help-26

[violet fractal]

you're not, stop it.

yes

this whole point was to see where you're at. the learning process is happening

[uncut crow]

No, you're not stupid. Problems like this are designed to show what you still need to learn

[bright trail]

Sort of to the "that's fucked" comment. Not the stupid thing.

[brave aspen]

so im learning that i almost need to completely restart trig because khan academy did not a fucking thing lmao

omg i get it

because even tho the cos is negative the sin isnt

[bright trail]

Yes!

[violet fractal]

yes I was about to draw the triangles

LOL

[uncut crow]

https://tenor.com/view/gandalf-yes-very-good-gif-19209604

[brave aspen]

i was imagining triangles with negative side lengths so thats why i got so stumped

[violet fractal]

good. now go do parts 2 and 3.

[brave aspen]

my mind reverted to 10th grade geometry instead of precalc trig lol

[bright trail]

You can kinda imagine the two angles like this

[brave aspen]

ye ik i kinda reverted to a geometrical headspace where things almost cant be negative

the hardest part about trig so far is separating geometrical concepts from the unit circle

like being able to go into the negatives

and using pi to describe triangles

anyways imma try the second part

[brave aspen]

can you repost the thingy

pwetty please

[violet fractal]

sure

[brave aspen]

woah

alr

ill give it a shot

uh

[brave aspen]

i think i did it wrong 😭

[violet fractal]

wutchu got

[brave aspen]

i ended the problem with sin^2 x = 1

let me walk you through it

[violet fractal]

k

[brave aspen]

(tan^2(x)+1/sin^2(x)+cos^2(x))cos(x)=sec(x)
(tan^2(x)+1)cos(x)=sec(x)
(((sin(x)/cos(x))(sin(x)/cos(x))+1)cos(x)=sec(x)
sin^2(x)+cos(x)=sec(x)
sin^2(x)+cos(x)=sec(x)
sin^2(x)+cos(x)=1/cos(x)
sin^2(x)=1

[violet fractal]

some illegal stuff up in ther

[brave aspen]

hm?

[violet fractal]

actually

start at your second line.

what's tan^2(x) + 1

[brave aspen]

i just took one peek at my notes and almost teared up

[violet fractal]

LOL

[brave aspen]

it's sec^2(x)

[violet fractal]

yup

ok finish it gogogo

[brave aspen]

i didnt have to do all that 😭

alr bet

FUCK

i wrote sex instead of sec

[violet fractal]

LOL

[uncut crow]

You're not the first to make that "error"

[brave aspen]

i tried writing sec(x) and accidently skipped the c lmao

[uncut crow]

!occupied

[topaz sinew]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[brave aspen]

omg tee hee i actually did it

idk why but this problem was easier and funner than the last

[violet fractal]

[brave aspen]

let me walk you through what i did this time

[violet fractal]

k

[brave aspen]

starting from the step i fucked up

[hasty light]

what is a+z?

[violet fractal]

!occupied

[topaz sinew]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[hasty light]

k

[brave aspen]

(tan^2x+1)cosx=secx
(sec^2x)cosx=secx
(secx secx)cosx=secx
(1/cosx)(1/cosx)cosx=secx
1/cosx=secx

cuh

[violet fractal]

first line should have multiplication right?

on the cosine?

[brave aspen]

oops

typoooo

[violet fractal]

yeh yeh perfect!

[brave aspen]

wowie

[violet fractal]

great, use sum and difference to find cos(15 deg)

[brave aspen]

and now number 3

that's angle addition right?

i havent learned that yet (properly)

[violet fractal]

yeh

[brave aspen]

also unit circle intuition just tells me it's 1/4

[violet fractal]

careful

might be

but

[brave aspen]

since cos 30 is 1/2

[violet fractal]

you'll wanna use

[brave aspen]

half of that is 1/4

[violet fractal]

oh no no

[brave aspen]

oops

wait

hold on

thats sin

1/8

hang on brb

im back

also i was using my number line and 4th grade math intuition for it lmao

yeah its probably neither 1/4 or 1/8th

[brave aspen]

uh yeah i havent even learned what i need for this yet

i'm probably gonna go back and work on unit circle intuition and trig identities

[violet fractal]

sure. for reference, you can use

[brave aspen]

its just khan academy has the most dogshit exercises known to mankind for trig identities

they did NOT teach them bruh

[violet fractal]

$cos(A \pm B) = cos(A)cos(B) \mp sin(A)sin(B)$ just gotta figure out how to get A+B or A - B

[thorny flame]

JayRoc (The Hurricane Panda)

[brave aspen]

uh

makes sense i guess

[violet fractal]

u sure?

[brave aspen]

absolutely not sure

[violet fractal]

XD

[brave aspen]

lets not go through this today lmao

i need to redo like half of trig

[violet fractal]

yeh no worries. I don thnk you need to redo. you just need to find ways to rigorously test yourself to ensure you have your knowledge base

[brave aspen]

i think the sinusoidal shit absolutely killed my trig intuition

[brave aspen]

i think my knowledge base has been severely cracked by the sinusoidal self torture and burnout

[violet fractal]

like

graphing sines and cosines and junk?

[brave aspen]

yes

fucking made me wanna cry

[violet fractal]

yeh a lot of ppl don like them

[brave aspen]

they fucking stink

[violet fractal]

it'll be ok you'll gettem

[brave aspen]

i fucking hate trig 🗣️

worst math ive ever done in my life 🗣️

i think i just went through it too fast since khan academy is dogshit at actually letting you practice

!close

/close

.close

[violet fractal]

.close

[topaz sinew]

Channel closed

Closed by @brave aspen

Use .reopen if this was a mistake.

[violet fractal]

there we go

lol

[topaz sinew]

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[lucid junco]

how do i find the centre i forgor

[drifting swift]

low tide and high tide are the same distance away from the center

[lucid junco]

but the maximum is 25 and the minimum is 5m

so theyre not the same

[drifting swift]

the maximum and minimum aren't equal to each otheer

what a shocking revelation amirite

[lucid junco]

you just said they are the same

[drifting swift]

no, i did not

[lucid junco]

high tide means max

low tide means min

[drifting swift]

low tide and high tide are the same distance away from the center

ffs

[lucid junco]

still dont know what you mean

[drifting swift]

the center is the same distance away from the min and max

[lucid junco]

but how does that help

[drifting swift]

the center is halfway between the min and max

[lucid junco]

so 25/2

5/2

?

oh

you mean like

25 + 5

30/2

is the center

[drifting swift]

yes that is what i mean

[lucid junco]

how do i find amplitude

[drifting swift]

amplitude is the distance between the center and either of the two extremes

[lucid junco]

15 - 25 so 10m

or 15-5

= 10

.close

[topaz sinew]

Channel closed

Closed by @lucid junco

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Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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• Be polite and have a nice day!

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[outer nacelle]

how do i solve b

[outer nacelle]

my answer is A + B (+) B + C' but im not sure if thats the right one

[knotty ledge]

shouldnt the middle (+) switch to + after you first use demorgan?

unless these aren't just the analogues of union/intersection, i shouldve asked what the symbols mean

[outer nacelle]

what about the normal +?

will it be converted too?

[outer nacelle]

it means exclusive or

in logic gate topics

[strange whale]

then not(A xor B) means A = B

A xor B is 1 when the two inputs are different

so not(A xor B) is 1 when the two inputs are equal

[outer nacelle]

where is not a xor b?

[strange whale]

the whole expression itself

,tex $ \overline{ (\overline{A+B}) \oplus (\overline{\overline{B} + C}) } $

[thorny flame]

aPlatypus

[strange whale]

it's not( [something with A and B] xor [something with B and C] )

@outer nacelle

[outer nacelle]

wait its not?

i thought thats what the equation mean

since the xor is at the middle

[outer nacelle]

so the final answer is just this?

this is the equation my lecturer gave

this isnt finished yet but can i do it like this?

[strange whale]

yeah it's the same thing I meant

not(A)not(B) + AB means the two inputs A, B are equal

either A=B=0 or A=B=1 for that formula to output 1

[outer nacelle]

yeah i do understand that

[topaz sinew]

@outer nacelle Has your question been resolved?

[strange whale]

right

so what other problems do you have ?

[topaz sinew]

@outer nacelle Has your question been resolved?

[outer nacelle]

nope i think i got it

thanks\

[topaz sinew]

Channel closed

Closed by @outer nacelle

Use .reopen if this was a mistake.

[topaz sinew]

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• Show your work, and if possible, explain where you are stuck.
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[sour sequoia]

Question 4

[sour sequoia]

I got it right by putting values and checking

It is multiple correct

Please give proof

<@&286206848099549185> plz help

[topaz sinew]

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.

[desert plank]

One way to see this is that whenever 3 numbers are in arithmetic progression, the middle number is the average of the outer 2.
How many ways are there to pick 2 numbers between 1 and n?
How many of those pairs gives you an average that's another whole number?

Hint: to get an average which is a whole number, either we must pick both numbers to be even, or we must pick both numbers to be odd

[sour sequoia]

@desert plank Then why are there two options; n even and n odd?

can't we just select two numbers with 1 or more numbers between them?

[desert plank]

well, when n is even, we have n/2 even numbers and n/2 odd numbers. when n is odd, we have (n-1)/2 even numbers and (n+1)/2 odd numbers. that affects how we use this hint

[desert plank]

not quite, if you picked 3 and 8, your average would be 5.5

we need the sum of the two numbers to be even so that it divides by 2

[sour sequoia]

So we need to do this

ok

[desert plank]

yeah

using that you'll get formulas when n is even and when n is odd

[sour sequoia]

But then for n even, it will be {(n/2)C2}^2

this is not matching the correct answer

[sour sequoia]

<@&286206848099549185> plz help

<@&286206848099549185> plz help

[desert plank]

Why do you have a square?

[desert plank]

please dont ping helpers over and over

[sour sequoia]

one for odd and other for even

[sour sequoia]

ok

[desert plank]

we can either have 2 evens, or we can have 2 odds

you would square if we needed to pick 2 evens AND 2 odds

but we pick either or, so instead it would be (n/2) C 2 + (n/2) C 2 (one for each possibility)

[sour sequoia]

ok

will adding do it?

[desert plank]

see if that ends up matching the answer

yea

[sour sequoia]

Thank you

.close

[topaz sinew]

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Remember:
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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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[gilded fractal]

I dont understand this

A and here a translation

Calculate the terms for the given values ​​of a b and c

<@&286206848099549185>

[past cargo]

so u just substitute right？

[gilded fractal]

What

[gilded fractal]

What does that mean

[past cargo]

on the worksheet

yea

you have

A=3

[gilded fractal]

Oh

[past cargo]

B=2

[gilded fractal]

That looks easy

Is basically 2nd class is t it

[past cargo]

[gilded fractal]

So theres no catch or anything its that easy?

[past cargo]

no catch

[gilded fractal]

Im in 8th grade why did he give us this

If its so easy

[past cargo]

so u plug it in

and then solve :）

[gilded fractal]

Wait

[gilded fractal]

So ab + c : b is 32+-6:2

[past cargo]

like 3(2)+-6:2

yea

[gilded fractal]

Not 32?

[past cargo]

ab

means multiplication yea？

[gilded fractal]

Huh

[past cargo]

just like 1x

you multiply 1 by x

but in this case

the 1 and x

are a and b

so ab

means a times b

[gilded fractal]

Why tho i dont get it

[past cargo]

it‘s just how it is

[gilded fractal]

Yea its just how it is but what do i do first

Theres a :

Wich would mean i have t9 do that first

[stable violet]

Okay

[gilded fractal]

But theres a negative number so how do i do that

[gilded fractal]

Dude what

[gilded fractal]

@past cargo

[past cargo]

PEMDAS

ab+c:b

you multiply first

[gilded fractal]

Oh and then?

[past cargo]

you do the ratio don‘t you？

-6:2

[gilded fractal]

But that doesnt work does it

[past cargo]

huh？

wdym

it‘s a ratio

[gilded fractal]

-6:2 doesnt work

[past cargo]

for what

[gilded fractal]

What does that mean im getman

German

[past cargo]

so you want me to translate？

Verhältnis：die quantitative Beziehung zwischen zwei Beträgen, die angibt, wie oft der eine Wert im anderen enthalten ist oder enthalten wird.

[gilded fractal]

What

[gilded fractal]

I just want to know the next step 😭

The next thing i should do is -6:2 but hoe that doesnt work

[gilded fractal]

Thats what i did for now

Now i dont know what to do

<@&286206848099549185> seems simple but i dont know what to do when theres a -6:2

Its a easy task but its just me being stupid

Idk what to do

[neon iron]

what do you think

[gilded fractal]

I dont know i just want to know what i have to do

In a situation like that

[neon iron]

u do know that u have to divide first?

[gilded fractal]

Really?

[neon iron]

yes

• and - are separater of numbers

[gilded fractal]

So i have to write it down again

[neon iron]

6-6:2
= 6-3
= 3

[gilded fractal]

Huh

What

Huh

What happened

[neon iron]

Operations are performed in the following order to solve numerical expressions:
First ‐ division.
Second ‐ multiplication.
Third ‐ addition.
Fourth ‐ subtraction.
.

[gilded fractal]

Alr i know that but idk how to do the -6:2

U just did it but

How

What what did u do

[neon iron]

oh u don’t know division?

[gilded fractal]

I do know it huh

[neon iron]

so do it

what u don’t understand

[gilded fractal]

But its -6

Not 6

[neon iron]

ohh

a/b = a/b
-a/-b = a/b

[gilded fractal]

What

[neon iron]

-a/b = a/-b

[gilded fractal]

What does that have to do with it

[neon iron]

its just a proprietie

[gilded fractal]

i still dont get what to do at -6:2:catthumbsup:

Bruh

[neon iron]

which grade are u in?

[past cargo]

he‘s in eighth

[past cargo]

nope by definition multiplication appears first from left to right so multiplication is first

[gilded fractal]

Chat gpt explained it to me

[past cargo]

damn

[gilded fractal]

Its just -3

[neon iron]

thats dmas rules

[past cargo]

no that‘s the mdas rule too

[gilded fractal]

I get it now just brain afk

[neon iron]

im not here not argue

[past cargo]

im just saying

from left to right

[gilded fractal]

So do i multiply or do i do division first

[neon iron]

what im saying its also foundable in books

[past cargo]

no

[past cargo]

u multiply first

[gilded fractal]

Why does the guy say something else

[neon iron]

dividing comes to multiply

[past cargo]

no

[gilded fractal]

🤣

[neon iron]

6 x 1/2 = 6/2

[past cargo]

well that‘s how i learned it in the US

[gilded fractal]

I think its gonna be the same

[past cargo]

you probably learned BODMAS

[neon iron]

im not here to argue help @gilded fractal him i leave it to u

i have no interest to prove something already proven

[past cargo]

no

it‘s false keed

[gilded fractal]

Dude its the same thing doing multiplication or division first no?

Youll come to the same thing

[past cargo]

multiplication is first

keed

left to right not right to left

[gilded fractal]

Still would be the same in this case i think

What do i do on (ab+c):b just multiply a and b and do the add c and division?

[past cargo]

[past cargo]

do the parenthesis first

within the parenthesis

you multiply first cuz of ab

[gilded fractal]

Whats a parenthesis

[past cargo]

brackets

[gilded fractal]

So i said it right

[past cargo]

yea

[gilded fractal]

Thats great me struggling at very simple things

Dude what 0:2 comes out!

?

[past cargo]

e

[past cargo]

so it‘s 0 right

[gilded fractal]

Yes so :2

Does that even make sense

[past cargo]

ya

[gilded fractal]

Alr

[past cargo]

what about the next one？

[gilded fractal]

-6

Yup

[past cargo]

for which one？

[gilded fractal]

The third

[past cargo]

ummmmmmmmmmmmmm

not quite

[gilded fractal]

(a(b+c)):b

Why

-6 should be it

[winged moat]

$(a(2-6)) \div b = (3(-4)) \div b = -12 \div 2 = -6$

[thorny flame]

USS-Enterprise

[winged moat]

It is -6, yes.

[gilded fractal]

See

Oh its you

[past cargo]

oh wrong box

[winged moat]

Hello there

[gilded fractal]

Want to help me with my math again

Got a exam tmr

[winged moat]

Sure thing

[gilded fractal]

Thanks for helping

[past cargo]

alr

[gilded fractal]

@winged moat simple thing gonna do it rq and ping u when arriving to the harder stuff

[winged moat]

👍

[gilded fractal]

How do i do division with 1/4:1/3 again? @winged moat

[winged moat]

Division is multiplication of the reciprocal of the second number

$a \div b = a \cdot \frac{1}{b}$

[thorny flame]

USS-Enterprise

[winged moat]

So $\frac{1}{4} \div \frac{1}{3} = \frac{1}{4} \cdot \frac{3}{1}$

[gilded fractal]

Oh now i know before doing that u always switch both numbers in the first thing right

I mean second

[thorny flame]

USS-Enterprise

[gilded fractal]

Yes

[winged moat]

Yes

[gilded fractal]

I know now

Just forgot

[gilded fractal]

The first one down there is 5,5/6 right?

[winged moat]

Give me a second

Not quite

[gilded fractal]

Huh

[winged moat]

$\left(\left(\frac{1}{2} \cdot \frac{1}{3}\right) + \frac{1}{4}\right) \div \frac{1}{3}$

[thorny flame]

USS-Enterprise

[gilded fractal]

Meant this one

[winged moat]

$= \left(\frac{1}{6} + \frac{1}{4}\right) \div \frac{1}{3}$

[thorny flame]

USS-Enterprise

[gilded fractal]

Ab+c:b

[winged moat]

OH

I'm dumbb

[gilded fractal]

Your not ur the one carrying me in maths

All good

Lol

[spark jackal]

i messed up

[winged moat]

The first one is 11/12

[gilded fractal]

Huhhh

[spark jackal]

i give up

[gilded fractal]

5,5/6 also works

Just made kt harder

It

[winged moat]

Oh

I thought you mean 5 5/6

[gilded fractal]

Nope

[winged moat]

Yes, 5.5/6 is also correct

Though we don't usually have decimals in fractions

[gilded fractal]

Stoll alr

Still

[winged moat]

Of course

Dividing both the top and bottom by the same number doesn't change the value

[gilded fractal]

Next one is 15/12

Math is even fun when understanding

[winged moat]

Correct

Gotta simplify though

5/4

[gilded fractal]

True

[slender grove]

git gud @ german

hi uss enterprise

[gilded fractal]

Huh

[winged moat]

Hello

[gilded fractal]

What can i bring the 6 and 8 to so that its the same number

[winged moat]

Try

[gilded fractal]

My brain isnt thinking

It isnt 16

Not 8

[winged moat]

nope

[gilded fractal]

Oh

24

[winged moat]

Yeah

[gilded fractal]

Mb

[winged moat]

If you don't know how to find them, try writing all the factors of both numbers

$6 = 2 \cdot 3 \ 8 = 2 \cdot 2 \cdot 2$

[thorny flame]

USS-Enterprise

[gilded fractal]

21/24 is the last

[winged moat]

Then take 3, 2, 2, 2

3 * 2 * 2 * 2 = 24

[gilded fractal]

So

Now to the harder stuff

[winged moat]

You don't have to take the 2 in 6 because you already took it in 8

[gilded fractal]

binomial formulas

[gilded fractal]

What do you mean

21/24 is right isnt it?

[winged moat]

Yes

But again simplify

Divide by 3

7/8

[gilded fractal]

Yes yes

[gilded fractal]

.

Gonna try myself first

[winged moat]

👍

[gilded fractal]

First one is s² and then r s

R+s

[winged moat]

Well, $(r+s)^2 = r^2 + 2rs + s^2$

[thorny flame]

USS-Enterprise

[winged moat]

Not $r^2 + rs + s^2$

[thorny flame]

USS-Enterprise

[gilded fractal]

Its not the solution

Look at a closely

Wait

What

[winged moat]

Pretty sure it's a typo

Should be 2rs

[gilded fractal]

Did they make a mistake

In the

Thing

[winged moat]

Because they want a square of sums

(r+s)^2

And that's r^2 + 2rs + s^2

[gilded fractal]

They made a mistake did they?

[winged moat]

I believe so

[gilded fractal]

Good

So i was right?

[winged moat]

Yes

[gilded fractal]

I think i have to learn all 3 of the formulas again just to not completly fail that shit in the exam

[winged moat]

They aren't hard

[gilded fractal]

Yes but i forgor

I do know the 2

But forgot how the 3rd works

Can u explain to me

[winged moat]

third?

[gilded fractal]

Yes

[winged moat]

Well

I don't know which one's third

They aren't numbered

[gilded fractal]

They are for us

[winged moat]

hm

[gilded fractal]

3rd

[winged moat]

Ah

If we multiply the parantheses out we get $a^2 - ab + ab - b^2 = a^2 + 0 - b^2 = a^2 - b^2$

[thorny flame]

USS-Enterprise

[gilded fractal]

Why tho

[winged moat]

This is called a difference of squares

What do you mean why?

[gilded fractal]

Can u make an example with real numbers

[winged moat]

Sure thing

[gilded fractal]

With x's and stuff

[winged moat]

$(4x - 3y) \cdot (4x + 3y)$

[thorny flame]

USS-Enterprise

[gilded fractal]

4x²-3y²

[winged moat]

Gotta square the numbers too

You get $(4x)^2 = 4x \cdot 4x = 16x^2$

[thorny flame]

USS-Enterprise

[gilded fractal]

Forgot the paratheses

Yup

[winged moat]

And if we do foil

we get $16x^2 + 12xy - 12xy - 9y^2$

[thorny flame]

USS-Enterprise

[winged moat]

Notice how the middle always comes to 0

12xy - 12xy = 0

[gilded fractal]

So the solutions would be (4x²)-(3y²)

[winged moat]

Well this is incorrect

[gilded fractal]

What

[winged moat]

The squaring should be on the brackets

[gilded fractal]

Oh

[winged moat]

Not on x and y

[gilded fractal]

Outside

[winged moat]

Yes

[gilded fractal]

Yeah i know that but too lost to do that

[winged moat]

$(4x)^2 - (3y)^2$

[gilded fractal]

[thorny flame]

USS-Enterprise

[gilded fractal]

Thanks

[winged moat]

$= 16x^2 - 9y^2$

[thorny flame]

USS-Enterprise

[winged moat]

No problem

[gilded fractal]

B is (121s+16t)-(121s-16t)

[winged moat]

Not quite

[gilded fractal]

The 3rd form is the easiest id say

[winged moat]

If we multiply everything out

We get $(121s)^2 = 121s \cdot 121s$

[thorny flame]

USS-Enterprise

[winged moat]

Which is quite large

You first gotta rewrite $121s^2 - 16t^2$

[thorny flame]

USS-Enterprise

[winged moat]

Into $a^2 - b^2$

[thorny flame]

USS-Enterprise

[winged moat]

Right now you are just squaring s and t

[gilded fractal]

What do you mean

[winged moat]

Same thing we did here

It's $(4x)^2$

[thorny flame]

USS-Enterprise

[winged moat]

Not $4x^2$

[thorny flame]

USS-Enterprise

[winged moat]

Not the same thing

$121s^2 \neq (121s)^2$

[thorny flame]

USS-Enterprise

[gilded fractal]

Huh

When did i say that

[winged moat]

Here

If we use the formula we get $(121s)^2 - (16t)^2$

[gilded fractal]

What

[thorny flame]

USS-Enterprise

[gilded fractal]

Cant read

It

[winged moat]

$14641s^2 - 256t^2$

[thorny flame]

USS-Enterprise

[winged moat]

What can't you read

[gilded fractal]

Now loaded

[winged moat]

Let me ask you this

$4x^2 - 9y^2$

[thorny flame]

USS-Enterprise

[winged moat]

What's this

[gilded fractal]

The 3rd formula

[winged moat]

Write it out for me

[gilded fractal]

(4x+9y)(4x-9y)

[winged moat]

No!

We'd get $16x^2 - 81y^2$

[thorny flame]

USS-Enterprise

[winged moat]

If we multiply everything

You assume that $4x^2 - 9y^2 = (4x)^2 - (9y)^2$

[thorny flame]

USS-Enterprise

[winged moat]

And use the formula

But it's not

[gilded fractal]

Now i get it but how do i come to the right numbers

[winged moat]

You gotta take the square root of the coefficients

So the square root of 121 and 16

Both are nice numbers

[gilded fractal]

Square root whats that

[winged moat]

ah.

$\sqrt{121}$

[thorny flame]

USS-Enterprise

[gilded fractal]

We never had that

[winged moat]

Such a number that when you square it you get the original back

I mean it's behind what you're doing here

[gilded fractal]

We still never talked about it

[winged moat]

You should try your best at guessing then

Which number do we square to get 121?

10?

[gilded fractal]

No

11

[winged moat]

12?

Correct

and 16?

what do we square to get 16

[gilded fractal]

4

[winged moat]

$121s^2 - 16t^2 = (11s)^2 - (4t)^2$

[thorny flame]

USS-Enterprise

[winged moat]

There you go

This is true now!

And you can use the formula

[gilded fractal]

Thank you so much

[winged moat]

No problem

[gilded fractal]

So just replace what i said with 11s and 4t

[winged moat]

Yes

[gilded fractal]

Alr

Gor ir

Now c

[winged moat]

$121s^2 - 16t^2 = (11s - 4t) \cdot (11s + 4t)$

[thorny flame]

USS-Enterprise

[gilded fractal]

Yes yes

Hm

[winged moat]

First things first

[gilded fractal]

2nd formula

[winged moat]

Do the same trick we did before

Convert those terms into a^2 form

[gilded fractal]

Its a other formula

[winged moat]

Correct but this is true for all of them

You still have a^2

[winged moat]

Which squares both the number and the variable

$49u^2 \neq (49u)^2$

[thorny flame]

USS-Enterprise

[winged moat]

What do we write instead of 49?

[gilded fractal]

7

[winged moat]

Correct

And 81?

[gilded fractal]

9

[winged moat]

So $(7u)^2$ and $(9v)^2$

[thorny flame]

USS-Enterprise

[gilded fractal]

I know a and b now

[winged moat]

You've already got the right part

Now just the middle term in the left part

What do we get in $(a-b)^2$

[thorny flame]

USS-Enterprise

[gilded fractal]

Thats the part i struggle with the middle is the hardest for me

Can we do some examples first

[winged moat]

Sure

$(3x - 2y)^2$

[thorny flame]

USS-Enterprise

[gilded fractal]

9x²-idk+4y²

[winged moat]

Remember this: $(a-b)^2 = a^2 - 2ab + b^2$

[thorny flame]

USS-Enterprise

[winged moat]

2 times a times b

[gilded fractal]

I know that

[winged moat]

Well then

What's 2ab in our example?

a = 3x, b = 2y

[gilded fractal]

E

E

I dont know

[winged moat]

Okay

We've got $2 \cdot a \cdot b$

[thorny flame]

USS-Enterprise

[winged moat]

We know a = 3x, b = 2y

So we just plug them in

We get $2 \cdot 3x \cdot 2y$

[thorny flame]

USS-Enterprise

[winged moat]

$= 2 \cdot 3 \cdot x \cdot 2 \cdot y$

[thorny flame]

USS-Enterprise

[winged moat]

We use commutativity

$= 2 \cdot 3 \cdot 2 \cdot x \cdot y$

[thorny flame]

USS-Enterprise

[winged moat]

$= 12xy$

[thorny flame]

USS-Enterprise

[winged moat]

You multiply the coefficients (the numbers) and the variables

x times y is just xy

Nothing to do there

[gilded fractal]

How did u get that as the solution

[winged moat]

That's just 2ab

[gilded fractal]

2times 3 is 6 and 2 times 2 is 4

Isn10

Is 10

10xy

No?

[winged moat]

$2 \cdot 3x \cdot 2y$

[thorny flame]

USS-Enterprise

[winged moat]

2 times 3 is 6

6 times 2 = 12

[gilded fractal]

Oh

I get it

[winged moat]

yeah

[gilded fractal]

So

Solution is 9x²-12xy+4y²?

[winged moat]

Correct

[gilded fractal]

Or do the squares disappear after squaring

Why dont they disappear

[winged moat]

What would disappear?

[gilded fractal]

²

[winged moat]

You've got $(3x - 2y)^2$

[thorny flame]

USS-Enterprise

[gilded fractal]

Yes

[winged moat]

$= (3x)^2 - 2 \cdot 3x \cdot 2y + (2y)^2$

You square the coefficients and the variables, x^2 is just x^2. can't do anything

[thorny flame]

USS-Enterprise

[winged moat]

$= 9x^2 -12xy +4y^2$

[thorny flame]

USS-Enterprise

[gilded fractal]

Whay

What

[winged moat]

What?

[gilded fractal]

I dont get it

Why does it ² stay when using it

[winged moat]

We've got $(3x)^2$

[thorny flame]

USS-Enterprise

[winged moat]

This is the same as $3x \cdot 3x$

[gilded fractal]

Yes

[thorny flame]

USS-Enterprise

[gilded fractal]

Yes

[winged moat]

$3 \cdot x \cdot 3 \cdot x$

[thorny flame]

USS-Enterprise

[gilded fractal]

Yes

[winged moat]

$3 \cdot 3 \cdot x \cdot x$

[thorny flame]

USS-Enterprise

[winged moat]

$9 \cdot x^2$

[gilded fractal]

Oh

[thorny flame]

USS-Enterprise

[winged moat]

x times x is x squared

[gilded fractal]

I get it

Thanks

[winged moat]

no problem

[gilded fractal]

So

Now for c

[winged moat]

So we've gotten $(7u - 9v)^2$

[thorny flame]

USS-Enterprise

[winged moat]

on the right of the equals sign

You get this right?

[gilded fractal]

162uv

Should be it

[winged moat]

$2 \cdot 7u \cdot 9v$

[thorny flame]

USS-Enterprise

[winged moat]

$2 \cdot 7 \cdot 9 \cdot u \cdot v$

[thorny flame]

USS-Enterprise

[gilded fractal]

What

[winged moat]

!occupied

[topaz sinew]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[gilded fractal]

No im stupid my dude

[winged moat]

Well it's 2ab right?

[gilded fractal]

Yes

[winged moat]

$2 \cdot 63 \cdot uv$

[thorny flame]

USS-Enterprise

[winged moat]

$126uv$

[thorny flame]

USS-Enterprise

[gilded fractal]

My bad i did ba

No i did

Bb

LMAO

[winged moat]

😂

[gilded fractal]

Alr understood

If i get a good grade in maths its because of you

[winged moat]

🙂

[gilded fractal]

How old are you or wich grade do you go to

[winged moat]

I'm in highschool

[gilded fractal]

How do you know so much

[winged moat]

I don't know, I like math

[gilded fractal]

What do i do on task d

[winged moat]

And having a good teacher is also very important

[gilded fractal]

True

[winged moat]

Well this is again going to be a square of difference correct

(your second formula)

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

[thorny flame]

USS-Enterprise

[gilded fractal]

If we got 34abc

And a is a

I have to find out what equals 34 times two so its 17

B is 17?

17bc

[winged moat]

Good thinking!

[gilded fractal]

Thanks

Is it correct?

[winged moat]

Of course

[gilded fractal]

Then just gotta square 17

Bc

[winged moat]

We've got $(a - 17bc)^2$

[thorny flame]

USS-Enterprise

[gilded fractal]

17tomes 17 is 289

[winged moat]

Yes

[gilded fractal]

289bc²

[winged moat]

b squared as well

[gilded fractal]

Mb

Thought so

[winged moat]

$17 \cdot b \cdot c \cdot 17 \cdot b \cdot c$

[thorny flame]

USS-Enterprise

[winged moat]

$17 \cdot 17 \cdot b \cdot b \cdot c \cdot c$

[thorny flame]

USS-Enterprise

[winged moat]

$289b^2c^2$

[thorny flame]

USS-Enterprise

[gilded fractal]

And done with that

Now the 3rd exercise

[winged moat]

There you go

[gilded fractal]

Gotta translate it

Rq

[winged moat]

uh

Solutions

To equations?

I learn german in highschool 😂

[gilded fractal]

Determine the solution sets of the following equations, note all equivalence forms and pay attention to the equivalence arrow

[gilded fractal]

Guten tag

[winged moat]

Hello to you too

[gilded fractal]

🤓in german please

[winged moat]

Yeah so pretty much just solve the equations

[winged moat]

😂

$\frac{3x}{8} - \frac{x}{6} = 5$

[thorny flame]

USS-Enterprise

[winged moat]

How would we start?

[gilded fractal]

E

Turn 3x/8 into 3/8x

And x/6 in 1/6x

[winged moat]

We can do that but that's unecessary

First thing we do if we see fractions in equations

We get rid of them

We don't like fractions in equations

[gilded fractal]

Id say its easier to move them

Makes it look simpler

[winged moat]

That won't get you closer to solving for x though

Right now we are dividing 3x by 8 and x by 6

[gilded fractal]

But it helps tho

Cant i do that?

Will it give me minus points

[winged moat]

Wouldn't it be easier if we just had 9x and 4x?

[winged moat]

Of course you can do that, but eventually you have to get rid of fractions

Everything you do before that is pointless

Anyway

Let me ask you this

[gilded fractal]

I want to do that it makes it easier for me aslong as its not something that counts as something wrong i could

[winged moat]

$\frac{x}{2} = 2$

[thorny flame]

USS-Enterprise

[winged moat]

How do we solve this?

[winged moat]

You can do anything you want as long as it it's allowed by math 🙂

[gilded fractal]

1/2x

[winged moat]

Doing so can't get you minus points

But you gotta get to x

Okay, $\frac{1}{2}x = 2$

[thorny flame]

USS-Enterprise

[winged moat]

Now what?

[gilded fractal]

Hm

I forgot

[winged moat]

😅

We gotta get 1x

Right now we've got half of x

So what do we do

[gilded fractal]

We make it bigger?

[winged moat]

How?

[gilded fractal]

Times 2

[winged moat]

Exactly!

[gilded fractal]

2/4

[winged moat]

We multiply both sides of the equation by two

We get $2 \cdot \frac{1}{2}x = 2 \cdot 2$

[thorny flame]

USS-Enterprise

[winged moat]

$\frac{2}{2}x = 4$

[thorny flame]

USS-Enterprise

[winged moat]

$x = 4$

[gilded fractal]

What

[thorny flame]

USS-Enterprise

[winged moat]

We gotta get rid of fractions

We've got $\frac{1}{2}x = 2$

[thorny flame]

USS-Enterprise

[winged moat]

This means 1/2 of x

We solve this by dividing both sides with 1/2

But dividing by 1/2 is the same as multiplying with 2

[gilded fractal]

Huh

But we want the x to stay

[winged moat]

You do know that we can add or substract on both sides of the equation right?

If we have $x = 2$

[thorny flame]

USS-Enterprise

[gilded fractal]

Yes i do know that

[winged moat]

We can add 1 on both sides

$x + 1 = 2 + 1$

[thorny flame]

USS-Enterprise

[winged moat]

This is the same

[gilded fractal]

We did it pretty much

[winged moat]

We can also multiply or divide on both sides

If we have $2x = 2$

[thorny flame]

USS-Enterprise

[winged moat]

We divide on both sides by 2 to get x alone

[gilded fractal]

I know all the simple stuff

[winged moat]

$x = 1$

[thorny flame]

USS-Enterprise

[winged moat]

But it's the same with fractions

We've got $\frac{1}{2}x = 2$

[thorny flame]

USS-Enterprise

[winged moat]

We divide by 1/2

To get 1x

But because 1/2 divided by 1/2 = 1 right

But dividing by 1/2 is the same as multiplying by 2

[gilded fractal]

Wouldnt we need to do 2xtimes not times 2

Necause it has a x

The others wont change if having a x

Only the ones woth x's

[winged moat]

That's not how this works

If we were to multiply both sides with 2x

This means multiplying every term with 2x

We'd get $x^2 = 4x$

[thorny flame]

USS-Enterprise

[gilded fractal]

What

[winged moat]

This is still correct

[gilded fractal]

Or teacher said something else

Our

Or is it me

[winged moat]

Not sure

Let's get to the beginning

We had $\frac{x}{2} = 2$

[thorny flame]

USS-Enterprise

[winged moat]

There's no point in turning this to (1/2)x

Because we just multiply both sides by the denominator

And fractions are gone!

$2 \cdot \frac{x}{2} = 2 \cdot 2$

[thorny flame]

USS-Enterprise

[winged moat]

$\frac{2x}{2} = 4$

[thorny flame]

USS-Enterprise

[winged moat]

$x = 4$

[thorny flame]

USS-Enterprise

[gilded fractal]

What

I still dont get it

[winged moat]

what part dont you get

[gilded fractal]

Why does it turn into 2

X/2 times 2 turn into 2?

[winged moat]

Multiplying a fraction by an integer

$a \cdot \frac{b}{c} = \frac{a \cdot b}{c}$

[thorny flame]

USS-Enterprise

[winged moat]

And then the 2's cancel

[gilded fractal]

I dont understand the words

[winged moat]

Multiplying a fraction

b/c

[gilded fractal]

OH

[winged moat]

By an integer

[gilded fractal]

x is 1

[winged moat]

a whole number

a