help-0

[alpine sable]

you have two powers

think of x as x^1

and apply the same rule

[green marsh]

its x^2 + 3x

this is the problem

[alpine sable]

I know

[velvet pelican]

If you have to find the derivative of 2x^2 + 1 then you can differentiate them separately and add the derivatives

[green marsh]

the answer is 2x+3

but idk how

but im not doing that

im doing $x^2+3x$

[ocean seal]

lard

[velvet pelican]

Ok, so differentiate x^2

[green marsh]

.. like.. the derivative?

[velvet pelican]

yes

[green marsh]

2x

[velvet pelican]

Now what is the derivative of 3x?

[alpine sable]

derivative of a sum = sum of the derivatives

[green marsh]

im doing it rn

$3x^0$

[ocean seal]

lard

[velvet pelican]

and what is x^0 ?

[green marsh]

um

1?

[velvet pelican]

yes

[green marsh]

idk

oh

[velvet pelican]

so you get 3

[fading zephyr]

what are you all doing

[green marsh]

so its 2x+3

[velvet pelican]

Yes

[green marsh]

ohhh

ty so much

[velvet pelican]

yw

[green marsh]

ill be back for more problems im working on chain rule hw

c: ill ask if im stuck

[alpine sable]

what's chain rule guys?

[velvet pelican]

the chain rule is used when differentiating composite functions

suppose you had to differentiate sin(x^2)

[alpine sable]

yeah I looked it up

thanks

it's because I don't know english terms for maths stuff xD

I already studied derivatives at school but I'm from Italy so I gotta learn all the words

[stoic hound]

Whenever someone says they don't know the English words for some math terms it always slightly surprises me, because so far they've been speaking perfect English

Lol

[alpine sable]

well thanks 😄

it's mostly because I use computers and stay on the internet for way too long

btw quick question, what are the last topics of high school math in the US?

or does it like depend on your level?

[stoic hound]

Sorry idk, I'm not from US

[alpine sable]

gotcha

[green marsh]

oki so im trying to find the derivative of :

$(2x+8)^3$

[ocean seal]

lard

[green marsh]

this is what i got

$2(1/3(2x+8)^2)$

[ocean seal]

lard

[green marsh]

i used the chain rule

[velvet pelican]

Why did you divide by 3 ?

[green marsh]

i can show y work

my

this is calc

ik the formula

[alpine sable]

wut

[green marsh]

This my work

Srry if it’s a bit light

Where

I flipped the fraction to get rid of it

[alpine sable]

I'm confused

what's the initial problem

[alpine sable]

this one?

[green marsh]

OH

SRRY

i mean $(2x+8)^-3$

[ocean seal]

lard

[green marsh]

thts the problem

[alpine sable]

oh ok

[ocean seal]

!ⓦⓔⓔⓟⓘⓝⓖⓛⓐⓤⓖⓗⓣⓔⓡ

[alpine sable]

I think he's helping him xD

[tough hatch]

when u have a negative exponent, u don't need to flip the fraction

[green marsh]

waluigi is confusing me

[tough hatch]

treat the exponent as a normal one

[alpine sable]

yeah just apply the rule like you would normally

[tough hatch]

sorry, meant to say -1/3 there

[green marsh]

but i thought an exponent shouldnt be negative

[tough hatch]

no such rule

maybe u have it confused with something else

[green marsh]

ill redo it then..

ill tell you wht i got

[serene jacinth]

@fading zephyr thank you

[alpine sable]

I mean, maybe in the final result you want to transform negative exponents into fractions

but during the process you can just apply the rule

[green marsh]

$2*3(2x+8)^-2 or 6(2x+8)^-2$

i flip it bc it asks you to plug in a number afterwards

[alpine sable]

its $

[tough hatch]

u can do that when u're already done

[green marsh]

oh

[ocean seal]

lard

[tough hatch]

nope

-3-1 = ?

and where did that negative 3 go

[green marsh]

with the wrk i gave you earlier

was i wrong

[tough hatch]

yes

[green marsh]

how

[tough hatch]

this is also

[green marsh]

where did i go wrong in my work

[fading zephyr]

lemme give it a shot

what's the original problem?

[green marsh]

so far i have $2*-3u^-4$

[ocean seal]

lard

[tough hatch]

yes

there u go

[green marsh]

now i will do it again

[tough hatch]

then substitute what value u has

and that's ur final answer

[green marsh]

i got $-6(2x+8)^-4$

[ocean seal]

lard

[tough hatch]

right

then u may transform the expression into one with a positive exponent

[green marsh]

so lets say i wanted to plug in an x value, i just make sure to flip the fraction

so its 1/myanswer

[tough hatch]

nah

if u're gonna flip it, make the exponent positive

[green marsh]

.. yes

thts how you do it

[tough hatch]

but u don't need to flip it anyway

just substitute

[green marsh]

yes but then i flip the answer

[tough hatch]

unless u find computing with negative exponents somehow difficult

[alpine sable]

no?

[green marsh]

so its 1/myanswer

[tough hatch]

no

[green marsh]

i dont get it

[alpine sable]

you're already accounting for that with the negative exponent

[green marsh]

ill plug int he values first

but idk..

i dont think i can

[alpine sable]

yeah you can try yourself both ways and see that's the same

[green marsh]

bc of the -4

[tough hatch]

u don't need to do that

just plug it in

[green marsh]

i dont know what texit is saying

but i cant solve if i have to do ^-4

[tough hatch]

why not

[green marsh]

ill get an error in the calculator

[alpine sable]

wut

[tough hatch]

weird

but if that's the case

[green marsh]

thts why i want to flip the expression

to get rid of the exponent

well

the negative

not the exponent

[alpine sable]

if you get it with - you'll get it anyway

maybe it's cause the bottom part is 0

[green marsh]

i dont get wht youre saying

ill do it first and show wht i have

[tough hatch]

if ure gonna flip it

[alpine sable]

yeah yeah nvm

flip it it's easier

[tough hatch]

dont forget to remove the negative sign from the exponent

i.e.

[alpine sable]

@green marsh what's the value you were substituting btw?

[green marsh]

flipping the fraction removes the negative sign

[tough hatch]

-6 / (2x+8)^4

[green marsh]

4

[green marsh]

4

[alpine sable]

lol such a weird result

[green marsh]

i got 1/ -393216

[alpine sable]

it's weird that your calculator does that btw

[tough hatch]

its just that u said this which implied u would also write the negative exponent

[green marsh]

i was taunt to always flip the fraction to get rid of negative exponenets

[alpine sable]

nah I mean it's a good habit to have for the final step I think

[green marsh]

my answer wouldnt have a negative exponent

bc its flipped

[alpine sable]

it's more straightforward

[tough hatch]

and easier to read

[green marsh]

am i correct

?

[alpine sable]

I can't really understand what you're asking tbh

if you wanted you could write it as $-6(2x+8)^{-4}$

[ocean seal]

Pointy

[alpine sable]

no problem with that

I mean it's the exact same thing

no need to flip the answer like you're saying

[tough hatch]

but he said that his calcu registers an error when he includes negative exponents

[alpine sable]

yeah yeah I just wanted to clarify this thing of flipping the answer

[green marsh]

i dont understand

am i wrong ?

i got 1/ -393216

[alpine sable]

well I get a different result

[green marsh]

oh

[alpine sable]

not sure if it's the same but written in different way

lemme check

[tough hatch]

same here

[alpine sable]

mh no it's a different result altogether

[green marsh]

:/ o

[alpine sable]

@green marsh can you like take a pic of your calculator

[green marsh]

yes

[alpine sable]

with what you did

[tough hatch]

u forgot to divide

by (8+8)^4

[green marsh]

?

[tough hatch]

-6 / (8+8)^4

[alpine sable]

you either write like this

[green marsh]

Divide what

[tough hatch]

u instead multiplied them in ur calcu..

[green marsh]

Wait where did you get this from

[alpine sable]

or like this $\frac{-6}{(2x+8)^4}$

[tough hatch]

i flipped

[ocean seal]

Pointy

[tough hatch]

yes this

[green marsh]

No

[alpine sable]

what the -4 does is it puts that parentheses in the bottom of the fraction

[tough hatch]

u're forgetting to put it in the denominator

[green marsh]

Thts wring

[alpine sable]

the - actually

[green marsh]

Wrong

[tough hatch]

how is it wrong

[alpine sable]

ok then

xD

[tough hatch]

this is the result all three of us agreed upon

but now u say it's wrong

[alpine sable]

$x^{-n} = \frac{1}{x^n}$ @green marsh

[ocean seal]

Pointy

[tough hatch]

instead of doing -6 / (2x+8)^4 or -6 (2x+8)^(-4) like we agreed upon, u computed
-6 (2x+8)^4

no negative exponent, no denominator

(2x+8)^4 is denominator

[tough hatch]

no

why did the -6 go there

[green marsh]

You said I was right

Before

[alpine sable]

then there was a misunderstanding

[tough hatch]

i said this was right

[alpine sable]

it's just the parentheses that's ^-4

[tough hatch]

which is very different from what u just encircled

[green marsh]

I’m lost

Can I see this on paper

[tough hatch]

-6 (2x+8)^(-4) is not equal to 1/[-6(2x+8)^4]

[green marsh]

I can’t follow wht you guys are saying

Where on my paper did I go wrong

Wht step

[alpine sable]

I'll show you

[tough hatch]

u typed the thing in latex

[green marsh]

Go away 42

[tough hatch]

not on paper

[green marsh]

No I sent you my work

[tough hatch]

this is my first time seeing that pic though

[green marsh]

No it’s not

[tough hatch]

yes it is

scroll up

lmao

[alpine sable]

,rotate

[tough hatch]

and see if u sent that pic before

[alpine sable]

that's what you got wrong

[green marsh]

This

[green marsh]

This

[green marsh]

I’m a bit confused on your work

I’m srry

[tough hatch]

u sent this latex later on and asked again

after that

u differentiated 2x+8 w.r.t. x and got 2

[alpine sable]

don't mind what's up there

[tough hatch]

not 1/2

and then u differentiated u^(-3) and got -3u^(-4)

am i right?

[green marsh]

Wht did I get right

[tough hatch]

d/dx (2x+8) = 2

[green marsh]

Is $-6(2x+8)^4$ correct?

[tough hatch]

d/du (u^(-3)) = -3u^(-4)

mind the negative exponent if u dont have denominator

[ocean seal]

lard

[tough hatch]

no

-4

[green marsh]

You said I was right :c

Oh

Yes

Typo

But is that part right at least

[tough hatch]

-6 (2x+8)^(-4) is correct

[green marsh]

Is that my number

[tough hatch]

now all u have to do is substitute

[green marsh]

I redid it

I’ll show wht I did

[tough hatch]

yes

[alpine sable]

yeah this is correct I think

yup

[narrow pumice]

Did you literally set x to a small number?

[green marsh]

How do I write that in a way that is smaller

[tough hatch]

u're going to write it in decimal form?

[green marsh]

Wdym

[tough hatch]

something like 0.121498706

[green marsh]

Can I?

[tough hatch]

what form should u write it in

fraction?

[alpine sable]

I mean there's a rational form for that

[green marsh]

I don’t think the calculator answer is a good answer Bc it’s on a computer and idk wht answer the computer may want

[alpine sable]

I don't know if your calculator gives you that as well

[green marsh]

Bc there’s the e

[tough hatch]

i mean

[green marsh]

I could do 10

But still

[tough hatch]

what form does ur teacher want

[green marsh]

Idk

[tough hatch]

fraction or decimal

[alpine sable]

E^-5means x 10^-5

[tough hatch]

then go with fraction

[green marsh]

It’s an online course

[tough hatch]

with decimal it's not precise

just simplify the fraction

[green marsh]

How do I do that fraction wise

[tough hatch]

-6 / ((2*4)+8)^4

[green marsh]

Why did you do that

[tough hatch]

= -6 / 16^4

[green marsh]

Why is 6 on top

[tough hatch]

did u just forget what u typed in ur calcu

[green marsh]

No

[alpine sable]

He typed with -4

[tough hatch]

mind the / symbol

and the parentheses

[green marsh]

i see why now

bc youre timesing it by 6

-6

[tough hatch]

from here it's quite easy to simplify

[green marsh]

i see

[tough hatch]

multiplying, but ok

[green marsh]

bc you do inside parenthesis first

[green marsh]

i said tht?

[tough hatch]

not sure if "timesing" is a word

[green marsh]

it is

[tough hatch]

but that's all irrelevant

[green marsh]

ill do it again

[tough hatch]

just simplify

no need to compute for the decimal value

[green marsh]

ok

[alpine sable]

@green marsh btw you may want to get a better calculator, mine gives me a fraction as a result by default

And it's nothing too fancy

[tough hatch]

that's prolly what we call two-liner

lard's calcu is one-liner

[green marsh]

i dont have money

this is a hand me down

[tough hatch]

with two-liner it lets u see the whole fraction without using /

[green marsh]

from my great uncle

[tough hatch]

and instead the horizontal bar

[green marsh]

i got -6(16)^-4

[tough hatch]

that's not yet simplified

and thats what i said above

-6 / 16^4

is the same

[green marsh]

ohhh

bc of the negative exponent

[tough hatch]

yes

[green marsh]

its the same answer

[tough hatch]

yes, not yet final

[green marsh]

... i dont get it

[tough hatch]

do u know how to simplify?

[green marsh]

i did

[tough hatch]

-6 and (16)^4 are both even numbers

[green marsh]

?

i dont understand wht youre implying

[tough hatch]

if numerator and denominator are both even, u still need to simplify

[green marsh]

so its like

[tough hatch]

that's what's simplifying is

[green marsh]

3/8^4

?

[tough hatch]

sorry, not even

they need to have no common factors

[green marsh]

i dont understand

[tough hatch]

for example 49/63

49 and 63 have common factor of 7

i.e. 49 = 7 times 7 and 63 = 9 times 7

[green marsh]

im not doing it your way, its too hard

i got the answer right

with my way

but ty so much

ill try to do the other problems

[tough hatch]

sure, it all depends on whether ur teacher needs u to simplify it tho

either way it's right

[green marsh]

my teacher doesnt grade this

its the computer

[tough hatch]

which is prolly stricter

it might not consider ur answer of -6/16^4

[green marsh]

it said im right

[tough hatch]

nice

then off u go

[green marsh]

ill get food and be back 😄 im on cos, sin, and tan

[alpine sable]

Ohh nice

A ladder should be set so that it forms an angle of between 60 and 70 frayers. The ladder is 4 meters long.

A: What is the highest point it can hit?

B: How high is the lowest point it can hit?

C:
Is the point that the ladder hits at an angle of 65 degrees exactly in the middle between the other two points?

what's a freyer

no

it's not

Ffs

Just believe, okay?

lmao

Ffs I need to get my phone because of this

Wtf?

retard

Imma just wait 5 min to prove I'm not in a hurry coz I cba to get my phone

[tough hatch]

"frayers" is probably meant to be "degrees" here

this channel is occupied, sorry

try other #questions- channels

[alpine sable]

hyp/mod = sin

[glossy remnant]

sorry, thanks

[tough hatch]

sine = opp/hyp

hyp = 4 m

[alpine sable]

4 * sin(70) =

[tough hatch]

yes

then u get the highest point's height

[alpine sable]

3.76

[tough hatch]

pretty straightforward for the other one

[alpine sable]

lowest point i do with 60 degrees or what

[tough hatch]

ofc

[alpine sable]

ight

4 * sin(60) =

[tough hatch]

this channel is occupied, sorry

u may use other channels

[ancient bear]

Wait didn't he solve the exercise?

[tough hatch]

@alpine sable have u got it down for the last question?

just use 65 degrees

[alpine sable]

yeah and see if it's between

well, i might have other assignments

but you can take the channel for now

[tough hatch]

@ancient bear

[ancient bear]

Yes, this is dog

So I'm getting cos(2x) + cos(x) = 0

not sure what to do next

[tough hatch]

how about

[ancient bear]

I studied it last year and I forgot

[tough hatch]

realizing the identity sin^2 x + cos^2 x = 1

then substitute that

[ancient bear]

o, shit

you is right

thanks

[alpine sable]

mh I'm interested as well, what do you mean

[tough hatch]

it's a pythagorean trig identity

[alpine sable]

yeah I know the identity

but what do you mean realizing it?

[tough hatch]

note the right side of the equation

2 sin^2 x - cos x = 1

= sin^2 x + cos^2 x

[alpine sable]

what's this?

[tough hatch]

the problem

[alpine sable]

so cos (2x) corresponds to 2sin^2 x?

I mean the initial question was $\cos(2x) + \cos(x) = 0$

[ocean seal]

Pointy

[tough hatch]

the initial equation was this

[alpine sable]

oh nvm I didn't scroll up enough

[tough hatch]

no

[alpine sable]

yeah yeah I was just confused because I thought the inital question was this one

I mean it should transform into a normal equation right?

you should get $-\cos^2(x) -\cos(x) = 0$ amirite?

[ocean seal]

Pointy

[alpine sable]

done?

nvm

[green marsh]

i can show work

oh srry shaky

[alpine sable]

lol

you removed exponent altogether

instead you should have done 4-1

A doorway is 1.2 meters wide and 2.2 meters high.
A: A giant picture with a frame is 2.4 meters high and 5 meters wide. Can it get through the doorway if it angles?

B: How high is the highest image that can come through the door?

have you already tried something?

something like this, idk if it's correct

yeah it is for the door

I'm confused about what it means if it angles

well the diagonal of the door is bigger than the height right?

so if you angle the picture that way it's gonna go in more easily right?

what

ok wait

I'll draw something

ight

I mean I don't really know how to explain this without giving you the answer

if you had something that was taller than the door

try

how would you try to get it through

make it smaller somehow

heh

you can't quite do that xD

ehm

you've never moved furniture?

yes

i have

like

take it a bad down

to the one side

or something

yeah exactly

we know the picture is too tall to pass if it's vertical

yes

but maybe if it's diagonal it can go through

so we don't even have to use trigonometry?

not really

you have this basically

you mean like this

yeah

just with the picture

instead of the other thing

door

huh?

nothing

[alpine sable]

yep

then what would you do

find the angle or something

it just asks you if it can go through though

you don't need the angle

split it into 2

split what into 2

take it to the one side

the pictur

e

lol I don't think that's allowed

[alpine sable]

I'm gonna help you a bit, you wanna figure out if the picture is taller or shorter than the diagonal of the door

if the picture is taller than the diagonal then there's no way it's going through

if the picture is shorter then it can go through

you know the picture height already

so try to find the diagonal

how do i find the diagonal

is there a formula?

well you could think of half the door as a right triangle

yes

then you know both sides

just need to find the hypotenuse

okay

let me try

a diagonal

do you draw one or two lines?

does it matter?

Ik what you mean

just wondering

just need one

1,2^2 + 2,2^2 = c^2

yeah

6.28

square root =

2.5

The hypotenuse is 2.5

yeah roughly

what r we gonna do now

well how tall is the picture

2.2

no that's the door

2.4

yeah

so can it go through or not

do i have to read that from the hypotenuse? if so, no

no??

you calculated diagonal of the door

since you used the sides of the door

and that's 2.5

the picture is only 2.4

well, then yes

nice

channel occupied

B: How high is the highest image that can come through the door?

Question B

you already calculated that

2.4

no

2.5

well yeah

but actually

it depends on how wide it is

if the width remains 5 then yeah

but if it was like 10cm wide you could have it like 20 meters long and carry it as a plank or something xD

Lol

what about this

A canal that will transport masses of water away from the city center, if there is heavy rain, has the shown goals.
A: Calculate the cross-sectional area of ​​the channel
B: Calculate the slope of the sides of the channel measured in relation to the vertical.
C: An engineer will change the slope to 50 degrees. How wide will the canal be now, when the bottom still has to be 5 meters wide?

@alpine sable

[alpine sable]

I gtg man

ahahahah ight

<@&286206848099549185>

[rich basin]

Only when f(x) is even.

[alpine sable]

thanks!

[cloud matrix]

hi

[paper temple]

U said hi lol

[cloud matrix]

we have a det of a diagonal matrix with its non zero elements as |A|
how is this det equal to
|A|³ × det of I with order 3x3

can we use the property of det that says if any row/column of elements is multiplied with k, the value of the det changes from x to kx if x was the value of det before multiplying a row/column of elements with x

<@&286206848099549185>

[deep whale]

@cloud matrix That's exactly right. Multiply the first row of the identity with |A| to get the diagonal matrix with first diagonal element |A| and determinant |A|. Similarly, multiply the second to get determinant |A|^2 and so on. Simply if you look at the definition of a determinant. For a diagonal matrix the determinant is the product of all its diagonal elements.

[cloud matrix]

are you sure?

[rapid horizon]

yo can someone help me on this

https://images-ext-2.discordapp.net/external/bZw-1g90i-uGVSMw-6L8L60F-aT071KBoJfSP3ri7fM/http/pays.host/uploads/50ac7278-d442-4fdd-be66-2487ff3b2505/fxszEcix_.png

[wooden saddle]

To get the intuition for this, take an even function like f(x) = x^2 and draw it on say 0 < x < 2. Then, draw it on -2 < x < 0

[alpine sable]

yeah it makes sense

[deep whale]

yeah

[cloud matrix]

ok

does division of det makes sense?

@deep whale

[cloud matrix]

use distance formula

[lean phoenix]

help

[cloud matrix]

choose a range for x so that C is equal or below 125000, using that graph

i mean they almost spoonfed you everything you need to that problen

[rustic star]

Can someone explain this step to me?

[alpine sable]

apparently this is advanced for others but it's literally grade 8 level here and i'm pissing myself being unable to solve it due to my dyscalculia, gotta pass it within the day and no formulas were given or anything

absolute pain, assistance required

[tired creek]

try utilising the triangle inequality for the first one

[alpine sable]

could some one help me phrase the answer to get the full two marks?

[tired creek]

channel is in use try another one

[alpine sable]

should i resend the question?

[tired creek]

yea just not here

[alpine sable]

oh okay

[cloud matrix]

the one n only

[tired creek]

@alpine sable

[cloud matrix]

doesnt that implies on me too

[alpine sable]

alright

[hallow niche]

Guys, am I stupid or is the system just bugging

[tall wing]

can you not

[alpine sable]

guys i forgot the calculator thing for this sin function, is it 17/sin(37)?

to find x

they're making us take basic trig again :harold:

[tired creek]

that crashes discord doesnt it

[tall wing]

yep

i tried to make sure lmao

[tired creek]

against TOS btw

[tall wing]

oh

brilliant

easy ban

[tired creek]

W

[glass lichen]

yeah I got crashed from it

[tired creek]

system bugging lol

[tired creek]

actually nvm the answers r different, its union not intersection

[hallow niche]

Yeah I got it sorted, thank you

[dire prairie]

Heyooo

could someone help me with this

:D

Please do ping me if you are ready to help!

[alpine sable]

tfw ignored :harold:

[alpine sable]

it says 8 meters lmao

ah nvm length

[dire prairie]

Thats the breadth though :3

8m WIDE

i dont know how to find the length

[dire prairie]

please

[alpine sable]

so there were 45 thousand bricks placed

now 20 by 15 cm i gotta find a way to calculate that w8

like what would the area of that be

cant believe i forgot fuckin geometry

ah thats a perimeter if i add it all up, to make 70

so there r like 40 bricks wide

and length is 3000 meters? idk tho

<@&286206848099549185> 15 mins have passed help this man

[naive dock]

How do you find rate of change from a table?

[alpine sable]

u can google that easily

ohhh the length is 3000 bricks i think

[dire prairie]

Ohhh

is length meters or bricks though. and if u dont mind could u tell me how u got 3000, cause i didnt understand the method

[alpine sable]

well do both ig

my brain hurts too much for this math lmao

[alpine sable]

uhh i did brain math :harold:

with basic algebra

[dire prairie]

Um okay

[alpine sable]

sec ill do it again in chat

[dire prairie]

thanks uwu

[alpine sable]

8m wide lane, size 20 cm wide, there is 100 cm in a meter
800 / 20 = 40 bricks wide

60750 / 1350 = 45
45,000 bricks long
45000 / 15 (bricks long) = 3000 meters

but i dont know if i did correct math so best to wait for a helper 🤷‍♂️

[dire prairie]

Thank you soo much

[alpine sable]

yw lol

did u learn trig yet? im stuck on a friggin sine function

[dire prairie]

Nopeee, im just in 8th grade

[alpine sable]

ah ok im in 10th rn

be ready for trig in 9th grade 😂

[dire prairie]

Where are you from?

[alpine sable]

im in israel but im from mongolia

[dire prairie]

Ohh cool

Have a nice dayyyyyyyyy

[alpine sable]

u too

[fathom field]

need some help with this

[fathom field]

where ive gotten up to now

how bad did i fuck it up :/

[alpine sable]

[question]

ok now I see that if I put t = x/a
dt = dx/a it will give me the same as in the table

I think

[rigid smelt]

You were wrong at the third equal sign

intergal of 1/sqrt(1-[x/a]^2) dx is not arcsin(x/a)

[hardy geyser]

<@&286206848099549185> how do I find the straight line distance I keep using soh can toa.. Idk what to do

[vale wigeon]

make a diagram!

[alpine sable]

You don’t need to use Soh Cah Toa.
To better visualise, you can draw the path. You would end up having a right-angled triangle. You need to find the hypotenuse. (clue: Pythagorean theorem)

[vale wigeon]

you can do this problem w/o knowing even a lick of trig

(also don't ping helpers right away youre not supposed to do that)

[alpine sable]

is this occupied?

did I do something wrong?

because mathway gives me this solution

<@&286206848099549185>

[coral pagoda]

Taking the square root leads to some problems

Instead, see if you can solve it from [\sin(x)=\frac{\sqrt{3}}{3}\cos(x)]

[ocean seal]

dackid

[alpine sable]

mh no I don't know what I could do apart from what I did

do you have any tip

also, what are the problems you encounter when taking the square root

[dreamy crypt]

anyone help?

[alpine sable]

kind of occupied

can you switch channel?

[dreamy crypt]

sure

[alpine sable]

ty

kind of occupied

can you switch channel

[alpine sable]

@coral pagoda sorry to tag you, could you help me further?

[shell widget]

@alpine sable What they did was rearrange 3sin(x) - sqrt(3) cos(x) = 0 to tan(x) = 1/sqrt(3)

Now just taking arcctan, we have x = pi/6, and since tan(x) has period pi, we have x = pi/6 + npi

[potent dust]

Please help

<@&286206848099549185>

[vale wigeon]

don't ping helpers right away

you're supposed to wait 15 min

[potent dust]

Sorry my bad

[plucky whale]

So this is function composition, it’s asking you to plug in N(h) for x in C(x)

So you would put 20h for x in the equation 12x+570, and simplify

[potent dust]

810?

[plucky whale]

Yea you’d get that for part b

For the first part it wants you to write out the equation you get

In terms of h

[potent dust]

So rewrite what you wrote at first

[plucky whale]

Wait nvm you don’t get that for part b

Yea rewrite the expression

h is another variable

[potent dust]

It says I’m wrong

[plucky whale]

What did you get

[potent dust]

I wrote 12(20)+570

[plucky whale]

You gotta simplify, and h disappeared

So part a isn’t asking for a number answer it’s asking for an equation

[potent dust]

What did you get for part a

[plucky whale]

For example if N(h)=3h then the equation would be 12(3h)+570, which simplifies to 36h+570

For the problem tho N(h) is 20h, what do you get when you plug it in and simplify

[potent dust]

I got 810

[plucky whale]

Don’t forget the variable

[potent dust]

810h?

[plucky whale]

You’re not just plugging in 20, you’re plugging in 20h

The 570 doesnt have an h

It sounds like you’re guessing Lol feel free to write out your steps so I can like see where you’re confused

[potent dust]

Alright I got, I understand now for part b how would I get it

[plucky whale]

Awesome! For b Plug in h=12 into the equation you got for a

[potent dust]

I got it

That helps out a lot

[plucky whale]

Awesome! I’m glad

[fluid tartan]

hi please mention me here or dm me!

[plucky whale]

Yea so sounds good same kind of procedure where you plug in f(x) for y in g(y)

To write it cleaner, it’s $g(f(x))=2.13(f(x))=2.13(5.56x)$, just multiply the two numbers

[ocean seal]

Mikey

[stone isle]

do you not know how to compose functions?

once you calculate the composition, just plug the value in

[tranquil tulip]

How do I solve for x?

do i do -9 * 4

so x + 8 = -36

[alpine sable]

yes

[tranquil tulip]

then subtract 8, so x = -44?

[alpine sable]

also yes

[velvet pelican]

You have to multiply the 8 by -9 too

[alpine sable]

yeah sorry

was about to say that xD

[tranquil tulip]

ohhhhhhh

tysm

[velvet pelican]

yw

[alpine sable]

oh, you can do that?

[runic swift]

Is this channel open? Or still in use

[alpine sable]

go ahead

heh actually Sup is already responding

[shell widget]

@alpine sable Just so you know, your working is also correct, but there's some more work to do, ie, look at the graphs of y=sin(x) and y=cos(x), etc

It took me like 15 mins to check it

some other time perhaps

[alpine sable]

dayum

to obtain the tan you divide the sin by cos right?

[shell widget]

yes

[lavish oriole]

I need to rotate A (-1,1) B (-1,4) C (-7,1) and D (-7,4) counterclock wise 90 degrees
and I know that x,y = -y,x

[runic swift]

oh welp guess he took the spot

[shell widget]

sorry

[alpine sable]

and you wouldn't be able to do that if that was an inequality?

[shell widget]

we would

[alpine sable]

mhhhhhh

btw can you show me the whole process the way you did it earlier?

because I can't really see that

the one with the tan

[shell widget]

not really a whole process

3sin(x) - sqrt(3) cos(x) = 0

3sin(x) = sqrt(3) cos(x)

sin(x) / cos(x) = sqrt(3) / 3

tan(x) = 1/sqrt(3)

[alpine sable]

mh ok yeah

that makes sense

but when you divide by cos

aren't you dividing by something that might be 0?

mh I guess you already account for that because tan doesn't exist at pi/2 and 3pi/2

[shell widget]

well when dividing by cos(x), just say x cant be an odd multiple of pi/2

but that doesnt matter since our solution x = pi/6 + npi wont contain any odd multiple of pi/2

[alpine sable]

at this point I think it's pretty easy to solve, but for the inequality I remember al3dium (don't wanna tag him) saying that you couldn't do that in that case

and it didn't give the right answer if you did

[shell widget]

when you have an inequality, you can still multiply/divide expressions by expressions

just gotta make sure if we're multiply/dviidng by negative, we have to reverse the sign

and not dividing by 0, etc

[alpine sable]

so

[shell widget]

when solving trig equations, ive never come across trig inequalities

[alpine sable]

to solve that you'd have to divide it in two cases or something?

[shell widget]

no

depends i guess

cant really say

since we dont have a specific inequality

[alpine sable]

wait I'm gonna go back to the same example

$\sin(x)+\sqrt{3}\cos(x)\geq 0$

[ocean seal]

Pointy

[shell widget]

so we have sin(x) >= -sqrt(3) cos(x), which gives us tan(x) >= -sqrt(3)

[alpine sable]

if u isolate x i think there will be two intervals

i think u can simply it to 1 sin expression tahts prob will be easier

[trail spire]

Hi guys .. i am new

Give me a math equation 😎

[shell widget]

1 = 0

[trail spire]

😱

[alpine sable]

try solving the one I sent a few messages back, it's an inequality

$\sin(\frac{\pi}{3}+x)\ge0$

[alpine sable]

then after that?

[velvet pelican]

Its 2*sin(...) btw

[alpine sable]

u sures?

wait mine?

[ocean seal]

square

[alpine sable]

no i think thats right

I don't know how you're so quick with those transformations, btw what I also don't understand is why Sup method doesn't work

that's my main concern right now

[velvet pelican]

Its 2sin(pi/3+x)

[shell widget]

what method of mine

[alpine sable]

the one with the tangent

[shell widget]

itll work

[velvet pelican]

Alright, his method works only when cos(x) > 0

You have to flip the inequality sign when cos(x) <0

[shell widget]

Oh yeah

[alpine sable]

here method that work for -1 to 1

ok so suppose we go on with the last example

i will write

we have tan x >= -sqrt(3)

but it work only if u do like me and make into 1 sin

[alpine sable]

that would be from -pi/3 to pi/2 and from 2pi/3 to 3pi/2 right?

[shell widget]

better to do it with square's method

[alpine sable]

no no I'm curious

[shell widget]

since it doesnt make us consider 2 cases when cos(x) < 0 or > 0

[alpine sable]

I wanna use yours

,, tex \sin(x) \ge a \\ \text{IF $-1 < a < 1$ then u can does} \\ \arcsin(a) + 2\pi n \le x \le -\arcsin(a) + 2\pi n

[ocean seal]

square

[alpine sable]

i think thats right

[shell widget]

Yeah then we have [-pi/3, pi/2) U [2pi/3, 3pi/2) and it keeps going on

[alpine sable]

and how do you continue? that's not the right solution yet, right?

[shell widget]

well we make sure that we also have the x values where cos(x) > 0

[alpine sable]

$\arcsin(0) + 2\pi n \le \frac{\pi}{3}+x \le \pi - \arcsin(0) + 2 \pi n$

[ocean seal]

square

[alpine sable]

uh

that probably right

[shell widget]

I have to sleep, but I will look at this tomrorrow

[alpine sable]

if I consider the unit circle

this is tan >= -sqrt(3)

[shell widget]

square is helping you, atleast listen to him

then you can consider "my way" later

[alpine sable]

I don't need to solve that inequality though

that's the point

that's not my priority

i didnt even know the question lol i just assumed u wanted inequality

,w arcsin(0)

yeah man no worries

[ocean seal]

Results provided by WolframAlpha

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

Requested by ⃟⃟#8027

[midnight merlin]

Rayan international school is managing by a board of trustees and they are worrying about the funds required for school maintenance in coming academic years due to economic crisis created by COVID-19. In order to face this problem, the board of trustees decided to deposit a certain sum of money in Bank Muscat account which pays interest at 12% (simple interest), so that it will give an interest of OMR 10,000 per year, which can be used for the school maintenance in coming academic years.
a) How much money board of trustees need to deposit in bank account

[alpine sable]

bruh they conditioning kids for covid crap

no i wont take the vaccine!!!

[midnight merlin]

hhhhhhhhhhhhhhhhhhhhhh

[midnight merlin]

anyone?

[glass lichen]

what does that have to do with anything?

[alpine sable]

look at his question

[glass lichen]

no im asking you why you felt the need to say that instead of helping

[oak chasm]

@alpine sable This isn't a debate channel.

[alpine sable]

because its an observation i made and nothing was happening so it wouldnt interrupt so i said it

[glass lichen]

$I=Prt$

[oak chasm]

@midnight merlin Do you know how simple interest works?

[ocean seal]

moshill1

[midnight merlin]

yup 0.12

[oak chasm]

That's the interest rate, not interest.

[midnight merlin]

how can i get

[ocean seal]

Chai T. Rex

[oak chasm]

So, which of those are known?

[midnight merlin]

im not sure
A = P(1+R/N)NT

[oak chasm]

That looks like compound interest, which isn't simple interest.

[midnight merlin]

how do i get T & N

[glass lichen]

That's (an attempt) at writing compound interest, which is not simple interest

there is no n in simple

[midnight merlin]

and t ?

[glass lichen]

says in the question

[tough ether]

I have a simple question. If we let alpha(G) and omega(G) be the independence and clique numbers of a simple graph respectively, is it necessary true that for every induced subgraph G' of G, we have $\alpha(G')\omega(G') \leq \alpha(G)\omega(G)$? This seems true based on some examples I tried, but I was wondering if anyone had a good counterexample or explaination

[ocean seal]

Mr.Hahn-Banach

[hearty orbit]

Does anyone know the formule for solving any cubic equations?

[oak chasm]

@hearty orbit Factoring is the easiest way, but there's also https://math.vanderbilt.edu/schectex/courses/cubic/.

[stiff pier]

can someone help me rationalize the numerator for:

because I'm not understanding how to do it correctly

,rotate

[stone isle]

you forgot the limit in each equality

also, what's the problem? have you tried to continue it

[stiff pier]

I don't know what to do anymore

1+1 = 2-h in the numerator? or cancel srqt(h+1) from the denominator with the h+1 from the numerator

(I'm not even sure if doing that is correct)

[hallow atlas]

in statistics, which takes priority? central limit theorem, or the success/failure condition?

[hearty orbit]

Is -2,5 - 1,936...i the same as -0,5i (sqrt(15) + - 5i)

[green marsh]

hi are you done with your problem

\sqrt{5x^2+3x+6}

$\sqrt{5x^2+3x+6}$

[ocean seal]

lard

[green marsh]

i am wondering how do i solve this, im using the chain rule but i never did a problem with a sqrt

i can show my set up

[oak chasm]

@green marsh You're taking the derivative?

[green marsh]

yes ma'am

ill show my work c:

[ocean seal]

Chai T. Rex

[green marsh]

ohhh

ty so much

[oak chasm]

You're welcome.

[green marsh]

i didnt know how to set it up

[oak chasm]

Yeah nth roots are the power 1/n.

[edgy cape]

i don't even know where to begin

[stiff pier]

I still can't rationalize my problem

[edgy cape]

its just integration

[green marsh]

are you guys done ?

[edgy cape]

no

[green marsh]

oki

[edgy cape]

whats the question

[green marsh]

ty jr

[edgy cape]

??

[green marsh]

i reference it in #help-1

[edgy cape]

ohh

[night jay]

this channel open?

[edgy cape]

i guess

no one answered my q :/

[night jay]

not sure what this means

i missed a class so idrk how to do it

[stiff pier]

,rotate

[oak chasm]

@alpine sable Nope, any math, though for harder math, you might get help in the topic-specific channels below. See #❓how-to-get-help for the rules on getting help.

[glass lichen]

You havent posted anything pertaining to a question

If you want help... you need to post the question

[oak chasm]

Fifth grade math is fine.

[glass lichen]

how old are you if you dont mind me asking?

have to be 13 to be on discord

<@&268886789983436800>

[flat gust]

Lmao

Report to discord

aw

evidence

[glass lichen]

I dont care enough to go to that effort

[edgy cape]

is 'calculus' like integration and differentiation and all the mini rules behind them?

[oak chasm]

@edgy cape Yes, though I haven't gone far into calculus, so there might be more to it.

[edgy cape]

ye idk if i should be putting my calculus questions on there or not

whats precalculus

[oak chasm]

Precalculus is like trigonometry and advanced algebra and such.

[edgy cape]

i c

[oak chasm]

You can go into the channel and click on the topic at the top of the chat.

It has a short explanation.

[edgy cape]

oh thats helpful thanks

[oak chasm]

Calculus and precalculus stuff can usually get help in the #questions channels, though.

[edgy cape]

ayt

[tranquil tulip]

I’m addicted to eating corn starch and flour

[timid birch]

oh

[fallen anvil]

The 50 cent Bluenose is one of Canada’s most famous postage stamps. In 1930 it could be purchased
for $0.50. In 2005, a stamp in excellent condition was sold at an auction fro $512. Determine the
annual rate of appreciation.

[obtuse charm]

Does anyone know how by o do this and explain it to me?

I missed class on this

[manic quail]

@potent dust What don't you understand?

@obtuse charm This is basic trigonometry.Do you know the sine cosine and tanent?

@potent dust Domain is the set of numbers you are allowed to put into the function. First you just subtract the two and then you determine its domain.

[obtuse charm]

No idk why I’m doing trig if I’m in geometry but I know how to find since cosine and ranger but it’s asking for two equations to solve it idk what it means by that

[manic quail]

@potent dust why +7?

4-3?

=1

Yes.

And I'd say the domain is $(-\infty, +\infty)$

[ocean seal]

veryhappyperson

[civic burrow]

Domain => possible y-values, right?. An x^2 function gives a U shape i.e. a lower bound

[manic quail]

I might be lost, but wasn't that the range? xD

Domain was possible inputs, I thought. But me not know english well

[civic burrow]

Lmao, me neither. You are correct, it's the possible input values, my bad.

[manic quail]

@potent dust +1

x²-5x+1

Yes, same process

Okay.

What are you not sure about?

Add the functions, then multiply by x

[civic burrow]

Multiply by x?

I assume (f+g)(x) means function notation like f(x)