help-19

[mystic saffron]

Wait do you also include a b c and d?

[mint mirage]

What do you mean A, B, C, and D?

[mystic saffron]

Look the correct answer has B in it

Why ?

[mint mirage]

Not what it means

[mystic saffron]

Ohhhh

I’m so dumb

[mint mirage]

You left it unchecked meaning that it was correct to be unchecked

[mystic saffron]

Sorry

Thank you guys- can you help me with the c now?

I still don’t understand those

[mint mirage]

Notice in this image that the choices with the arrows at the correct answer choices, s m a g, like what you said above

[mint mirage]

Which?

[mystic saffron]

C and underlined c

[mint mirage]

So as I mentioned, $\subseteq$ means subset

[clever fjord]

CaptainNova22

[mystic saffron]

What’s a subset

[mint mirage]

So it's asking if a, c, m, p, s, w is a subset of A

[mint mirage]

A set within the overall set

So what is set A?

Meaning what are the terms in set A?

[mystic saffron]

cwpmsa

?

[mint mirage]

Yes

Now is a, c, m, p, s, w part of set A?

[mystic saffron]

How about without the underline

Yes

Right

It is part of it

[mint mirage]

That just means proper subset

[mystic saffron]

What does that mean?

Is it everything in the set ? So same answer

[mint mirage]

Upon some googling I found this https://mcckc.edu/tutoring/docs/blue-river/math/reasoning/Sets_and_Subsets.pdf

That will help a lot

[mystic saffron]

Ty !

[mint mirage]

It should help with the terminology

[mystic saffron]

Thank you but quick question so the underlined c and regular c is the same

So it’s just everything in the set?

The circle ?

[mint mirage]

You mean $\subset$ and $\subseteq$?

[clever fjord]

CaptainNova22

[mystic saffron]

Yes sorry

I mean those

What’s the difference

[mint mirage]

So $\subset$ is a proper subset and $\subseteq$ is just subset

[clever fjord]

CaptainNova22

[mystic saffron]

But in this circle thing what’s does that mean

[mint mirage]

That pdf will explain the difference fyi

[mint mirage]

What circle thing?

[mystic saffron]

The picture I sent you

[mint mirage]

Can you show what you mean

[mystic saffron]

Is says the proper subset for a is asm

Why?

Is it what intersects with B?

[mint mirage]

A proper subset is when all the terms exist in set A but is not the same as set A

[mint mirage]

No it doesn't

It says asm is a subset of set A

[mystic saffron]

Would cwp also be a proper subset?

[mint mirage]

As a proper subset or subset?

So $\subset$ or $\subseteq$?

[clever fjord]

CaptainNova22

[mystic saffron]

The one with the line

Without the line

Idk what’s the difference

Like in this scenario

[mint mirage]

I'm telling you, $\subseteq$ is when a set of elements is part of the overall set, ie pwc $\subseteq$ A while $\subset$ is a proper subset, where if all the elements in that set are part of the overall set but not the overall set itself

[clever fjord]

CaptainNova22

[mystic saffron]

Oh alright I get it

Thank you

🙏🏽

[mint mirage]

This is in that link I sent

[mystic saffron]

Okay thank you so much

I’ve got it!

🙂

Idk how to close this chat

[odd edge]

If you are done with this channel, please mark your problem as solved by typing .close

[mystic saffron]

.close

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[deep lava]

I can't figure out how to go about solving this question:

"Given that lg2 ≈ 0.3 and lg5 ≈ 0.7

Find an approximate value for lg2.5, lg0.4 and lg0.8"

[mystic saffron]

2.5 = 5/2

convert the required things in fractions

[deep lava]

okay! can you show me how you would do it with lg0.4 please

[main flame]

0.4 = 4/5 = (2^2)/5

lg0.4 = 2*0.3 - 0.7 = -0.1

[deep lava]

but i'm supposed to get -0.4 as the answer for lg0.4

[odd edge]

@deep lava Has your question been resolved?

[deep lava]

<@&286206848099549185>

[wanton bison]

You can write the decimals as fractions

2.5 = 25/10
0.4 = 4/10
0.8 = 8/10

[clever fjord]

bacc

[wanton bison]

4,8,10 and 25 can be written as factors in terms of 2 and 5 that you are given

For example 4 = 2²

[clever fjord]

bacc

[wanton bison]

You may try that now yoursefl!

[deep lava]

thank you sm!

[main flame]

slight mistake sorry
0.4 = 2/5

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[spiral basin]

.close

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[spring smelt]

differential equations

[soft terrace]

I don't think that PDE can be integrated by parts.

[spring smelt]

do i do substitution instead?

[soft terrace]

you can do it using an integrating factor, or by undetermined coefficients

[spring smelt]

okay

[soft terrace]

just to clarify

• by integrating factor method is where you find some function f(t) such that f(t)y' + f'(t)y = (d/dt)( f(t) y ) = f(t) 2t e^(2t).
• by undetermined coefficients is where you assume y = f(t), where f is some good guess function (probably an exponential here), and you solve for the undetermined coefficients.

[spring smelt]

erm

am i heading the right way

[soft terrace]

p(t) = -1

[spring smelt]

oh yes

[soft terrace]

here's an example if you wanted to follow along with it.

[spring smelt]

oh but what about the + c for my e^-t

[soft terrace]

I'm being silly, you've got the right answer.

[odd edge]

@spring smelt Has your question been resolved?

[spring smelt]

oop

[spring smelt]

nice!!!!

is it okay if i ask just one more....?

its ok ill open another

.close

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[wooden lintel]

plugin formula

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[wooden lintel]

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[mystic saffron]

do you know certain "well-known" limits with sine and cosine, something like sin(x)/x ?

[warm horizon]

no

my teacher mentioned it but i dont understand

sinx/x equals 1?

[mystic saffron]

$\lim_{x\to 0} \frac{\sin x}{x} = 1$ and there is another one for cosine

[clever fjord]

uop

[warm horizon]

sin(0) is 0

0/0 is und i thought

[quasi sparrow]

0/0 is undefined yes. But the limit exists

Maybe review the definition of limit

[warm horizon]

uhhh

how does the limit exist

[mystic saffron]

$\lim_{x\to 0} \frac{2x}{x}$ exists and it is equal to $2$ despite evaluating it at $x=0$ gives you $0/0$.

[clever fjord]

uop

[quasi sparrow]

Review the definition of limit

[warm horizon]

hmm

[quasi sparrow]

https://tutorial.math.lamar.edu/classes/calci/thelimit.aspx

[warm horizon]

im so lost

[mystic saffron]

which part? The fact that limit is not simply plugging in number?

[quasi sparrow]

Did you read the definition and the example problems in the link

[warm horizon]

yes

[warm horizon]

i read the def

but this cant factor and cancel so idk how they got -4

[quasi sparrow]

It can factor

[warm horizon]

but cant cancel

[quasi sparrow]

Factor more

[warm horizon]

oh it can factor

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[ancient rampart]

stuck now

[ancient rampart]

ik i have to use that

result

but

not sure about the sub

[south plume]

this has to be a typo, the 2 needs to be on the tan on the sec

[ancient rampart]

oh shit

i made a mistake

🤦🏻‍♂️

.close

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[delicate nebula]

How do i solve thi further

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[craggy matrix]

For which value of k does the polynomial function p(x)=8x3−12x2−2x+k have two opposite zero vallues?

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[mystic saffron]

.Don't occupy a whole lotta multiple channels

[summer lava]

what abt midpoint?

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[drifting pine]

find exact values of the six trig functions for each angle.
405 deg
i subtracted 360 from it to get 45 deg
do i then draw a 45-45-90 angle on a graph, label the sides, and the find the six trig functions?

[forest sky]

that should work

[drifting pine]

i hope so, cause i dont have a way to check my answer

the sides of a 45-45-90 triangle are 1 and the hypotenuse is sqrt(2)?

[forest sky]

any scientific calculator should have that capability

[drifting pine]

thanks

.close

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[lone coral]

idk how i would decompose a vector along axes that aren't just the x/y axes

[wanton niche]

Well, think of how you do it along x,y.

It's the same method, with a different choice of basis

[lone coral]

but x/y has a right angle so u can use sin and cos

[wanton niche]

What angles are "right" depends on your choice of basis

[lone coral]

wdym

[wanton niche]

Oh, nevermind, I misread the question. I thought this was a different way of decomposing the vectors

[lone coral]

do u know how to do it?

[wanton niche]

I haven't used the method you are probably expected to use in a years.

[summer river]

isn't this quite standard

you can either recognize that axes are orthagonal to each other

and take <F_1cos(30 deg),F_1sin(30 deg) = F_1cos(60 deg)>

[lone coral]

they're not tho

<@&286206848099549185> pretty please

[odd edge]

@lone coral Has your question been resolved?

[lone coral]

<@&286206848099549185>

[ashen holly]

You can always make an orthogonal projection if you know what the other vectors are

It doesnt matter if they are the x and y axes

[lone coral]

how would i do that

[ashen holly]

You can watch this video for a full explanation on orthogonal projections :

https://www.youtube.com/watch?v=Rw70zkvqEiE

but yea I'm not teaching allat on discord lol

srry

[ashen holly]

and tbh, if you have to complete this problem, you should already know about orthogonal projections

[lone coral]

yeah i took calc 3 last year i thought u were talking abt something else

bc the prof hasn't mentioned projections in class at all

[bronze canyon]

ignore everything but a single axis and vector, lets say the u-axis and F2

we want to make a right triangle like so, then we can use trigonometry immediately

do the same for v axis, then repeat for F1

[lone coral]

like that?

,rccw

[lone coral]

ignore the bottom part

[bronze canyon]

hang on

consider the angle between u and v

[lone coral]

it's 75

right

[bronze canyon]

yes

im gonna solve this first before i embarass myself like i usually do

so what is the angle F2 to v, that angle will give us Fv

[lone coral]

F2 doesn't matter

the question only asks about F1

[bronze canyon]

oh i see my b

[bronze canyon]

yeah this works

[lone coral]

it's wrong

answer key says 2.93 kN

[bronze canyon]

for Fv?

key is wrong

F1v*

[bronze canyon]

yeah key is wrong

its 3.46

[lone coral]

so i've just wasted 45min of my life thinking i'm braindmged then

[bronze canyon]

thats really weird that the key would mess up a simple problem

[lone coral]

that's why i thought i was wrong

[bronze canyon]

yeah its wrong 100%

[lone coral]

well

ggs

thx for help

.close

[bronze canyon]

tell prof

[odd edge]

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[young sedge]

i dont understand this one

[young sedge]

is this the answer?

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[winter granite]

I need help!

[winter granite]

On part b, is it wrong to split up the integral? I’m not sure how to start this problem.

[uneven path]

you use integration by parts

[winter granite]

But they are two functions?

[uneven path]

yeah thats what integration by parts is for

alternatively theres tabular method

but thats harder for this case imo

and its the same process really

[winter granite]

I actually don’t remember this but I rlly appreciate your help

Thanks! I’ll try it out

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[fickle spade]

i'm not too sure how to start the solution for this question aside from plugging 2 in on the x^3 - c(x)

[olive needle]

What are the conditions for a point to be continuous?

Actually, have you learned about limits?

[fickle spade]

yes i have but it kind of goes right over my head

i know that polynomials, rational functions, trig and root functions are always continuous

[fickle spade]

i've seen the top 2 but not that last one

[olive needle]

It just means that where the two limits are equal, then then actual value of f(a) must also equal to both limits.

https://www.geogebra.org/classic/ja3f9q3e

In that graph, you can change c to see how it affects both conditions of the piece-wise function.

There is one value of c in which both piece-wise functions approach the same value at x = 2.

[fickle spade]

ohh

how would i solve for it?

like i dont know how to start off the equation

[olive needle]

Set both conditional functions equal to each other.

You know the value of x which is equal to 2, this will allow you to solve for c.

[fickle spade]

like this?

[olive needle]

,rotate ccw

[olive needle]

Yes.

[fickle spade]

would i then subtract c(2) from both sides or no

[olive needle]

Solve for c.

So yes.

[fickle spade]

i got 4

[olive needle]

You mathed wrong.

[fickle spade]

oh

[olive needle]

Oh wait, you add 2c to both sides, not subtract.

[fickle spade]

ohhh

should i have ended up wuth c(2)^3 = 4

[olive needle]

No. There is no cx^3 in either conditional function.

[fickle spade]

what happened to the cx^2

oh

omg the 4

omg tysm for helping me 😭

i finally got 2/3

[olive needle]

🙂

[fickle spade]

have a nice dayy

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[charred blade]

My homework is asking: What is the coefficient of x^6*y^14 in the expansion of (x+y)^20. I believe we need to use the binomial therom to calculate this but im not sure how to do so

[pale atlas]

nC0 x^ny^0 + nC1 x^n-1y^1 + nC2 x^n-2 y^2 + ... + nCn-1 x^1y^n-1 + nCn x^0y^n

nC0, nC1 these are coefficient

You need to find the coefficient of term where x^ay^b = x⁶y¹⁴

[static totem]

when you expand a product, you get every combination once
so if you have (x+y)(x+y)(x+y) you get xxx + xxy + xyx + xyy + yxx + yxy + yyx + yyy

so you know x²y has coefficient 3, you got x²y 3 times

if they don't want steps you can just ask google

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[fair briar]

what am I doing wrong here? i used FOIL first

[runic swift]

its x squared

not x^4

[fair briar]

https://tenor.com/view/fml-end-the-simpsons-lisa-rolling-gif-15532621

[fair briar]

my answer still wrong tho

[mystic saffron]

why so

[runic swift]

-4x not -8x

[fair briar]

i'm getting -(4)x^2 not -(2)x^2

[mystic saffron]

oh true

[fair briar]

the answer key is wrong? or i messed up somewhere

[runic swift]

you messed up

[fair briar]

https://tenor.com/view/fml-theoffice-michael-gif-5219520

[fair briar]

oh

ty

.close

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[mystic saffron]

guys

[mystic saffron]

how !?

[fringe bough]

0 < x < y < x ? 🤔

[quasi sparrow]

Did you write the domain wrong

[mystic saffron]

sorry

yes infinity

but i still cant do it

[mystic saffron]

this is what i have so far

[mystic saffron]

do you have an idea?

[quasi sparrow]

No

[mystic saffron]

<@&286206848099549185>

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[woeful rivet]

How did my teacher get 5-3(2-1)

and then -1 + 3i

i got 11-3i

[weary pelican]

so you got u = 2-i

[woeful rivet]

yes

[weary pelican]

and...

[woeful rivet]

and v = 11-3i

oh..

-3u + 5

um

ok i got it

thx :D

wait one more question..

[weary pelican]

👍

[weary pelican]

?

[woeful rivet]

uh

can u check my working for this q

[woeful rivet]

question b i got it wrong here

[woeful rivet]

i redid it here

[weary pelican]

yes this is better

[weary pelican]

you got it wrong here because you interpreted 7*7^k - 1 as 7*(7^k-1)

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[grand turret]

I don't really know where to start

[grand turret]

I want all complex solutions

[tacit wasp]

Do you remember the cartesian/rectangular form of a complex number?

[grand turret]

the z=x+iy?

[tacit wasp]

Yep

[wooden lintel]

a+bi

[tacit wasp]

Instead of z write that and the rest is only calculations

[grand turret]

alright, i'll try and see where i get stuck

Do I know that's the only solution

[mystic saffron]

yea

[grand turret]

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[wise zodiac]

this is what i have so far and i know im wrong and im not sure what to do
f(x)=-(1/2)x^2 + 3x - (1/2)
-1/2(2x^1)+3x-1/2 power rule
-1x+3x-1/2
2x-1/2 combine like terms

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@wise zodiac Has your question been resolved?

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@wise zodiac Has your question been resolved?

[paper quartz]

so f(x) = g(x) + h(x) + c with g(x) = -1/2 x^2, h(x) = 3x, c = -1/2

f'(x) = g'(x) + h'(x)

[paper quartz]

the problem is that you need to apply the appropiate derivative rule (power rule) to each of the terms

you've applied it only to the first term

[wise zodiac]

do you know how i would apply it to the other 2 terms?

[paper quartz]

so did you understand what I did with f(x) = g(x) + h(x) = -1/2 x^2 + 3x - 1/2 ?

I split up the terms with an $x$ into their own function

[clever fjord]

龙傲天

[paper quartz]

and then I know that the derivative of a function composed of the sum of other functions is just the sum of the deritatvies

i.e. f'(x) = g'(x) + h'(x)

you took the derivative of -1/2 * x^2

but then forgot to take the derivative of 3x

and the deriatvie of -1/2

[wise zodiac]

ok thx

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[glad sun]

hello!

[glad sun]

how do i find a interval in this function?

[granite ferry]

[a, b]

Do you need to some something specific about that?

[glad sun]

why are the square brackets used instead of the round brackets?

[granite ferry]

See that they have allowed f(x) = 0 also

So including the terminals makes sense in this case

[glad sun]

so this would be the correct answer?

[granite ferry]

Did you notice the question asks for <= 0, not >=0

[granite ferry]

Another thing about [] is that

When the starting and end points are the same of two [] intervals

Then you can join them as one

[a, b] U [b, c] = [a, c]

Also, just ping me when replying 😄

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[earnest garden]

Im having a little trouble thinking this through

[earnest garden]

ive graphed the eqation somewhat in desmos

still a little confusing

It looks like there is a horozontal asymptote at -6

Its undefined at 6

so should the answer be all real numbers but -6, 6

[brittle beacon]

What does "it" refer to, the function f or the fraction?

[earnest garden]

the function like

[brittle beacon]

The function f is defined everywhere!

[earnest garden]

inside the picewise function

you are right

i agree but like

its not continuous everywhere

there is disconuity at -6, 6

so that should be the answer?

B, (6 and -6)

[brittle beacon]

Not quite...

[brittle beacon]

While the fraction is undefined at 6, that doesn't mean the limit as you approach 6 doesn't exist (and you should check if it exists, and if it does, what it is - does this match up with f(6), as per the definition?)

[earnest garden]

ohh okay i see

okay so the limit for x approaching 6

it is 9

so that just makes it continuous

but for -6, there is a vertical asymptote where the function goes in two different directions so it doesnt equal anything

So the function is continuous on all numbers except -6

[brittle beacon]

Yep, that's it, the function is continuous everywhere, including 6, but excluding -6

[earnest garden]

Okay thanks for help pointing that out to me!

[brittle beacon]

(a massive hint is that on graphing it, there wasn't a corresponding asymptote at x = 6, while there was one at x = -6, so likely the limit is defined there!)

[earnest garden]

Ohhh okay

[earnest garden]

that helps a lot

Thank you so much

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[outer wadi]

Am I understanding this right?

[outer wadi]

I've tried getting the probability by scaling up the experiment but im getting 1

[sharp oak]

I haven't checked your code yet. I'm guessing the odds are likely 100%. 100 people is a lot

Or, very near 100% I mean

[outer wadi]

by day do you think they mean

I should put 1:365

or mon-sun

[sharp oak]

Oh, I think it means "Jan 22, 2AM"

Same day, within the same hour

I think this, because the traditional birthday problem is only considering the same day

[outer wadi]

hm yeah

with using 365 days im getting around 0.44

This is what I have currently let me know if anyone thinks otherwise

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[lyric meteor]

am I tripping or is there supposed to be a + sign over here?

[brittle beacon]

sin(...) integrates to -cos(...)

[lyric meteor]

sure, but where is the negative sign on the other cos

oh did it cancel out 😭

[brittle beacon]

Yea, with the - from the -k

[lyric meteor]

im tripping i need sleep

thanks!

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[outer wadi]

Is there something wrong with my experiment or my probability reasoning?

[outer wadi]

even when I let replace=FALSE I get 0.14

It has to be my probabillity reasoning right

my experiment looks good to me

Ok so part b is right

hmmm

[outer wadi]

ohhhh

My experiment is wrong

I have it so that it is true if they are 11 and 11 or 10 and 10

and they can only be one or the other

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[zenith ledge]

how do i add 2^(k+1) and 2^(k+1)

how did they do it

[carmine storm]

x + x = 2x

[zenith ledge]

so 2(2^(k+1))

[carmine storm]

and a*a^b = a^(b+1)

[zenith ledge]

how does that turn into

2^(k+2)

oH

BECAUSE

2^1

2^(k+1+1)

ohh

ok

thx

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[loud rune]

Howdy! My question has to do with finding the domain of a composite function and expressing it interval notation. Additionally I'd like to see if someone can help me clarify something about domains when it comes to radical functions.

The function I'm attempting to find the domain of is (f o g)(x) where f(x)=1/(x-6) and g(x)=sqrt(x+1)

My answer was (-infinity, -1]U[-1,6)U(6,infinity), but it is incorrect.

I came to this conclusion by finding the values that had to be excluded for each function. For f(x) we can't divide by 0, so x != 6. For g(x) the radicand can't be negative, so x > -1.

[odd edge]

@loud rune Has your question been resolved?

[loud rune]

Ok, I've figured out the error with my calculation - needed to plug 6 in as the output for g(x) to find the excluded output for the other value. This clarified my question about domains for radical functions too. Thanks!

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[cyan pasture]

Hello, I have a simple and quick question, because I need confirmation, the matrix is ​​written only in square brackets or in regular round brackets, and if so, what is the difference? The question arises from the fact that in the book I am learning from there is a square bracket all the time and suddenly in one example a regular bracket appears, which is terribly strange

[low locust]

the bracket doesnt really matter

not sure why your book did that

[cyan pasture]

That's what I thought, thanks for the help

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[cyan pasture]

I have one more question because if we assume that the matrix is ​​assigned to each pair of natural numbers (i,j)(i=1,..n; j=1,...,m), can we make a matrix A=[a( ij)] with dimensions other than n x m, e.g. n-3 x m-2 I know that the dimension cannot be larger than m in columns and n in rows because it is not logical, but can it be smaller?

[cold sage]

how would that work? What about the left over i and j values

you may as well just redefine the set of values they take

dont see any benefit in trying to do otherwise

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[pallid badge]

this true?

[royal herald]

ye

,calc 15(17) - 10 == 14(17) + 7

[clever fjord]

Result:

true

[royal herald]

there u go

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[long tinsel]

Do you know what a Frullani integral is

[clever fjord]

ananas

[long tinsel]

I think everything is alright now

[heady plover]

f(infty) wait what's f(x) here?

[long tinsel]

for you it's e^(-x)

in general it's a function that is differentiable on R^+ and has limits at 0 and infinity

[heady plover]

So ww get (0-1)lna/b

-lna/b

Then the range of ab is ab>0 ..?

[long tinsel]

be careful now

I just used a notational shorthand

do you know how improper integrals are defined?

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@heady plover Has your question been resolved?

[mystic saffron]

what does converges mean?

just give me an example

so the limit just needs to exist?

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[mystic saffron]

i got it do you still need it?

[long tinsel]

hey sorry dipped

yeah Inthink ab > 0 is right

and b != 0

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[fiery lotus]

How would you find the domain for this function

[odd edge]

@fiery lotus Has your question been resolved?

[fiery lotus]

No

[odd edge]

@fiery lotus Has your question been resolved?

[wanton bison]

this is an inequality

are you looking for the solution set?

[fiery lotus]

Yes

To find the domain from this

[wanton bison]

ok i guess

[fiery lotus]

So how do you do it

[wanton bison]

algebra

you can do something with the -6 and 4

[fiery lotus]

I did it

And I got four different answers

I’m just confused how do you put it in domain form

[wanton bison]

,, (4x^2-6)^2 \geq \frac{3}{2}

[clever fjord]

bacc

[wanton bison]

What did you do next here?

[fiery lotus]

I did the algebra

Look

[wanton bison]

more specific

[fiery lotus]

I solved it

But how do I put four different answers as a domain

[wanton bison]

Wait

When you pull the square root

you end up with absolute value

[fiery lotus]

Boy oh boy

[clever fjord]

bacc

[wanton bison]

when you do the minus thingy the inequality sign flips

4x²-6 is an open upwards parabola so between its roots it will be negative and outside of it positive

,w roots of 4x^2-6

[clever fjord]

Results provided by WolframAlpha

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

Requested by adoniszgks

bacc

bacc

bacc

[wanton bison]

From here I wouldn't continue to do this algebraically as it yields more absolute values

I would now do it graphically

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[fluid socket]

show on the coordinate plane all points (x,y) for which the propositional form $2x+3y > 6 \implies x \leq y^2$ is a tautology

[clever fjord]

syecko

[fluid socket]

i am familiar with showing contradiction

<@&268886789983436800>

[pulsar elbow]

don’t advertise unsolicited here.

[fluid socket]

i tried thinking of it as if it were a truth table

with P being $2x+3y >6$ and Q being $x \leq y^2$

[clever fjord]

syecko

[fluid socket]

if P is false, as in $2x + 3y \leq 6$ then $P\implies Q$ is true

[clever fjord]

syecko

[fluid socket]

but if P is true how would I show that Q is always true?

because i can think of instances when it wont be

let x = 4 and y =1

P is true

yet Q is false

so i guess all that means is that it is not all real numbered pairs

which should be obvious

i then tried considering the boundary points

and sort of graphing it to see where the inequalities overlap

<@&286206848099549185>

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[obtuse haven]

im so scared to ask a question but here 😭

idk how to awnser this question in an image i sent.

its: predict which awnser is positive or negative, then evaluate, but its all negative numbers

[quasi sparrow]

use pemdas

[thick fiber]

if your exponent is even, then any negative number inside will become positive

if your exponent is odd, any number inside will keep its sign

[obtuse haven]

OH

i forgot that

thx

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[spark wolf]

How would I minimize the distance in part b?

[cold sage]

get the vector between two general points on the line
then you can do the dot product with the direction vectors
two variables two equations

[odd edge]

@spark wolf Has your question been resolved?

[spark wolf]

Between two general points? So could I get the vector from (-3,1,-1) and (2,0,4)?

[green elm]

you could use the hint, you want a vector that is perpendicular to both lines

and you're in R^3

so there's a simple way to get a perpendicular vector

[spark wolf]

hm. I'm not sure I really understand what the hint is saying to be honest. The only way I can think of to get a perpendicular vector here is through the cross-product.

[green elm]

so try that

[spark wolf]

I got <4,10,-2>

I did the cross product of (3,1,-3) and (2,0,4)

[cold sage]

the general points i meant were
(-1-3t, t, 2-t) and (2s, -2, 1+4s)

[spark wolf]

oh

hm

I could try that

and you said to do the dot product with that?

[cold sage]

once you get the vector between those points you can dot it with the two direction vectors

which should equal 0 in both cases

[spark wolf]

ok, so i need to figure out how to get a vector between those points then

[cold sage]

treat them like position vectors if that makes more sense to you

[spark wolf]

ok, so I ended up with <2s+1+3t,-2-t,1+4s-2+t>

[cold sage]

looks good to me

[spark wolf]

you said that the dot product should equal zero yes? maybe I did the dot product with the wrong thing

[cold sage]

yeah the dot product between two perpendicular vectors is always 0

[cold sage]

what do you mean?

[spark wolf]

I mean I didnt get zero

[cold sage]

nor should you? but the value you get is equal to 0

[spark wolf]

oh i misunderstood what you meant then

[cold sage]

you should get two algebraic expressions from the two dot products, theyre both equal to zero since the vectors were perpendicular, is what i meant

then you can solve them simultaneously

[spark wolf]

ok, the two equations I got were -10s-11t-4. and 20s+10t-2. So, now I would want to solve the system of equations?

[odd edge]

@spark wolf Has your question been resolved?

[odd edge]

@spark wolf Has your question been resolved?

[odd edge]

@spark wolf Has your question been resolved?

[odd edge]

@spark wolf Has your question been resolved?

[mystic saffron]

just take a perpendicular line

[odd edge]

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[fathom steppe]

(Repost cause my channel got closed due to timeout) Hello, l've found this problem online. I deduced some information but I don't know how to arrange it properly. Any help is greatly appreciated

[odd edge]

@fathom steppe Has your question been resolved?

[fathom steppe]

<@&286206848099549185>

[fathom steppe]

<@&286206848099549185>

[fathom steppe]

<@&286206848099549185>

[worldly tree]

that looks fire

gimme a bit

[fathom steppe]

Sure thing! Thank you

[mystic saffron]

in my country i have learned this at grade 9

[fathom steppe]

Oh that’s cool, can you tell me how to proceed then?

[mystic saffron]

k wait

ill write down my solution

[worldly tree]

would be crazy if he actually did

[mystic saffron]

gonna be very very long

[lethal folio]

(surely a spam)

[brisk coral]

is it going to be something like
u find conditions to make a set of equations of lengths of certain segments, and the equation can be solved but extremely messy and complicated

like i didnt actually find these equations but i can see this is possible

[lethal folio]

Yeah... But even that way, it isn't that obvious... I am trying it from a while now... There are many conjectures that I see, but they don't seem to have a nice prove.

[worldly tree]

anything can be solved using coordinates

but its kinda cringe

[lethal folio]

real

[brisk coral]

ye most certainly not the intended way to solve it

very complicated and at that point one might as well let computer do the work

[worldly tree]

could be tbh

the conditions feel so random

[brisk coral]

i have a feeling that i have seen this question or a similar one, and i dont remember it using a lot of calculations

[lethal folio]

Someone earlier tried to do it with coordinate bashing, but I am pretty sure they messed up... They assumed that CA=CD which might not be true...

[worldly tree]

i can assure you CA is not equal to CD

[worldly tree]

hopefully ur right

[lethal folio]

mhm

[worldly tree]

i lied lemme check

[lethal folio]

But how do we do it 😭

Is there even a synthetic solution?

I mean, it can be done by trig...

But a synthetic solution is much appreciated...

[worldly tree]

naaaaaaah i gotta solve it using some random ass extra line or circle

[lethal folio]

Yeahhh or maybe reflection...

I dunno

[worldly tree]

but that CB=2CA is so bad T_T

[lethal folio]

Just some has to do it!

[lethal folio]

Dude real!! Dunno why it's even there...

Maybe it's a hint to use trig...

I dunno

[worldly tree]

hell nah

i hope . ..

[brisk coral]

ok ig ill bash it

the sunk cost fallacy

[worldly tree]

noooooooo

[brisk coral]

i already invested too much in it

[worldly tree]

[lethal folio]

yeah go for it ✊

[worldly tree]

hope you come back in one piece

[lethal folio]

let them cook 🦾

[worldly tree]

[brisk coral]

ig i have to bash it another way
as rn its a quartic function :-:

[worldly tree]

dw bro

i found something

very very huge

[brisk coral]

?

[worldly tree]

im 99% sure AC=CD

i just need to prove it

[brisk coral]

ok im dumb enough to not see 1:2:sqrt5

lemme try again

ok i arrived at the answer
OO' = (10-5sqrt5)/10 u

idk if this is correct i might make a mistake practically anywhere

lemme redo all of this to give a pic as well as to make sure nothing is wrong here

[mystic saffron]

aw man some one solved it

[brisk coral]

i mean u can verify if im right or not
rn my draft is a mess

[mystic saffron]

i think ac = cd do nothing

anyone in this server got the imo medal

i need to ask him some

book

to prepare for it

nvm sorry my bad

[fathom steppe]

I’d still love to see your process!

[mystic saffron]

im afraid

[brisk coral]

alr calculated it all over again and i miraculously did not make any obvious mistakes
that said i still might make some mistakes that i missed in the second try
anyways let my phone connect and ill post the bashing process

well at least the bashing was neater than i anticipated

no crazy quartic functions

@fathom steppe

[worldly tree]

i just spent 20m trying to see if it does something and

yea

i couldnt do anything

BUT

thats because im bad

not because you are right

fight me

[worldly tree]

why did you retreat like that 💀

i was 1 mark away from medal so maybe i can help

[fathom steppe]

Thank you so much! I’ll take a look at it right away

[brisk coral]

np

[odd edge]

@fathom steppe Has your question been resolved?

[lethal folio]

PLEASE DON'T CLOSE RN

I MIGHT BE CLOSE TO A SYNTHETIC SOLUTION

[fathom steppe]

Got it!

[lethal folio]

OK SO I GOTTA GO! I'LL BE BACK TOMORROW... BUT I AM REALLY CLOSE

I HAVE DRAWN MULTIPLE DIAGRAMS

AND I AM PRETTY SURE THAT CA=CD

AND IF WE PROVE CA=CD, THEN I HAVE AN EASY SOLUTION FOR THE REST

I JUST NEED A LITTLE TIME TO PROVE CA=CD

[fathom steppe]

Alright then! See you tomorrow!

@mystic saffron can you show me your work? I’m curious

(Sorry for the ping btw)

[brisk coral]

alr i bashed my way through and apparently AC=CD

then again that is bashing so ig not the synthetic solution ur looking for

but at least bashing gives us hope for synthetic solution

also ping me when u find a synthetic solution
kinda curious how that will be like

[odd edge]

@fathom steppe Has your question been resolved?

[fathom steppe]

<@&286206848099549185> can someone demonstrate that AC = CD?

[brisk coral]

(in a way that is not bashing)

[fathom steppe]

<@&286206848099549185>

[fathom steppe]

<@&286206848099549185>

[fathom steppe]

<@&286206848099549185>

[fathom steppe]

<@&286206848099549185>

[fathom steppe]

<@&286206848099549185> please

[fathom steppe]

<@&286206848099549185> ?

[rancid falcon]

@fathom steppe

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

[rancid falcon]

dont cry bro

[barren coral]

what even is u here

AB = 1u, what is u here

[odd edge]

@fathom steppe Has your question been resolved?

[fluid tundra]

one approach

[odd edge]

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[mystic saffron]

khan academy wants me to move to -4 when the numbers dont even line up with the lines?

[mystic saffron]

or am i actually dumb?

[shell bolt]

uh well since each tick corresponds to a number then the first tick must be -5 and the second tick is -4

each number corresponds to the previous tick

[mystic saffron]

then i must be right?

[shell bolt]

yes you are right

[mystic saffron]

okay ty

[shell bolt]

just .close if youre done

[mystic saffron]

wow why do they do it like this though, i swear i never seen it like this

ty

[shell bolt]

np

[mystic saffron]

!close

[odd edge]

@mystic saffron Has your question been resolved?

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[glossy drift]

Add the following vectors using the component method.

2. 100 km/h [S50], 350 km/h [N], 65 km/h [W72N]
3. 65 km [N85W], 35 km [S10W], 60 km [E70S], 54 km [N60E]
4. Add the following vectors.
   a) [4, 2], I-3, 4] and [5, -1]
   b) [3, 01, [10, -5] and [-6, - 2]

• IF U COULD DO ALL THATD BE GREAT BECAUSE I DONT UNDERSTAND ANYTHING BUT PLEASE DO #2 so ik how to do the rest

[odd edge]

@glossy drift Has your question been resolved?

[odd edge]

@glossy drift Has your question been resolved?

[odd edge]

@glossy drift Has your question been resolved?

[odd edge]

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[odd edge]

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[fluid socket]

what would a sufficient but not necessary condition for a triangle being equilateral be

[median quiver]

three sides

[fluid socket]

i cant think of anything that isnt something along the lines of all sides are 10 feet

[fluid socket]

thats not sufficient

[median quiver]

i must not understand the question then sry

[fluid socket]

im trying to connect it to a similar problem along the lines of a quadrilateral being a rectangle is sufficient but not necessary for a quadrilateral

could i say all 3 sides and all 3 angles are congruent?

[viscid jacinth]

So are you asking for minimum requirements or the requirement that includes everything?

[fluid socket]

there is no special name for a shape that contains the equilateral triangle as a rectangle contains a parallelogram

[viscid jacinth]

A suffient statement would be all the three angles are equal

[fluid socket]

its logic

[fluid socket]

but isnt that also necessary

because no equilateral triangle isnt equiangular as well

[viscid jacinth]

It is

A equal side triangle is also an equilateral triangle

That's a sufficient logic

[fluid socket]

well thats precisely what it means to be equilateral lol

that is sufficient and necessary

becasue they are logically equivalent

[viscid jacinth]

I mean the triangle with three equal sides

[fluid socket]

the assumption implies the conclusion and the conclusion implies the assumption

i need the assumption to imply the conclusion but for the conclusion to not imply the assumption

google says all three angles are 60

but it doesnt make sense

how would that not be a necessary condition

[feral scaffold]

may I ask, why do you need this?

[fluid socket]

practice for midterm

[feral scaffold]

ah

[fluid socket]

so i guess ill just stick with what i had

[viscid jacinth]

You are over complicating

[feral scaffold]

yea, or the length to be a subset of real numbers or something

[viscid jacinth]

Just make it simple

[fluid socket]

i came up with all 3 sides are 10 feet

or any other unit of measure

doesnt matter

thats sufficient but not necessary

i just dont know how satisfactory or formal of an answer that is

any objections

[feral scaffold]

the opposite angles are equal to the lengths?

nvm, I'm not sure if that's sufficient

[odd edge]

@fluid socket Has your question been resolved?

[odd edge]

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[glacial pollen]

https://cdn.discordapp.com/attachments/903486479064522752/1283658841116119116/image.png?ex=66e3cbf4&is=66e27a74&hm=a05f38167b9c0e88b33823fe2561f2d266ae2f9c89e336a2c6b2aa8d0cb7dd25&

1. How did they remove X? Did they factor X into X to remove it? And, if so, how does that work? What operation did they do (division, subtraction, etc).

2. I am generally confused about what operations they did exactly across the problem.

3. I understand how it works now, but I dont understand why they keep moving things to the other side of the equation (ik it keeps equivalency i mean what they chose to do that when making the formula)```

[olive needle]

They Completed the Square.

[glacial pollen]

oh that

[median quiver]

woah

[glacial pollen]

halp

xD

[median quiver]

nah its all good

[glacial pollen]

its not that i cant solve it but like

i need some pointers and if someone just tells me what they did to x to get rid of oh wait

the reason i didnt get what he said was i just have to watch that video again man i hated CTS (complete square)

CTS was like quad factoring which i didnt like but on steroids lol

shrug

so do you have any info?

[odd edge]

@glacial pollen Has your question been resolved?

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[willow wraith]

https://www.desmos.com/calculator/4sb7if15nt

how to restrict a line to the origin and a vertex

[willow wraith]

or between two points

[summer cradle]

restrict?

[willow wraith]

yeah the thing's not working for me

[summer cradle]

wdym restrict?

[willow wraith]

$y=\frac{b}{a}x\left{x^{2}+y^{2}\le\sqrt{a^{2}+b^{2}}\right}$

[clever fjord]

Tetronix

[willow wraith]

where a is cos theta and b is sin theta

[summer cradle]

but what about it?

[willow wraith]

im trying to restrict it such that when each point on the line is not on the quadrant of the ellipse in this graph it doesnt render

[summer cradle]

https://www.desmos.com/calculator/q2f7pfeg0n like this?

[willow wraith]

like that yeah

thanks

.close

[odd edge]

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[odd edge]

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[gentle flare]

how do i solve this?

[gentle flare]

this is the farthest i got im not sure what to do after

Like this?

And if so what do I do after to find the inequality

someone help plz

[crisp quest]

mb, you were right

[crisp quest]

that final term needs to be less than 0

[gentle flare]

which one?

[crisp quest]

this one

$\frac{7x^{2}-24x+29}{\left(x-3\right)\left(9x-7\right)}\le0$

[clever fjord]

snorlaxboi