiple of 180 then sin 75 theta is also 0

Now we just need to find the lowest theta that does this

So if you remember back to your primary school days when you did LCM and HCF for the first time

Try doing the LCM of 75 and 180

I don’t blame u if u forgot it lol

[gleaming juniper]

💀

15

[spark geyser]

Uhh

[gleaming juniper]

900

[spark geyser]

yes

[gleaming juniper]

😩

[spark geyser]

LCM is lowest common multiple

So like for 3 and 4 it’s 13
W

Because multiples of each are
3, 6, 9, 12
4, 8, 12

12 is the first multiple where they are the same

So we are doing the same for 75 and 180

Anyway

[gleaming juniper]

ahhhh

[spark geyser]

Now that you have the LCM just divide by 75 to get n

n = 12

[gleaming juniper]

i seeeeee

[spark geyser]

Do u have the answers so we can check if it’s right?

[gleaming juniper]

i dont

[spark geyser]

Ah rip

Well I’m pretty confident we got it

[gleaming juniper]

grand

you love to see it

thanks a lot mate

[spark geyser]

Np

[gleaming juniper]

🙏

.close

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[frozen harbor]

Im trying to find the derivitive of this using natural logs rules

But I dont know what Im doing wrong

[dull sequoia]

Shouldn’t the fractions be the other way

When you differentiate the ln(2e^x-6)

[frozen harbor]

What other way?

I think that when you differentiate ln of something, it gives you 1/that something and then times that by the derivitive of the something

[dull sequoia]

Well d/dx ln(f(x)) is what

[frozen harbor]

f'(x)/f(x)

[dull sequoia]

Ok I’m just not awake enough today

[frozen harbor]

That's ok

[dull sequoia]

It doesn’t look wrong

Have you tried simplifying it further

Like cancelling out the 2’s

[frozen harbor]

I can get this

But photomath and mathway give me really different answers and they dont look like theyre the same

[dull sequoia]

Try expanding

And finding common denominators

[frozen harbor]

Is that when you distribute the outside to the insides

[dull sequoia]

Yeah

Then refactorise

[frozen harbor]

This is the best I could do

[dull sequoia]

ab-ac ≠ b-c

[frozen harbor]

?

[dull sequoia]

You cancelled it wrong

Look at the numerator

[frozen harbor]

Oh

How do I cancel things then

[dull sequoia]

Factorise first

[frozen harbor]

How do I do that

[dull sequoia]

Factorise the thing you drew red over

[frozen harbor]

What does that mean

[dull sequoia]

Do you see the numerator is in the form ba-ac

Un-expand

[frozen harbor]

I dont know the ba ac thing but

I see that theres some things in both fractions that look similar

[frozen harbor]

If i multiple e^x by itself does it give me e^x^2? Like the x is squared?

[frozen harbor]

I understand the a b c breakdown now

But how do you even come up with the thing on the middle of the page

Also in what you wrote you have two things in the denominator but mine has three

This is confusing

[dull sequoia]

I squared it

[frozen harbor]

Oh ok

So first thing I'd do is combine the two fractions

Cause they have the same denominator

And then I would pull out a common factor

[safe radish]

@frozen harbor Has your question been resolved?

[safe radish]

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[ember sphinx]

Opposite angles add to 180

[edgy cape]

like this?

(2u+32)+(u+74)=180

[ember sphinx]

Yep

[edgy cape]

but then i get a decimal

[worthy hemlock]

I don't think that's right

I'm pretty sure it's opposite angles are equal to each other

[edgy cape]

oh yeah they are congruent

(2u+32)=(u+74)

which then goes to 42

[ember sphinx]

Oops

Too many circle theorems

[worthy hemlock]

That's not a circle?

[ember sphinx]

Yea but I thought it was in one

[edgy cape]

so was i right?

[worthy hemlock]

Sure

[edgy cape]

it was wrong

the answer is 64

[worthy hemlock]

Well, you found the value for u

The question asks to find the measure of y

[edgy cape]

damn

[worthy hemlock]

In that case, sum of angles equals 180, so angle y + angle x = 180

[edgy cape]

what abt this one?

[worthy hemlock]

Opposite sides are equal

[edgy cape]

so

(u+6)+(4u-63)=180?

[worthy hemlock]

What?

[worthy hemlock]

.

[edgy cape]

idk how to do this ngl

.close

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[opaque sorrel]

hi can someone tell me if my approach makes sense?

[safe radish]

@opaque sorrel Has your question been resolved?

[safe radish]

@opaque sorrel Has your question been resolved?

[safe radish]

@opaque sorrel Has your question been resolved?

[safe radish]

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[mortal sandal]

what have you tried?

[dreamy mirage]

plugging in

[mortal sandal]

and you got infinity over infinity after you distributed?

[dreamy mirage]

indeterminant

i just dont know how to lhopital this

[mortal sandal]

What if the problem didn't have the sin part in it?

could you solve it then?

[dreamy mirage]

dont know

[mortal sandal]

$\lim_{x\to\infty}\f{x^3}9*\f{10}x$

[flat frigate]

monikanicity

[dreamy mirage]

the answer would just be infinity

cause the top power is higher than the bottom power

[mortal sandal]

right so

importantly

your first step wasn't to plug in, right?

what was it?

[dreamy mirage]

distribute?

[mortal sandal]

to multiply the fractions yeah

so can you apply that to the full problem

[dreamy mirage]

ok what now

[mortal sandal]

distribute in the full problem too

before plugging in

[dreamy mirage]

i got 10x^3/9x -10x^3/9(sinx10/x)

[mortal sandal]

right

[dreamy mirage]

sin undefined??

wth is this

[mortal sandal]

?

sin(10/x) you got right

not sinx10/x

[dreamy mirage]

yeah

when u plug in inf dont u get 0

like the limit for that part

the sin part

because 10/inf is just 0

[mortal sandal]

right

[dreamy mirage]

so is this answer just infinity?

[mortal sandal]

Ah damn does this become infinity minus infinity

I should have thought about that, that's indeterminant

[dreamy mirage]

why inf minus inf

if sin 10/x is mult by the other part

and sin 10/x kinda reduces to 0

[mortal sandal]

x^2/9 - x^3sin(10/x)/9

oh you have infinity*0 on the right then

ah I messed this up

[dreamy mirage]

is that indeterminant>

?

im new to lhop sorry

[mortal sandal]

yeah

it's indeterminant whenever the two parts aren't working in the same direction

0*infinity, one is small and one is big

infinity - infinity one is positive and one is negative

you don't know which one is more important

[dreamy mirage]

so what do i do now?

derivative?

[mortal sandal]

we'd need to get it in the right form first

This one is really cruel

I don't suppose you'd know the Taylor series for sin(x)?

[dreamy mirage]

no

[mortal sandal]

This isn't a hw problem surely, right?

[dreamy mirage]

sure is

its like the final boss

breezed through the others

then i reached this monstrosity

[mortal sandal]

well you could write it as x^3 / everything else and apply L'hopitals 3 times in a row

as in x^3/ (9 * (10/x-sin(10/x))^-1)

would take a long time

[dreamy mirage]

howd we get there

[mortal sandal]

without a calculator

[dreamy mirage]

it says use analytical methods

am i missing something there

[mortal sandal]

You can rewrite x*y as x/(y^-1)

I.e. don't just plug a large x into a calculator?

it seems like to do this without great pain you would need to know Taylor series

[dreamy mirage]

bruh

[mortal sandal]

limit as x->∞ of (x-sin(x))/x^3

maybe solving this would help somehow

though it's not lhopital-able

[mortal sandal]

yeah you'd use this expansion. The first term cancels with something else, the second one becomes relevant, and all the rest are too small to matter

[dreamy mirage]

this is unbelievable

[mortal sandal]

I think my lhopital method might not work anyways so

[dreamy mirage]

lets say the /9 didnt exist from the original problem

[mortal sandal]

a simpler way to solve (1-cos(x))/x^2

if I have a way to solve that without Taylor series I can work from it

[dreamy mirage]

this /9

[mortal sandal]

ye makes sense

[dreamy mirage]

if i could solve the problem then

would i be able to divide the answer by 9

and get the answer

[mortal sandal]

yes

since lim cf(x) = c*lim f(x)

If you want to simplify the starting problem to the same thing I'm working on now

This is a bit absurd

[dreamy mirage]

im trying the x^3 approach that 9 looks intimidating

[mortal sandal]

But you can apply a substitution like u = 10/x

@lean otterow help

shoot

@toxic stratus

sorry random person for the ping

[toxic stratus]

nani

[mortal sandal]

No Taylor series allowed

You just learned L'hopitals rule

[mortal sandal]

best I can do is u=10/x followed by 1 application of L'hopitals which gets you to something like this which I believe has some kind of squeeze theorem solution

is there better?

and when I say "some kind of squeeze theorem" solution I mean pretty sure I vaguely remember this as a Mr Ou problem

[dreamy mirage]

wait putting the x^3/9 on the bottom is allowed right?

[mortal sandal]

/(9x^-3)

[dreamy mirage]

i just saw a rule about that but i dont see how that helps anything

[mortal sandal]

like that it would be

yeah sadly it doesn't eventually become a constant if you keep deriving it

[dreamy mirage]

so put it as another complex fraction as 1/x^3/9?

on the bottom

[mortal sandal]

1/(9/x^3)

unless I misunderstand

[dreamy mirage]

i got a decent looking derivative

by some miracle

probably wrong

[mortal sandal]

ah

idk of what but gl

[dreamy mirage]

yeah gg

[safe radish]

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[hallow surge]

Can someone tell me how to derrange 5 letters in such a way that first one occupies the 5th position

[hallow surge]

.close

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[zinc vale]

Stuck at (2)

Thought that it is about invariant space or Cayley-Hamilton theorem

[safe radish]

@zinc vale Has your question been resolved?

[zinc vale]

<@&286206848099549185>

[safe radish]

@zinc vale Has your question been resolved?

[zinc vale]

<@&286206848099549185>

[safe radish]

@zinc vale Has your question been resolved?

[safe radish]

@zinc vale Has your question been resolved?

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[atomic totem]

would it just be X squared -5 squared

[compact ferry]

no

[atomic totem]

can you explain how to do it pls

[uneven jacinth]

you have to use the (a-b)^2 identity

[modest sky]

(a-b)²= a²- 2ab+b²?

[uneven jacinth]

yup

just plug in x= a and 5 = b

(a-b)^2= a^2 -2ab + b^2

(x-5)^2 = x^2 - 2 * x * 5 + 5^2

x^2 -10x + 25

[atomic totem]

I’m a bit lost

[modest sky]

(a-b)²= (a-b) * (a-b)

[atomic totem]

where do you get -2ab from

[modest sky]

=a²-ab-ab+b²

Do you understand?

[atomic totem]

oh so you do -ab but since it’s squared you do it twice?

so is this right? this is the next question

[modest sky]

Yes that's right!

[atomic totem]

so surely almost every answer is the same just the signs is different?

[modest sky]

Yep if there is a +, then it's "+2ab". If it's a -, then it's "-2ab"

[atomic totem]

oh that’s easy, thank you

.close

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[leaden scaffold]

I'm so confused, a calculator is telling me that the antiderivative of :e^x-3x^2+sin (x) is e^x-x^3-cos(x)+c...

[leaden scaffold]

I thought it would be e^x-3x^3/3-cos(x)+c..

[peak estuary]

and what is 3/3 ?

[leaden scaffold]

Wow this is embarassing

[peak estuary]

happens

[safe radish]

@leaden scaffold Has your question been resolved?

[leaden scaffold]

One quick question, why would this be the answer to this:

Why would 4sin(2x) turn into -2cos(2x)?

[peak estuary]

try differentiating -2cos(2x)

[leaden scaffold]

How would I know intuitively though with 4sin(2x)?

I know the antiderivative of sin is cos, but Idk how we get -2 and (2x) from 4 and (2x)

[peak estuary]

well first, the antiderivative of sin is -cos

so that takes care of the minus

and like you hopefully noticed, when you differentiate -cos(2x), you have to multiply it by 2 from the chain rule

so if you are integrating you have to do the reverse and divide by 2

[leaden scaffold]

so you get 4-cos(2x) because the antiderivative of sin is -cos, then divide by 2 because you have to multiply it by 2, and get 2-cos(2x)?

[peak estuary]

please dont write the numbers and the minus in that order without brackets

but yes that's the idea

[leaden scaffold]

Why would this not be (sin^3/3)-sin(x)?

[leaden scaffold]

This is for calculating anti derivative btw

[safe radish]

@leaden scaffold Has your question been resolved?

[leaden scaffold]

<@&286206848099549185>

The answer to this is (sin^3/3)+C but not sin^3/3-sin(x)+C, why is that so?

[safe radish]

@leaden scaffold Has your question been resolved?

[leaden scaffold]

Dsssaas.close

.close

[safe radish]

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[karmic hedge]

Let the height be x

Since x is adjacent to 35 degrees, and you know the hypotenuse

[patent musk]

am i right with D**

[patent musk]

yea

[karmic hedge]

Which trigonometric identity can you use

Yea

[patent musk]

okayy thank you i alr solved it i jus wanted to make sure

[karmic hedge]

I thought you picked something else and d was the correct answer

My bad

[patent musk]

i forgot to write this before 😭

[patent musk]

ty tho

am i right with B here?

[karmic hedge]

Yup

[patent musk]

okayy

i got a few more am i right with D here?

[shadow sparrow]

yup

soh cah toa 😎

[patent musk]

yess

[shadow sparrow]

yuh

[patent musk]

kk

wish i could give medals on here

am i right wit D here

@shadow sparrow are you still here?

[shadow sparrow]

o ya

uhhhhhhh

i think so

i dont wnana do the math but B is definitely taller

and definitely not by more than 60 ft so must be D

[patent musk]

okay yea

am i right with A?

@shadow sparrow im srry i dont want to bother you but what abt this one 😭 am i right with A?

[shadow sparrow]

sin 30 = x/120 sooo

120*sin 30

is uhh

yea 60

[plucky elk]

.close

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[white basalt]

Hello can anyone verify if I am correct the wording is tricky

[buoyant shadow]

you need to → both ways to express "only if"

[rich stratus]

Both ways means it goes both directions
1 "I'll see you at dinner if i have time"
2 "I have time if i see you at dinner"

Oh ok you can say 2 since it says only if

[buoyant shadow]

or you can like, "(q & r) or (~q & ~r)"

[white basalt]

so the one directional arrow changed to a both bi would be correct?

[buoyant shadow]

yes

i'm not sure what's the shortest way but it should be correct

[rich stratus]

I don't think so
It doesn't say "only if" at the raining part

So there's a chance i am seeing you at dinner but it isn't raining

[buoyant shadow]

right, i got confused

[white basalt]

i thought if and only if was <->

[buoyant shadow]

that'sfor the second half

p −> (q <−> r)

straightforward

[rich stratus]

I don't know the notation
Does "a -> b" mean "if a, then b" or the other way

[buoyant shadow]

yes

[white basalt]

yeah a->b would mean if a then b

[buoyant shadow]

pretty certain it means if a then b

[white basalt]

so then based off that this would be the correct way to do this one?

[buoyant shadow]

yeah

but it's equally correct to do r <−> ( ... )

[white basalt]

@buoyant shadow ok thank you very much enjoy your day

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[buoyant shadow]

thx

[safe radish]

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[tawny path]

why is the solution to this

this

and not minus 2

[tall bough]

Minus 2?

[tawny path]

i mean x^2 - 2 / 2x^2

thats the formula i used

[tall bough]

Show your work

[tawny path]

basicly i have u' = 2x and v' = 2

so its
2x * 2x - 3x^2 - 1 * 2 / 2x^2

like this

and then this

and this is my solution

[tall bough]

Umm

[shadow glade]

when you square the bottom:

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

[flat frigate]

Sooshon

[shadow glade]

you forgot to square the coefficient in the bottom, that maybe cancels out with the one in the numerator? Haven't checked your whole solution but that's first thing i caught

[tall bough]

How u come at 3x+1

Should be

[tawny path]

give me a sec

bruh

[tall bough]

$\frac{(2x*2x)-(x^2 +1)*2}{4x^2}$

[flat frigate]

Fucktalogist

[tawny path]

i looked at b)

but i was doing d)

guess that solves the problem

thx guys

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[tawny path]

.reopen

[safe radish]

✅

[tawny path]

i still dont get it ._.

i dont know what to do after this

[stray socket]

What are you differentiating

d)?

[tawny path]

this

ye

[stray socket]

This is your work?

[tawny path]

yep

[stray socket]

Just simplify what you have

4x^2 - 2x^2 = 2x^2

Factor out 2

2/4 = 1/2

[tawny path]

could it be that it should be -2 instead of +2?

then everything would make sense in my head

because the brackets had a - before right?

am i correct?

im just so unsure if im doing it correct

.close

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[hidden merlin]

i dont know where my mistake is ?

[plucky elk]

why do you think you're wrong

[hidden merlin]

i dont see how you can go from the top half to the answer

this i mean

oh wait

mb sorry

just to clarify, have i broken any rules this time, i dont mean that in a satire sense i genuinely want to know.

[plucky elk]

multiply the x^(x-2) through and you'll get your expression

you can check by plotting them both using desmos

[hidden merlin]

thank you, ye it matches

[hidden merlin]

ooh i didnt think of that, thank you

.close

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[turbid path]

is 3(t)^t in a(b)^c form ?

[plucky elk]

yes

[turbid path]

even though b

& c

are the same variable?

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[gentle shoal]

How many times does the graph f(x)=a(x-h)^2+k and g(x)=a|x-h|+k intersect?

[gentle shoal]

i need an explanation

in

an 8th grade to 9th grade

way

please help

i need a simple way

to find

it

without graphinh

graphing

please

help

yes

ty

question

[glass terrace]

If you want to simplify it algebraically, you can set f(x)=g(x)

[gentle shoal]

could u explain

[glass terrace]

So that a|x-h|+k = a(x-h)^2+k

Are all the variables of f(x) and g(x) equivalent?

[gentle shoal]

i never learned partial factoring

[glass terrace]

In your problem?

[gentle shoal]

wdym

[glass terrace]

Is the "a" variable in f(x) and g(x) the same?

[gentle shoal]

yeah

so is x

k

h

[glass terrace]

Gotcha

[glass terrace]

Can you simply a|x-h|+k = a(x-h)^2+k up until you get stuck?

[gentle shoal]

yeah

|x-h| and (x-h)^2

@glass terrace

dont leave me

please

[glass terrace]

I'm still here

[gentle shoal]

ok

[glass terrace]

So, do you know how to make two algebraic equations when you have absolute value?

[gentle shoal]

yeah

but

after i got

|x-h|=(x-h)^2

what do i do

[glass terrace]

Let's rewrite the right side first

[gentle shoal]

wdym

by

right side

[glass terrace]

(x-h)^2 side

It just makes it easier to see

Would you agree that (x-h)^2 = (x-h)(x-h)?

[gentle shoal]

wait

OH YEAH

so

(x-h)(x-h)= |x-h|

right?

skitten?

u there

[glass terrace]

Yep

Working on my own hw, don't mind my slow responses

So, let's work with the absolute value side

[gentle shoal]

ok

[gentle shoal]

is this correct

[glass terrace]

Do you remember how to create two equations when you have two abs value?

[glass terrace]

Correct

[gentle shoal]

ok

we can do

one with plus

and one with minus

[glass terrace]

Yes

[gentle shoal]

ok

[glass terrace]

Can you write it out?

[gentle shoal]

(x-h)(x-h)=x+h

and

(x-h)(x-h)=x-h

right

?

[glass terrace]

Not quite

[gentle shoal]

ok

so what would it be

[glass terrace]

Here's an example

[gentle shoal]

OH

wait

[glass terrace]

The side opposite to the side of the absolute value side is what changes 👍

[gentle shoal]

how would we do it with this

so

im confused

[glass terrace]

Let me get the equation, hold on

So

|x-h| = (x-h)(x-h)```

[gentle shoal]

yeah

[glass terrace]

x-h = (x-h)(x-h)
x-h = -(x-h)(x-h)

[gentle shoal]

wait

huh

so

only one negative

distributes to one

(x-h)

[gentle shoal]

whats next

[glass terrace]

Would it be more clear if I wrote it out as x-h = -[(x-h)(x-h)]?

Basically you make one entire side negative

[gentle shoal]

ok

i see

[glass terrace]

Do you notice what both sides have in common?

[gentle shoal]

x-h

is equal too

[glass terrace]

Mhm!

So what you can do is cancel a (x-h) from both sides

x-h = (x-h)(x-h)

I am going to use the positive equation as an example

When you simplify that, what do you have next?

Wait actually, is this equation solveable? God I would feel bad if this can't be taken further. I think there are equation has two unknowns tho so it should be

Oh yeah it definitely is, carry on ^^

[gentle shoal]

ok

wait

so

[gentle shoal]

so (x-h) would be remaining

[glass terrace]

Yes

What about the left side?

What's left on the left side?

[gentle shoal]

im confused

(x-h)

[glass terrace]

Like, what's left on the x-h side once you divide both sides by x-h?

[gentle shoal]

what about the negative one

like

[glass terrace]

By my question, or how to continue?

[gentle shoal]

what u ment

by canceling

i do that to both equations

too

so

what would be left

[glass terrace]

Once you understand how to do it to the positive side, you'll pretty much be able to figure out how to do the negative side too

[gentle shoal]

id get it

this is what i have

oh nvm

it isnt readable

[gentle shoal]

wdym

so

[glass terrace]

I was saying that after you simplified it, you could eliminate x-h

[gentle shoal]

so

for the (x-h)(x-h)=x-h

[glass terrace]

Until you got 1 = x-h

[gentle shoal]

only

x-h

[glass terrace]

Mhm?

[gentle shoal]

would be remaing

[glass terrace]

Ah, I don't think so

Let me rewrite it in a way that is more clear

[glass terrace]

So, given the equation

x-h = (x-h)(x-h)

[gentle shoal]

this is what i have

so far

could u check

[glass terrace]

Looks right except that on the negative side, it should be -(x-h)(x-h) = x-h

[gentle shoal]

ok

so what to do

[glass terrace]

Would you agree that the equation 1(x-h) = (x-h)(x-h) is the same as x-h = (x-h)(x-h)?

[gentle shoal]

then

[gentle shoal]

yes

[glass terrace]

And you have an (x-h) on both sides, right?

[gentle shoal]

yeah

so

[glass terrace]

So how would you simplify it so that you can eliminate the (x-h) on both sides?

[gentle shoal]

ok

um

[glass terrace]

Try dividing both sides by (x-h)

Does that make any sense?

[gentle shoal]

skitten

i did this

i gtg eat

dinner

so

could

u just explain

the steps and the answer

?

that will be nice

thanks

@glass terrace

SKitten

u there

please

dont bail

when we are this close

@glass terrace

<@&286206848099549185> could someone help me continue the work so far

#help-23 message

this is what i did so far

and

i need to continue it'

please

<@&286206848099549185>

[shadow sparrow]

can you actually read that?

the pic

yourself

[gentle shoal]

yeah

zoom in

[shadow sparrow]

yea idk

not about reading it

just in general

[gentle shoal]

aw man

i really need help

[shadow sparrow]

yea idk

my best guess would just be 2

because u have two solutions

-(x-h) and (x-h)

[gentle shoal]

yeah