help-10

[short spruce]

ah

[hot hazel]

please read before you ping mods

[short spruce]

yes namington

[odd magnet]

I assume they want to be able to do this problem mentally

and thus are just like

[astral ivy]

@lone shore are you sure you can’t write anything down? Trying to do algebra in your head will likely cause mistakes, not prevent them

[odd magnet]

doing it mentally now no matter how long it takes

[lone shore]

I can but that just beats the whole purpose of this

[short spruce]

so to recap

you've been sitting here for an hour

staring at this sentence

[lone shore]

not exactly an hour

almost an hour

[nocturne minnow]

Beats the purpose of what exactly?

[short spruce]

so for almost an hour you've been staring at a sentence

try attempting the problem?

[lone shore]

of doing it mentally and in a certain speed

[nocturne minnow]

It’s not useful to do it mentally

[astral ivy]

Trust me, there is no reason to practice algebra mentally. Wouldn’t you rather finish 90% of the questions all correct, than do 100% and get half wrong?

[short spruce]

i don't know if it's possible to do it mentally

[lone shore]

it is possible I did it with few others but im stuck on this one

[astral ivy]

Dude you’re wasting your time

[lone shore]

How so

[short spruce]

if you want to stare at a sentence for an hour and do absolutely nothing go for it

[astral ivy]

If the question gets even a little harder you won’t be able to do it in your head

[short spruce]

as long as you do that, i'm out

[nocturne minnow]

It’s not easily achievable and you’d waste more time doing it mentally than on paper

[astral ivy]

If you want to minimize time on your exam, you should practice solving problems faster on paper

Yeah mentally you’d (1) make mistakes and (2) take more time than scribbling on paper

It’s just pointless

[nocturne minnow]

There’s too much math to mentally do

[tardy epoch]

Works on tests too?

[obtuse pebble]

@lone shore Has your question been resolved?

[obtuse pebble]

@lone shore Has your question been resolved?

[nocturne minnow]

@lone shore Did you not solve your problem yet?

[lone shore]

no

[nocturne minnow]

Are you still doing it mentally?

[tardy epoch]

ptsd reading math papers

[short spruce]

lmao

[nocturne minnow]

Are you still working on that problem?

[lone shore]

yes

I wrote it down and I got an answer but im not sure

[nocturne minnow]

Did you find W?

[obtuse pebble]

@lone shore Has your question been resolved?

[tardy epoch]

.close

[obtuse pebble]

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[little trench]

help

[obtuse pebble]

Please don't occupy multiple help channels.

[little trench]

okay

[obtuse pebble]

@little trench Has your question been resolved?

[tardy epoch]

.close

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[tardy epoch]

,w simplify 0.2(-2x+4) + 0.5(7x-4) + 5x-3

[warm shale]

Results provided by WolframAlpha

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

Requested by riemann#2529

[tardy epoch]

are you supposed to learn rules of algebra?

i guess you're supposed to learn something like
https://www.cuemath.com/algebra/basic-of-algebra/

[obtuse pebble]

@timid silo Has your question been resolved?

[obtuse pebble]

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[mild kernel]

Isnt the x values for interval notation just these coordinates with the appropriate parentheses and brackets

[royal basin]

you've got [ and ( backwards

[ includes boundaries, ( excludes them

[timid silo]

Yes

[mild kernel]

ok

so just flip the signs for the bottom 2

[royal basin]

flip all the parentheses

well

swap round for square and vice versa

but still, all of them, not just the bottom two.

[mild kernel]

ok

it worked

thank you

.close

[obtuse pebble]

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[mint whale]

how do you do this question? How can the plane which contains the xy-plane have an angle of 45° with the plane on xz-plane?

[royal basin]

"the plane which contains the xy-plane"

??

[mint whale]

yes because one of the conditions say the plane contains the z-axis which is the xy-plane?

[royal basin]

no

the z-axis is not the same as the xy-plane

[obtuse pebble]

@mint whale Has your question been resolved?

[mint whale]

idk

how do I interpret the z-axis?

[royal basin]

it's that blue vertical line right there lol

that's the z-axis

it is a line

[mint whale]

oh ok

how come geogebra gives me the plane on the xy? when I set z=0

[royal basin]

the equation z=0 describes those points whose z-coordinate is 0

the z-axis does not consist of such points (other than the origin)

[mint whale]

ok I see

for the problem at hand, there are a total of 2 planes then that satisfies the condition?

[royal basin]

it appears so.

[mint whale]

thank you!

.close

[obtuse pebble]

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[fading heron]

im horrible with FTC

[obtuse pebble]

Please don't occupy multiple help channels.

[fading heron]

how did they solve for g'(x)

i see that x^2 and 2-x was substituted into tan(u^3)

but where does the 2x come from

?

[obtuse pebble]

@fading heron Has your question been resolved?

[fading heron]

ah nvm i think i got it

you have to take the derivative of each of the bounds and multiply it to the thing

x^2 becomes 2x and (2-x) becomes (-1)

so 2xtan(x^6)+tan((2-x)^3)

instead of just tan(x^2)-tan((2-x)^3)

.close

[obtuse pebble]

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[timid silo]

Hello

[timid silo]

Would someone please explain me this property: 15.26

Do you think the property written in the first image is incorrect?

.close

[obtuse pebble]

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[zinc cairn]

.reopen

occupied

[zinc cairn]

Hello im from ph can you teach me how to

solve that

[pine sail]

So do you know what zeros are?

[zinc cairn]

no sir

i dont know sir sorry

[pine sail]

It's alright.

[zinc cairn]

sir

how can i

[cerulean ridge]

A square field is 60 m long. Find the cost of levelling the field at the rate of `10
per sq. metre.

[zinc cairn]

sir i dont know sir

[cerulean ridge]

A square field is 60 m long. Find the cost of levelling the field at the rate of `10
per sq. metre.

[pine sail]

Channel is occupied.

[zinc cairn]

oh

[pine sail]

#❓how-to-get-help
@cerulean ridge

[zinc cairn]

i thought that question is for me

im sorry sir

@pine sail sir

how can i

[pine sail]

Right so

Zeros of a polynomial are the values for which it is zero.
Basically you do
$x^2(x-1)=0$

[warm shale]

Sakata Yaksha

[pine sail]

So what values do you get?

[cerulean ridge]

A square field is 60 m long. Find the cost of levelling the field at the rate of `10 per sq. metre. Tell The Answer Please Bros

[zinc cairn]

sir i dont know how to sir

[pine sail]

Leave this channel, this is occupied.
If you want to know how to ask questions check
#❓how-to-get-help

[zinc cairn]

im really sorry sir

[pine sail]

Alright, do you understand x intercept or y intercept?

[pine sail]

Don't call me sir, and don't repeat it man. Relax we're good.

[zinc cairn]

sir 😦 im so sorry

[pine sail]

Bruh

[zinc cairn]

i dont know sir

[pine sail]

Alright, I want you to revise all that before you ask a question then.

[zinc cairn]

okay sir im very sorry sir

i stop 4 years in school sir and now i pursue sir thats why i have no knowledge at all sir

i will revise the lesson you said

and i will going to ask sir again

sorry to bother you sir

thanks

[cerulean ridge]

i am a 13year old kid

[zinc cairn]

@pine sail

this one ?

can you help me bro

just last one question bro

sir

i needly this badly

@pine sail sir im sorry sir thanks and i appreciate sir

.closed

.close

[obtuse pebble]

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[obtuse pebble]

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[obtuse pebble]

@celest gorge Has your question been resolved?

[obtuse pebble]

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[tough coral]

i got the answer of (-∞,-3.5) U (-1,∞) but in photo maths its different answer? can someone help pls

[high lily]

show work

[tough coral]

ok wait

[raven spire]

Great work but you forgot to include the absolute value function's condition

|x| = +x only when x > 0

|x| = -x whenever x < 0

[obtuse pebble]

@tough coral Has your question been resolved?

[obtuse pebble]

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[tough coral]

um i dont understand? can you elaborate it more?

.reopen

[obtuse pebble]

✅

[raven spire]

ara ara

[tough coral]

;-;

[raven spire]

XD

so umm

[raven spire]

here

you removed the absolute value function right!?

[tough coral]

yes..?

[raven spire]

but that comes under some premises

oops- so badly phrased

*it's always better to keep tabs on the conditions before removing the absolute value function

[warm shale]

Ansh

Ansh

[tough coral]

can you give a little explanation about absolute value? because i started learning rational inequaties from the organic chemistry tutor who didnt cover absolute value

[raven spire]

O_O

[tough coral]

sory

[raven spire]

🙊 no no.. I mean .. sure

So the thing is, basically

absolute value always gives a positive value right?

[tough coral]

yes

[raven spire]

what will happen when the thing inside absolute value is negative?

[tough coral]

becomes positive

[raven spire]

yeah

but how does the function make it positive

[tough coral]

idk

x -1?

[raven spire]

nope

[tough coral]

times it by -1?

[raven spire]

Exactly

whenever the function looks within itself (@_@;) and finds that its insides are negative

it multiplies itself by -1, and then releases the positivity

$\abs{-5} = -1 \times -5 = 5$

[tough coral]

ye

[warm shale]

Ansh

[raven spire]

similarly

$\abs{-19} = -1 \times -19 = 19$

[warm shale]

Ansh

[raven spire]

Right?

[tough coral]

yes

[raven spire]

so 😱 what happens when you don't really know what's inside it...

inside the absolute value function, I mean-

what is $\abs{x}$

[warm shale]

Ansh

[tough coral]

x

[raven spire]

well, the answer's simple now isn't it?

[raven spire]

yes.

$\abs{x} = x$

[warm shale]

Ansh

[raven spire]

but,

only when $x$ is positive

[warm shale]

Ansh

[tough coral]

so what if |-x|

is it x?

[fierce ruin]

then x

yes

plug in absolute value in a graph calculator and you can see for yourself, any negatives get reflected about the x axis

[raven spire]

oiiiiiiii

(@_@;)

[tough coral]

?

|-x| is x right?

[raven spire]

only when x is positive

whenever "x" is negative, you'll have a minus x coming out of the absolute value function

[glossy ibex]

|x| = sign(x)*x

[raven spire]

DETOX 😱 sgn(x) comes after defining \abs{x}

[glossy ibex]

|x| is x if you drop the sign

-x becomes x

[raven spire]

-(-9) becomes -9?

[glossy ibex]

|-x| is x just drop the sign from inside

[raven spire]

|-(-9)| is -9 dropped the sign 👀

[glossy ibex]

assuming x is positive !!

[raven spire]

exactly what I'd been saying all along XD

[tough coral]

whats happening ;-;

[raven spire]

you ditched class

ara ara

@tough coralremember this

[tough coral]

this is 1 grade above me

im learning for fun ;-;

[raven spire]

Learn

[tough coral]

im learning litterally of youtube

[raven spire]

Ohh want me to share a video then?

[tough coral]

:= is wut

yes pls!

[raven spire]

just equal to

[glossy ibex]

it says |x| is defined to equal x when is x is positive and -x when x is negative

ensuring |x| is always positive

[raven spire]

https://www.youtube.com/watch?v=ZJvOGkykJ44

Gooooooo goooooooo

[tough coral]

ok pls guide me if i have anyother questions next time

sorry for my incompetence!

[raven spire]

heyyyyy nuuuuuuuu

also, sure :D hit the help channels whenever

[obtuse pebble]

@tough coral Has your question been resolved?

[obtuse pebble]

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[modest ruin]

is this incorrect use of sig figs???

she proceeded to mark me wrong

in future assignments

[short spruce]

seems she just doesn’t like the dot for multiplication

both answers have 2 sig figs

[balmy mortar]

Wow rejecting dot

[short spruce]

though using an x for multiplication is normally bad practice

[balmy mortar]

in some cases the dot might look confusing.

I guess it is true in scientific notation usually an 'x' is written.

[short spruce]

if only implied multiplication worked with scientific notation :(

i vote we change to that :)

[balmy mortar]

in any context where you are writing decimal fractions

dot for multiplication would be confusing.

[short spruce]

confusion is weak

dot master race

[modest ruin]

ikr

i’m just going to use x to make her happy

thanks

.close

[obtuse pebble]

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[unreal kernel]

Looking for help with a calculus question concerning change of velocity

[obtuse pebble]

Please don't occupy multiple help channels.

[unreal kernel]

Looking for help with a calculus question concerning change of velocity

[halcyon tulip]

Post question

[modest ruin]

hello

[unreal kernel]

car is traveling at 11 m/s and decelerates at -1.2 m/s^2 how much time does it take to fully stop

v(t) = -1.2t + 11, I believe but not sure how to proceed

[modest ruin]

time is in seconds right?

i’m guessing it is

[unreal kernel]

Yes, Im assuming. That is the only unit of time given

[modest ruin]

you would just find the root of v(t)

[modest ruin]

oh nonono

i mean like

when you graph it, you get the x root

when x is = 0

[unreal kernel]

Not allowed to graph this homework

[modest ruin]

or you could just do 0 = -1.2t + 11

and solve for that

[unreal kernel]

then t = time?

[modest ruin]

yea

[unreal kernel]

Ok and how to determine distanced traveled in that timeframe?

[modest ruin]

you would take the integral of that function between x=0 and x = the time you got

for me, it’s coming up as 9.1(6) repeating

[unreal kernel]

right

[modest ruin]

i’m in phone so i can’t show you the equation and how to integrate it

but someone else could prob help u

[modest ruin]

yup

[unreal kernel]

ok

[unreal kernel]

are you available?

[modest ruin]

hello

i’m back

[unreal kernel]

Hi

[modest ruin]

have u integrated yet or do i have to step u through it

[unreal kernel]

I am unsure

[modest ruin]

okay,

whoops

v(t)=1.2t + 11

[unreal kernel]

-1.2t

[modest ruin]

for the integral,

yeah my bad

[halcyon tulip]

Yes

[modest ruin]

the first term can be gotten with the power rule

so (-1.2t^2)/2

2nd term is just power rule again

so 11t

and of course, + constant

so it would be

-0.6t^2 + 11t + c

[unreal kernel]

Not sure what the limits are for the integral

[modest ruin]

the first bound is 0 since the time starts at 0

[unreal kernel]

Ah.

[modest ruin]

and the second bound is what you got for the first question

have you gotten it yet?

for the first question?

[modest ruin]

yup

[unreal kernel]

solve for c now?

[modest ruin]

you can’t solve for c

[unreal kernel]

So thats the distance traveled during the 9.16666 seconds?

[modest ruin]

yeah if that’s what u got

let me use paper

[unreal kernel]

Ok

[modest ruin]

phone is a pain

[unreal kernel]

Indeed

[modest ruin]

i had to do this fast cus i got class but

evaluate that

c cancels out

again, take this with a grain of salt

i haven’t even taken official calc yet

lol

it would be right

what you got

i just checked

[unreal kernel]

lol and youre helping others? Thats awesome

[modest ruin]

lol

[unreal kernel]

.close

[obtuse pebble]

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[celest gorge]

As the question says the curve touches the axis at (3,0) i know that the equation of the line must be
(Ax + b)(x - 3)^2 but I don't really know how to answer any of the questions

[royal basin]

actually you know it's $y = (x-a)(x-3)^2$

[warm shale]

Ann

[celest gorge]

how so

[royal basin]

it crosses the x axis at (a,0)

so it has a as a root

[celest gorge]

oh I didn't see the y value was 0

Ok I see that

But I still have no clue how to solve this problem

[royal basin]

which part

[celest gorge]

Well lets start with part (i)

as if I understand how to do that I can probs do part 2 and 3

[royal basin]

the point (1, a^2 - 10a + 12) lies on the curve y = (x-a)(x-3)^2

[celest gorge]

when the y value of part a is (a^2 - 10a + 12) does it mean the curve passes through x = 1 twice or is only one of the values correct

I get that yeah

[royal basin]

does it mean the curve passes through x = 1 twice or is only one of the values correct
???

why would the curve pass through x=1 twice

[celest gorge]

Well the quadratic gives 2 values

thats why im confused

[royal basin]

what do you mean

[celest gorge]

a^2 - 10a + 12 gives me a = 5 - sqrt13 or 5 + sqrt13

[royal basin]

no

[celest gorge]

Maybe im just doing the wrong thing

[royal basin]

you're setting a^2 - 10a + 12 equal to zero despite there being no reason to

[celest gorge]

o

that makes sense ig

[royal basin]

just because the problem states a quadratic somewhere does not mean you have to drop everything and find its roots right there and then

[celest gorge]

ok I see

So what should I do as a first step to solve part i)

[royal basin]

plug the point in

get a^2 - 10a + 12 = (1 - a)(1 - 3)^2

[celest gorge]

1 sc

im a little confused

you're setting the y value of that point equal to the entire equation of the curve?

[royal basin]

????

i'm plugging in x = 1 and y = a^2 - 10a + 12

don't overthink it lol

[celest gorge]

srry im just trying to understand why im doing these steps

a^2 - 10a + 12 is the y value of the point correct?

[royal basin]

yes

[celest gorge]

OH

I see

mb i was being stupid

so I expand the brackets on the right side then set it all equal to 0 and find values for a?

[royal basin]

overthinking it again

all you have left to do here is clean this equation up

[celest gorge]

huh

[royal basin]

and you don't even need to expand (1-3)^2 unless you refuse to rewrite 1-3 as -2

[celest gorge]

i dont get what you mean

so I get a^2 - 10a + 12 = 4 - 4a

?

then dont I rearrange it to
a^2 - 6a + 8 = 0?

or am i doing something wrong again

[royal basin]

yes now you've got it right

[celest gorge]

thats what i meant here

worded it badly i guess

[royal basin]

you don't need to find the values of a tho

all you were asked for is the quadratic that a satisfies

[celest gorge]

which we found

I should be able to do part ii) then but part iii) i think i could do with some help

oh wait nvm

i got this

ty

.close

[obtuse pebble]

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[orchid lintel]

https://gyazo.com/91e109827824361c72a79ca877b5d2bf

[orchid lintel]

i am very confused

This is how I did it

[short spruce]

do you know log rules?

[high lily]

simplify your fraction

[orchid lintel]

simplify what fraction

[high lily]

that skyscraper fraction

[short spruce]

oh i thought you said "this is how they did it" lmao

just heed ramonov's advice and you're good

[orchid lintel]

i know the answer is (x^14 * z^8) / y^10 right

i just confised as how you move the z

[high lily]

would you be able to simplify
$$\frac{a}{\br{\frac bc}}$$

[warm shale]

ℝamonov

[orchid lintel]

i confused on how

i know this is basic sorry

[high lily]

division is the multiplication of the reciprocal

[orchid lintel]

so that would equal a * c/b

[high lily]

yes

[orchid lintel]

so a/1 * c/b is just ac/b

OOOOOO

ok i get it now

[obtuse pebble]

@orchid lintel Has your question been resolved?

[obtuse pebble]

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[sly cargo]

hello

[violet ruin]

Hi, please send a problem here.

[sly cargo]

sorry for the late reply

i do not know how to answer this

[obtuse pebble]

@sly cargo Has your question been resolved?

[obtuse pebble]

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[sly cargo]

Thank u

[somber hedge]

Hi there, could i get some help with this i am really struggling

[violet ruin]

Whenever you see x you add 1

Like f(x+1) is x+1 / 2x+3

[short spruce]

don't do people's work for them

also that notation is awful

[obtuse pebble]

@somber hedge Has your question been resolved?

[obtuse pebble]

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[timid silo]

I have a problem and I've done some research but cant seem to find anything that would help
The roots of the equation ax^2 + bx + c + 0 are -12 and 2
find the values of a b and c

[short spruce]

nothing that would help?

[timid silo]

like guides or methods

[nocturne minnow]

Reverse factoring

[short spruce]

if i gave you a similar quadratic, say x^2-4x-12=0, could you solve that?

[timid silo]

is it x = 6 x = -3

[short spruce]

oop

that ain't right

[timid silo]

oh

i found the factors of -12 so i came to 2 and -6 which add to -4 then but them in brackets to get (x-6)(x+2) then x-6=0 x=6 and x+2=0 x=-2

oh yh -2 not -3

[short spruce]

right

[timid silo]

i think

[short spruce]

(x-6)(x+2) this is the important part to notice here

you went from (x-6)(x+2)=0 to (x-6)=0 and (x+2)=0, then to x=6 and x=-2

so, with your question... go backward

you have x=-12 and x=2

[timid silo]

so put them into brackets and back into the equation?

[short spruce]

well what would your factored equation look like?

given that x=-12 and x=2

[timid silo]

?x^2+10x-24

so b is 10 and c is 24

but how do you find a

[short spruce]

a is 1

[timid silo]

how did you find that?

or is it because there is no answer

[short spruce]

1x^2=x^2

the ? you wrote is just an imaginary 1

we just don't write it cause there's no point

x*1=x

[timid silo]

ah ok

is a ever a number apart from 1 then?

or is it always 1

[short spruce]

it could be something other than 1

say you were given x=2/3 and x=5 as your roots

,w expand (3x-2)(x-5)

[warm shale]

Results provided by WolframAlpha

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

Requested by a disappointing son#0540

[timid silo]

ah ok

thanks man you have really helped

.close

[obtuse pebble]

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[latent panther]

Can anyone walk me through this?

[latent panther]

I know for pi(sin(u)) it is pi(cos(u)) but how about the -2^u?

[gloomy valve]

write 2^u as e^(ln(2) * u)

[latent panther]

Alright

So then u'/u so would it just become 0/2 * u?

so 0*u

[gloomy valve]

u' / u?

do you know how to take the derivative of an exponential?

[latent panther]

but it is a log

[gloomy valve]

the log is a constant

log(2) = const, not dependent on u

[latent panther]

so the log is 0

log(2)=0

[gloomy valve]

no

[latent panther]

how is it not?

[gloomy valve]

what is the derivative of e^(2x)?

[latent panther]

where does that come from?

[gloomy valve]

because you're taking the derivative in the wrong way

[latent panther]

How am I doing it in the wrong way

[gloomy valve]

you have to use the chain rule

[latent panther]

I am so lost

[gloomy valve]

.

now replace the 2 with ln(2), same thing

[latent panther]

but I dont get where that even came from

[gloomy valve]

you're trying to differentiate the log in the exponent

but its just a constant number like 2

[latent panther]

but arent the derivatives of constants 0?

[gloomy valve]

but you have ln(2) * u

not just ln(2)

[latent panther]

but where does the e come from

and where does the x come from

[gloomy valve]

that was just an example

you can use any letter

[latent panther]

so with ln(2)*u how do you set that up

[gloomy valve]

wdym?

the derivative of that or where it came from?

[latent panther]

how do you set it up to find the derivative of that?

[gloomy valve]

the derivative of ln(2) * u is simply ln(2)

[latent panther]

how?

oh is it because u^1?

[gloomy valve]

factor rule?

[latent panther]

and then power rule is u^1-1

so u^0?

[gloomy valve]

yes

[latent panther]

Ok

so then is the answer pi(cos(u))-ln(2)?

[gloomy valve]

nono

you know that the derivative of e^u is e^u right?

but in our case we have e^(ln(2) * u). we need to apply the chain rule because the exponent is a function of u itself

[latent panther]

this is so confusing

I thought the u was gone

the * u

because it becomes u^0

[gloomy valve]

yes the inner derivative becomes ln(2)

[latent panther]

so then we are just left with ln(2) and no * u

[gloomy valve]

but you also need the outer derivative

e^(2u) => 2 * e^(2u)

[latent panther]

so you put the u inside the ln?

[gloomy valve]

e^(ln(2) * u) => ln(2) * e^(ln(2) * u)

[latent panther]

I dont get where the e comes from

[gloomy valve]

because we have rewritten 2^u as e^(ln(2) * u)

[latent panther]

how though?

I dont get how you just do that

[gloomy valve]

well you know that exp and ln are inverse functions of each other?

[latent panther]

why does it have to change around

I am so lost

[gloomy valve]

did you learn about exponential derivatives in class?

[latent panther]

I am just completely failing to understand what you are saying

no

Im trying to right now I guess

[gloomy valve]

well you have to because otherwise it's not possible to solve

[latent panther]

is it possible to learn how to do that in 15 minutes?

[gloomy valve]

if you know exponent rules and basic differentiation rules, yes

[latent panther]

what should I do to learn it

[gloomy valve]

Well first you have to know that e^x and ln(x) are inverse functions. So e^(ln(x)) = x and ln(e^x) = x.

[latent panther]

Alright

so in the case of this problem it becomes e^(ln(2))

which means e^(ln(2)) = 2?

[gloomy valve]

Now why did we rewrite 2^u to e^(ln(2) * u)?

[gloomy valve]

Right

but you multiply by u as well

[latent panther]

that is because the u is not included in the inner part of the function

so it isnt ln(2u) it is ln(2)*u?

[gloomy valve]

e^(ln(2) * u) = e^(ln(2))^u

now you said that e^(ln(2)) = 2 right

[latent panther]

Yes

[gloomy valve]

so e^(ln(2))^u = 2^u

[latent panther]

wait it is -2 right and not 2?

[gloomy valve]

no its 2

[latent panther]

oh

[gloomy valve]

e^(ln(a)) = a for any a

[latent panther]

so then we do 2^u * u^1?

[gloomy valve]

how did you get that?

[latent panther]

I dont know honestly

ok so it becomes e^ln(2)^u which then becomes e^2^u?

@gloomy valve

[latent panther]

So that is the answer?

[gloomy valve]

Tell me which step you don't understand

[latent panther]

I think I see how you break it up

thank you

.close

[obtuse pebble]

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[stiff fog]

1+1=x x+x=y solve for y

[stiff fog]

.close

[obtuse pebble]

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[timid silo]

Stuck on question 5

[wicked cedar]

This channel in use

[timid silo]

Oh oops

[wicked cedar]

It ok

[obtuse pebble]

Channel closed

Closed due to the original message being deleted

[wicked cedar]

can someone help me with this

please

[carmine bear]

You deleted the message so your channel is probably going to "reset" in a second but use the fact that angles in a triangle sum to 180, and that the shape BOA is a triangle

[wicked cedar]

Ok

Idk these ones either

[carmine bear]

radius is always perpendicular to the tangent, so angle BAX + angle OAB = 90 if i'm right (not 100% sure tbh)

[wicked cedar]

yeah that is correct

[carmine bear]

yeah so q is 90-p

because of that

[obtuse pebble]

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[wicked cedar]

Ok I got it back

I know that angle BOA is double of BCA

[carmine bear]

Yeah

[wicked cedar]

Oh wait angle BAX = BCA

[carmine bear]

The fact that the radius is perpendicular to the tangent should help you

OA is a radius and XY is a tangent so using that you know what OAX is

[wicked cedar]

90

[carmine bear]

yeah

[wicked cedar]

hmm

Now I am confused here

[carmine bear]

Essentially, to prove that angle BAX = angle BCA you're being asked to show that angle OAX = 90 (radius and tangent are perpendicular) and that angle BAX = angle OAX - angle OAB

[wicked cedar]

I believe that and BAX = BCA

That doesn't help me though

[carmine bear]

What part do you need help with

[wicked cedar]

Finding angle OAB and OAX

Actually I have OAX

[carmine bear]

You're basically using other facts that you know already to find them. Just like how you got BOA

angle OAB is one of the three angles in an isosceles triangle because OB = OA

because OB is the radius of the circle and OA is also the radius of the circle

[wicked cedar]

Its an isosceles so both angles at the bottom are the same

[carmine bear]

yes

you don't know what both angles at the bottom are so you just assign them a letter. In this case they've chosen q. It's just like saying how i know that 2 * a number + 5 = 15. Since i don't know the number yet i'd just assign it as x so that 2x + 5 = 15

they did the same thing with angle BCA and assigned it the letter p

[wicked cedar]

I don't understand how to find it out

[carmine bear]

how to know it's an isosceles triangle?

[wicked cedar]

Ik it is an isosceles

Because it says in the question

I don't know how to find the angles

[carmine bear]

You write them in terms of p and q

i think

[carmine bear]

angles in a triangle sum to 180 so 2p + 2q = 180

[wicked cedar]

I know that:
OAX = 90
OBA = OAB

Im just gonna skip it

[carmine bear]

ok

[wicked cedar]

.close

[obtuse pebble]

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[wicked cedar]

.reopen

[obtuse pebble]

✅

[wicked cedar]

.close

[obtuse pebble]

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[obtuse pebble]

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[eternal garden]

Which way is the correct way to evaluate 3^3^3?

[haughty coyote]

top one

[short spruce]

with no parenthesis, the first way

[eternal garden]

Okay thanks

.close

[obtuse pebble]

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[dry phoenix]

Ok so ik that a. is under all conditions bc of symmetry properties, but idk about b anc c.

[obtuse pebble]

@dry phoenix Has your question been resolved?

[tardy epoch]

b is harder

positive definite is easier to prove. use the definition

[mental solstice]

b is dead easy

[tardy epoch]

[mental solstice]

hint: determinant

[tardy epoch]

oh duh

alright well that's probably enough hints to get you started

[obtuse pebble]

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[next aspen]

I personally give up and feel ashamed that I haven't been able to solve this simple exercise

[next aspen]

Can someone help me?

[spiral maple]

compute f(f(f(x)))

[next aspen]

f(f(f(x))) is a(a(ax+b)+b)+b = 8x +21

but that's not enough info to find a and b

[spiral maple]

it is.

[next aspen]

I put X = 1 ?

I tried that

[spiral maple]

sure

or further simplify the LHS

[next aspen]

lhs?

[spiral maple]

Left
Hand
Side

[next aspen]

ok i'll try expanding it?

[spiral maple]

ok

But it sounds like you did 1 step then gave up tbh

[next aspen]

well ye cause i got an equation with 2 variables and i have to found a numerical solution

[spiral maple]

🤨

a and b are the real variables

you compare coefficients..

2 polynomials are equal iff their coefficients match exactly

[next aspen]

I got a³+a²b+ab+b-29 = 0
by expanding it replacing x = 1

[spiral maple]

so yeah, don't plug in values

just expand and compare coefficients

$f(ax+b)=a(ax+b)+b=a^2x+ab+b \
f(f(ax+b))=a(a^2x+ab+b)+b$

[warm shale]

Mosh

[next aspen]

a³x+a²b+ab+b-8x-21=0
what do I even do with this tho

[spiral maple]

read what I said

[next aspen]

I still never get it

[spiral maple]

compare coefficients

$a^3x+a^2b+ab+b=8x-21$

[warm shale]

Mosh

[balmy mortar]

@fast mantle u ok there lol

[next aspen]

a³ = 8
and (a²b + ab +b )= -21 ?

[spiral maple]

yes

so you clearly know what a=

[next aspen]

me is low iq sorry

i solved it thanks

[balmy mortar]

Its fine, you didn't know how to equate coefficients

[spiral maple]

you managed to understand f(f(f(x))) without problem, so you're not.

[balmy mortar]

you're not going to know unless someone tells you the 1st time.

[fast mantle]

The way you type is so condescending :/

[next aspen]

it's not fine. I am in grade 12 🤣

[spiral maple]

Your reaction also wasn't needed.

[next aspen]

.close

[obtuse pebble]

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[balmy mortar]

If you have a better way of helping people, please feel free.

[obtuse pebble]

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[teal eagle]

Just wanted to check if I evaluated this equation correctly.
Equation:
e^2x+2 + e^x+1 - 3 = 0
My Answer:
x = ln[ (-1 + sqrt(13)) / 2 ] - 1

[short spruce]

is that $e^{2x+2}+e^{x+1}-3=0$

[warm shale]

a disappointing son

[short spruce]

or are the +2 +1 not in the exponent

[teal eagle]

yes this is correct

[balmy mortar]

this is a quadratic equation

[teal eagle]

yep

i solved it with u-sub

[balmy mortar]

oh wait u solved it.

[teal eagle]

yeah i just wanted to know if my answer was correct

[balmy mortar]

You can just verify your answer with a calculator

or just substituting back in...

[teal eagle]

oh ok lemme try that

im really tired my brain isnt working

i didnt think of that lol

ok i checked it with a calculator - it is correct

thanks for firing up my brain again @balmy mortar

.close

[obtuse pebble]

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[summer cloud]

help

[long sinew]

You do know what factoring is right?

[nocturne minnow]

Determine the highest common factor

[summer cloud]

yes

ik how to do all that

like ik that its

2d(d-4)

but idk where exponents go

[long sinew]

Ok then, what is the greatest number that can multiply into 2d^3 and -8d^2

[long sinew]

This is so close

[summer cloud]

ik but like im

missing exponents

[long sinew]

Yes

[summer cloud]

but how do i decide

where exponents go

[long sinew]

If you look a the exponents, there is a ^3 and a ^2, so you can do d^2 as a factor

Use this with what you already have

And you will have the answer

[summer cloud]

ok

[long sinew]

After that I will give you another and see if you can factor it too

@summer cloud hows the first question going

[summer cloud]

well

this happened

[long sinew]

?

What did you put as the answer

Oh I see

[nocturne minnow]

And extra d^2

[long sinew]

Well if you do 2d^2(d^2) you get 2d^4

but the original was 2d^3

[summer cloud]

oh

[long sinew]

So the correct answer would be 2d^2(d - 4)

(Which it says up there)

Try 3x^4 + 9x^3 factor by the greatest common factor

[summer cloud]

ok

3x^2(x^2+3)

would this be right

[long sinew]

Close

3x^2 (3) = 9x^2

But the original was 9x^3

[summer cloud]

ohhh

i think i get it now

[long sinew]

Try another one 2x^4 + 4x^2 + 2x

[summer cloud]

2x(x+4+2)

[long sinew]

You are missing a lot of exponents @summer cloud

[obtuse pebble]

@summer cloud Has your question been resolved?

[obtuse pebble]

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[boreal lantern]

I'm trying to clamp a value to a circle

[boreal lantern]

for example

[sudden fox]

use sin and cosin

[sudden fox]

its easiest to use it if u are working with a circle of radius 1

[timid silo]

so you moving the green dot? and trying to find the red dot?

[boreal lantern]

yes

and this behavior is needed

[timid silo]

OH

[crude cloud]

@boreal lantern i think it goes as alpha +r costheta,beta +rsin thetha

Where r is the distance from the centre

[timid silo]

you trying to move the red dot as close to the green one while keeping it in the circle?

[boreal lantern]

yep

I've got clamp that I can use

[boreal lantern]

I dont have theta and want to use atan as a last resort

[boreal tree]

just move the circle :)

[timid silo]

what are you trying to do this in? like is this a program you have to make? are you trying to come up with a algarabic equation that fits this?

[boreal lantern]

this is for ui in a program, yes

I have been messing around with the math for a bit now

x=clamp(x,-1,1)
y=clamp(y,-1,1)
makes a square ofc

[timid silo]

are there if statement avaible?

[boreal lantern]

kinda

I can do an inline if

also I have atan2 which is arctan that includes the imaginary plane

so if I need to I can do x= cos(atan2(y/x)),y= sin(atan2(y/x))

omg

I can use normalize

🤦 vector math

[timid silo]

you could try something like
if ( distance from origin to green point < 2 ) {
red = green point
} else {
blah
}

[boreal lantern]

I think I can normalize the (x,y) vector (set it to a unit vector) and then just use that

[timid silo]

normalise the vector? sorry im not very falmialr with vector math

is that the thing where you make thje length of the vector 1?

oh yeah im dumb lol,

[slate zephyr]

The unique criterium to be along the circle is that it is length 1

just calculate the vector's length and scale the vector in reverse by it.

[boreal lantern]

it works!

clamp(x,a,normalize(a).x)

.close

[obtuse pebble]

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[mental mortar]

yo i'm still confused on how to evaluate these expressions

[mental mortar]

can someone teach me the process on how to evaluate these expressions

[slate zephyr]

Use i² = -1

also usual commutativity etc

so for example 4i * 4 = (4 * 4)i = 16i

[obtuse pebble]

@mental mortar Has your question been resolved?

[obtuse pebble]

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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.

[wintry stream]

can someone please explain how to do c

[obtuse pebble]

@wintry stream Has your question been resolved?

[obtuse pebble]

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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.

[pearl nymph]

hey, i need help with an optimization question

[pearl nymph]

pls ping me if you help, greatly appreciated, thanks!

[austere tree]

is this a calc problem?

[pearl nymph]

yes

im confused on how to do it with abs minimum

im having trouble finding the critical points

[austere tree]

yeah ok I could help but I might be a little shaky

prob should wait for someone else

[pearl nymph]

oh

are u in calc too or

[austere tree]

I took it last year so I don't really trust myself with it lol

[pearl nymph]

oh fair

well @austere tree got any good studying recommendations

could really use them

[austere tree]

khan academy

[pearl nymph]

oh fr

ok

[pearl nymph]

for anyone who tries to help me, still need help, plz ping me, thanks!

[austere tree]

and this https://www.youtube.com/watch?v=WUvTyaaNkzM&list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr

well I can give it a try while we wait (I'm waiting for my own question to be answered)

[pearl nymph]

oh ok cool sure

[raven spire]

:O

[austere tree]

👀

[raven spire]

Do you know what a derivative is!?

[pearl nymph]

yeah ofc lol

[raven spire]

rate of change!?

[pearl nymph]

@raven spire can u help me with my question

yes

i dont know how to get the critical points in that certain question tho

[raven spire]

._.

can you frame three equations for me using the info from question?

[pearl nymph]

wat

wdym

[timid silo]

where do i get help with my math

[pearl nymph]

@timid silo #❓how-to-get-help

[raven spire]

Given:

VOLUME IS CONSTANT

and r and h are your variables

[pearl nymph]

ye

[raven spire]

can't you frame an equation with that?

[pearl nymph]

i used the constraint to get teh equation in terms of r

but im having trouble using that to find

critical points

[raven spire]

$\pi r^2 h = 8$ ?

[warm shale]

Ansh

[pearl nymph]

that's the constraint yes

so i used

[raven spire]

what's the equation for Surface Area?

[pearl nymph]

2x^2 + 4xh = s

[timid silo]

someone help me

with my math pls

i cant do it

[raven spire]

$2\pi rh + 2\pi r^2 = S.A.$

[warm shale]

Ansh

[pearl nymph]

yup

[pearl nymph]

wait what

oh wait right

[timid silo]

help pls

[pearl nymph]

im tired

@timid silo ..

ive already said lmfao

#❓how-to-get-help

go to an open channel

[raven spire]

Dude get your own channel or ...

[pearl nymph]

this one is in use