help-39

[delicate beacon]

But on my second equation I have sqrt5 How do i make it complex

<@&286206848099549185>

Oh i see my problem

4-1 isn’t 5 ffs

.close

[pearl pond]

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[echo pebble]

Why does the ending point of the infinite product stay n when the change of variables is made?

[pearl pond]

@echo pebble Has your question been resolved?

[echo pebble]

<@&286206848099549185>

[pearl pond]

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<@&286206848099549185>

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<@&286206848099549185>

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[thorny stream]

could someone please help me with this problem:
So cartons of milk have weights that are normally distributed with mean 10 and standard dev 0.5. If 15 cartons are selected, what is the probability that the mean weight is less than 10.2? (assume normal distribution)

[thorny stream]

the way i went about this problem was that i declared a random variable z = the sum of all 15 weights. So right now im finding the probability that z/15 < 10.2

multiplying both sides by 15, now im finding the prob that z < 153

is this correct so far?

<@&286206848099549185>

[pearl pond]

@thorny stream Has your question been resolved?

[thorny stream]

<@&286206848099549185>

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[thorny stream]

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[stiff olive]

would i start with substitution here?

[tropic saddle]

imagine you have an antiderivative G of the integrand

then F(x) = G(x^2)-G(2x)

and now differentiate, don't forget chain rule

[stiff olive]

ok

[tropic saddle]

dont solve the integral

[stiff olive]

would i use d/dx( f + g ) = d/dx(f) + d/dx(g)

[tropic saddle]

yes you need that here

[stiff olive]

but how would i identify what if f and what is g?

from just the sin(t^3)?

or from the upper and lower limit?

[pearl pond]

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[quartz echo]

Hey, can anyone maybe explain to me how you can conclude that a=2? (SA means "oblique asymptote" i think)

[quartz echo]

tell me if you need any more information

its about rational functions btw

<@&286206848099549185>

Can anyone help me with this pls?

Just tell me if my question doesnt make sense or anything like that.

<@&286206848099549185>

[jade tide]

Bro idk much but standard procedure to find oblique asymptote is putting y = MX +c and then equating two highest degree terms to zero

Try doing reverse engineering

[quartz echo]

the oblique asymptote is: "y = 2x + 8" but somehow the teacher used that to calculate that a = 2

<@&286206848099549185> anyone?

a is the a from "ax^3 + bx^2 + cx + d" i think

[pearl pond]

@quartz echo Has your question been resolved?

[quartz echo]

<@&286206848099549185>

[midnight haven]

what's your function

cancel the top and bottom where you can

and then I then if it doesn't cancel all the way I think you do fraction division

can you write it again but neater

oh I see I think

yeah I'm still not sure about exactly what part you're having trouble with or how what's written down relates. write out your problem and what's given a bit more clearly

[pearl pond]

@quartz echo Has your question been resolved?

[quartz echo]

ill send the whole exercise later to give it a bit more context

[quartz echo]

@midnight haven this is the whole excercise

the information you get is on the top

in b you have to make the prescription of the function using the information about asymptotes and perforation

tell me if you cant read something bc its not in english

it says: Vertical asymptote: x=1

Slanted asymptote: y=2x+8

[jolly parrot]

ExAllocatePool2

[quartz echo]

theres a perforation in the function for x = 3

x-3

[jolly parrot]

ExAllocatePool2

[quartz echo]

probably

[jolly parrot]

ExAllocatePool2

[quartz echo]

but it says a=2

and how are you supposed to calculate a?

the teacher is apparently using the slanted asymptote y=2x+8 for that

its not that

its so annoying that the teacher is asking stuff not featured in our textbook

the class average for maths was under 50% last month

yeah but if i change the asymptote to y=3x+8 and the a value in the function to 3 then the asymptote isnt an asymptote anymore

if you know what i mean

ah but if i change the asymptote to y= 3x + 12 its al good

so its probably the slope

thx for the help

yeah XD

.close

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[slate grotto]

i tried

to do it

lol

<@&286206848099549185>

everyone died

like

no-one here

[tacit mulch]

Dude it's been like 5 minutes -_-

[warm current]

why did you do 40000*4?

[slate grotto]

to get total force

oh wairt

i shouldnt have

[slate grotto]

7*

[slate grotto]

its still wrong

[warm current]

how

show your work

[plush bramble]

• After 15 minutes, feel free to ping <@&286206848099549185>.

[slate grotto]

its baso the same thing but 40000/1.6 pi

[warm current]

Let's look at the pressure equation again

pressure is the ratio of total force to total area

What is the total force?

[slate grotto]

30000

(its changed now)

(the question)

[warm current]

uhhhh

[slate grotto]

its the same but 30000 instead of 40000

[warm current]

sure okay?

And then what's the total area?

[slate grotto]

1.6 pi??

[warm current]

how'd you get 1.6pi?

[slate grotto]

0.2^2

then x 4

[warm current]

0.2² is not 0.4

[slate grotto]

what is it then

[warm current]

figure it out

[slate grotto]

0.04

finaly

donr

done

now help w this

<@&286206848099549185>

[warm current]

what have you tried

ugh please stop pinging helpers, it's literally been 0 seconds

[slate grotto]

ok sorry

[slate grotto]

nothing

i dont understand it

[warm current]

what don't you understand

[slate grotto]

everything

so 150 = 3

3 parts

so i do 150 / 3

which one is width

nvm

i figured it out

now help w this one

[long flicker]

@slate grotto I would set this up algebraically...

20 people per 90 m2 per 6 days...

13 people per x m2 per 4 days...

8 people per y m2 per 10 days...

Solve for x and y.

[slate grotto]

simutanious equations?

[quartz echo]

I would calculate how much one person can weave in one day and then you multiply it by the amount of people and the amount onf days

[long flicker]

No...

So for an example.

[slate grotto]

i dont know how to do that

[slate grotto]

so i / by 20 the / 6?

[long flicker]

@slate grotto are you taking algebra? or what is your math class?

[slate grotto]

im doing factorising

lol

[quartz echo]

so you take the 90/20, this is how much one person can do in 6 days and then you do that /6 and thats how much one person can do per day

[slate grotto]

thats too complex algebra 4 me

[quartz echo]

i can be wrong though

[slate grotto]

alr ill try

[quartz echo]

i had 0.75 sqm/person/day

and then you multiply that by the people and days in the question to get how big the carpet will be

[slate grotto]

i got it right thanks

[slate grotto]

yes thanks

[quartz echo]

np

[pearl pond]

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[pearl pond]

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[buoyant trench]

Hello I need some help with question 13

Differential equations

Not sure how to do part iii onwards

<@&286206848099549185>

[merry carbon]

!15m

[pearl pond]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[buoyant trench]

oops

sorry

[merry carbon]

Also, show what you've done beforehand please?

[buoyant trench]

ok

[merry carbon]

I'll let you off, you're new here

[buoyant trench]

Did part iv as well

I’ve checked answers in back of text and got right but I don’t know how to finish off part iii I don’t understand the integration

And don’t know how to show limit for part v

[merry carbon]

cool just reading through now

[buoyant trench]

thank you very much

[merry carbon]

Are you saying you don't know how to do this, to be clear?

[buoyant trench]

yes i dont understand how it comes out as -e^-t +1 -ln 2 on the right hand side

also part v of the question

[merry carbon]

Right, you can integrate $e^{-t}$ can't you?

[jolly parrot]

chartbit

[merry carbon]

(Gonna guess that cause you've reached partial fractions, you've gone over integrating e)

Try to fill in the right hand side?

[buoyant trench]

i would've put -2e^-t

[merry carbon]

Good, try put that in there then...

I also see you've remembered your +c, always forgot it when I did A level 😂

[buoyant trench]

So I get to this but then I don’t get how I get to the answer

[merry carbon]

You don't need two integrating constants, you already have one 😉

Unless you were trying to move it to the RHS?

[merry carbon]

Read your question 😉

[buoyant trench]

Oh

I see

Damn I’ve had a mare

Wasn’t really that hard

It’s been a long day😅

[merry carbon]

Hahah fair fair 😂

Have you been enjoying the snow btw?

[buoyant trench]

Yeah it’s been sick

[merry carbon]

Hahah I was so shocked to see it when I looked outside 😂

[buoyant trench]

been out with the mumsy

No school today it’s been calm

[merry carbon]

Ayy, gotta have fun while you can!

[buoyant trench]

on the revision grind for mocks coming up

[merry carbon]

Best of luck for them man! Hope you smash them 💪

Is the rest of the question all good btw?

[buoyant trench]

yeah all good thank you

[merry carbon]

Cool cool, I shall leave you to it then have a good one (from the south east 😉 )

[buoyant trench]

thanks boss appreciate the help

[merry carbon]

No worries my g, take it easy 😎

[pearl pond]

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[frozen nacelle]

lg x sqrt(1000x) How do you simplify this?

[frozen nacelle]

I’ve started with

lg x (1000x)^0,5

lg x • 0,5 • 1000x

lg 500x^2

[pearl pond]

@frozen nacelle Has your question been resolved?

[patent flame]

Uh is this log_x((1000x)^1/2)

?

[pearl pond]

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[rough raft]

idk if this server accepts physics but can someone help with this one?

[iron cove]

Mass never changes regardless of your distance from a gravitational source.

[rough raft]

ok

thats true

let me see here

so b is correct

[iron cove]

As for the force, that decreases as the distance from the source increases.

[rough raft]

and so is c

does b and c seem correct?

[iron cove]

Yes to both! Good work. :>

[rough raft]

alright thanks a lot

I understand this now

.close

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[frail oxide]

can someone Please help with this problem. All I get is that arccos(u) has to be a number between -1 and postive 1

[light helm]

drawing a reference triangle would be helpful

[frail oxide]

ok

[light helm]

as well as considering the range of arccos and where sin is positive/negative

[frail oxide]

oh arc cos is 0 to pi I think

[light helm]

your diagram doesn't indicate anything about u

[frail oxide]

well

u = a/h

and arccos has to be betwen -1 and 1

so u between that

[light helm]

express o and h in terms of u

[frail oxide]

what does that mean

[light helm]

pretty common terminlogy

also note that in this case for convenience you can even set
a = u and h = 1

[frail oxide]

ok

[light helm]

using that you can the apply pythagoras to get o

[frail oxide]

sqrt(1 - u^2 )= o

oh

@light helm

[light helm]

and then sin(theta) = ?

[frail oxide]

sqrt(1 - u^2 )

sqrt(1 - u^2 )/ H = 1

is it wrong?

@light helm

but why

[light helm]

bad notation

what's with

sqrt(1 - u^2 )/ H = 1

[frail oxide]

to show the 1 was from the hypotenuse

[light helm]

bad notation

because that is effectively saying the whole expression
sqrt(1 - u^2 )/ H is equal to 1 which it isn't

[frail oxide]

i meant (sqrt(1 - u^2 ))/H

H = 1

[light helm]

yes

[frail oxide]

but what do I do with that knowledge

[light helm]

well you have it

sin(theta) = sqrt(1-u^2)/h = sqrt(1-u^2)/1 = sqrt(1-u^2)

[frail oxide]

so I dont have to do anything with the arcos

[light helm]

you used that to set up your triangle

[frail oxide]

ok

thank you

.close

[pearl pond]

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[brisk flare]

If UV=p+2 and WY=p–36, what is the value of p?

[brisk flare]

i def need help

i tried to think

i was sleep in class tbh

[opal moss]

diagram missing

[opal moss]

use similar triangles

[brisk flare]

BRUH I AINT EVEN KNO WHAT THAT MEAN

Speak english pl;ease

[shell dew]

very good way of getting rid of ur helper

[brisk flare]

i was kidding 💯

[pearl pond]

@brisk flare Has your question been resolved?

[pearl pond]

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[ancient phoenix]

if someone said mod 30 what would yo uassume?

[ancient phoenix]

basically tryna solve an arg

lol

[cinder flower]

in what context?

[old geyser]

Long division from 3rd grade

[cinder flower]

i would assume they are in a discord with at least 30 moderators and they labelled them all for some reason and are talking about the 30th mod

[pearl pond]

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[pearl pond]

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[midnight haven]

<@&286206848099549185>

[midnight haven]

Can someone help explain this to me

[chrome lynx]

!15m

[pearl pond]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[midnight haven]

I didn’t use this 🤣

[cinder flower]

wat is that question asking lol

[midnight haven]

It’s a number puzzle , thats what my teacher calls it

There’s no question to it

[cinder flower]

[midnight haven]

Me too

[midnight haven]

Alright I’ll try that

[haughty crest]

i think it means there's an assumption that if the top is x and the bottom is +, you need to figure out which of the other two are - and / and figure out the numbers

[midnight haven]

Me too gurl

I’ll figure it out

I’m on the verge of dropping out and becoming a stripper

[cinder flower]

understandable

[rustic gate]

layla dont encourage this behaviour

[haughty crest]

so there are two numbers where if you divide or subtract them, you get 2.5 or 6

[cinder flower]

i mean

[haughty crest]

they want you to tell them what happens when you add or multiply them

[cinder flower]

stay in school!

[midnight haven]

Alright

[midnight haven]

I’m trying but life is telling me no

[cinder flower]

:c

[midnight haven]

That sounded very sad

School is just hard

This isn’t a therapy session

Thank you guys

.close

[pearl pond]

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[honest bough]

What do you think it should be

You are asking why it's 3sin(3x)/(7sin(7x))

What part specifically confuses you

What do you get when you use L'H

Show your work

Where did you get sec(7x)/cos(3x)

That doesn't answer my question

Also, that top part is just wrong

f(x)g(x) ≠ g(x)/f(x)

f(x)g(x) = g(x)/(1/f(x))

Though you could just recognize sec(7x) = 1/cos(7x)

[midnight haven]

oh is

ic*

so when I find the derivative of cos it'd just be -sin

thank you!

.close

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[pearl pond]

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[verbal escarp]

The sum of Patricks age ang mako's age is 58. Eight years ago, Patrick was twice as old as Mako then. How old is Mako?

[midnight haven]

Define current Patrick age as P, current Mako age as M.

You know that: P + M = 58

And that 8 years ago:
2(P-8) = M-8

Solve the system of equalities

[verbal escarp]

how?

[midnight haven]

solve for one variable and substitute it in the other equation

[verbal escarp]

Huh? Can you give an example

[midnight haven]

Do you know how to solve a system of two equations?

[verbal escarp]

no

[midnight haven]

If I gave you something like
2x + 5y = 19
x - 2y = -4
Would you be able to find the x and y to satisfy those two equalities?

[verbal escarp]

i think...

[midnight haven]

If not, watch this video before attempting your problem https://youtu.be/oKqtgz2eo-Y

[verbal escarp]

i thnk i can

wait

[midnight haven]

Okay great!

How would you do it

[fervent crescent]

elimination or substitution. in this case take
P = 58 - M
and
2P - 16 = M - 8.
now add both equations. M will cancel out and you can solve for P. then substitute P in one of the equations to solve for M

[verbal escarp]

wait

[pearl pond]

@verbal escarp Has your question been resolved?

[verbal escarp]

waitt

[pearl pond]

@verbal escarp Has your question been resolved?

[verbal escarp]

i can't solve it.....

[verbal escarp]

.close

[pearl pond]

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[pearl pond]

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[sleek zenith]

hello

[sleek zenith]

i started learning integrals and watched some videos

however i dont quite have an overview yet on what rules exactly i have to learn for this

I heard of something called substitution for example

but im a little overwhelmed so i was wondering if somebody could tell me in simple terms what there is apart from that one

[timid spindle]

Substitution and integration by parts are the main two methods you should focus on to start with

[sleek zenith]

thank you!

and there are different types of integrals right?

i didnt quite understand yet what thats all about

[timid spindle]

I wouldn't worry too much, basically most of all youll ever need to do is done by @plush bramble integrals

Which are the "standard" ones

[sleek zenith]

im not sure what riemann integrals are, i will look it up, thank you

[pearl pond]

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@full obsidian Has your question been resolved?

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.close

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[raw lintel]

Can someone help me find the formula for optimization

[pearl pond]

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[hot osprey]

calc question

[pearl pond]

Please don't occupy multiple help channels.

[hot osprey]

idek where to start

related rates, i have some stuff written but idnt how to find dr/dt

i know it has something to do with the graph in the question burt idk what

<@&286206848099549185>

[pearl pond]

@hot osprey Has your question been resolved?

[hot osprey]

<@&286206848099549185>

[modern fjord]

dont spam ping helpers

[hot osprey]

i thought i could every 15 mins

i didnt meant to spam

[modern fjord]

this was before 15 minutes was up

[hot osprey]

sorry

[modern fjord]

use chain rule

$\frac{dr}{dt}=\frac{dr}{dV}\cdot \frac{dV}{dt}$

[jolly parrot]

ed

[hot osprey]

what?

im asking how to find the other things to plugin

i did the deriv of the volume equation already

[modern fjord]

how am i supposed to know you just sent the question

show me your working

oh wait

you did im a clown

sorry

[modern fjord]

this is wrong

if you differentiate with respect to time you need to use product rule

try finding dV/dr

[hot osprey]

ohhh product rule

gotcha

[hot osprey]

it has to be with respect to time

i never learned any other way and all the operators shit confuses me]

[modern fjord]

why?

[hot osprey]

idk

[modern fjord]

why does it have to be with respect to time?

[hot osprey]

its how we did it

[modern fjord]

ok @hot osprey

[hot osprey]

im solving for dr/dt anyways

[modern fjord]

$V=\frac{1}{3}\pi r^2\cdot \frac{r}{3}$

[jolly parrot]

ed

[hot osprey]

so i have to do with respect to t

[modern fjord]

no you dont

you need dr/dV for chain rule

[hot osprey]

i dont know what that means

hold on lemme do produce rule here and show you

[modern fjord]

its just this but h=r/3

[hot osprey]

im not saying ytour wrong its just not how we did it

[modern fjord]

the way you're gonna do it is really slow and time consuming

you have to use product rule like ten times

[hot osprey]

isnt it 3r=h

[hot osprey]

no lemme show you

[primal nexus]

can I get some help pls and thank you

[modern fjord]

no base radius is 3 times its height

[hot osprey]

i may not be explaining it right but it wont be that long

[modern fjord]

#❓how-to-get-help

...

we'll see @hot osprey

[hot osprey]

hold on lemme redo the deriv and send

[modern fjord]

do your "method"

[hot osprey]

there

so my original question

is how do i solve for all of the other variables so i can isolate dr/dt for the answer

ik it has something to do with this graph

[modern fjord]

ok that actually works

i thought there was 3 variables

[hot osprey]

HUAH HUAH

i also know that 3r=h

[modern fjord]

its still a pain in the ass

[hot osprey]

yeah its just a crummy problem

[modern fjord]

then its simple

no if you do this

oh shit

you can solve for r and h

[hot osprey]

what did you do

[modern fjord]

the problem is trivial

[hot osprey]

yeah

but how do i solve for dv/dt

[modern fjord]

find r and h at t=6

the nyou're done

[hot osprey]

i have to plug something in for that

[modern fjord]

why would you do it like this..

[hot osprey]

idfk its how we wer taught

im not in college this is highschool calc so maybe you know of easier ways but this is how ive been doing it this unit

i know it has somkething to do with the given graph

[modern fjord]

im in highschool too...

[hot osprey]

oh

well idk this is how it is

[modern fjord]

just try it

[hot osprey]

try what

[modern fjord]

try this

differentiate with respect to r

[hot osprey]

like derive that

[modern fjord]

here

[hot osprey]

IDK HOW

[modern fjord]

dV/dr

wdym you dont know how

[hot osprey]

like idk what that means

[modern fjord]

...

[hot osprey]

wut

[modern fjord]

you just showed me you know how to do product rule and chain rule

[hot osprey]

its not going to be accepted if i do it that way nyways

[modern fjord]

and you're telling me you cannot differentiate that

[modern fjord]

...

[hot osprey]

i can but i dont know how to with respect to r

[modern fjord]

well then the marker is stupid if they dont accept a better solution...

[hot osprey]

like i dont understand operator language

[modern fjord]

why does it matter whether its t or r

they're just variables

[hot osprey]

because weve never ever take a deriv in this class all semester that wasnt with respect to x or t

[modern fjord]

$V=\frac{1}{3}\pi t^2\cdot \frac{t}{3}$

[jolly parrot]

ed

[modern fjord]

so if i write the same thing

but with ts

[hot osprey]

i still dont get it

[modern fjord]

and say find dV/dt

now you can do it...

[hot osprey]

ok but

[modern fjord]

its just a letter.

[hot osprey]

im solving for Dr/Dt

[modern fjord]

yes but you need dV/dr to find that

[hot osprey]

so why would i rtake deriv to a different respect

[modern fjord]

thats why im asking you to find it...

[hot osprey]

idk how

we didnt do it that way

[modern fjord]

find dV/dt in this

[hot osprey]

can you just help me with the way we were taught\

[modern fjord]

we'll be here for another hour

[hot osprey]

no we wont

[modern fjord]

you have to find r and h

you cant even find dv/dt

...

[modern fjord]

why can't you just try

[hot osprey]

we havent even addressed this\

this is included in the prob

[modern fjord]

yes its just a (t, V) graph

yeah ik you first need dV/dr first

[hot osprey]

so what can we find from this?

[modern fjord]

the volume at t=6

bro im done find someone else if you want to do it your way

in maths theres many ways to solve every problem

[hot osprey]

can you get another helper in here

[modern fjord]

you should learn as many as you can

[hot osprey]

no im aware and im not saying your wrong but i need to do it the way were were taught in this class

[modern fjord]

no you dont

i have never heard of a math class where they punish doing questions a bit differently

ping me if you think you want to do it the easier way

i think there might be a fundamental problem with your differentiation because variables are just letters, we just choose "t" for time. would it matter that much if "Q" was the letter we chose for time?

[hot osprey]

all im saying is weve never done it this way and my midterm is thursday, im not changing how ive been doing these problems, if you cant help me with it the way im asking thanks but you can help someone else

[modern fjord]

well gl under timed conditions...

this is multiple choice as well

[hot osprey]

im breezing through this ill be fine this question is just fucked

midterm wont be this hard

[modern fjord]

sure it wont

going into a math test expecting it to be not hard is like the worst i know from personal experience

#❓how-to-get-help

[pastel mango]

sorry

[hot osprey]

ok i did it

you find dv/dt because the question tells you to approximate dv/dt at t=6

@modern fjord

.close

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[glad kettle]

part c

Also when you look at this problem.... how do you know what method to use? like what tells the brain to know 😭

Ig because its a count weknow its binomial exp

[pearl pond]

@glad kettle Has your question been resolved?

[glad kettle]

nop

[haughty crest]

make a truth table

[glad kettle]

Wat

[haughty crest]

list out all the options

[glad kettle]

Nvmm

we're not supposed to do that XD

i'll try to figure it myself

.close

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[vivid pilot]

i need a hint please

[earnest ivy]

Good question

🤔

[vivid pilot]

is there something interesting about this number perhaps?

[earnest ivy]

I suspect it's a misdirect, like it could be any big number

I think you always end up with 9, from 10-19 is obvious why

[pearl pond]

@vivid pilot Has your question been resolved?

[vivid pilot]

how about any bigger?

do you think that we would always arrive at a number from 10-19?

[earnest ivy]

I'd argue that because the sum of digits is never really large, then the number will be decreasing slowly

[earnest ivy]

And we can say something like that, 10-9 reaches 9 in one step, 20-29 in at least two, and so on

[vivid pilot]

yeah i could do something like that

but its not exactly convincing

[earnest ivy]

Yeah, we can probably show that any number reaches 9 by induction

Complete induction

Any number larger than 9 also

[wooden sleet]

Unnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn

[earnest ivy]

Do you have a better suggestion?

Also, for any number larger than 19 the difference between the number and the sum of its digits is larger than 10

[vivid pilot]

idk if were supposed to use induction

right so it will eventually get to that range

[vivid pilot]

for this

i think ill use that

tysm!

[earnest ivy]

[vivid pilot]

.close

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[clear lance]

I got this problem that i can't figure out and neither can my friends, it says
Determine a and b so that when x^3-ax^2-bx-10=0 is divided by (x+1)(x+2) the remainder is zero.
I have been trying to find a and be with system of equations but when i go to check my answer with synthetic division, it doesn't work out

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[prime drift]

There are point P and Q on a cube ABCD.EFGH, if AP:PB = 1:2, and BQ:QP= 1:1. P between A and B, Q is between B and C

This statement is wrong isnt it? Since BQ and QP make a rightangle triangle, so the hypotenuse cant be the same of one of its side

[pearl pond]

@prime drift Has your question been resolved?

[prime drift]

<@&286206848099549185>

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@prime drift Has your question been resolved?

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[midnight haven]

X=7y-sqrt(5-y) make y the subject

[midnight haven]

What did u try

y^2-14xy+49y^2=5-y this is where iended

[rustic gate]

x^2

[inland cove]

50y^2 -y(14x-1) -5=0

Solve quadratic eqn ig

[rustic gate]

,w expand (x - 7y)^2

[jolly parrot]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by 夢雪#2250

[inland cove]

Theres 50y^2

[rustic gate]

[pearl pond]

@midnight haven Has your question been resolved?

[midnight haven]

Prove the Highschooler+ in you! @rustic gate

[jolly parrot]

♡LexQa♡

[midnight haven]

[pearl pond]

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[split gazelle]

is xlogx defined at 0?

[wind wigeon]

logx is not defined at 0

so xlogx cant be either

[split gazelle]

thanks

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[outer hare]

how would you solve this

I have the answer key but idk how they did it

[leaden wadi]

What is your understanding of a Riemann Sum?

[pearl pond]

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[hazy horizon]

Hey, am I solving these correctly?

[smoky terrace]

Yes

[mossy canopy]

looks good

[smoky terrace]

Tho you dont really need to multiply them since you can simply seperate it to two roots

[mossy canopy]

true, we always deal with perfect square here which is quite nice

[pearl pond]

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@elder citrus Has your question been resolved?

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@elder citrus Has your question been resolved?

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[dire tartan]

Is the absoulte value of this expression < 1 or > 1, when b,B > 0?

[earnest ivy]

Nominator is larger than denominator so <1 because of the sign, unless bc>B

[pearl pond]

@dire tartan Has your question been resolved?

[dire tartan]

I forgot the absolute value in the question

[earnest ivy]

Ah, then it's larger than 1

Nominator > denominator, so the fraction is like 4/3

[dire tartan]

Do you have time to explain it to my tired european brain?

nvm it's so simple math

[dire tartan]

Thanks ❤️ Much appreciated

.close

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[ember furnace]

how would u do these two problems?

[neat mountain]

Integration yayyyy

[ember furnace]

for 4. would u like change the -1/x^5 to negative exponent

[neat mountain]

you may

For starters it will help u

[ember furnace]

is there another way

[neat mountain]

$$ \int$$

[neat mountain]

Do it directly

[ember furnace]

wdym

[neat mountain]

Ig for now just change it bro its better

[ember furnace]

I just started learning this and I'm not very good at it

okay

[neat mountain]

Like when u break it $$\int 2 = 2x$$

[jolly parrot]

anand

[neat mountain]

No prob with that ig

[ember furnace]

so that part was right?

2x

[neat mountain]

Ofc

[ember furnace]

ok

how about 6.

[neat mountain]

Wait ya done with the whole sum alr?

No 5?

Wait I mean 4

[ember furnace]

4. I can do it, I'm just wondering how to start these off because that's what I have trouble with

[neat mountain]

Oh

For no 6

We can apply chain rule

But I'll tell ya use substitution for starters

Ya have learned substitution?

[ember furnace]

uhh

just reverse power rule I think

[neat mountain]

Oh-

[ember furnace]

teacher said like everything goes back to technique 1?

[neat mountain]

Oh wait

I see

Its just (a±b)²

[old geyser]

Well you could either expand it, which is what I would do since it's really simple, or do a u-sub

[neat mountain]

Expand it and integrate it my bad

[ember furnace]

so just expand it to x^2-18x+81

and find anti derivative of that?

[old geyser]

Yeah

[neat mountain]

Ye

[ember furnace]

okay

uh back to 4.

I turned -1/x^5 to -x^-5

[neat mountain]

Yes

[ember furnace]

idk how to do it in latex sorry if it's hard to read

[neat mountain]

Nah I can understand

[ember furnace]

when I do the anti derivative of that would it be - x^(-4)/-4

like do I divide it by -4 or just 4

[neat mountain]

-4

[ember furnace]

like this?

[neat mountain]

Exactly

[ember furnace]

ok

[neat mountain]

@ember furnace dm me if ya need any help for integral further

[ember furnace]

tyty i appreciate it

😭

[neat mountain]

[ember furnace]

i have my exam on friday and im trying so hard to understand this stuff

[neat mountain]

What's the syllabus in integrals?

[ember furnace]

wdym

ion think we have a syllabus

we just learn whatever

im also struggling bc my alg 1 and alg 2 isn't 100%, alg 2 i learned online in 8th grade and alg 1 is from 7th so its hard to remember

[neat mountain]

Jesus wtf

[ember furnace]

well not whatever I just don't have a list of what we learn

[neat mountain]

Oh

[ember furnace]

my teacher is really good but I'm just bad at math

[neat mountain]

Anyways ig you should proceed with next problems

[ember furnace]

yeah ok so

[neat mountain]

Feel free to add me as fren and dm me for doubts

[neat mountain]

Oh already? 💀

[ember furnace]

for this one should I split the numerator over the denominator

[neat mountain]

Yupp

[ember furnace]

no I'm just looking at problems I might need help with

[neat mountain]

Split denom

Ez

[ember furnace]

ok

what about for trig

like

sec t ^2 - csc t ^2 + 1

how do u find anti derivative of trigs

[neat mountain]

Obh

You need formulas

[ember furnace]

oh

[neat mountain]

Yeee

[ember furnace]

how

[neat mountain]

few

[ember furnace]

ohhh yeah

so opposite of the derivatives of trigs

that was obvious

[neat mountain]

💀

[ember furnace]

tyty

I think I get it now

[neat mountain]

Oki

[ember furnace]

tysm

.close

[pearl pond]

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[neat mountain]

Can 2 options be the answer hehe

[cinder flower]

9(3x + 6) = 27x + 54 and 14 - (x + 2) = 14 - x - 2

so the eq is equivalent to 27x + 54 = 14 - x - 2

can you simplify more?

[opaque lantern]

see

that’s what i had

but after that i didn’t know what to do next

😢

[cinder flower]

i cannot see how 2 options could be the answer

[haughty crest]

you'd be better off factoring the 3 out of (3x+6)

[coarse dawn]

Get all the terms with x on one side, everything else on the other

[haughty crest]

27(x+2) = 14 - (x+2)

[coarse dawn]

Not really, if you're solving for x, better to expand

[opaque lantern]

hmmmm

[fleet sky]

You just need to open your mind to the possibilities

[coarse dawn]

If this is what you have, what math manipulations can you do to get all the terms with x on one side and everything else on the other?

[neat mountain]

Are y'all bullying me Or what

Coz the x I got

Is definitely under both op 1 and 2

[cinder flower]

solution set (-inf,inf) means every real number makes the equation true

[neat mountain]

Oh-

[opaque lantern]

so for the numbers after the = i wouldn’t distribute those

[old geyser]

Expand and isolate the x term and divide by its coefficient and voila answer (yay)

[opaque lantern]

thank you

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[pearl pond]

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[split berry]

If Sin 0 = -3/5, then the value of tan0 could be;
-4/3 or 4/3
-3/4 or 3/4
-3/4 only
3/4 only

[split berry]

(0 is theta)

.close

[pearl pond]

Channel closed

Closed by @split berry

Use .reopen if this was a mistake.

[split berry]

.reopen

[pearl pond]

✅

[split berry]

different question

[vocal lark]

ok

[split berry]

If the terminal arm of 0 passes through the point (-3k,k) where k > 0, then the exact value of Sin0 must be?

[vocal lark]

have you drawn a picture of this yet?

$\theta$

[jolly parrot]

Disorganized

[split berry]

I have

i can send a pic hold on

[vocal lark]

you don't strictly need one but it's helpful

[split berry]

here ill send the work ive done so far

[vocal lark]

for example, what quadrant is this

[split berry]

basically what i did was follow the restriction since K must be greater than 0

[vocal lark]

based on the given info

[split berry]

i let K = 1

[vocal lark]

ok

[split berry]

then drew this

[vocal lark]

ok

[split berry]

re did it in paint because i didn't wanna grab my phone since it charging

but thats what i did

[vocal lark]

that's all fine

so the reference triangle is in what proportion

[split berry]

pardon?

[vocal lark]

your reference triangle

[split berry]

what do you mean by proprotion

proportion

[vocal lark]

the acute angle drawn (above, in your case) the -x axis

ratio of the legs of the right triangle

[split berry]

oh wait it is a right triangle

would i have to use pythagorean to solve this then?

let the x be -3

and y be 1

[vocal lark]

you can fill in the hypotenuse for the Sine value

[split berry]

3^2 + 1^2 - C^2

[vocal lark]

but you can get the angle value right now

or rather the reference angle

use arctangent.

[split berry]

I see

[vocal lark]

yes

[vocal lark]

yes

[split berry]

so the hypotenuse would be sine value of this expression

1/square root of 10

[vocal lark]

sine, by definition, involves the hypotenuse of the right triangle

[split berry]

i missed the first trig lesson im kinda scrambling to get my base knowledge atm forgive me

[vocal lark]

well how about this

whatever the angle is, it's

$\tan^{-1}\left({-\frac{1}{3}}\right)$

hang on I did that wrong

[split berry]

sorry for interupting i had a quesgtion

if sin can usually be defined by the hypotenuse of a right angle triangle

what would cos and tan be

or do they not have that type of relationship with triangles

[jolly parrot]

Disorganized

[vocal lark]

it's not

the definitions are Soh Cah Toa

[split berry]

oh right

opposite and hypotenuse

I did not consider that

[vocal lark]

for a unit circle, sine and cosine are just the opposite and the adjacent sides, respectively (since the hypotenuse is 1 on a unit circle)

so anyway

$\theta = \pi - \tan^{-1}\left({-\frac{1}{3}}\right)$

[jolly parrot]

Disorganized

[vocal lark]

do you see why

or back up

do you understand why arctan is the angle of the reference triangle

|\
|
__________@

[split berry]

hold on i forgot to add the answers

[vocal lark]

?

[split berry]

A: Square root of 5
B 1/square root of 5
C square root 10
D 1/square root 10

its a multiple choice i forgot to put this in the actual question

[vocal lark]

great.
are you good with why we used arctangent here?

[split berry]

we used Tan because the opposite and adjacent were provided and that would give us the hypotenuse right

[vocal lark]

most of what you just said is correct

[split berry]

1 being adjacent -3 being opposite

[vocal lark]

the last part is not

tan = opp/adj

[split berry]

oh

arc tan is just tan-1 right

[vocal lark]

you know...

you can totally just solve this directly for sine without using arctangent

probably less work

[split berry]

o

how

[vocal lark]

what did you get for the hypotenuse. sqrt(10)?

[split berry]

ye

[vocal lark]

sqrt(3^2 + 1^2) = sqrt(10)

yep

[split berry]

9 + 1

[vocal lark]

ok

so then directly we can say that

$\sin{\left(\theta\right)} = \frac{1}{\sqrt{10}}$

[jolly parrot]

Disorganized

[split berry]

but

why is 1 over root 10

and not just root 10

[vocal lark]

you can tell me that

(I was just messing up a min ago wasting time with arctan)

but you can remind us both

what the definition of sine is

[split berry]

opposite / hypo

oh

[vocal lark]

so what is the 1?

[split berry]

oh oh oh

[vocal lark]

yeah

[split berry]

the opposite is 1 and the hypo is root 10

I see I see

[vocal lark]

now, for these kinds of things, triangles, planar figures...if every side is multiplied by k or whatever...we're saying that all the sides scale together

we're talking about similar triangles

the angles are always the same

so it was convenient and easy to use k=1

good choice, btw

[split berry]

thank you

your a good teacher

[vocal lark]

:D

ok, good luck

[split berry]

if you have time

i had a few more questions

[vocal lark]

ok

[split berry]

so

A triangle has <A = 30 degrees, <B = 80 degrees and a =12.0cm. The measure of c must be.

22.5
B 6.4
C 23.6
D 7.1

[vocal lark]

so, is this a quiz?

[split berry]

no

its a worksheet im doing for practice

my teacher recommended i do it

[vocal lark]

they shouldn't give students multiple choice homework

practice is good though