help-26

[opal vault]

yep

So if this is true, what can we say about angle 3pix?

[normal vapor]

x multiplied by 3pi is pi/4, 3pi/4

well

[opal vault]

yes

[normal vapor]

sin x

yeah

[opal vault]

no you're right, either $3\pi x = \frac{\pi}{4}$ or $3\pi x = \frac{3\pi}{4}$

[thorny flame]

rafilou2003

[normal vapor]

yeah

sin just goes away right

[opal vault]

Oh but I think there might be some missing, are we solving for x in [0,2pi]?

[normal vapor]

ok then solving for x is 1/12 and 1/4

yeah

we want all the instances i think

[opal vault]

I think there's a problem on the domain we're solving on

You'll ask your teacher but I think he intended for x to be in [0,2/3]

[normal vapor]

it’s 2pi

[opal vault]

This way, 3pix is in [0,2pi]

[normal vapor]

idk

[opal vault]

so having this

what are the possible values for x?

[normal vapor]

1/4 and 1/12

[opal vault]

Yep

[normal vapor]

but there’s more than that

answer

[opal vault]

technically

if x is indeed in [0,2pi]

[normal vapor]

need to find up until yes

up until 2pi

[opal vault]

Well, add 2/3 to each solution

[normal vapor]

i saw someone do it in a recursive func?

like 2/3pi

i mean

sorry

2/3n

[opal vault]

The solutions are 1/4 + 2/3n and 1/12 + 2/3n

[normal vapor]

up until 2pi

ok makes sense

[opal vault]

Knowing that 2pi is approximately 6.28, the last value that should work is 1/4 + 2/3*9 = 6.25

[normal vapor]

yea

and repeat for 1/12

ahh makes sense ok

thank you

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[elfin slate]

Could I please just have some of my work checked?

[frail fiber]

wow so detailed

looks good to me

[elfin slate]

I have a couple more 🥲

[elfin slate]

If I do not have the detail and those extra notes, I have a harder time understanding the material.
Thank you for the compliment!!

[topaz sinew]

@elfin slate Has your question been resolved?

[elfin slate]

I just need my work checked

[knotty ledge]

you can check these things yourself on wolfram just so you know

,w int 0 to inf xe^(-x^2/2)

[thorny flame]

Results provided by WolframAlpha

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

Requested by icaird

[elfin slate]

Oh! I did not know that!

I will use that from here on, thank you!

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[knotty ledge]

of course feel free to ask people to check things that arent just calculations a robot can do:)

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[muted forge]

X1 = 1

X2 = 28

X3 = 55

X4 = 83

X5 = 110

Delta_t = 0.3s

--

a) (110-83)/0.3 = 90cm/s 

b) T = 0.35s , X = V_o * T + 95 = (0.35)*(77) + 110 = 133.1cm

c) Vy = -g*T

Theta = 102.6

1.10 + 0.90 * (0.139) = 1.2251m <- x position

Delta_y = 0 - (1/2) * (9.81) * (0.139)^2 = 0.01932

0.6 - 0.01932 = 0.5807m <- y position```

[muted forge]

This is my procedure above^

I am quite certain I followed the correct steps, yet I am getting the wrong result. Is there something wrong in my procedure?

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[noble laurel]

I'm working on this, but unfortunately exercise 4.1.15 is not completed and I'm not sure how to begin with the rest of the hint

[jade thunder]

Coooooose

[empty sail]

.coose

[opal vault]

the hint is to divide the numerator and the denominator by a same factor...

no

[sweet shard]

The hint is use Cauchy's MVT

[opal vault]

you want the derivatives of f and g to appear

so how can one make derivatives appear out of f(x)/g(x)?

[noble laurel]

I'm confused, also I know what cauchy's MVT is but I haven't yet covered it in this course chapter

[noble laurel]

i mean, take the derivative??

[opal vault]

no

maybe something that has f'(c) as its LIMIT

and same for g

[ivory wraith]

hey guys if what the question said

{x|x ∈ R, x is ?}

this si set builder notation

[noble laurel]

difference quotient as x->c?

[noble laurel]

this channel is occupied, please read #❓how-to-get-help and open an available help channel

[opal vault]

#❓how-to-get-help

[opal vault]

yes

[ivory wraith]

aw ok sorry

[opal vault]

make the difference quotients appear out of f(x)/g(x)

[noble laurel]

Okay Ill try that later ty

I gtg for now

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[dense estuary]

i feel so damn embarassed asking such a simple question but its 3 am and my brain cant work it out

A = B
1 = 1
2 = 7
3 = 13
4 = 19
5 = 25

What is the formula to get A to B?

[sweet shard]

Take the difference of consecutive terms in B

[dense estuary]

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[spark spire]

How to solve this

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[hard vigil]

hey, just want to ask, for this question I got -9*10^12, But its not standard form so what should I do?

[hard vigil]

<@&286206848099549185>

[nocturne obsidian]

simplify

[topaz sinew]

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[hard vigil]

oh ok

I was told that standard form is when the base is $0 \leq < x < 10$

[thorny flame]

aaryan : )

[hard vigil]

Like I don't really know what to do becauase my calculator showed -9*10^12 but how would i make the base 1 to 10

[empty sail]

I'm pretty sure the more proper way is $0 \leq |x| < 10$

[thorny flame]

dldh06

[empty sail]

So you can have a negative as a base

[hard vigil]

oh, i thought its always supposed to be between 1 to 10, i just copied and pasted what you told me before haha

Does this mean it cant be negative?

[empty sail]

That's standard form for a Linear Equation

[hard vigil]

oh:/

[empty sail]

That's why I adjusted it to say $0 \leq |x| < 10$

[thorny flame]

dldh06

[empty sail]

The absolute value of the base

[hard vigil]

what does the "|x|" mean?

[hard vigil]

what is that?

I heard of it

[empty sail]

Magnitude of a number basically the distance from 0, on a number line, like |-2| = 2 and |2| = 2 because if you drew it on a number line, you'll see that 2 is 2 units from 0 and -2 is also 2 units from 0

[hard vigil]

I see, so the distance it is from 0?

[empty sail]

That's what absolute value is

[hard vigil]

ok so the absolute value of -9 is 9

[empty sail]

Yes

[hard vigil]

so itd be 9 * 10 ^ - 12 ?

instead of - 9 * 10 ^ 12 ?

[empty sail]

No

You keep the negative sign

[hard vigil]

oh ok

[empty sail]

I'm saying if the value is this, $0 \leq |x| < 10$, then it's in standard form

[thorny flame]

dldh06

[empty sail]

Because |-9| = 9, that's still between 0 and 10

[hard vigil]

so it is -9 * 10 ^ -12 ?

[empty sail]

.

[hard vigil]

oh

[hard vigil]

lik this?

[empty sail]

The one in front of the 9 too

[empty sail]

Yes

[hard vigil]

ok now is it right

[empty sail]

That's better

[empty sail]

.

[empty sail]

So that base is valid for standard form

[hard vigil]

it says its wrong

[empty sail]

Can you show your work

You editing that answer multiple times didn't help

[hard vigil]

ok

so when i input to calculator it gave me -9*10^12

but I need to do the absoulute value so would it b 9*10^-12

right?

[empty sail]

$0 \leq |x| < 10$

[thorny flame]

dldh06

[empty sail]

I said that because you were asking about standard form

That is to check and make sure that the base is proper for standard form

[hard vigil]

hm

okayy

[empty sail]

If the absolute value of the base is not between 0 and 10, then it is not in standard form

[hard vigil]

im quite confused

ohh

so it dosent matter abt the base it matters abt the absolute value and the absolute value of -9 is 9 and thats in between 1 and 10 so its ok right?

[empty sail]

For example -27, |-27| = 27, 27 is larger than 10 therefore it is not in standard form. -27 = -2.7 x 10^1
|-2.7| = 2.7, and 2.7 is in between 0 and 10 therefore -2.7 x 10^1 is in standard form

[hard vigil]

so it should still b positive

[empty sail]

What should be positive?

[hard vigil]

sorry i mean it shoudl b negative

-9 shoudl stay liek that right

[empty sail]

Yes

[hard vigil]

ok

and now what do i do

whats wrong with the answer then

[empty sail]

It's this

Because the power

[hard vigil]

ohso its positive?

[empty sail]

Yes

[hard vigil]

great its correct

ill try the next one

2 more questions to go

heres my 2nd last question

sorry for wasting so much of your time

for this I got -1.75 * 10^-22

[empty sail]

Is it in standard form?

[hard vigil]

yes

[empty sail]

So that's it

[hard vigil]

ok

ok last one now

this gave me -1100 @empty sail

It said this was wrong

[empty sail]

You typed that into a calculator wrong

Negatives cancel, therefore it should be +1100

[hard vigil]

oh its 1100

yea

so -1 * 10 ^ 2

[empty sail]

No

[hard vigil]

oh wait

-1.1 * 10 ^ 2

[empty sail]

No

[empty sail]

Reenter that into a calculator

[hard vigil]

I did and i got 1100

[empty sail]

Is that in standard form

[hard vigil]

1.1 × 10^3

[empty sail]

Yes

[hard vigil]

Oh yay, its correct. Thanks so much, I think il need to watch some videos and prac more as im finding it quite challenging

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[edgy quail]

i just want clarification

[edgy quail]

so does this mean

jumpy swaps the 2021st positioned nut with the 2nd pos nut

then the 1st and 3rd positioned nut

all the way to 2020st and 1st positioned nut

[craggy haven]

yes

[edgy quail]

that's stupid

jumpy is stupid

he did nothing

that solves nothing at all

[craggy haven]

he did his best

[edgy quail]

if youre unhappy just dig the walnuts out and

not do whatever this shit is

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[craggy haven]

jumpy's very upset at bushy and is freaking out

[stuck forum]

[edgy quail]

smh

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[undone flicker]

Can anyone explain why cross products give us area?

[undone flicker]

I want to visualise cross and dot product in 3d?

[final jungle]

https://youtu.be/eu6i7WJeinw?si=OeGdFpGeSlZwOU6Y

[undone flicker]

I just searched it

Thanks

. close

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[knotty ledge]

test

.close

[knotty ledge]

.close

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[knotty ledge]

.reopen

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✅

[knotty ledge]

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[near nebula]

The angle of elevation of a cloud from a point h metres above the surface of a lake is θ and the angle of depression of its reflection in the lake is ϕ. Prove that the height of the cloud above the lake surface is : h(
tanϕ−tanθ
tanϕ+tanθ

).

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[left urchin]

hii, is B a subset of A if B = { {2}, √2, 1} and A={1, {2}, √2} ?
i think iz not cuz it should not use all the elements if it is a subset

[neon iron]

Any set is a subset of itself

There are 2 types of subsets

Proper/scrict subset

And uh

I forgot the other one lol

A set cannot be the proper subset of itself

But yeah it is the "normal" ig¿ subset of itself

[neon iron]

Reason being the way subsets are defined

B is subset of A if every element of B is present in A

[left urchin]

so is it vice versa? a is also a subset of b?

[neon iron]

Right

In this case yes

[left urchin]

thank uuu

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[topaz sinew]

@grave timber Has your question been resolved?

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@grave timber Has your question been resolved?

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[zenith nimbus]

Can someone help me with problem 10?

[fierce zealot]

,rotate

[zenith nimbus]

<@&286206848099549185>

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[granite hull]

how can I prove that A is congruent to B? I forgot.

[granite hull]

<@&286206848099549185>

[craggy haven]

A and B are points

they can't be congruent

[chilly trail]

i think they mean AB

or circle A and cirlce B

[frozen pagoda]

same radius

[chilly trail]

if u mean circle A and circle B then circles with congruent radii are congruent by definition of a circle

if u mean AB then reflexive property

[chilly trail]

(a circle with center A and radius R is defined as the set of points called the circumference that are distance R away from A)

[limber iron]

you can say that they intercept the same arc

[chilly trail]

so if two circles have the same radius they are congruent by definition

[granite hull]

ah

is what I wrote good?

[chilly trail]

you might want to write that circles with the same radii are congruent by definition of a circle and then yeah

just to be safe

[granite hull]

alright

?

(tweaked)

[frozen pagoda]

you should right how AB = AC

they are both radii

[granite hull]

good @frozen pagoda?

[frozen pagoda]

yep thats good, you proved all three sides are equal 👍

[granite hull]

thanks @frozen pagoda

[frozen pagoda]

np

[granite hull]

much love everyone.

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[icy pilot]

What am I doing wrong ??

[icy pilot]

Am doing the factor by grouping method

4x^2 +4x - 1

First, multiply a and c

-4

Find factors of -4 that add up to b, 4

Now I don’t think thats possible

[craggy haven]

it's not possible

[icy pilot]

So what do I do ?

Is it not factorable

[craggy haven]

it is not factorable over the integers / rational numbers

[icy pilot]

I’m trying to find the solutions so the only way is quadratic formula then?

[icy pilot]

Can you show doing it with imaginary

[craggy haven]

"only" is slightly broad but like yeah

$x^2 + 5ix - 4 = 0$ \
$ab = -4$; $a + b = 5i$ \
$(x - 4i)(x - i) = 0$

[thorny flame]

hayley!

[craggy haven]

in general if you can't factor it then just reaching directly for the QF is the best way

or completing the square if you're more comfortable with that

[icy pilot]

Hm let me try completing the square I thought it was only for graphing

[craggy haven]

completing the square is how the QF is usually derived! it's great

[icy pilot]

Am I right in doing

4(x^2 + x + .25 -.50)

[craggy haven]

yep! (do you find decimals useful like that? most ppl prefer fractions there)

[icy pilot]

Ok so I just need to find the factors of .25 that add up to 1

Easy

[craggy haven]

uh

[icy pilot]

Ok nevermind its .5

[craggy haven]

yeah that's why you did that :P

[icy pilot]

I was having trouble thinking how a factor of 1/4 can get you 1

But I just remembered

[craggy haven]

well the whole point is that it's b/2

[icy pilot]

Why isnt the solution -1/2

[craggy haven]

remember what you did here

$4(x^2 + x + \f14 - \f12)$

[thorny flame]

hayley!

[craggy haven]

and you took those first three terms and made them into a square

$4[\lp x+\f12\rp^2 - \f12]$

[thorny flame]

hayley!

[craggy haven]

(this is a really annoying way to factor polynomials)

now you can use difference of perfect squares to factor it

[icy pilot]

Can I also get the another via multiplying both with 4

Or do I have to simplify parenthesis first

[craggy haven]

yeah let's distribute that 4 it's annoying me too

$(2x+1)^2 - 2$

[thorny flame]

hayley!

[craggy haven]

now you can factor this with difference of squares

[icy pilot]

Shouldnt it be 4x

[craggy haven]

no because it's inside the square

so like

$4(x+\f12)^2$

[thorny flame]

hayley!

[craggy haven]

$2^2\cdot(x+\f12)^2$

[icy pilot]

Right

[thorny flame]

hayley!

[craggy haven]

$(2(x+\f12))^2$

[thorny flame]

hayley!

[icy pilot]

Dropping bombshells like its nothing

[craggy haven]

i've done this a few times ;)

[icy pilot]

Where does ^2 in 2 go?

[craggy haven]

where?

[icy pilot]

When its 2^2

[craggy haven]

$\green 2^2 \cdot \blue{\lp x+\f12\rp}^2$

[icy pilot]

What about the ^2

[thorny flame]

hayley!

[craggy haven]

which one

[icy pilot]

Oh

When you multiply common exponents you add ???

[craggy haven]

when you multiply common bases you add exponents

,tex .exp rules

[thorny flame]

hayley!

[icy pilot]

So where is the ^2 on the 2^2 going

[craggy haven]

we're using "distributivity" here

$\lp\green2\blue{\lp x+\f12\rp}\rp^2$

[thorny flame]

hayley!

[craggy haven]

see how these are the same?

[icy pilot]

I see…..

Never ran into this before

$(2x+1)^2 - 2$

[thorny flame]

geoxcaliber

[icy pilot]

So whats the square root of -2

[craggy haven]

we dont' need sqrt of negative 2 here

because we're using difference of perfect squares

[icy pilot]

How is 2 a perfect square

[craggy haven]

the pattern here is $a^2 - b^2 = (a-b)(a+b)$

[thorny flame]

hayley!

[craggy haven]

that's the fun part, it isn't

but it is the square of $\sqrt2$

[thorny flame]

hayley!

[icy pilot]

Is this different or the same as just “difference of squares”

[craggy haven]

same

we just learned it by the acronym DOPS in middle school so that's stuck in my brain

[icy pilot]

Yeah and am supposed to know that

[craggy haven]

well

[icy pilot]

What is math

[craggy haven]

i mean that's what a square root means

so if we write it as like

$(2x-1)^2 - (\sqrt2)^2$

[thorny flame]

hayley!

[craggy haven]

now can you factor it?

[icy pilot]

But if you had -81

You could make it (9)^2 and sqrt[81]^2?

[craggy haven]

i mean yeah

or you could just say 9^2

[icy pilot]

So 2x -1 + sqrt2 and 2x-1 -sqrt2

Are the two solutions

[craggy haven]

those are the two factors

[icy pilot]

Solutions to be

[craggy haven]

i mean, yes if you have an equation

if you just have the quadratic then it ends there

anyway yeah now you see why i said it was a PITA to do it this way

[icy pilot]

What do you mean

[craggy haven]

if someone just handed you the quadratic and said "factor this" then... well, you've factored it

if someone gave you $4x^2 + 4x - 1 = 0$ then you'd factor it and then set factors = 0, solve for x, etc

[thorny flame]

hayley!

[icy pilot]

Gotcha

$2x = -1 + \sqrt{2}$

[thorny flame]

geoxcaliber

[icy pilot]

Idk where to go from here

[craggy haven]

well

if you had 2x = 7 what would you do?

[icy pilot]

So I divide by 2

[craggy haven]

yeah

[icy pilot]

$x = \frac{-1}{2} + \frac{\sqrt{2}{2}}$

[craggy haven]

missing close brace on the second frac

because of the sqrt

[thorny flame]

geoxcaliber
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[craggy haven]

$x = \frac{-1}{2} + \frac{\sqrt2}{2}$

[thorny flame]

hayley!

[craggy haven]

yes :)

[icy pilot]

Lmao

Ok so how do I divide the last 2?

[craggy haven]

wdym

[icy pilot]

Is that just the answer like that

[craggy haven]

pretty much yeah

and if you try the QF you should get the same

[icy pilot]

Wait so why is it -1/2

Arent you adding +1 to the right

[craggy haven]

why is what -1/2?

[icy pilot]

Here

[icy pilot]

If you set this = 0

[craggy haven]

oh you baited me

$2x - 1 + \sqrt2 = 0$

[thorny flame]

hayley!

[craggy haven]

$2x = 1 - \sqrt2$

[thorny flame]

hayley!

[icy pilot]

Lol

But then why is it -1

[craggy haven]

i typod this

[icy pilot]

https://tenor.com/view/meme-spooky-month-funny-spooky-month-dance-task-failed-successfully-gif-24413020

[craggy haven]

should be 2x + 1

so $(2x + 1 + \sqrt2)(2x + 1 - \sqrt2)$

[thorny flame]

hayley!

[icy pilot]

Oh I see

Got it thank you @craggy haven, learned some things today

[craggy haven]

yeah np! this is a really weird way of factoring and you would normally want to just use the formula

but it's good that you've gone through it

[icy pilot]

Haven’t used the quadratic at all yet, just really used to factoring. But I ought to now

Have a good day/night!

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[shadow smelt]

No idea how to go about this to be honest

[old crypt]

What is the length of the fence in terms of x and y?

[jade thunder]

There’s a relationship between x and y, do you see that?

They can’t just be any arbitrary amount

[shadow smelt]

I mean, sure?

[sweet shard]

Write down the equation of the relationship

[shadow smelt]

1000 = y * x ?

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[sleek haven]

is this correct?

I'm sorry that it's blurry

[stuck forum]

It looks good

[sleek haven]

okay, just checking

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[graceful leaf]

Hi

[graceful leaf]

Can someone make me a problem like this

So i can practice

SInce i already did this one in the picture

THank very much

[frozen goblet]

Multiply by both x+1 and x-1

[restive willow]

Um

Search up on google and you will find plenty of problems like this

[spare smelt]

Take the derivative

Then a few applications of newtons method should work

[mellow arrow]

well, you can multiply both sides by (x+1)(x-1). That would result in a quadratic which can be solved using the quadrartic formula

[graceful leaf]

Oh

THank yall but

I know how to do this specific problem I was wondering if someone can make me a problem similar to this one

[restive willow]

Search in google

You can find practice online with this problem

I do it all the time

[mellow arrow]

Like you need more such problems?

[graceful leaf]

Yes

[mellow arrow]

https://media.discordapp.net/attachments/1133228142589378642/1145724017123262564/eqn.gif

[graceful leaf]

Idk what to search up @restive willow

THNX

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[ionic token]

How do i sketch x^3 - x?

[ionic token]

With turning points and roots

And asymptotes

[surreal idol]

Find the turning points and roots

[tender quartz]

Will it be okay to solve this with basic proportionality theorem?

[surreal idol]

and any asymptotes, if any

[surreal idol]

Please read #❓how-to-get-help

[tender quartz]

Sorry, I don't understand what was wrong with my question.. Can you please guide me to correct it?

[surreal idol]

This help channel is occupied, please ask in an available one like #help-24

[tender quartz]

Oh

[surreal idol]

have you found the roots?

[ionic token]

No

I’ll do that and make another help channel if i have a doubt

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[left urchin]

hii, is {x} an element of {{x}, {y}, {z}}?
it is right?

[surreal idol]

Yes

Do you see why?

[left urchin]

can u explain it tyyy

[craggy haven]

${\blue{{x}}, {y}, {z}}$

[thorny flame]

hayley!

[left urchin]

owhhh tyyy

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[chrome sierra]

what does B even mean, what is going on here

[surreal idol]

B means that

the red marble is to the left of the green marble

and the red marble is to the left of the yellow marble

[chrome sierra]

yeah so its like RGYW, RYGW, WRGY, WRYG

those are all the possibilities right?

how does that = 8/24??

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[forest nova]

Absence - for example a number
Absence rate - in %
Right?

For example a student attended 10 times but absence 4 days, then you would find how many % 4 of 10, and then it’s 40%, so 100% - 40% = 60% absence RATE does the word rate mean like this?

[forest nova]

@drifting swift Ok let’s talk about it

Cause previous times I didn’t have time

And it closed the ticket

[drifting swift]

as i understand right now, there are 14 classes in total, of which the student went to 10 and missed 4

this would maake her absence rate 4/14

,calc 4/14

[thorny flame]

Result:

0.28571428571429

[drifting swift]

about 29%

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@forest nova Has your question been resolved?

[forest nova]

Uh

[forest nova]

So the word “rate” means %?

[drifting swift]

not necessarily

but it is normally expressed as a percentage unless it's close to 0

otherwise it can be expressed in such ways as "1 in __" or "x parts per million/billion/etc"

[forest nova]

So for example I have a sheet that has “Attendance”

So if they’re attended 10 times

And then I wanted to another column

That for example 10/15 days they attended

And I’d convert that in %

Would then i name the column attendance rate?

[drifting swift]

sure, why not

[forest nova]

But would that make sense

Can a rate always go up?

For example 10/15 attended

Then

11/16

or no

it cant go up

@drifting swift

[drifting swift]

yes it can go up

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@forest nova Has your question been resolved?

[forest nova]

But it can’t reach 100%?

[forest nova]

@drifting swift

[drifting swift]

if you have at least one absence on record then yes of course it can never reach 100%.

100% attendance rate <=> zero absences.

[forest nova]

Ok, what’s the highest number it can get?

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[obtuse trench]

How does this inverse functions work?

Like if we say $x=-100$ since $C=]-\infty, 0]$
$$
-\sqrt{-100^2}
$$

,w -\sqrt{-100^2}

[thorny flame]

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SimonWin

[obtuse trench]

Or am I missing something?

$$
-\sqrt{x^2} \quad x=-100 \quad -\sqrt{-100^2} = ...
$$

[thorny flame]

SimonWin

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[winged ferry]

did i do this correctly..? am i missing something?

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[winged ferry]

<@&286206848099549185>

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[thorn lily]

can someone help pls

[thorn lily]

is two lines around a variable absolute value?

or something involving vectors?

like for the first one I have 6u^2-2uv but idk what to do with that

[torpid pendant]

It's the vector magnitude, so the length of the vector.

You can use the identity $u \cdot u = {\lVert u \rVert}^2$.

[thorny flame]

The__Innkeeper

[thorn lily]

uhuh...

@torpid pendant so am I right to plug in 6(1)^2-2(2)?

[torpid pendant]

Yes, that should be right.

[thorn lily]

so then the second one simplifies to u^2-v^2

i'm guessing that's (1)^2-(3)^2?

[torpid pendant]

That should be correct.

[thorn lily]

awesome, thanks

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[safe mica]

how do you do these? when im looking at a graph i can do it, but in a piecewise function i just cant get it to click in my head, am i not supposed to visualize this in a graph but rather use the if parts of the function?

[thick oyster]

oops

[safe mica]

lol

same time

[thick oyster]

i didnt mean to post in your channel lol

[safe mica]

youre fine

it was close

[thick oyster]

👍

[simple orchid]

Piecewise functions are functions that are just seperate

Cut-off functions shall I call?

[safe mica]

so do i just imagine its apporaching -3 from the right side of any positive value

to help with the conditional statements

on a graph i can do it but these just throw me off

[thick oyster]

as x approaches -3 from the right, what is f(x)? To the right means greater than -3. So find the piecewise function used where x > 3

and plug in

boom

[safe mica]

i see alright that helps a bit more

thanks

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[restive willow]

Rationalize the denominator

So basically i started on it and here is the pic :

No clue tho

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[restive willow]

help plz

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[restive willow]

I beg

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[dim dune]

i’m really struggling with part A i don’t understand it

i got g(3) = 1.5 f’(1.5) = 1/4 and g’(3) = 1/2 and when you multiply them shouldnt you get .125? but it’s wrong??

[tall wolf]

you have to do chainrule first

[dim dune]

i thought that’s what i did

[tall wolf]

nope

chain rule is f'(g(x)) = g'(x)*f'(g(x))

nvm you did

sorry

[dim dune]

yeah lol that’s why i’m confused

[tall wolf]

g'(3) =3

not 1/2

[dim dune]

how is it 3

[tall wolf]

g(3)=7

you find the slope of the line

f'(3)=1/2

you probably switched up the functions

[dim dune]

oh

wouldn’t it be f(7)

f’(7)

[tall wolf]

right

oops

[dim dune]

f’(7) = 3 right

[tall wolf]

ye

[dim dune]

so 3 x 3 h’(3) would be 9?

[tall wolf]

why are you doing that

3*3 yes but what's the h'(3) doing

oh nvm

yeah

[dim dune]

ty

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[runic basin]

3x(y-2x)

Then, distribute the 2x

So it becomes, 3x(y+2xy+2zy)

[drifting swift]

3x(y-2x)
nope

if the expression was $(3xy -6x)(y - z)$ you could have been correct but even then only halfway

[thorny flame]

Ann

[drifting swift]

remember your order of operations

$3xy - {\color{gray}(}6x (y-z){\color{gray})}$

[thorny flame]

Ann

[wide tusk]

Do you guys know calculus

[drifting swift]

this pair of parentheses is invisible but it is there

@wide tusk please open your own channel and post your question there. read #❓how-to-get-help for instructions.

@runic basin you are better off here expanding -6x(y-z) into -6xy + 6xz and then combining 3xy - 6xy into -3xy.

[runic basin]

Wait hi

So 3xy - 6x(y-z)

[runic basin]

First thing is HCD

So

3x

Then, 3xy/3x so that becomes X then - 6x/3x is 2

[drifting swift]

........................

[runic basin]

So first, its 3x(y - 2x)

[drifting swift]

you are talking straight nonsense.

[runic basin]

Huh

Can u teach me step by step

[drifting swift]

expanding -6x(y-z) into -6xy + 6xz and then combining 3xy - 6xy into -3xy.

1. expand -6x(y-z) into -6xy + 6xz. the full expression is 3xy - 6xy + 6xz.
2. combine 3xy - 6xy into -3xy. the full expression is -3xy + 6xz.
3. factor out 3x from all terms.

[runic basin]

Oh

Lemme try

This is not what my teacher taught me

She taught me other method

Solving for factor

@drifting swift

[drifting swift]

well, you CAN first factor out 3x, but it'll look like this:

3x[y - 2(y-z)]

which i think is a lot easier to fuck up than my suggestion.

[runic basin]

I thought u group them by two

[drifting swift]

but given that your teacher might be the kind that punishes the SLIGHEST deviation from her teachings with a ZERO ON THE ENTIRE ASSIGNMENT,

you might be forced to work strictly under her methods.

[runic basin]

Oh

[drifting swift]

we do not have a sum of 4 terms here.

so no, "group by two" does not apply.

[runic basin]

3 terms?

[drifting swift]

we have a more complicated expression.

in which there's two terms, except one of them is the product of some shit and a parenthetical.

expanding it as i suggested, you'll get 3 terms.

which then collapse into 2 terms once you collect like terms.

[runic basin]

Ok

You know what

Am skipping this

What are the term words, expanding

And collapse

May I ask

[drifting swift]

"expand" means going from a(b+c) to ab + ac

"collapse" is not an 'official' term but i use it to mean several like terms becoming one

like x+3x+3x+7x+99x collapses into 113x

[runic basin]

Oh, alright. Tysm

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[kindred elm]

how do i obtain the domain and range of this graph

[drifting swift]

which values does the graph cover on the x axis (for domain) and on the y axis (for range)?

[kindred elm]

for the domain, the first line seems to go from -inf to near -2

is that right

[drifting swift]

that's only one part of the graph

[kindred elm]

the 2nd line goes from -2 to +4, and the 3rd one goes from +4 to inf

the range would be -inf to in-between 0 and -1, 2nd line is inf to -inf, and the 3rd line is inf to 0

[wild brook]

Range seems to be (-inf, +inf)
domain is a bit tricky but try (n epsilon integers, n not equal to 4, -2

)

[kindred elm]

i feel like im about to get an aneurysm lmao

ty anyway

.close

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[surreal idol]

Where are you stuck

[drifting swift]

!status

[topaz sinew]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[hot belfry]

i do not know how to solve it

[surreal idol]

do you know what the circle symbol means?

[hot belfry]

thats the problem

[surreal idol]

It means you do the right one first, then the left one

[drifting swift]

did you learn about composition of functions?

[surreal idol]

I realized my blunder right after

[hot belfry]

composite function?

[drifting swift]

same-ish thing.

so yes

did you learn about that

[hot belfry]

yes

[drifting swift]

ok then that's what the funny circles mean

does that enable you to do the problem?

[hot belfry]

this

???

help

.close

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[surreal idol]

Do you know the definition of even and odd functions

[hot belfry]

nope

time for part 2 ig

[surreal idol]

have you been taught them

[hot belfry]

yes

[surreal idol]

an even function is a function satisfying the condition that for all x in the domain, f(x) = f(-x)

[hot belfry]

ok

so basically f(x)=f(-x) is a even function?

@surreal idol

[surreal idol]

it needs to satisfy that for all x, not just one

[hot belfry]

ok

@surreal idol what about odd

[surreal idol]

an odd function is a function satisfying the condition that for all x in the domain, -f(x) = f(-x)

[hot belfry]

and what does 'A' mean. like we have 'I' for integer.

[hot belfry]

k

[surreal idol]

a is some number, like 5, or sqrt(7)

[hot belfry]

ok

[hot belfry]

back to this

how to solve it

@surreal idol

[surreal idol]

check if it is even

then, if it is not, check if it is odd

[hot belfry]

for some it doe

does*

for some it does not

[surreal idol]

Which ones?

[hot belfry]

+x

and even -x

[surreal idol]

which ones

[hot belfry]

even -x

im getting confused

[surreal idol]

can you show your work

[hot belfry]

i cant take photo

im on pc

[hot belfry]

when did you learn about functions?

[surreal idol]

Why do you ask

[hot belfry]

cuz im learning this in 9th ;-;

@surreal idol

[surreal idol]

I forgot when I learned about functions

[surreal idol]

What country

[hot belfry]

i dont think this is good

india

[surreal idol]

Is that the normal curriculum?

[hot belfry]

this is not normal

[surreal idol]

Oh

[hot belfry]

we learrn this in 12th

[surreal idol]

you learn functions in 12th grade??

[hot belfry]

yes

[surreal idol]

no way

[hot belfry]

no 11th

[surreal idol]

are you sure

that seems late

[hot belfry]

that seems early

[surreal idol]

you are supposed to check numbers, like whether f(3) = f(-3), for example

[hot belfry]

which country r u from?

[surreal idol]

11th grade to learn what a function is is early???

[hot belfry]

ye

u learn this in?

[surreal idol]

I happened to have my textbook from that year with me

and it said 10th grade

or form 4

but I knew the concept of function way before that

[hot belfry]

u learnt that in 10th??

[surreal idol]

Yes

[hot belfry]

which country r u in

[surreal idol]

I am in the region of hong kong

[hot belfry]

k

they are teaching us very hard things which is not normal

like electro chemistry

chemical kinetics]

[surreal idol]

we also learnt that in 10th grade

[hot belfry]

im learning in 9th

what about trignomentry

[surreal idol]

compulsory for all people?

[hot belfry]

no

[surreal idol]

elective only?

[hot belfry]

our school is weird

[surreal idol]

we learnt the basic concepts of that in 8th grade

then expanded on that later

[hot belfry]

we learnt that in 6th

[surreal idol]

back to the question

[surreal idol]

compulsory for all people?

[hot belfry]

NO

THEY STILL TORTURING US

[surreal idol]

do you understand what compulsory means

[hot belfry]

yes

and in my countrry it is not it is only from 10th

[surreal idol]

so they let you pick electives in 6th grade?

[hot belfry]

nope

[surreal idol]

just to be sure, it means you have to learn it

[hot belfry]

they just started it

we didnt know what the hell was going on

[surreal idol]

huh

are you still going to do the question

[hot belfry]

oh ye forgot about it so how to do

[surreal idol]

here

[hot belfry]

what should i take a as?

@surreal idol

[surreal idol]

just let it be some number like 5(but not 1)

[hot belfry]

why not 1

can u just solve it if i have any doubt ill ask'

[surreal idol]

the solution is: consider f(-x). when we evaluate it there using algebra, we get -f(x). Therefore the function is odd

can you fill in the algebra

[hot belfry]

ye got it

oh shi-

i have to go

i have an exam

.close

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[surreal idol]

Do you know the special angles

,tex .unit circle

[hot belfry]

its me mario

[thorny flame]

rti

[hot belfry]

ok so

i dont have much time

i have to go in few mins

if you could tell me the answer it would be helpfull

[surreal idol]

we don’t do that here

[hot belfry]

just tell me the solution

[surreal idol]

but if you look at the unit circle, and keep in mind that sec x = 1/cos x, you can get there quickly

[hot belfry]

thank you for your kind hearted help

ill be back do not worry

i must go now

-unknown

.close

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[wintry thunder]

hi, I have a theory problem, my book has a typo and I just wanted to make sure. In the second line the midpoint between AB = 1/2(a**+**b)?

[surreal idol]

Yes

You can see this from the parallelogram law

[wintry thunder]

thank you :D

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[ionic token]

How do i sketch f/g

i know where the x intercept and asymptotes r

But idk what shape it shuld be

[sturdy oracle]

Start with plotting x intercepts of f/g and using dashed lines to represent vertical asymptotes

[ionic token]

Yeh thats what i did

[sturdy oracle]

Then use some kind of sign analysis

For intervals where the sign of f and g are the same, f/g is gonna be positive

Otherwise they're gonna be negative

g ≠ 0

So just gonna freehand that

It's a sketch

[ionic token]

Is it gonna be like an exponential

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@ionic token Has your question been resolved?

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[woven kettle]

what is the negative reciprocal of -20/20?