help-26

[cunning kayak]

lmao

[fiery badge]

I swear I saw this on here before

[cunning kayak]

yes i think it's a common question

[fiery badge]

The trick is to not look for f(x) at all, but just write out all you can, setup a system of equations and just plug in those constants

it solves itself in the end

or in this case, since you have 4 given answers, you could try and brute force it somehow

[cunning kayak]

lemme try

the first way you told XD

[fiery badge]

Proofs by exhaustion are always my favourite

Actually proof by hindsight and proof by intimidation come first

[cunning kayak]

uhm

you sure?

[cunning kayak]

this would work?

[fiery badge]

As far as I can remember, yes

[cunning kayak]

okay

let's try

[fiery badge]

The tricky thing here is the y

so like, there's two variables to determine the parameter, but then f in itself is a single variable function

so you have to kinda think about that

when you differentiate things

[cunning kayak]

I thought if y is causing issues, we keep y=0

and then diff

but it turned pretty useless as you said

[fiery badge]

But then would (5x-3y) / 2 get wacky?

[cunning kayak]

no like in ques f(0) = 3

so it will be like uh

f(5x/2) = 5f(x)/2 + 9/2

[fiery badge]

uhhhhh

you can't do that

wait

oh

nvm

[cunning kayak]

yup

wait I have better idea

[fiery badge]

wait

proceeds to wait

[cunning kayak]

yes better idea was to google

and they have just

just

just done

https://www.toppr.com/ask/question/if-fleft-x-rightsatisfies-the-relation-fleft-dfrac-5x3y-2-right-dfrac/

[fiery badge]

Nooooo, don't googleittt

that's cheatingggggg

Have you no honor?

[cunning kayak]

couldnt resist

[fiery badge]

shakes bell

SHAME

shakes bell

SHAME

[cunning kayak]

starts villain arc

BWHAHA

jokes asidr

they have used section formula

tbh still need to solve it with diff method

in exam, it's hard to think abt it

[fiery badge]

Well they used that property to prove that f(x) must be linear

and then they used the given constants to calculate the function

and then you know the dril

[cunning kayak]

pretty much I guess

and I am inevitable
snaps

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[distant totem]

How would I solve by making a complete square

[distant totem]

I started out by doing

x^2 - 8x + (8/2)^2 - (8/2)^2 + 12

[inner wren]

8x = 2 * (x * 4)

so add 4 to make it 4^2

x^2 - 8x + 16 - 4
(x-4)^2 - 2^2
(x-6)(x-2)

x = 6, 2

[distant totem]

so just a bit of confusion on my side

how do we go from (x-4)^2 - 2^2 to (x-6)(x-2)

[inner wren]

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

x-4 = a
2 = b

[distant totem]

but how do we come to x-6?

if x-4 = a?

[inner wren]

(x-4)^2 - 2^2 = [(x-4-(2)][(x-4+(2)]

The cause is that b = 2 and that it adds to -6.

[cunning kayak]

yo conan?

[distant totem]

ah i see

[cunning kayak]

need help with previous ques

like of genral form I gave?

[distant totem]

new question of same sort, but i seem to slowly understand ^^

[inner wren]

find two numbers such that ab = 12 and a+b = -8

[cunning kayak]

I think he meant, conversion of ax²+bx+c to (x+b/2a)² = smthin

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[languid dagger]

solve using de movire's the following:

[languid dagger]

Hi how did this turn into this

[acoustic pecan]

subtract 2pi

since its periodic it has the same sine value

[languid dagger]

subtract it?

But why exactly 2pi

[acoustic pecan]

because sin has a period of 2pi

any multiply of 2pi added or subtracted would work

but getting the result in the range [0, 2pi] is just nicer

[languid dagger]

im sorry if i sound stupid but they told us to always just divide 15 by 4 and get the remainder

I have no idea what is period

[acoustic pecan]

im not sure what to make of that

[rigid ivy]

oh. Get the remainder

That's bad advice because it makes assumptions and doesn't always work

do you know what the shape of a sine graph is like?

[languid dagger]

uh

no?

[rigid ivy]

very odd that you're learning complex euler form conversions before even knowing what a sine function is

[languid dagger]

if it was like middle school or 1st class of highschool stuff then i probably didnt learn it

because corona and that stuff

[rigid ivy]

that's unfortunate

[languid dagger]

they just didnt teach us

[rigid ivy]

Then you're going to need to learn it.

Does anyone in your class know it?

[languid dagger]

uh no

everyone just divides

[rigid ivy]

that's bad

you're not learning math

you're learning a procedure, which won't help you

[languid dagger]

Is there a specific video on how to do this

maybe i can watch it

[rigid ivy]

https://www.khanacademy.org/math/trigonometry

[languid dagger]

Wait one moment!

Lemme get my 5th highschool book

[rigid ivy]

The site is also in arabic, but I'm not sure if they offer trig
https://ar.khanacademy.org/

[languid dagger]

Is that the one ur talking about

[rigid ivy]

That's the period of the function, yes

Your book is a bit unfortunate. From what I can see, it looks like it just says "this is the property of something" but isn't explaining why

Is this a cram school?

[languid dagger]

just normal school

[rigid ivy]

pretty unfortunate if it's not giving the reasons for all of this then

[rigid ivy]

I recommend checking this out if your English comprehension is good (it seems to be)

[languid dagger]

yeah even though im native i understand english better

Lmao

anyways thank you

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[merry hawk]

hi

[merry hawk]

I need help on this word problem

it's rationals precalc 11

[acoustic pecan]

any idea?

[merry hawk]

no I habe a learning disorder

on vocab

[fiery badge]

This problem has a grammar disorder

"difference in their reciprocals"

lmao

Did you solve it?

How would you approach it?

[merry hawk]

wdym

[fiery badge]

It should be "difference of" not "in"

[wary tulip]

i do not think "in" instead of "of" is all that egregious here

[mint crescent]

If anything "difference between" is better

but I digress

[mint crescent]

Do you remember what "reciprocal(s)" means?

[merry hawk]

sorry for not responding quick i was watching a youtube video on simplyfing rational expressions

[merry hawk]

what does egregious mean?

[mint crescent]

egregious = extremely bad

[wary tulip]

it's not important

[merry hawk]

okok

so

sorry im just reuploading

so i dont need to scroll

[mint crescent]

Do you remember what "reciprocal(s)" means?

here's what I asked that's relevant, the rest is just vocab chatter

[merry hawk]

its the

uh

the thing where

9/2

is ratrional?

then thats the opposite

i remember that cus i searched it up

yesterday

[mint crescent]

uh

The reciprocal is the result when you "flip" the numerator and denominator

more rigorously, the reciprocal of a/b is b/a (where both a, b are nonzero ofc)

So let's sps the numbers are x, y

What are some eqs we can make?

@merry hawk

[merry hawk]

what does rqs mean

eqs*

[mint crescent]

eq = equation, eqs = equations

[merry hawk]

im so sorry could u pls reply with the @ when yea

[mint crescent]

yeah I forgot to press it

so I just pinged after

[merry hawk]

its alright

thank u tho

[mint crescent]

anyway, back to this

[merry hawk]

so what i know is

+=12

what

omg

uhh

number+number=12

[mint crescent]

you could (you really should) use variables

like x, y

a, b

etc

[merry hawk]

ohh

thats what u meant

so x+y=12

then i dont understand 2/9

i seriously dont understand

[mint crescent]

The difference in their reciprocals is 2/9

in their reciprocals

what are the reciprocals of the numbers if we call the numbers x and y?

[merry hawk]

so 2+9=12?

thats wrong tho

its 11

[mint crescent]

.

@wary tulip can I drag you back here cause I gotta dip

[merry hawk]

i dont understand

at all

y am i like

stupid

like its just not getting in my brain

[wary tulip]

sorry i was never any good at math don't know how to do this one

[mint crescent]

oh actually I kinda forgot to say

It might be helpful to note x = x/1 and y = y/1

[merry hawk]

why

[mint crescent]

The reciprocals should be much more obvious now

[mint crescent]

B/c anything divided by 1 … is itself?

[merry hawk]

x/1+y/1=12

uhh

[merry hawk]

i dont understand

im actually so sorry

what does the reciprocals like

supposed to help with

[hoary burrow]

You can form a simultaneous equation with them
x+y=12
(1/x)-(1/y)=2/9

[merry hawk]

huhh

wait

wait what

what does simultanceus mean

wait why -

[hoary burrow]

Wait what age are you?

[merry hawk]

16

i just have a learning disorder

sorry

on vocab

and i also have adhd if that is any relevence

[hoary burrow]

Uh idk do they call it systems of equations here

If you heard of that

[merry hawk]

no im not sure

i just got this worksheet off my friend

to practice on rationals

[hoary burrow]

Ok so uh

[merry hawk]

but i dont know how to do word problems

[hoary burrow]

Two integers are equal to 12

[merry hawk]

yes

[hoary burrow]

So x+y=12

[merry hawk]

yes

[hoary burrow]

Where the x and y are the two integers

x=12-y

From that

[merry hawk]

uhuh

[hoary burrow]

So then we sub this in to the second equation

(1/x)-(1/y)=12

Then becomes

(1/(12-y))-(1/y)=2/9

Got that

?

[merry hawk]

do u think

theres going to be alot of questions on the final test

like that question

or no

[hoary burrow]

How the hell would I know

[merry hawk]

cus its just so hard

wait

do u know what this is called specifically

this question

[hoary burrow]

Idk simultaneous equations ig?

[merry hawk]

ok thaNK U

sorry my keyboard

[hoary burrow]

You should get two solutions

y= 9 and - 6

So there are actually two solutions

x=3,y=9
x=18,y=-6

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[topaz sinew]

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3. I got an answer but I was told that it's wrong.
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@pallid harness Has your question been resolved?

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[brave brook]

for this question I got 110 but the answer says 82, so I coded in python to go through all possible pairs and got 110 as well, but I still dont understand why the answer says 82

[brave brook]

I did this question by going through the maximum points like (0, 17) = 51, so that means I can safely decrease 17 all the way to 0

so (0, 17) ... (0,0)
(1, 16) ... (1, 0)
(2, 14) ... (2,0)
(3, 12) ... (3, 0)
(4, 11) ... (4, 0)
and so on

until (10, 1)

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@brave brook Has your question been resolved?

[hollow drum]

I believe that it's not including 0 as a valid x or y value since it says positive (x, y) and 0 is neither positive or negative

[brave brook]

oh that makes sense thank you

[brave brook]

thank you very much

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[topaz sinew]

Please don't occupy multiple help channels.

[twilit thistle]

How to do please

[pseudo sonnet]

,rotate

[cinder sequoia]

you have f'(x), you also have f'(-1) and f(-1)

if f' is the derivative of f, integrating f' should recover f up to some constant, which you can find using the initial condition f(-1)

i assume a future part asks you to find k, which is where knowing f'(-1) is probably useful to solve for k

[twilit thistle]

Lemme try the working for ur thing 1 sec

There is no part 2

Could I find a point of f(x) as I know 2x+1 lies on the line on f(x) @cinder sequoia

[cinder sequoia]

yes

[cinder sequoia]

if y=2x+1 is tangent to f at -1, then you know that f(-1) is the same as 2(-1) + 1 since the tangent line shares a point

yeah so you know a point of f(x), f(-1)

so you can solve for c

you also know the slope of the tangent line at x = -1 so you know f'(-1), and you can solve for k

[twilit thistle]

I think I did that just then

Would this be right?

[cinder sequoia]

yes k = -1

[twilit thistle]

How do I now find C?

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[inner swan]

Yo

[inner swan]

sup

Need help 1-5

[half glade]

isn't the altitude half the length of the hypotenuse if its a right angled triangle?

[inner swan]

yes

I think

<@&286206848099549185>

[sudden temple]

!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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[half glade]

i think you have to use the Euclidean Theorem in 5

[inner swan]

can u state it for me?

[half glade]

AD = (AB * AC ) divided by BC

the hypotenuse in your question should be 10, which is the BC in the picture, and the legs of the triangle are 6 and 8

so AD or the altitude of your triangle should equal to ( 6 * 8 ) divided by 10

so it should be 4.8

[half glade]

and in question 1 the answer should be obtuse, since 4^2X > 2^2X + 3^2X

which is 16X > 4X + 9X

16X > 13X

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[urban raptor]

Why not just say x = h

[fallow igloo]

Where is h?

[urban raptor]

But h is -b/2a right

[urban raptor]

He solved it earlier

But h = -b/2a right?

[fallow igloo]

yeah, but we don’t know what does h stands for

You need to show us what he said

[urban raptor]

He said the vertex is at (h,k)

And h =-b/2a

[fallow igloo]

Alright

[urban raptor]

So I guess he just put the formula for h

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[fallow igloo]

?

Are you good with the question?

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[celest crypt]

can someone help me on where to start with number two

[celest crypt]

i understand i plug 3/2 in

but what about the root

is it just sqrt 3/2 everywere

[shadow salmon]

?

[celest crypt]

like would it be f( sqrt 3/2) = 4(sqrt 3/2) and so on

[shadow salmon]

No

The square root is outside

You’re square rooting the value you get from f(3/2)

So start from the inside, i.e plug 3/2 in

Evaluate f(3/2)

Then square root

[celest crypt]

ah

okay lemme attempt it

[shadow salmon]

Always go from inside to outside

[celest crypt]

Like this??

i dont think i did it right...

[shadow salmon]

Don’t put equality at the end there, you’re saying, f(3/2) = sqrt(f(3/2))

[shadow salmon]

It’s correct, but don’t write equality like that

[celest crypt]

alrgight

tysm for the help

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[clever citrus]

I am given Y bar = 16.2, s = 3.6, sqrt(n) = sqrt(120) for this but I am not sure how to find tstar.

df = 120 - 1 so I have to look for df = 119 at 92% but the problem is my table doesnt the 119 row..so how would I approach this question?

[clever citrus]

wait should I use z_alpha/2 instead?

16.2 pm 1.75(3.6/sqrt(120)) ?

wait so am I expected to use the t method for smaller sample sizes?

because in my lec we only used it on sample sizes that seemed to be rlly small

[verbal crater]

i suppose you can take the 100 row

[clever citrus]

[verbal crater]

your results wont change much anyways

[clever citrus]

will it give me the same answer as the z method?

[verbal crater]

possibly, with minor differences

[clever citrus]

I see

[verbal crater]

since its a large sample size

[clever citrus]

tysm

also one more question

when they used the t test on this in R

this is what they got

how did they get df = 191

that would mean n = 192

[clever citrus]

but reading from this I dont understand how they can find that

wait im slow as shit. I skipped this slide

so im guessing that len(taxes) was 120 here?

[verbal crater]

i mean it says a random sample but didnt specify the size

[clever citrus]

oh my badf

bet ty

[verbal crater]

possibly just took 120 samples

[clever citrus]

ye I get it now

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[vivid venture]

is the formula 1/2 x b x h to find the area of a triangle applicable to all types of triangles e.g. ones without 90 degrees?

[wooden osprey]

yes

[verbal crater]

well for non 90 degrees you have to multiply by the sin of the angle made by the two sides

[dense crescent]

Yes

[wooden osprey]

what

[verbal crater]

no?

[dense crescent]

If u consider 2 sides yes

But if u consider breadth and height no need

[vivid venture]

so for e iii

how come we can use 1/2 x b x h

[wooden osprey]

^

[verbal crater]

oh height

then yeah

[dense crescent]

If u know vectors

It's pretty easy

But if u don't

[vivid venture]

why do we need vectors?

[dense crescent]

There are like many methods to find area

And vector method is one of them

So basically

[vivid venture]

well im not trying to use vecotrs here tho

im just asking why 1/2 x b x h can be used

is it cus we found bc and ad?

[dense crescent]

Yes u can

Consider one

Side as breadth

Draw perpendicular to that line to find height

Of triangle

Then use formula

[vivid venture]

yea alr

[dense crescent]

Mhm

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[brittle void]

are these correct?

not sure bout 3

[unborn jewel]

Tan is negative in 2nd and 4th quadrants

[neon iron]

,w tan(150deg)

[unborn jewel]

So your answer is correct

[thorny flame]

Results provided by WolframAlpha

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Requested by dickdoesbackflip

[unborn jewel]

And cos is negative in 2nd and third quadrant

So yeah, second one is correct too

[brittle void]

ayyy

thank you very much

[unborn jewel]

Haha, never mention

[brittle void]

.close

[topaz sinew]

Channel closed

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

Here I formed a new function h(x)

such that h(x) =g(f(x)

But there will be two functions h(x)

Can someone verify that the functions I have formed are correct

wait

These are the two functions

g(f(x)) could be equal to either one of them depending on a

right?

[topaz sinew]

@raw zenith Has your question been resolved?

[raw zenith]

<@&286206848099549185>

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@raw zenith Has your question been resolved?

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• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

@quasi mist Has your question been resolved?

[quasi mist]

<@&286206848099549185>

[topaz sinew]

@quasi mist Has your question been resolved?

[topaz sinew]

@quasi mist Has your question been resolved?

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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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[slow flower]

.status

!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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[slow flower]

1 and im just kinda confused on the concept of log cause my alg 2 teacher was trash lmfao

[pseudo sonnet]

do you recall the logarithm rules?

[slow flower]

almost none of them

but my sheet has them

[pseudo sonnet]

okay, nice

notice rule (vi)

try to see where you can use it here

[slow flower]

is there a way to do subscript on discord

wait hold up

for e it would be

this would be E

wait no

e would just be 45 i think

for a tho i dont know where to start lmfao

[blazing mauve]

you can start by rewriting whatevers inside the logs as powers of 3

since 3, 1/27, and 81 are all powers of 3

and its straightforward from there

[slow flower]

okay ill see

and then b is

[blazing mauve]

good, but you can simplify that further

[slow flower]

yea to -2

[blazing mauve]

yeah

[slow flower]

wait uh

thats correct right

[blazing mauve]

yes

[slow flower]

can you possibly further explain number 1

sorry im a little confused

[blazing mauve]

ok let me post it again

wait

so 3log_3(3) can be just simplified to 3*1

[slow flower]

okay

which is just 3

[blazing mauve]

yes

and (3/4)log_3(81) can be written as (3/4)log_3(3^4)

since 81 is 3^4

and so it becomes just 4

[slow flower]

it says it comes out as

3

[blazing mauve]

oh sorry it is 3

[slow flower]

so then

[blazing mauve]

the last one, 1/27 can be written as 3^-3

and so it becomes -3*(1/3) which is just -1

[slow flower]

ooooh

so then what do i do with them all after

3-3+(-1)

which is -1

so is that the answer

[blazing mauve]

yes

[slow flower]

okay makes sense

ty

so then for c you could do

log_9(27) is the same as

log_9(3)

[blazing mauve]

huh

[slow flower]

wait hold up

okay i did c

d) = log_125(1)-log_125(5)

which is -0.33 or -1/3

[blazing mauve]

yes

[slow flower]

what do i do for f

[blazing mauve]

ln is just log with base e

so its just log_e(e) which is 1

[slow flower]

ah

[slow flower]

so then ln 1 would be 0

[blazing mauve]

yes

[slow flower]

and then lne^2 would be 2

okayb et

[inner wren]

wait question?

which question?

[slow flower]

.close

[topaz sinew]

Channel closed

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[topaz sinew]

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Send your question here to claim the channel.

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>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[final fossil]

im so fucking tired of solution sets without explanations to the solution

[clear nova]

youre trying to learn how to do it but get screwed over, probably a cost cutting measure

[final fossil]

ignore the blue

my working is in red

solution

what is this nonsense about 1/y dy/fx = ln(c)

like the x just disappears

[sudden temple]

it is correct

differentiation of x wrt x is 1

[final fossil]

so y= xLn(c)

dy/dx = Ln(c) + x/c

hmm

Ln(y)

so d(Ln(y))/dx = 1/y dy/dx

[strange whale]

yea

[final fossil]

but this

[strange whale]

derivative of ln(c) is 0 though

ln(c) is constant

[final fossil]

yes

[strange whale]

I assumed you tried to use product rule or something

[final fossil]

yes

[final fossil]

this is result of product rule

[strange whale]

no

[strange whale]

^ we're taking the derivative with respect to x, not c

so you get 1*ln(c) + x*0

or just ln(c)

[final fossil]

i should go to bed

😭

[strange whale]

might be a good idea if it's night

not a good idea if it's 2pm where you are

[final fossil]

so dy/dx = Ln(c)?

but 1/y dy/dx = Ln(c)

wait

[strange whale]

d( ln(c)*x )/dx is ln(c)

d( ln(y) )/dx is 1/y dy/dx

you had the equality ln(y) = x*ln(c)

you take the derivative on both sides of the equation

you get 1/y dy/dx = ln(c)

[final fossil]

ty

my soul is crushed

im so tired

.solved

[topaz sinew]

Channel closed

Closed by @final fossil

Use .reopen if this was a mistake.

[topaz sinew]

Available help channel!

Send your question here to claim the channel.

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>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[unborn jewel]

!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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[unborn jewel]

And you want help for a or b or both

[slow flower]

both

just dont know where to begin

[unborn jewel]

Oh, there's a c too

[slow flower]

yea

[unborn jewel]

Yeah, so let's begin with a

To solve this, we gotta get rid of log6

This thing ruins all

[slow flower]

lol

[unborn jewel]

So, what we do now is...

We can rewrite 1 as

log6(6)

Got this?

[slow flower]

how did you get the 6 in parathesis

[unborn jewel]

Clear?

[slow flower]

ohh

okay yea that makes sense

[unborn jewel]

Okay, so RHS is now log6(6)

Now let's come to LHS

Do you know this rule: log(ab) = log(a) + log(b)?

[slow flower]

I did not

[unborn jewel]

Yeah you never be successful in life without knowing this rule

[slow flower]

LOL

[unborn jewel]

This is very crucial rule

[slow flower]

[unborn jewel]

And note: this rule only applicable when bases are same

Which in our case, is 6 for both terms

[slow flower]

ok

[unborn jewel]

So, we can write our LHS as log6[(x+3)(x+4)]

Clear?

[slow flower]

yep

[unborn jewel]

So, now since at both sides, of equal to sign, there's log6, we can oliberate this demon

So now our question simply becomes, (x+3)(x+4) = 6

Clear?

[slow flower]

yep

[unborn jewel]

Now, you know to solve this?

[slow flower]

yes give moment

[unborn jewel]

Sure

You stuck?

[slow flower]

a little

i thought i had it

[unborn jewel]

Right, go ahead

[slow flower]

but im assuming 3-4 = -1 is one of them

[unborn jewel]

Yes

Correct

And second one?

Wait -1 is correct but why you had to do 3-4?

[slow flower]

well i mean i put it in

i was just to lazy to say it

im not sure what hte other one is tho

if you could explain it

[unborn jewel]

You get -1 by solving a quadratic equation right?

Reply with yes or no

And I explain all

[slow flower]

no

explain pls

[unborn jewel]

Hmm, you are in trouble!!!

[slow flower]

yea my algebra 2 teacher was really bad

so its kinda hard for me

sorry

[unborn jewel]

Okay you clear till the equation (x+3)(x+4)=6 ?

[slow flower]

okay okay

[unborn jewel]

Yeah, now to find values of x, we gotta solve this quadratic

First, I want you to expand (x+3)(x+4)

Do it

[slow flower]

x^2 + 4x + 3x + 12

x^2 + 7x + 12

[unborn jewel]

Yeah

Now we have that stupid 6 at rhs

Take it to lhs

Do it

[slow flower]

then i set it to 0?

[unborn jewel]

Yessir

[slow flower]

x^2 + 7x + 6 = 0

[unborn jewel]

Hell yeah

Now you know the "splitting the middle term to find roots"?

Yes or no

[slow flower]

i think

[unborn jewel]

Hmm try it

If u stuck, lmk

[slow flower]

okay

[unborn jewel]

Are ya winning son?

[slow flower]

noo lmfao

[unborn jewel]

Okay so you want me to explain to split the middle term?

[slow flower]

yes please

[unborn jewel]

Okay, so our equation is x^2 + 7x + 6 = 0

Now, we have to adjust the middle term, 7x

[slow flower]

okay

[unborn jewel]

We have to split 7x in two terms

Such that when we multiply them, it gives product of first and third term

Read this peacefully

2-3 times

Slowly

[slow flower]

okay

split 7x in 2 terms

when we multiply them it gives ax and c multiplied

okay i get that

[unborn jewel]

Yes

So, what's the product of ax and c in our case?

[slow flower]

6x^2

[unborn jewel]

Yes

[slow flower]

cause we dont know x yet

so

[unborn jewel]

Now, can you break 7x in two parts, whose product is 6x^2?

[slow flower]

uh

[unborn jewel]

What if we write 7x as (6x + x)?

[slow flower]

ouu

[unborn jewel]

And guess what's the product of these terms

[slow flower]

6x^2

[unborn jewel]

Booyah

So now, our new/modified equation is...

Write it

Put 6x+x in place of 7x

[slow flower]

okay

x^2+6x+x+6=0

[unborn jewel]

Yess

Now from first two terms, we can take x as common

Right?

[slow flower]

yea

[unborn jewel]

Then our equation becomes x(x+6) + x + 6 = 0

Clear?

[slow flower]

okay

[unborn jewel]

And there ain't anything common in third and fourth terms, so we will take 1 common from them

So our equation becomes x(x+6)+1(x+6)=0

Got this?

[slow flower]

yea

[unborn jewel]

And now, we can take (x+6) common

So our equation becomes, (x+6)(x+1)=0

Clear?

[slow flower]

yea

[unborn jewel]

So now we have 2 terms (x+6) and (x+1) whose product gives zero

Clear?

[slow flower]

mhm

[unborn jewel]

So, of anyone of the two terms becomes zero, then the product becomes zero

Clear?

[slow flower]

\mhm

[unborn jewel]

So for what value of x will our first term be zero?

[slow flower]

-6

[unborn jewel]

Nice -6 is our first answer

[slow flower]

other is -1

[unborn jewel]

And for what value, second term becomes zero?

Yesh

You got htis

So, our answer is -1, -6

I would recommend you to save this conversation by screenshots or whatever you gonna do

[slow flower]

[unborn jewel]

And read this to get a hang of factorising a quadratic equation to get roots

[slow flower]

okay sounds good

[unborn jewel]

So, after all this bloodshed, we done with first question

[slow flower]

haha

[unborn jewel]

Can you resend the question pic

Have to scroll a lot

[unborn jewel]

Now, this ones ezier than previous one

You remember that rule log(ab) = log(a) + log(b)?

[slow flower]

ye

[unborn jewel]

Now there's another rule...

log(a/b) = log(a)-log(b)

Similar to previous rule

Just opposite sings

[slow flower]

k

[unborn jewel]

This rule is just as crucial as previous one

[slow flower]

okay

[unborn jewel]

And here, no base is given

Like in first question, it was 6

Here, it's air

[slow flower]

lol

[unborn jewel]

So, we don't have to worry when base becomes invisible, it just means that base is 'e'

That's it, for now just know that e is a number that's it

[slow flower]

ok

[unborn jewel]

Since for all terms our base is same

We can apply the above discussed rule

You wanna give a try?

[slow flower]

sure

[unborn jewel]

Rewrite the RHS using this rule

[unborn jewel]

This rule

[slow flower]

wait so

[unborn jewel]

Get it in log(a/b) form

[slow flower]

does that mean i just swap the sides basically

[unborn jewel]

Nah nah nah

We write log(x^2) - log(100) as log(x^2/100)

In rhs

[slow flower]

ah

thats what i was gunna do

[unborn jewel]

Oh

[slow flower]

so then its just

[unborn jewel]

Good

[slow flower]

lhs = log(x^2/100)?

i mean

rhs

[unborn jewel]

Yes

Now again we have ONE SINGLE LOG on both sides

So oliberate it

So now, our question becomes x^2/100 = 1

Got this?

[slow flower]

did you just cancel all the logs out

wait im dumb i get it

[unborn jewel]

Theres only one log on both sides

[slow flower]

I didnt change the lhs

to

[slow flower]

this

[tepid oxide]

HEEEEEELP

[slow flower]

lol

[unborn jewel]

rhs right?

[slow flower]

wait

so

[tepid oxide]

hellp meeeeee

[slow flower]

its just

[unborn jewel]

Find another channel mate

[tepid oxide]

meany

[slow flower]

logx^2 - log100 = log(x^2/100)

[unborn jewel]

Yeah

[slow flower]

im confused how you got one log on both sides though

sorry im slow haha

[unborn jewel]

Clear now?

[slow flower]

oh thats why i was confused

its cause

my lhs was literally logx^2 - log100

and my rhs was literally log(x^2/100)

LMFAO

[unborn jewel]

Oh lmao

So, now we remove logs

x^2/100=1

You can solve this ig

if not, you shall die

[slow flower]

LMFAO

ofc

x^2 = 10

100/100=1

[unborn jewel]

Eh

What

[slow flower]

wdym

[unborn jewel]

Look at this carefully

Do again

[slow flower]

ahhh i hate factoring

asd moment

[unborn jewel]

No factoring here

[slow flower]

x=10

10^2 = 100

[unborn jewel]

Yeah

[slow flower]

I meant to say x=10 not x^2=10

oops

[unborn jewel]

Yeah

But there's another answer too

[slow flower]

is it -10

[unborn jewel]

Yes

You got this

So the answers are -10, 10

[slow flower]

yep

now for the finale xd

[unborn jewel]

Wait a min

What I am going to tell you will blow your mind

[slow flower]

lets see

[unborn jewel]

Your mortal brain is incapable of this dovone knowledge

So, you ready...

[slow flower]

yep

[unborn jewel]

Log1 = 0

Irrespective of base

So, the question we did now

[slow flower]

was it wrong

😭

[unborn jewel]

Could have been solved in an easier way

[slow flower]

oh

dang

[unborn jewel]

We could have straight up wrote that log(x^2) = log(100)

[slow flower]

rip

[unborn jewel]

You get this?

[slow flower]

ye

[unborn jewel]

Haha

I was about to tell you before

But shortcuts hit good after hardwork

[slow flower]

yea

[unborn jewel]

So, now we can move to final one

[unborn jewel]

I have to think a little for this

Gimme a min

Please...

[slow flower]

kk

[unborn jewel]

👉👈

Ok, I got it

So, you know basic definition type equation for log?

Lemme write it forst

If a^b = c

[slow flower]

im back

[unborn jewel]

Then b = loga(c)

[slow flower]

okay

[unborn jewel]

This is like definition of log

Or standard form of log equation

Now, I want you to compare this pic to our question, and write our question in log form

[slow flower]

so you could do like
3^(x+1)=15 = (x+1)= log_3 15

[unborn jewel]

Hell yeah boy

Correct

Hey, I am getting lazy to type the steps, it be okay if I write a step and send pic?

[slow flower]

yep

[unborn jewel]

Cool

Okay, now focus only and only on RHS

Clear?

Clear?

[slow flower]

uh

where did you get rhs from

oh wait

log3(3x5)

is the same

right

as log3(15)

[unborn jewel]

LoL yeah

[slow flower]

okay

okay i get that

[unborn jewel]

Clear?

[slow flower]

ye

[unborn jewel]

Clear?

[slow flower]

ya

[unborn jewel]

Now this is our new RHS

So our question now becomes...

[slow flower]

(x+1)=1+log3(5)

[unborn jewel]

x + 1 = 1 + log3(5)

Yess

Now 1 gets cancelled

[slow flower]

ah

[unborn jewel]

And here we have our x

[slow flower]

so x = log3(5)

and thqtas the answer

[unborn jewel]

Yessir

[slow flower]

tysm

[unborn jewel]

np,

Since these are basics

And very important

And you not very strong at em

I would recommend you to somehow save this whole conversation

This is far far far better than any notes

The conversation style always better than monotonous reading

[slow flower]

ye

okay thanks

i gotta go now

i appreciate u

[unborn jewel]

Ok cool

[slow flower]

.close

[unborn jewel]

Cya

[topaz sinew]

Channel closed

Closed by @slow flower

Use .reopen if this was a mistake.

[topaz sinew]

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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>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[spark ibex]

Just a really quick question

[spark ibex]

is this how you would divide this figure

[fiery badge]

Looks good

[sudden temple]

to calculate areas stuff, yes

[spark ibex]

yes

[fiery badge]

There's another way that's equally efficient though

[spark ibex]

is it a line to the left?

[fiery badge]

ye

[spark ibex]

I don't know which would be correct because apparently you can only divide the figure in a specific way

[fiery badge]

Who told you that?

You can divide it as much as you like