help-42

[calm coral]

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[knotty moat]

What does question number 1 want

Im confused

[tired tusk]

You must have a formula that has force as a function of the coefficient of friction no?

[knotty moat]

I think so

Ff = 60 therefore force = 60

But how do I get N

TO HAVE

MsN

Isn't it

Like tan the number

The rule js

N sqrt 1- ms²

[calm coral]

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[remote mural]

this is my homework and this is the step it showed

how does he get -4

from just grouping the trinomial

in the denominator

[sick plover]

-4 where?

There's a lot of -4s

[tough prism]

lol

its probably hard to see

but in the first image you sent

that fractoin is negative

[remote mural]

ohh

thank u

for the clarification

.close

[calm coral]

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[remote mural]

Need help with the HW question, I am a bit confused on how to tackle it

[calm coral]

@remote mural Has your question been resolved?

[cloud nexus]

"certain school inside a certain castle"

everyone and their dog have read harry potter at this point what's the point of trying to hide it

[calm coral]

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[calm coral]

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[plush dust]

does anyone know the pronunciation for F(c,0) and F'(-c, 0) and 2c

[plush dust]

like how to you say it

[prisma mango]

You mean the word "foci"?

Because you can just google pronunciation of foci

[plush dust]

how about the c?

is that center

[prisma mango]

It's just a letter to denote the coordinate point

[plush dust]

is this right?

the pronunciation for F(c,0) and F'(-c, 0) is F of (c,0) and F ' derivative of the function (-c,0).

[calm coral]

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[calm coral]

@plush dust Has your question been resolved?

[calm coral]

@plush dust Has your question been resolved?

[calm coral]

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[ebon abyss]

Hi i need help with this question

[ebon abyss]

I’m not really know the meaning of the question 😔

[calm coral]

@ebon abyss Has your question been resolved?

[ebon abyss]

<@&286206848099549185>

Can anyone help me

[round sonnet]

How much have u done by urself

@ebon abyss

[ebon abyss]

I’m not done with that

[round sonnet]

Like have u started

[ebon abyss]

I’m started but dont know much the meaning of the question

[round sonnet]

Ok

[ebon abyss]

Its like if we need to finalize the assigiment, we just plus all the tasks

Like: 5+ 5+ 3+2+2

But i think i’m wrong

[round sonnet]

Yea

[round sonnet]

The number of lines represent the number of days

[calm coral]

@ebon abyss Has your question been resolved?

[ebon abyss]

And then??

<@&286206848099549185>

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@ebon abyss Has your question been resolved?

[calm coral]

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[worldly schooner]

"As an aspiring computer programmer who grew up playing lots of video games, I plan to one day go into game engine development. I think that nearly all types of video games use vectors, whether it is realized or not. I'll use Super Smash Bros as an example, a two-dimensional fighting game in which two or more players are positioned on floating platforms suspended in the air where they duel in a goal to achieve dominance over the other players. In these games, there are coordinates which point to positions on the screen, an x-coordinate and a y-coordinate. Let's say you were trying to design an AI character for players to practice against. This AI character will have an ability in which it becomes a ghost and floats to your character over a set interval of time, which does not change no matter how far the AI is away from your character. Whether it is 5 units away or 10 units away, it will arrive in exactly one second. How could you calculate the velocity the AI should travel with in order to achieve this? One way you could do it is to first compare the coordinates of both players on the screen. If the AI has coordinates (3, 5), and the player has coordinates (8, 12), you could find the angle at which the AI should travel by finding the slope between these two points, (y2-y1)/(x2-x1) = 7/5"

[worldly schooner]

This is what I have so far, I am trying to make a point about the application of vectors in video games for a physics class but I am a bit unsure of myself and unsure how to finish

[flint pilot]

Sheesh

[worldly schooner]

That sounds bad.

[tender coral]

If you're applying vectors, why don't just calculate the length of the vector with phytagoras

[worldly schooner]

Oh yea... 3:30AM brain

[glass heart]

the nice thing about vectors is that we don't have to use slopes anymore. we can just subtract the two points from each other and get the vector which points from one to the other. and then we can travel along that vector

[worldly schooner]

I can't believe I can't remember how to make calculate the speed it needs to travel in order to get their in one second

I guess cause there is no units of length besides coordinate points I am confused

Units / 1 second I guess?

God I need sleep

[glass heart]

yeah go to bed and tomorrow it will be easier

[calm coral]

@worldly schooner Has your question been resolved?

[worldly schooner]

"As an aspiring computer programmer who grew up playing lots of video games, I plan to one day go into game engine development. I think that nearly all types of video games use vectors, whether it is realized or not. I'll use Super Smash Bros as an example, a two-dimensional fighting game in which two or more players are positioned on floating platforms suspended in the air where they duel in a goal to achieve dominance over the other players. In these games, there are coordinates which point to positions on the screen, an x-coordinate and a y-coordinate. Let's say you were trying to design an AI character for players to practice against. This AI character will have an ability in which it becomes a ghost and floats to your character over a set interval of time, which does not change no matter how far the AI is away from your character. Whether it is 5 units away or 10 units away, it will arrive in exactly one second. How could you calculate the speed and direction the AI should travel with in order to achieve this? If the AI has coordinates (3, 5), and the player has coordinates (8, 12), you could find the distance the AI needs to travel by using the pythagorean theorem. The difference in the character's x-coordinates is 5 and the difference in their y-coordinates is 7, so inputting these values into the pythagorean theorem (a^2+b^2=c^2) you get (5^2+7^2)= 74 and the square root of 74 is 8.6. So the distance the AI needs to travel is 8.6 units (magnitude). The angle, or direction at which the AI needs to travel can be calculated using the trigonometry function arctan(7/5) which yields a result of 54 degrees. Lastly, we need to calculate the speed at which the AI must travel to arrive in one second, which is 8.6 units per second.
Therefore, in this case using the teleportation ability, the AI should travel 8.6 units per second at 54°."

Okay I think I have a tangible answer thrown together

Would you say this displays an application of vectors in a computer science career?

[glass heart]

sure. although I'd probably just say that it travels at 8.6 units along the vector (5, 7). instead of reducing it to angles

angles don't work as easily in higher dimensions

btw, please use paragraphs

[worldly schooner]

Makes sense, thanks. I will format my messages better in the future

.close

[calm coral]

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[glass heart]

and now go to bed

[calm coral]

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[north plover]

Hello

[calm coral]

Please don't occupy multiple help channels.

[north plover]

How do I even start bruh

[feral meteor]

Which chapter does this belong to @north plover

I was thinking to solve it like a simultaneous equation

[calm coral]

@north plover Has your question been resolved?

[modest viper]

HAHA I sent the answer

[modest viper]

oh u can actually just use substitution

[north plover]

No clue brotha it’s a practice paper

[north plover]

Thx for the answer lmao, posting on multiple servers does help

.close

[calm coral]

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[feral meteor]

Simplest way would be to just find x and substitute.... This question got me slightly confused

[modest viper]

welcc!

[modest viper]

o the qn said that can’t solve

so I think that’s what made this qn harder

[calm coral]

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[spice jasper]

Hey

[spice jasper]

Task 5 b

B

I’ve made the equation based on the regression analysis

But don’t know how to solve B

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[spice jasper]

Hi

[spice jasper]

Still in need

<@&286206848099549185>

[calm coral]

@spice jasper Has your question been resolved?

[remote mural]

Write your question

Oh its up there

[calm coral]

@spice jasper Has your question been resolved?

[spice jasper]

Yeh

[calm coral]

@spice jasper Has your question been resolved?

[spice jasper]

Man this is fucked up

From yesterday I tried getting help

No one helps me

[spice jasper]

<@&286206848099549185>

But this is highschool math

Then stop being here dude

Valuta

Danish krones

Wut?

[spice jasper]

Man i’m gonna send the work in a bit

<@&286206848099549185>

Help please

I waited 2 days

[calm coral]

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[spice jasper]

Worst services ever

[calm coral]

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[brisk folio]

can someone please explain to me how to tell the difference between a unique/one equation vs infinite equation matrix in linear algebra? like just by looking at it

[brisk folio]

like for example, an inconsistent would be 0=3

[calm coral]

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[brisk folio]

thanks to whoever sent that

[calm coral]

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[plush lantern]

i am completely lost

does anyone have any clue on what to do

[fickle gate]

We know they are not parallel since one of them is on the 2nd quadrant and the other in 1st quadrant and non of them are on the axis

[calm coral]

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[simple hornet]

How can I go to vertex form?

[simple hornet]

I want to do 9-4 but does that follow BEDMAS?

[sick plover]

a + bc ≠ (a + b)c

What's vertex form?

[simple hornet]

y=a(x-h)^2+k

[sick plover]

It's already in that form

Wrong way around, but still

[simple hornet]

do I just add 9 to the end?

[sick plover]

If you mean flip the order so 9 is at the end, yeah

[simple hornet]

How would I show my work?

[sick plover]

There's not much work to show

You're basically turning a - b into -b + a

[simple hornet]

Ok

One more thing

For going from factored form to vertex

Basically you find the axis of symmetry and then sub it into the equation to find y right?

[sick plover]

You could, yeah

[simple hornet]

ok

That's all

[calm coral]

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[calm coral]

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[remote mural]

would anyone mind helping me with this equation

[jaunty sigil]

1. add 3 on both sides
2. raise each side to power of -3/4
3. simplify

[remote mural]

ok thank you sorry for bothering

.close

[calm coral]

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[worldly plover]

How do I do b. and c.?

[calm coral]

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[calm coral]

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[pulsar girder]

i dont have a drawing but i need to find 3 angles from this. i swear its an impossible equation

[dull wagon]

i dont have a drawing
have you tried making one?

[pulsar girder]

i dont need one to understand it im just saying i didnt post one here

its a quadrilatical

theres 4 sides one angle

[dull wagon]

i dont need one to understand it
its better if you had a diagram

[pulsar girder]

k ill make one quick then

[dull wagon]

it gives you a much clearer idea of where things are and what you can use

[pulsar girder]

shitty drawing but thats the idea.

[dull wagon]

and the side lengths?

[pulsar girder]

shit righ

sorry im so tired

the angles arnt proportional to my drawing. so theres no 90s even

my math teacher said only thing u could try is splitting it into 2 triangles but that doesnt even work

because u wont get tthe same angles

[dull wagon]

how much trig have you learned?

[pulsar girder]

Not hella advanced. This is supposed to be more of review

But it's post secondary

[dull wagon]

that doesn't give me a clear indication of what you know

[pulsar girder]

I basically wanna know if you guys can even solve this cause my teacher is supposedly insanely smart and even he was confused

[pulsar girder]

I know law of sin and cosine

Idk much else what to say

[dull wagon]

say that

[pulsar girder]

I know Pythagorean Therom 💀

[dull wagon]

cos law could be used to find AC,
and then again to get <ABC

[pulsar girder]

That's what I thought too but because one side is 63 and one is 71 then whatever answer I get for AC will be different for either triangle

And there's no more info on the other side

[dull wagon]

That's what I thought too but because one side is 63 and one is 71 then whatever answer I get for AC will be different for either triangle

[pulsar girder]

The hypotenuse of ADC and ABC are not the same. That's what I'm saying

[dull wagon]

hypot is not the correct term to use there,

[pulsar girder]

And because I have no info on the other side I can't even get the Hypotenuse of ABC

[dull wagon]

and I wasn't finished with my explanation

[pulsar girder]

If I were to split it into triangles

Okay

[dull wagon]

note that BD is common for both triangles ABD and BCD,
and you could set up a system of equations using more cos law
and angle sum of quadrilateral

[pulsar girder]

Wdym BD is common for both

Oh wait

[pulsar girder]

🤦 I tried doing it the other way like from AC

I might be able to get it now. Thanks

[dull wagon]

actually you don't actually need to set up a system

[pulsar girder]

But then u have no starting angle to get bd

Like if ur tryna get Ac u have 93 but to get BD u don't have anything

[dull wagon]

you can just apply sine law a few times after finding AC and <B

[pulsar girder]

How will sine law from AC help

Sorry I'm slow

Yeah you can get an angle for A and C but like I said those angles don't matter since they can't merge with ABC

[pulsar girder]

Yes but what would u do from there with half angles?

It's not like I know the total is 90 or 180 so whatever I get I can't just add to find the full angle

[dull wagon]

well you knew how to determine B earlier

[pulsar girder]

I thought I did..

[dull wagon]

sine law can be applied for that triangle too

[pulsar girder]

But there's no angles in ABC

[dull wagon]

wdym

[pulsar girder]

There's just the 2 sides

[dull wagon]

recall what was mentioned at the very start?

AC could be determine from the bot left triangle
which could then be used to determine <B from applying cos law again

in fact after knowing all 3 sides, you can determine all the angles from cos law

[pulsar girder]

How do u get B from 3 sides and no angle tho

[dull wagon]

cos law

[pulsar girder]

I thought u need 2 sides one angle

[dull wagon]

the cos law relates 3 sides of a triangle and an angle

[pulsar girder]

But there's no givin angle yet I would just have 3 sides

[dull wagon]

knowing 3 sides allows you to determine the unknown angle

[pulsar girder]

Ok I didn't know the SSS rule. That's why I was lost

[dull wagon]

determining c from a,b,C isn't the only thing the cos law is capable of

the cos law is just an equation with four variables

knowing 3 of them allows you to determine the value of the fourth

[pulsar girder]

Oh okay I thought cos law was just SAS

I'll get it from here ty

i lied im lost again

nvm

@dull wagon

I have the angle of B and I got lost

I can do law of sin but then I have sin on denominater and I get confused asf. How do I get my last 2 angles

Nevermind honestly I can't do this anymore

[calm coral]

@pulsar girder Has your question been resolved?

[calm coral]

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[safe chasm]

Can someone help me solve this one

[winter hazel]

what is this terminal side

[safe chasm]

is it x+2y?

What its asking for is Give the exact values of the six trigonometric functions of theta
.

[calm coral]

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[twin creek]

what does

f([a;b]) is included in [a;b]

mean?

and how different is it from

f([a;b]) = [a;b]

[calm coral]

Please don't occupy multiple help channels.

[graceful dust]

"is included in" probably means "is a subset of"

does that help?

[twin creek]

yeah so i cant say they re equal sets?

[graceful dust]

I wouldn't think so

not from that alone

[twin creek]

f is continuous on [a;b]

f([a;b]) is included in [a;b]

prove that
there exists c in [a;b] such that
f(c)=c

im stuck on this question and i dont know what to do. could you help me

[graceful dust]

intermediate value theorem is a good place to start

[twin creek]

i did try it but nothing

i have to prove that f is continuous. already done

now i gotta prove that f(a) < c < f(b)

how?

[graceful dust]

umm I don't think that's what you need to prove

like one thing, f(a) could be equal to f(b) or greater than f(b)

[calm coral]

@twin creek Has your question been resolved?

[twin creek]

dude im lost

honestly

[untold compass]

does this help?

[twin creek]

oh

so

umm

wait

okay

i see

it does

help

i ll see now

[calm coral]

@twin creek Has your question been resolved?

[calm coral]

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[lucid apex]

So for the parkland formula is there a better way to communicate to use the whole number of the percent instead of the actually percent?

[lucid apex]

4ml x TBSA (%) x body weight (kg)

for example lets say they are 50 kg. and the burn percent is 20

to communicate that hey use the 20 would I say use the W of TBSA %?

[calm coral]

@lucid apex Has your question been resolved?

[lucid apex]

<@&286206848099549185>

Can someone help me or no?

<@&286206848099549185>

[lucid apex]

<@&286206848099549185>

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[noble cedar]

Looking for help with understanding this

The “Vertex Form: y= …” in purple text is throwing me off

How do I convert “y = -2(x + 4)² + 3” into the same “y = a(x - h)² + k” format?

Oh I get it now

It’s just the opposite of whatever h is

If h is positive x is negative and if h is negative x is positive

Whatever makes x - h = 0

So the vertex of this quadratic is (-4,3)

Am I using the right word “quadratic” or is there a better word to use?

[sick plover]

No, everything you're saying is correct

[noble cedar]

Parabola / quadratic I get them mixed up

Parabola is the shape of the line?

[sick plover]

A quadratic equation draws a parabola

Quadratic is the name of the equation, parabola is the specific shape the equation draws

[noble cedar]

Oh so quadratic is just any monomial, binomial or polynomial with power of 2 as the highest power?

[sick plover]

Yep

[noble cedar]

Got it thanks

[sick plover]

Polynomial includes monomial and binomial, so you could just say "polynomial of degree 2"

[noble cedar]

I like to use monomial for x², binomial for x² + 2 or x² + 2x and polynomial for x² + 2x + 2, etc and anything beyond 3 terms

That way it’s more specific

Personal preference 🙂 don’t know if I’m shooting myself in the foot for doing that lol

But yeah an all encompassing term is much easier lol

Poly is the one that rules them all

[sick plover]

It's just a little redundant. There's already terms for higher numbers, such as "trinomial"

Why cut off at binomial and not trinomial?

[noble cedar]

True, I forgot trinomial

Haha

I thought I was missing one

But no such thing as a quadnomial right? Even iPhone is giving a red underline to that word

At that point it’s nothing else but a “polynomial”

Same goes for 100 terms.. also a polynomial

[sick plover]

Quadrinomial is occasionally used, but yeah, there's no real reason to name higher number term polynomials beyond trinomial

[noble cedar]

OK 🙂

Ty

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[pliant garnet]

What equation am I supposed to use for this ?

[jaunty sigil]

didnt i help u on this alr

[pliant garnet]

Yes big man

I came looking for the specifics on that equation

I solved it but

Like I said there were some details I was questioning

[hard trout]

What sort of details? The general solution? Or what?

[pliant garnet]

Well I wanted to know what the default format for the equation is. The equation I got was A=P(1- X/100) ^y which was a good help but I wanted to know what each part of it meant so I can use it for more problems like this

[hard trout]

Yeah ok

Let's say your computer costs $1000 dollars right now, and you know that after each year it'll be worth 10% less of its value during the prior year

How much is it worth after one year?

[pliant garnet]

$900

[hard trout]

Yes, exactly. Now, how much is it worth after the second year?

[pliant garnet]

$810

[hard trout]

Ope sorry got busy

@pliant garnet
Yep. So how much is it worth after N years?

[pliant garnet]

That's fine. But um. It's worth 10% less? Or X percent less depending on the years? I'm not too good at algebra

[hard trout]

That's all good

So how did you go from $1000 to $900

[pliant garnet]

The computer devalued 10%

[hard trout]

Yea

But what was the calculation?

i.e. what was the work you did to reach $900

Did you
• subtract $100, or
• multiply by 0.9, or
• halve it, then add $400
or did you do something else?

(When working out where a formula comes from, it's very helpful to show all the work done.)

[pliant garnet]

I'm gonna be honest I kinda just used common sense but mainly subtracted $100

[hard trout]

Yeah that's fair

Where did $100 come from (even if it's common sense?)

[pliant garnet]

The 10%

[hard trout]

Alright

So to put it into one formula, would you agree that you did

$900 = $1000 - ($1000 * 0.1)

[pliant garnet]

Yes

[hard trout]

Alright

So a similar process I imagine was done to get to $810?

$810 = $900 - ($900 * 0.1)

[pliant garnet]

Ohhh yeah

I see

[hard trout]

Yeaa

So let's make it a bit nicer and pull out the $900 and $1000 from their equations

$900 = $1000 * (1 - 0.1)

$810 = $900 * (1 - 0.1)

Do you see how I did that or would you like me to show my work?

[pliant garnet]

I see it

[hard trout]

Alright

Since we know the former equation, we can substitute it in

$810 = [$1000 * (1 - 0.1)] * (1 - 0.1)

which is equivalent to

$810 = $1000 * (1 - 0.1)^2

Looking at our formula for $900, we can also write it as

$900 = $1000 * (1 - 0.1)^1

Do you think from here you might be able to determine how you might make a formula for N years?

If not, consider how much the computer's worth after 3 years and see how that compares to the formulae we have

Also, are any of these steps unclear? I'm open to showing more work

[pliant garnet]

No this is perfect I'm just trying to think of the formula

N=(1-0.1)^X

[hard trout]

Close

[hard trout]

That gives us a number between 0 and 1; how could we make sure that reflects the price of the computer?

Or wait

Is N the number of years or the price? And the same with X

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[hidden pivot]

Hello, I dont know how to continue this question. I have filled in the things that I know how to do but I dont understand how I should continue it.

[hidden pivot]

should it be this:

the next one is

and then after that this

and then the entire thing?

[sick plover]

No, you do the entire thing after this

[hidden pivot]

ohh but how should u do it then? I have only been taught how to do it with one of those things in the middle

[sick plover]

Once you get this

You already know the truth tables for the left hand side and right hand side of a <-> b

So you can evaluate the truth table for a <-> b

[hidden pivot]

omgg thank you so much i finally get it

have an amazing day!

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[sour halo]

I don't know what to do next can anyone help!?

[mellow crater]

are we supposed to solve equation?

[sour halo]

No i need to prove this

[mellow crater]

aa

ok so you can factor out 2cos(2x)

[sour halo]

I don't have any single clue what to do next!!

By taking common ?!

[mellow crater]

then 2cos(2x)(cos(6x) + cos(4x))

then use cosA + cosB

formula

it will produce cos5x

but hmm

a

ye

and cosx

that's it

[sour halo]

How?!

[mellow crater]

look at the formula

(6x+4x)/2 = 5x

you could use this at the beginning but nvm

[sour halo]

Oh okk I got it now

[sour halo]

Really ??

How?!

[mellow crater]

yes, it would take 2 lines to prove it

[mellow crater]

in the 1st line you have cos(6x) + cos(4x) as you can see

[sour halo]

Seriously 🙂🙂

Ahh yes but what about the the cos(8x) and cos(2x)

[mellow crater]

maybe not two lines, but I guess it would be easier

proceed your solution

[sour halo]

Ok, that's not a problem I need to know the alternate way to do this math! Nvm

[mellow crater]

Ok I'll try

give a minute

yeah it works

[sour halo]

That you very much for the help dude 🌹

[mellow crater]

I'll show it

$$\cos (6x) + \cos (4x) = 2\cos (5x) \cos (x)$$
$$\cos (8x) + \cos (2x) = 2\cos (5x) \cos (3x)$$
So we have:
$$\implies 2\cos (5x) \cos (x) + 2\cos (5x) \cos (3x) =$$
$$= 2\cos (5x) (\cos (x) + \cos (3x))$$
Now:
$$\cos (x) + \cos (3x) = 2\cos (2x) \cos(x)$$
Finally:
$$\implies 2\cos (5x) \cdot 2\cos (2x) \cos(x) = 4 \cos (5x) \cos (2x) \cos (x)$$

[potent lotus]

Modus

[sour halo]

I see it bunches of thanks dude for showing me the easier way to do that math!

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[remote mural]

can someone just explain how to solve the problem, I don’t need the answer, just the solving process

[remote mural]

Problem #8

[remote mural]

i was trying to get a photo 🥲

<@&286206848099549185>

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@remote mural Has your question been resolved?

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@remote mural Has your question been resolved?

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[wanton blaze]

For

To find the domain and range
Its x >= +- 3
But how does one know which 3 is greater than or less than.

[cloud topaz]

Domain for square root function is >=0

So solve x^ - 9 >=0

As for range, the output of a square root function is always >= 0

[wanton blaze]

x^2 = 9

x >= +-3

how do ik if its

-3 > x > 3

[cloud topaz]

That’s not the right way to solve it

[wanton blaze]

3 > x >-3

[cloud topaz]

Draw a graph

Sketch y=x^2 -9

[wanton blaze]

I should prolly mention questions asks to solve it algebraically

[cloud topaz]

And see when it’s greater than 0

Then you just have to think about it

If x<=-3 then x^2 >= 9

If x>=3 then x^2 >= 9 as well

if -3<x<3 then 9>x^2

So we need x<=-3 or x>=3 as our domain

[wanton blaze]

one sec

let me write this down and re-read it

[wanton blaze]

but what abt the square root?

[cloud topaz]

What do you mean?

[wanton blaze]

cs this was the original question

[cloud topaz]

Just consider the inside

Cause we need that to be >= 0

[wanton blaze]

So we can just disregard the sqrt?

[cloud topaz]

Well we need the inside of the square root to be positive or zero for y to be defined

[wanton blaze]

Ahh ic.

[wanton blaze]

How did you get x^2 >= 9

the bolded part

[cloud topaz]

Because you need x^2-9 to be positive or zero

So you need x^2 to be more than or equal to 9.

[wanton blaze]

dont i want it to equal more than 0 or equal to it?

[cloud topaz]

Yeah you need the inside of the square root to be more than or equal to 0

So x^2 - 9 >= 0

Socx^2 >= 9

[wanton blaze]

OHHH

SHIT

Sorry.

I read that so wrong.

[wanton blaze]

But the exponenet

Shouldn't we like sqrt it to

remove it?

[cloud topaz]

It’s not an equation

So have to be careful

[wanton blaze]

isnt it like the same as saying
x^2 = 9

except we want to find values greater than or equal to "X"

[cloud topaz]

Yeah but you have to think about it carefully

I suggest drawing a graph

And see where the graph is greater than 0

[calm coral]

@wanton blaze Has your question been resolved?

[wanton blaze]

the x^2 = 9?

[cloud topaz]

https://youtu.be/8J_m-hMp8lY

[wanton blaze]

hmm i sorta get it

tysm.

[wanton blaze]

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[spark pagoda]

How should I learn advanced algebra and geometry?

[worthy willow]

start off with youtube is what I'd do

[leaden thunder]

Ask in #book-recommendations or one of the #discussion channels. Not a good use of a help channel

[spark pagoda]

Oh my bad.

.close

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[tepid estuary]

Hey

[tepid estuary]

How do I make this in a fracture

I understand how to make the ones with 0.676767 in a fracture but idk about 0.050505

Damn

Anyone else knows?

It’s like that

But I’m not sure on 0.05

Example of 0.63

[tall onyx]

put the repeating fraction over 99 and simplify

[tepid estuary]

Yea but how do I do it with 05

[tall onyx]

05/99

[tepid estuary]

There’s a 0 before 5

Isn’t that just 5

[tall onyx]

yeah

you have two digits so its 99 instead of 9

[tepid estuary]

Wouldn’t 5/99 be 0.05555555

[tall onyx]

no

[tepid estuary]

Oh

Ok thanks

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[tender coral]

You can devide the sum one with the k and the other one with the 3

[tawny oyster]

ik

[tender coral]

OK, then show your work please

[tawny oyster]

no no i didn't dive deep into sigma notation yet, i saw this somewhere and thought it was cool and wanted to know how to solve

can you solve it and show me?

[tender coral]

Yes, but I won't

[tawny oyster]

why not

[tender coral]

If you want to try it use Gauß Formula

[tawny oyster]

idk that

my curriculum has the very basics of sigma notation

i wanna see how this one is solved

[tender coral]

The sum 1 to n is n(n+1)/2

[tawny oyster]

and from n to 2n

?

[tender coral]

The sum of 1 to 2n - the sum 1 to n-1

[tawny oyster]

oh yea

substitute k with n and boom solved

just add the 3(n)

ty man

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[burnt citrus]

hi, i need some help with some questions, where im differentiating

[burnt citrus]

How would I go about this

[jaunty sigil]

factor out r^3/2

then simplify

then differentiate using product rule

[burnt citrus]

oh , we haven't been taught product rule yet

[jaunty sigil]

its a rule which differentiates products of differentiable functions
like (f.g)' = f'.g + f.g'

U can try simplifying until this form
Cus the steps after this require product rule

[burnt citrus]

hmm , alright

wait, did you factor out the r^3/2 or r^1/2

[calm coral]

@burnt citrus Has your question been resolved?

[burnt citrus]

do i distribute the r^1/2 or ? this is new to me sorry

i got it , lets go

What about this one ?

[jaunty sigil]

,

[jaunty sigil]

Differentiate using power rule

Apply sum rule first , then differentiate using power rule

[burnt citrus]

alright, thank you for your help

.close

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[kind forge]

When integrating 1/e^-x , why must we convert it to e^x

[kind forge]

why can't it stay and then become ln|e^-x|

oh nvm

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[frank gull]

lol

nice catch!

[ancient thistle]

chain rule...

[calm coral]

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[simple burrow]

can anyone help me with this pls

[velvet osprey]

where are you getting stuck on this one?

[simple burrow]

uhh um im not really sure where to start

ok so idk how to find a secant line

or tangent line cuz there are more problems that involve finding the tangent line

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[primal tusk]

I honestly completely forgot how to do slopes and my friend needs help. I have my guesses, I think #3 is = 0.2 or 1/5, and I also think #4 is = 5 but not 100%

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[dim sail]

Which solution is correct?

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[pine schooner]

I need help with an induction proof pertaining to the Euclidean algorithm. I have the proof written out, but I’m not sure if it really qualifies as an induction proof in its current state

[winter hazel]

yes, show it

[calm coral]

@pine schooner Has your question been resolved?

[pine schooner]

Thank you so much!

I’m pretty certain the reasoning is sound for some of the operations and substitutions in the inequalities, but I’m not sure if I successfully proved P(n+1) like at all, so I just added it on in a sentence toward the end

[pine schooner]

<@&286206848099549185>

[pine schooner]

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[random stratus]

Idk how to demonstrate that

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@random stratus Has your question been resolved?

[glass heart]

if you pick p+1 elements out of n+p+1, how many options are there if the p+1th element chosen is at position p+k+1

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[calm coral]

@grim idol Has your question been resolved?

[grim idol]

<@&286206848099549185>

[grim idol]

.close

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[calm coral]

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[clear pier]

is this correct?

[lapis blaze]

oh that's toxic lol

[clear pier]

not sure whether the left or right are the right work or if neither are

whats worse is its a study guide so im sure the answers on the real thing will be much worse lmao

latex is not a term ive heard LOL but does that mean just like 3(x+5) you would multiply 3 into x and 5?

[lapis blaze]

ah i just meant the colour of the text

[clear pier]

... lmao it doesnt matter

[lapis blaze]

ok anyway ¯_(ツ)_/¯

[clear pier]

yea got that

[oblique current]

Maybe check their work, you're explaining what they've already done on the left hand side

[lapis blaze]

sure its left side

close it ¯_(ツ)_/¯

[clear pier]

im assuming hes gonna do something like P(AxB)

2^AxB?

[lapis blaze]

yep

[clear pier]

ok thanks! appreciate it

.close

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[noble cedar]

Is this function odd, even, or neither?

I’m guessing even root is also a unique case.. neither odd nor even

[oblique current]

What's f(-x)?

[noble cedar]

But I just want to confirm if this graph passes as even (y-symmetry) or not that simple…

[noble cedar]

Ah yes that is the definition…

Even if f(x) = f(-x)
Odd if f(x) = -f(x)

[noble cedar]

I hope I have that correct?

-f(x) is strange to think about…

Just means flip 180 degrees? Or 1 pi?

[oblique current]

Well use f(x)=b

Or do you mean in general

[noble cedar]

It would not pass as odd.. origin 0,0 would cause 1 pi rotation to be Q3 and Q4

[noble cedar]

Yeah

But it has y-symmetry

So I suppose it is even

But wait.. it’s not really the same thing is it?

[oblique current]

Use the definitions you correctly wrote
If f(x)=b, what is f(-x)?

[noble cedar]

For y symmetry it needs to be opposite input gives same output

So I think this is incorrect

[oblique current]

I assure you its even

[noble cedar]

Oh…

Lol

[oblique current]

Answer this

[noble cedar]

f(-1) = b
(-1, b)

f(1) = b
(1, b)

Both have same output for y value

[oblique current]

So f(-x)=...?

[noble cedar]

b

[oblique current]

Which is f(x)

[noble cedar]

Right

[oblique current]

f(-x)=f(x)

Yay even

[noble cedar]

Interesting…

[oblique current]

Why are you surprised

[noble cedar]

So easy lol just seems. Like a trick question bc I’m used to parabolas

[oblique current]

Graphically even function are symmetric when reflecting over the y axis

[noble cedar]

Yeah

[oblique current]

You can see that by just looking

[noble cedar]

Odd is. Symmetric on origin

All even functions have (1,1) (0,0) (-1,1)

All odd functions have (1,1)(-1,-1)

[oblique current]

That's not true

[noble cedar]

But not all odd functions have (0,0) 😉

Hyperbolas

[oblique current]

Your even function here doesn't have (1,1) if b is not 1

[noble cedar]

That’s what professor Leonard states in pre calc

[sick plover]

You must've misheard or misremembered

[noble cedar]

No

[sick plover]

That's odd

[oblique current]

f(x)=x²+1 is even, it has none of those points

[sick plover]

Pun not intended

[noble cedar]

So professor Leonard is wrong on this one?

I think he’s stating before transformations

[oblique current]

Well he's just written some coordinates, without context we don't know what he meant

[noble cedar]

That’s all I can assume…

[oblique current]

Your interpretation isn't correct regardless

[noble cedar]

It is.. exactly what he states I can link the YT video

It’s called Graphs You Must Know in his Precalculus playlist

He calls them basic functions

“All of our odds”

Just to be clear he hasn’t discussed transformations yet

[oblique current]

All the graphs in that video happen to have the point (1,1)

[noble cedar]

OK

[calm coral]

@noble cedar Has your question been resolved?

[calm coral]

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[crude wagon]

I need help with “Basic Exponent properties” and the question im stuck on says “fill in the missing portion of each product to make the question an identity “

[crude wagon]

<@&286206848099549185>

[prisma mango]

!15m

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[fickle tide]

alright

do you know the basic exponent rules?

[crude wagon]

I kinda forgot

I think something to do with Associative and Commutative

[fickle tide]

well

all you need to do is divide the 2 terms given here

for the first question

18x^6 / 3x^2

[crude wagon]

Oh

Hold on

[fickle tide]

do yk the dividing rule of exponents

[crude wagon]

Uh no?

[fickle tide]

x^a / x^b = x^a-b

[crude wagon]

Do i need to divide the whole thing or something like 18/3 and 6/2

[fickle tide]

2^4 / 2^2 would be 2^4-2

[fickle tide]

divide the like terms with each other

[prisma mango]

You should know these

[fickle tide]

yeah

[crude wagon]

My teacher goes too fast

[prisma mango]

Then ask them to slow down

[crude wagon]

I did💀

[prisma mango]

If they didn't slow down, I doubt you asked

[crude wagon]

Wait for my first question

U told me to divide

[fickle tide]

yeah

divide the like terms with each other

18/3 is 6

[crude wagon]

And i got 6x^4

[prisma mango]

It's factoring, which is pretty much dividing that by the LCM

[crude wagon]

Do i have to do that to all of them?

[fickle tide]

yeah

[fickle tide]

yeah

[crude wagon]

Ohkk i get it now

[fickle tide]

👍

[crude wagon]

Thanks

[prisma mango]

@crude wagon Close this using .close

[crude wagon]

.close

[calm coral]

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[minor bronze]

help

[minor bronze]

i dont know what im doing wrong, did all this work to find the normal vectors of the planes to then find the angle between those two normal vectors

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@minor bronze Has your question been resolved?

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@minor bronze Has your question been resolved?

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.close

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[tawdry spruce]

Can someone explain how you get from the first to the second step in this?

[leaden thunder]

,calc 125*4

[potent lotus]

Result:

500

[tawdry spruce]

I'm trying to understand the methodology so that I can replicate it.

Does one of the numbers need to be able to be rooted to whatever power is outside?

Anotherwords, I dont want a simple answer based on this specific equation, I would like a general answer revolving this style of equation

[leaden thunder]

The method is to factor your number inside the square root

[tawdry spruce]

why 125 and 4 specifically though? why not 50 and 10?

[leaden thunder]

Because neither of the 2 that you wrote are perfect squares

[prisma mango]

Cubes*

[leaden thunder]

You want to factor into its prime factors

Squares or cubes 😛

[tawdry spruce]

okay so that does make sense. thank you, but how does the division of the x's work?

Theres three 5s and one 4 in the prime factors so 3/4 of the x's go to the 125?

im overthinking this arent I. 8 isnt divisible by 3 but 6 is the next greatest number that is...

[leaden thunder]

It's arbitrary. You can treat that independently of the number 500

sqrt(500x^n) = sqrt(500) * sqrt(x^n)

[tawdry spruce]

gotcha. thanks so much.

.close

[calm coral]

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[glacial oasis]

<@&286206848099549185> Hey, i've been working on this problemm for a while, and I feel like I am working on it completely wrong, here is some work of me doing some work:

[languid sphinx]

!15m

[calm coral]

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.

[languid sphinx]

.

[glacial oasis]

sorry, new to the server

[winter hazel]

its ok

[languid sphinx]

It's pretty messy, can you quickly explain what you've tried?

[glacial oasis]

so i found the derivative of the volume of a cone

[languid sphinx]

One mistake I'm seeing it the formula for the volume

It's not 1/3πr², but 1/3πr³

Maybe that's the mistake

[winter hazel]

wait its

[glacial oasis]

i see

[winter hazel]

4/3

4/3πr³

[languid sphinx]

That's for the sphere

[glacial oasis]

i just used the formula given in the example haha

[winter hazel]

wait im

sry

ive only seen spheres

[glacial oasis]

maybe the prof showed the wrong formula

[languid sphinx]

Oh I'm wrong too lol

It's actually 1/3πr²h, it's correct

[glacial oasis]

ah ok, good

[winter hazel]

[languid sphinx]

I just woke up ahah

[glacial oasis]

so after that I applied 3(h) for radius since the diameter is 3 times the height, which i see now as a mistake, because to find radius, r would be equal to 3(h)/2

[languid sphinx]

Yep

[glacial oasis]

ahh ok, i think i found my problem

thanks for the help guys!

[mighty bronze]

[languid sphinx]

Yw, not that we helped much... You found your mistake by yourself lol

Anyway once you're done you should close the channel with .close

[glacial oasis]

talking to others about how i reached a conclusion help analyze ones mistakes

.close

[calm coral]

Channel closed

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[winter hazel]

we misguided

so they would work extra hard to come back

[languid sphinx]

Yeah ahah

We actually did that on purpose

Not really I'm just really tired

[calm coral]

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[signal elk]

At this point, I am terrible in proving similar triangles

specifically speaking tho, I need help with 4)

c

to find the value of x

[calm coral]

@signal elk Has your question been resolved?

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[signal elk]

.reopen

[calm coral]

✅

[signal elk]

can anyone help

write yes if you can

[calm coral]

@signal elk Has your question been resolved?

[vocal lava]

Ive never understood these, can someone help ?

[calm coral]

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[remote mural]

hi

[remote mural]

can someone help me with rationalising this

[mortal orbit]

Hello, there are 2 ways of simplifying square roots :

1. factor the number inside the square root as much as possible, you might be able to find square factors, thus simplifying whats inside the root a bit more
2. when a square root is on the denominator, multiply the numerator AND the denominator by the same square root. Example :
   b/sqrt(a) = b•sqrt(a)/(sqrt(a)²) = b•sqrt(a)/a

[remote mural]

can you show me how to do this example?

[mortal orbit]

Sure

Let's start with square root of 48 (notation sqrt(48))

[remote mural]

4sqrt3

[mortal orbit]

Can you factor the number 48 ?

[mortal orbit]

Yes exactly

[remote mural]

this is what i’ve gotten up to

[mortal orbit]

Alright

Now, continue with 10/sqrt(3)

[remote mural]

multiply it by sqrt3?

after this idk what to do

[mortal orbit]

Thats it

Now, is there a common factor between 4sqrt3 and 10sqrt(3)/3 ?

[remote mural]

ohh they both have sqrt3?

[mortal orbit]

Yes

And now i think you can finish

[remote mural]

and what can u do w that

i rlly dk

[mortal orbit]

Since they have a common factor, you can factor them

[remote mural]

how?

[mortal orbit]

Like this :
4sqrt3 - 10sqrt(3)/3 = sqrt(3)*(...)

[remote mural]

um

i don’t know what that is

[mortal orbit]

Like ac + bc = (a+b)c

We know c = sqrt3 in that case

So what is 'a' and 'b' ?

[remote mural]

ok so is it

sqrt3(4-10/3)

[mortal orbit]

Exactly

The last trick is knowing how to simplify 4 - 10/3

[remote mural]

ohh ok

i got it now

thanks

[mortal orbit]

You're welcome

[languid sphinx]

.close

[calm coral]

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[shell rune]

$\alpha$ and $\beta$ are angles of a right triangle.

$$sin(\beta) = \frac{\sqrt{6} + \sqrt{2}}{4}$$
What is $sin(\alpha) * cos(\alpha)$

[potent lotus]

Pluton

[shell rune]

This is prob so easy but im so bad at trig

I only ask for what knowledge do you need to know to solve this type of questions.

Like some identity and that stuff

A link to some yt video that has in it the knowledge i need to solve this would be most helpfull

[wintry glacier]

well you can use pythagoras

try drawing the triangle

[pulsar granite]

you can use sin^2 + cos^2 = 1 to find cos

[pulsar granite]

same as this essentially

[shell rune]

That would give me cos(\beta)

Which ig is sin(\alpha)

[pulsar granite]

oh i misread