help-0

[runic basin]

oi u wot r u reading this for

[fallen patio]

Okay, thanks.
Just to confifm,
Since in this question, the -t² has the highest degree and it's coefficient is -1 so it is facing downwards and hence dh/dt will be equal to maxima

[fallen patio]

Am I right?

And if it was +t², would it have been minima?

[runic basin]

Yeah, bc quadratic. For higher degree polynomials just double check with second derivative/gradient table

[fallen patio]

Okay
Thanks

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[lone heart]

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[alpine sable]

In order to determine the distance between two points A and B on opposite sides of a lake, a surveyor chooses a point C that is 900 ft away from A and 225 ft from B. If measure of angle at C is 70 degrees. Find the distance between A and B

I need help with this i drew a diagram the helper might need to draw one too idk. I just need somebody to talk me through

[alpine sable]

ping if seen

[fringe ember]

trig question

draw a diagram

send ur diagram

[warm brook]

@alpine sable So you have that AC = 900, and CB=225
The angle of C is 70 degrees, so you just need to find AB
You have 1 angle and 2 sides, so from here, you can use law of cosines.
Drawing a diagram can help you see this fact, as well as what the a,b, and c sides of the triangle are

[alpine sable]

i have myself a diagram it's on paper so i can't send

so

to get ab

it's

sqrt{900^2+225^2-2(225)(900) cos 70}

@warm brook is that it

[warm brook]

That appears correct to me

[alpine sable]

and i just enter that whole thing into calculator

to get ab

<@&268886789983436800>

<@&268886789983436800> hate to ping again but

[daring hedge]

Oof spammers so annoying.
I'm actually using this server to brush up on Algebra for my class as well, but I have a question about this- why would that be the equation rather than 900 cos(70) ? I don't get the sqrt part, wouldn't that only be applicble for 90 degree triangles?

[alpine sable]

Man's typing an essay rn

[daring hedge]

I could be incorrect though

lol I'm kinda also a slow typer haha

[alpine sable]

yes u are correct

BRO

<@&268886789983436800>

[daring hedge]

HOW

they'r really putting effort into this?!

[alpine sable]

but yeah u have to add the last bit when u aren't looking at a right triangle

[daring hedge]

Oh I see

thank you for explaining

[alpine sable]

nw

The helped becomes the helper

[daring hedge]

<@&268886789983436800> .sigh.

[alpine sable]

seems we in a riad atm

[sly mantle]

takes em 10s to join. takes me 1s to ban

[alpine sable]

@warm brook i actually have another question regarding trigonometry in geometry portrayed by a cheese wedge. If you are still here can u help on that

[fringe ember]

send

[alpine sable]

ok

[fringe ember]

there are other people who might know trig

[alpine sable]

A wheel of cheese in the 2hape of a right circular cylinder is 18cm in diameter and 5 cm thick. If a wedge of cheese with a central angle of 15 degrees is cut from the wheel, find the volume of the cheese

[fringe ember]

use the formula of area of an arc

and extend this formula to find the volume of the wedge

[alpine sable]

u mean s = r theta?

[fringe ember]

yes

theta in radians

[alpine sable]

so

9*15*5

why in radians

so is it 9*(15pi/180) * 5

@fringe ember

<@&268886789983436800>

<@&286206848099549185>

<@&268886789983436800>

btw

the channels are all ded

[fringe ember]

yes

it's righ

[alpine sable]

damn u let for half an hour bro i gottsa sleep

.close

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[night geyser]

but that isnt sin(x), its sin(pi*x/2)

use u-substitution

with u = pi*x/2

note then that du/dx = pi/2, hence the integral of sin(pi*x/2) dx is equal to the integral of 2/pi * sin(u) du

thats where the 2/pi comes from

(du/dx = pi/2 so dx = 2/pi du)

alternatively, differentiate -2cos(pi*x/2)/pi to convince yourself that its the antiderivative.

[fallen patio]

Thanks

.close

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[torpid plover]

how

it says to express the shaded area in terms of x

i got 22x² but the answers at the back said 18x²

[tiny minnow]

find area ABC-not shaded

ABC= $24x^2$

[ocean seal]

IVMC Gaming CH

[tiny minnow]

not shaded=$6x^2$

[ocean seal]

IVMC Gaming CH

[tiny minnow]

shaded=$18x^2$

[ocean seal]

IVMC Gaming CH

[tiny minnow]

done?

[torpid plover]

what $

[tiny minnow]

i just code to make x^2

read the texit below

[torpid plover]

wait wait

so my answer is halfway done?

this is sosussy

[tiny minnow]

i think ur answer are wrong at calculation

[torpid plover]

heh?

.close

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[limber tendon]

Can I have help pls

[bold lion]

what

[limber tendon]

?

A shop keeper buys a crate of eggs as $1.50 per dozen. He buys another crate, containing 3 dozen more than the first crate, as $2.00 per dozen. He sells them all for $2.50 a dozen and makes a $15 profit. How many dozens were there in each of the crates?

the answer btw is 9 dozen and 12 dozen

idk how to write it as an equation

[tiny minnow]

example crate 1 has x dozen

crate 2 has x+3

if we use crate 1 we get profit 1$/dozen

crate 2 we get 0.5$ profit

@slow gobletgo in math help alva

[limber tendon]

oh ok

I understand now

tysm

[slow goblet]

where?

[tiny minnow]

nope

in help 1

@limber tendon if ur done do .close

[limber tendon]

oh ok

sorry

.close

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[wary nacelle]

cant figure it out, tried manipulating but cant seem to get the expression to fit

[wary nacelle]

.close

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[minor yacht]

is the only way a function is bijective if it is strictly increasing?

[minor yacht]

what if i have f(x) = 3x-1, is this only injective but not bijective?

[bold lion]

What topic

[chrome salmon]

It's bijective for f : R to R

[minor yacht]

(0,-1),(1,2),(2,5)

so its not bijective?

[minor yacht]

functioncs

[chrome salmon]

What has this to do with it?

[bold lion]

I wanna learn functions

Brb

[minor yacht]

i tried inserting some value for x

[bold lion]

Ima learn advanced physics

[minor yacht]

since there are some gaps, its not injective right?

[chrome salmon]

What's the domain of the function

And co-domain too

[minor yacht]

domain are 0,1,2

co domain are -1,2,5

[chrome salmon]

Not like that

What's the question as in book

[minor yacht]

Determine whether each of these functions from R to R is a bijection.

[chrome salmon]

Yes so domain is R

Why are you deciding bijection of function by 0,1 and 2

[minor yacht]

im testing if it will be strictly increasing(injective) so i used some numbers

but im not sure on how to test if its surjective

if i understood it right, for something to be bijection it has to both be injective and surjective right?

[chrome salmon]

You have to check if for every element in co-domain if there exists a pre image

[chrome salmon]

Yes this is right

[lyric cedar]

It will depend on the domain and range of f

[chrome salmon]

Btw I gtg now so if anyone else is ready to continue then you can ping helpers

[minor yacht]

do you guys know of any video i can watch to deepen my understanding on this

im having a hard time understanding just from the lecture of our prof

[lyric cedar]

on functions?

[minor yacht]

on bijections

and how to test

or even just channels that has good vids on functions

[lyric cedar]

https://youtu.be/xKNX8BUWR0g this should be good

[minor yacht]

thank you

[lone heart]

@minor yacht Has your question been resolved?

[lone heart]

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[vale wigeon]

,w {{1,3,0},{9,2,1},{1,2,0}} * {{1},{0},{1}}

[ocean seal]

Results provided by WolframAlpha

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

Requested by Ann#0413

[vale wigeon]

yup @timid sky

what's troubling you?

B' is just a name

as is B

in this context anyway

you have two bases: one for the input space, one for the output space

you have the map T defined for you in the first sentence

you're asked to write down the matrix of T wrt these two bases

how so?

can you show the examples you're talking about?

maybe it's not as different as you think.

so you know the basic principle that the cols of the matrix encode the values of T at the domain's basis vectors, yes?

i take the 👍 react as a yes.

the principle is exactly the same here.

you will need to compute T(x^2), T(x) and T(1)

and then you will need to express those results in terms of the basis of the codomain, which in your problem is called B', and write down the coordinate vectors you get as the columns of your matrix

does this all make sense to you or should i take you through it step by step?

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[next pulsar]

I saw this when looking at the wolfram page on bessel functions of the first kind, how do I prove this?

[fringe ember]

use the definition of Bessel fxns, I guess

[next pulsar]

well that was my first instinct but the algebra got nasty so i was wondering if theres a cleaner method

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[ocean rampart]

Is there anyone who can show me what todo withe minus here.

X^5=-100

[fringe ember]

take the fifth root as you would normally

[ocean rampart]

but what with the minus, do i put it inside or before the root

so i just do it like this then?

x^5=-100
x=- 5√100
x=-2.51

[lone heart]

@ocean rampart Has your question been resolved?

[ocean rampart]

x^5=-100
x=- 5√100
x=-2.51

is this correct

thank's

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[chilly panther]

I'm terrible and I keep forgetting how to deal with natural logarithms and log laws. How can I simplify this:

[chilly panther]

$e^{2\ln{t}}$

[ocean seal]

mcacutt

[full marsh]

Bring 2 to the inside

And cancel

[chilly panther]

thank you, I'm screencapping so I have that with me, thank you!!!!!!

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[glacial pier]

if there is a set {a,b}* what does that * means?

[chrome salmon]

Does this have to do with strings?

[lone heart]

@glacial pier Has your question been resolved?

[halcyon grove]

someone in #proofs-and-logic asked a question with this notation

he said its reflexive transitive

[glacial pier]

yes sir

[glacial pier]

dun think it's correct?

[vale wigeon]

{a,b}* sounds like the set of all strings you can make by concatenating any number of a's and b's in any order, as well as the empty string

[chrome salmon]

||It's set of all finite strings||

[vale wigeon]

||no||

[chrome salmon]

||why not?||

||You mean I missed empty set?||

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[chrome salmon]

#❓how-to-get-help

[fading rampart]

ah i'm sorry

[lone heart]

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[glacial pier]

thanks

[lone heart]

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[formal spoke]

It's question c (I)

. close

.close

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[edgy cape]

I differentiated

got d/dx=(2x+4y)/(-2x-2y)

said 2x+4y=0

and then said x=-2y

substituted back into original function

I got y^2+3=0

idk how to get the right answer:

[lone heart]

@edgy cape Has your question been resolved?

[edgy cape]

<@&286206848099549185>

[fringe ember]

@edgy cape which question do you have a doubt in?

[gray isle]

I got y^2+3=0
can u show how you reached that

[edgy cape]

5

[gray isle]

also missing the y in dy/dx here

got d/dx=(2x+4y)/(-2x-2y)

[edgy cape]

1 sec

[gray isle]

why'd you sub x= 2y

[edgy cape]

to solve the eqn

[gray isle]

where's x=2y coming from

[edgy cape]

when I set the derivative to 0

so the denominator cancels

then 2x+4y=0

x=-2y

[gray isle]

last I checked -2y isn't the same as 2y

[edgy cape]

where did you get t

[gray isle]

what's t

oh

typo

and your 4xy term also changed into something completely different

[edgy cape]

oh wait 4xy=-8y^2 when subbing in -2y

.close

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[knotty sky]

I need help w/ 26 and question 5 under 18

im pretty sure 26 is 1/2 the size of line A is the size of line X.. im not sure tho

and is this part correct?

[lone heart]

@knotty sky Has your question been resolved?

[knotty sky]

how would i measure too get x

oh

and add em up?

[lone heart]

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[knotty sky]

so i was right?

im not that good at doing segments

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@knotty sky Has your question been resolved?

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[quasi granite]

Out of three people in a shop, one buys something and the other two don't. What's the probability that out of eight people, three buy something and the other five don't.

[quasi granite]

How do I apply Bernoulli here?

[proper pilot]

i think you do 8 chooses 3

so 8! divided by 3!x5! which if you use cancellation would be 56

so there are 56 ways that 3 people buy something while the others don't

then you put it over 8! or 56/8! which is 1/720, because you're looking for the probability it happens

[quasi granite]

but this isn't bernoulli

[glass lichen]

The random variable is a negative binomial distribution iirc

[quasi granite]

not sure about negative, but it is a binomial distribution yes

[glass lichen]

X is the number of people until 3 buy something
X~NegBin(3,1/3) I believe

[quasi granite]

not sure I understand

what's NegBin(3,1/3) equal to

[glass lichen]

It's the distribution

[quasi granite]

can you write the whole equation mathematically please?

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[alpine sable]

hi

[alpine sable]

can i please get help

[north needle]

So could you set an equation up like:

R: (2i + j - 4k) + ¥( i + 2j - k)

¥ is lamda

Because if I remember correctly likes perpendicular to a plane would share the same normal

Then (if I’m right which I hope I am) you would set up an equation in terms of lambda (¥)

X= 2 + ¥
Y= 1 + 2¥
Z= -4 - ¥

Substitute this into the plane and it should give you a value for lamda

[alpine sable]

hmmm

what would x,y and z be though

[north needle]

14 - (2 + 2 + 4) = ¥ + 4¥ + ¥
6 = 6¥
1 = ¥

3, 3, -5

[north needle]

@alpine sable

You understand the working?

[alpine sable]

lemme try

one sec

damn you smart

wait gimme a sec

[alpine sable]

i understand this

[alpine sable]

im confused with this?

[north needle]

I substituted in and brought the non ¥ values to the RHS

[alpine sable]

just curious

what method is this called?

like i tried to do point normal form but i got stuck

[north needle]

I don’t know the method name sorry. I was just taught it this way

But it’s just using the normals and standard vector equation form

[alpine sable]

ah okay

can i ask another math q?

do you know how to solve this?

[north needle]

Yes

[alpine sable]

how do you solve that?

[north needle]

Give me a few mins and I will send a photo of my working

[alpine sable]

okay thank you

[alpine sable]

sorry im confused, how did you get (2+2+4) and 6lambdas?

[north needle]

I subbed the lambda into the plane equation.

[north needle]

These values replaced the X Y and Z

[alpine sable]

ohhh

that makes sense

thank you for that

[alpine sable]

sorry is it possible if i can get assistance on this please

[north needle]

Is the lighting good enough?

[alpine sable]

yeah it is good

thank you

if i need help on it, is it possible if i can private message you about it?

[north needle]

Yup 👍

[alpine sable]

thank you

[north needle]

Though what is it?

[alpine sable]

on the working out you did

im currently busy atm

i need to leave and will look through it later

if there is a misunderstanding and im confused, its cool if i private message you right?

[north needle]

Yeah

It’s 1am in my time zone so if you message and I don’t reply I’m most likely asleep though 🥴

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@alpine sable Has your question been resolved?

[lone heart]

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[jade atlas]

How do I calculate the first moment of area of Inertia of a hollow cylinder

[lone heart]

@jade atlas Has your question been resolved?

[lone heart]

@jade atlas Has your question been resolved?

[charred flint]

around the center? just MR^2

[jade atlas]

my double integral doesnt make sense

@charred flint thats the 2nd moment of inertia

when i try and go from 0 to pi i just get 0

but when i go to pi/2 i get half the correct answer

[charred flint]

oh you're meant to sum the distance

so like y should be |y|

[lone heart]

@jade atlas Has your question been resolved?

[lone heart]

@jade atlas Has your question been resolved?

[lone heart]

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[orchid python]

hi

[orchid python]

how can I solve this?

please help me

[quaint trout]

Wtf is this picture lol

[chrome salmon]

Is this for a test?

[vague coral]

nice pic

[chrome salmon]

Seems like they avoiding the cam

[orchid python]

here

if you're curious where it comes from

i'm not cheating man

[quaint trout]

Write (1,-2,3) as a linear combination of (1,0,0) , (0,1,0) and (0,0,1) then apply the linearity of L

[orchid python]

let me try

so I will multiply 1 with the first matrix, -2 with the second one, and 3 with the last?

or it looks like this

[chrome salmon]

,rotate

[chrome salmon]

Yes

[orchid python]

should I do as the image or ??

[chrome salmon]

Yes as the image

[ocean seal]

it's Sam

[orchid python]

but what can I derive from it?

since it's the reduced form already

[chrome salmon]

L(1,-2,3)= L( 1 (1,0,0) -2 (0,1,0) + 3 (0,0,1))

[orchid python]

then??

[chrome salmon]

Apply this

[orchid python]

how can I solve this one @chrome salmon

will this becomes ((x + h) ^ 3 - x^3)/h?

but I am confused because as we treat f(x+h) the same as f(x)?

[fringe ember]

expand

use the formula for (a+b)^3

[orchid python]

yeah I know

but

[fringe ember]

you'll get a common factor of h

[orchid python]

((x + h) ^ 3 - x^3) this is correct for f(x) right?

[fringe ember]

yes

[orchid python]

but f(x+h) and f(x) in the quotient need to simply is not the same

why we just apply x^3 to both of them

[fringe ember]

f(x)=x^3

so f(x+h)=?

[orchid python]

yeah (x+h)^3

but there you have f(x)

and it also equal x^3

how can I know if a set is independent?

@fringe ember

[orchid python]

apply what exactly 😦

[fringe ember]

any linear combination of independent vectors is also independent

https://en.wikipedia.org/wiki/Linear_independence

[orchid python]

ok so 2 is correct because the set is linear combination of X, Y, and Z?

if 1 <= f(x) <= x^2 + 6x -6 for all x, find the limit lim x->1 f(x)

what should I do with this?

[chrome salmon]

Bruv L(1,-2,3)= L( 1 (1,0,0) -2 (0,1,0) + 3 (0,0,1)) = 1 L(1,0,0) - 2 L(0,1,0) + 3 L(0,0,1)
After this it's just answer

[orchid python]

ok I see this

thank you bro

[orchid python]

can you help me with this @chrome salmon

[lone heart]

@orchid python Has your question been resolved?

[lone heart]

@orchid python Has your question been resolved?

[jagged imp]

Apply squeeze theorem

[orchid python]

what should I do exactly?

[fluid shadow]

just show that lim x->1 (x^2+6x-6) = 1

which you can do by just plugging it in since its continous as a polynomial on R

then you get lim x->1 f(x) = 1 by the squeeze/sandwich theorem

[lone heart]

@orchid python Has your question been resolved?

[lone heart]

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[jagged jetty]

Someone can help me?

[glass lichen]

https://dontasktoask.com/

[jagged jetty]

oh ok

the problema is physics

(Fatec-SP/Adapted) A wave propagates on a string, from left to right, with a frequency of 2.0 hertz, as shown in the figure. (a) Show in the figure where the crest and valley are, mark and state the value of the wavelength, and for that value of frequency calculate the speed of propagation of the wave in cm per second. (b) Now compare the value you found for the wavelength of this wave with the wavelength values that appear in the spectrum on p.10 of the workbook. Can you identify a region in the spectrum where the wavelength is measured in cm? Thinking about this region, are the frequency values close to 2 Hz? How could you use the fundamental equation of undulatory (v=f) to justify this difference?

Translated with www.DeepL.com/Translator (free version)

[lone heart]

@jagged jetty Has your question been resolved?

[severe sluice]

i think it's quite obvious that:

1. this question refers to 2 figures
2. we can't answer the question without those figures
3. you haven't sent them yet

[lone heart]

@jagged jetty Has your question been resolved?

[lone heart]

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[pure sage]

<@&286206848099549185> i got -30 when its supposed to be -32

[pure sage]

and yes im a 18 year old

[severe sluice]

you might want to read the rules again

and discord's community guidelines

[pure sage]

??

i just want help thats all

[severe sluice]

anyways

you edited this

he's 9

[pure sage]

cap

[severe sluice]

(signature cringe look and stuff)

[pure sage]

i wrote ol so i edited to old

[pure sage]

thats to make a meme outta fortnite

[severe sluice]

is it sUpPoSeD to be -32 though?

[pure sage]

yes some hwo

[gray isle]

who's telling you its -32

[pure sage]

how

[pure sage]

techer

its -30 right?

[severe sluice]

,w (-2)^3-5(-2)^2 - 2

[ocean seal]

Results provided by WolframAlpha

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

Requested by ARGHdavocowana#6194

[gray isle]

time to get a new teacher

[pure sage]

yes

[severe sluice]

wolfram's word is law
:|

[pure sage]

snitching to the principal

thank you

3𝑥 + 1 − 20% of (4𝑥 − 1) = 1.2 ...could you use the bot for this too?

[hidden tundra]

wait leme try to solve it

[pure sage]

Im supposed to get 0 but i get it wrong

If you could show me the working it would be great

[hidden tundra]

mk for sure

i cant solve it sry

[pure sage]

oh its fine

<@&286206848099549185>

3𝑥 + 1 − 20% of (4𝑥 − 1) = 1.2 . please show me working

of this

[chrome salmon]

What's 20% equivalent to?

[hidden tundra]

🤦‍♂️ thats why i couldn't solve it

[chrome salmon]

Can you now?

[hidden tundra]

not if i dont know that

[pure sage]

ummm

[chrome salmon]

20/100

[pure sage]

arent we supposed to do 20 upon 100 and cancel them out?

[hidden tundra]

the answer is 0.6

3x + 1 −
100
20 − ( 4x − 1) = 1.2
3x + 1 −
2 · 2 · 5 · 5
2 · 2 · 5 − (4x − 1) = 1
3x + 1 −
5
1 − ( 4x − 1) = 1.2

x=0.6

unless im totally doing it wrong

[pure sage]

answer was 0.

[hidden tundra]

o

[pure sage]

nice try tho

I have my math exam tomorrow

[pale kestrel]

gl

[slender gull]

x equals zero.

[hidden tundra]

😑 your not on thanksgiving brake?

[slender gull]

I have language exam tomorrow. 🥲

[hidden tundra]

😑 your not on thanksgiving brake?

sad

[pure sage]

Can you show me the working ?

[ocean seal]

Been a Dad since Forever
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[slender gull]

Sure.

[pure sage]

thanks

[slender gull]

$3x+1 - \frac{20}{100}(4x-1) = 1.2$

[ocean seal]

Been a Dad since Forever

[slender gull]

Any issues here?

[pure sage]

umm

what do we mulitply the 4x and -1 by?

[slender gull]

1/5.

As 20/100=1/5.

[pure sage]

and when we cancel 20/100 . 5 goes to each side right?

[slender gull]

It doesn't!

[pure sage]

ohk

ty

[slender gull]

Sure.

[pure sage]

you helped me a lot

[slender gull]

I really didn't.

Goodluck for your exam.

Underage guy.

👀

[pure sage]

shhh

dont expose

[slender gull]

What country are you from?

[pure sage]

Uk

[slender gull]

Nice.

[pure sage]

We use words like lads, innit, etc

[slender gull]

Bruh.

[pure sage]

Im assuming you're american?

[slender gull]

Please don't guess randomly you won't get anywhere.

I'm Asian.

[pure sage]

india?

thailand?

[slender gull]

While if your question is over you could first close the tab and for any further doubts I don't mind dms.
Or you could move this to general channels.

[pure sage]

.close

[lone heart]

Channel closed

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[pure sage]

lost to pakistan in cricket L for you guys.

[lone heart]

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[gray isle]

<@&268886789983436800>

[night geyser]

ty, dealt with

[keen shoal]

thank u

[night geyser]

apologies plex

[lone heart]

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[keen shoal]

.close

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[keen shoal]

i know this is an invariant problem

and i tried different permutations of -1 and 1

but idk how to generalise it

[lone heart]

@keen shoal Has your question been resolved?

[keen shoal]

<@&286206848099549185>

[lone heart]

@keen shoal Has your question been resolved?

[lofty axle]

Have you tried the same problem, but with smaller matrices?

Try it for a 3x3 first

@keen shoal

[lone heart]

@keen shoal Has your question been resolved?

[lofty axle]

Looks like @keen shoal gave up

[keen shoal]

Haha sorry

Went to class

Thanks

.close

[lone heart]

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[green hazel]

HELP

srry caps

[thorny patio]

iirc, volume of these prisms is:

Area of Face (triangle in this case) * Length of the prism (the rectangle's Length)

[green hazel]

how do u find the height of the traingle

Volume = 1/2 base times height times lentgh

[thorny patio]

It's a right triangle

[green hazel]

yeah but its not a perfect triangle

u get a radical

[thorny patio]

It's given by callint it right triangular

[green hazel]

i agree

but u would get rad 72 as the height correct

[thorny patio]

So base is one leg and height is the other

Because they make a 90 degree angle either one is a height

6*6 / 2

Height is where 90 degree angle is

Not the hypotenuse

[green hazel]

ah okay

thanks

so answer is 180

This was on my SAT that I took in October

I got it wrong

It was a no calculator section

I paid extra to get my questions back

[thorny patio]

Just remember height is always found by making a 90 degree angle

[green hazel]

got it

[thorny patio]

Because of this right triangles havw easy to calculate areas

[green hazel]

can you help me with one more

[thorny patio]

Always the 2 legs

Yea go ahead

[green hazel]

I picked Answer choice B

I don't know why it's not B

Like A doesn

make any sense to me

[thorny patio]

It's A right?

[green hazel]

yes

[thorny patio]

So this is a weird question but

This is wht

Why*

Half the rooms

Means 180/2

So all the equations that say 1/2 on the left are out

You dont end up with 180/2 when expressing the rooms cleaned

You end up with 9r doing 360 rooms

When it should have been 90

[green hazel]

whayy

but listen

u should do 1/2 times r

1/2 times r is equal to 90

[thorny patio]

How many rooms do the 9r workers clean

[green hazel]

180 rooms

[thorny patio]

No

[green hazel]

half of them

[thorny patio]

They clean only half

90 rooms

So the equation should say 9r = 90

The one you chose is not equivalent to that

[green hazel]

So A is equibalent?

[thorny patio]

A is equivalent to that statement

You can use algebra

[green hazel]

oh cuz u divide by 2

[thorny patio]

Divide by 2

Yea

[green hazel]

this was tricky

[thorny patio]

And it reads 9r = 90

Yes

I agree

[green hazel]

im so bad at SAT

[thorny patio]

Thats a harder SAT problem

[green hazel]

I scored a 1250

[thorny patio]

It's just about practice

[green hazel]

i want a 1500+

[thorny patio]

Can guarantee your math score will improve just from practice

[green hazel]

Do u think it's possible for me

[thorny patio]

Practice official SAT practice tests

[green hazel]

ok

[thorny patio]

There are only so many different kinds of problems

And tons of tests you can find

But make sure it's official college board tests

The other review books dont write them the same way

[green hazel]

thanks

[thorny patio]

Yw GL you can 100% get a good math score

[green hazel]

.close

[lone heart]

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[harsh ocean]

Which is better to use in this case? $\iff$ or $\Rightarrow$ ?

[ocean seal]

JSGF

[harsh ocean]

And what are the differences?

[placid zinc]

If I wrote:
x = 2 ⇔ x² = 4
I would be incorrect

[harsh ocean]

oh

yeah

[placid zinc]

If you knew that x² = 4, that would not be enough to determine that x = 2. So, the "if and only if" is the wrong symbol

[harsh ocean]

So is it better the imply or derivation arrow?

[placid zinc]

x = 2 → x² = 4
Is a true statement

[harsh ocean]

Well if it's reversed it wouldn't

[placid zinc]

Now, in your case the ⇔ works perfectly

[harsh ocean]

ok

[placid zinc]

However, you only need the → to get your point across

So it's a matter of preference

[harsh ocean]

When deriving a solution what should I use then?

What do you prefer?

[placid zinc]

Both work fine. Just watch out for using ⇔ where it isn't legal

If your goal is to start with one equation and show that you get certain solutions, then → is safer haha

[harsh ocean]

Yeah that's what I normally do.

[placid zinc]

(If you have no interest in showing that the process can be done backwards, then ⇔ offers no advantage)

[harsh ocean]

$\Rightarrow$ is for horitzontal derivation preferably

[ocean seal]

JSGF

[harsh ocean]

Makes sense

If not you could just solve the equation line by line one on top of each

[placid zinc]

I often see people do that, and then start lines with → or ⇔

So it works vertically if you do that

[harsh ocean]

Yeah, I also saw it

Ok

[placid zinc]

All a matter of style, no best solution imo

[harsh ocean]

Got it, thanks!

I'll close

.close

[lone heart]

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[solar pebble]

What technique should I use

to get a general solution?

[lone heart]

@solar pebble Has your question been resolved?

[turbid nacelle]

Hello guys, can you please Help me with examples num. 3 and 5

[topaz grove]

@turbid nacelle been a while, but if i recall correctly, l'hopital's method should work?

or you could just try to graph it at a few spots as they get closer and closer to zero, i suppose

for both of them, they look like they should be undefined at x=0 (or holes with jumps), but i'm guessing you could already figure that out on your own

[turbid nacelle]

mmm, thank you the third one is already i got it with lhopital i tried also the fifth but i got ln(2)/2 and i have no idea if it possible to simple the equation so we get zero which is in the brackets

[topaz grove]

if you do lhopital with number 5, don't you get 0 for the numerator bit and zero for the denominator bit?

[lone heart]

@solar pebble Has your question been resolved?

[lone heart]

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[daring tulip]

can someone do that question

i did a proof for it

but Its not very good

[static geyser]

no bro he did not do a proof hes capping he has no idea how to do it

i would know im literally sitting next to him rn

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[daring tulip]

.reopen

[lone heart]

✅

[devout summit]

You can try proving that sum of length of the arcs passing through black cells is minimised when the centre of the circle coincides with centre of the white cell

[main beacon]

Uhhh

Can somebody give me some question about Root Of 3, Volume Of Cube And Rectangle?

[static geyser]

well we worked out that when the circle's center is the same as the white cell's center, it creates 4 equilateral triangles. Each triangle has 60 degrees (obviously) and then since the 4 equilteral triangles leaves the angles of the arcs within the white cells only. so 360 - 60 * 4 = 120 which is 1/3 of the total circle angle which is the largest the angles can get

[devout summit]

60° is the minimum angle we can get from each of the arcs passing through black cells

[static geyser]

and why is that?

[devout summit]

Sorry, meant minimum

[static geyser]

yeah but why is it that

[devout summit]

We know that arc passing through one of the black cells is a minor arc...

[static geyser]

yep

wouldnt the arc angle stay the same wherever we move the circle?

[devout summit]

So, if we join the chord corresponding to that arc, minimising the chord length will minimise the length of the arc

[static geyser]

but when we move the circle, doesnt the chord stay the same length?

[devout summit]

No it doesn't! Depends on how you move it

[daring tulip]

dang smart guy

we are 8th graders

[static geyser]

shush the adults are talking

[devout summit]

A diagram is helpful

[static geyser]

oooh wait ok thanks so much i get it now

[devout summit]

There is a direction in which we can move such that the lengths of opposite arcs remains the same. But while doing that, lengths of arcs of the other pair changes

[daring tulip]

k

.close

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[cinder sundial]

its weird when i put the fraction on calculator i get 0.11252813203

that doesn't match to my calculation

its 0.03/0.2666 in the decimal form right

[buoyant kayak]

no

[cinder sundial]

3/100=0.03

[buoyant kayak]

yeah

[cinder sundial]

2/75=0.02666

[buoyant kayak]

yeah

[cinder sundial]

then 0.03/0.02666=(3/100)/(2/75)= 0.11252813203

right

[buoyant kayak]

no

[cinder sundial]

why?

[buoyant kayak]

because it's wrong

[cinder sundial]

where i did wrong? its looks reasonable

[buoyant kayak]

this

[cinder sundial]

but 3/100 does equals to 0.03

i just convert it from fraction into decimal

[buoyant kayak]

yeah

your fractions are right

[cinder sundial]

could you point out the mistake i have made

[buoyant kayak]

.

maybe try putting in your calculator again

not sure what to tell ya

[cinder sundial]

(3/100)/(2/75)=1.125

[buoyant kayak]

yep

[cinder sundial]

then i have another question

why its different

[buoyant kayak]

you probably put it in your calculator incorrectly

[cinder sundial]

why those two results are diffrent

[buoyant kayak]

perhaps because this is wrong

[buoyant kayak]

.

[cinder sundial]

can someone explain why those two underlined numbers are different

[cursive badger]

well the bottom one you are off by a factor of ten

2/75 is .0266...67

@cinder sundial

and the -7 ending instead of 5 is a rounding error

because you used .266 instead of .2666666666666 or the even more accurate 20/75 (since you were off by a factor of ten)

[cinder sundial]

yes i did put the exact numbers on calculator this time:(0.03)/0.02666666666 and i got 1.12500000028 as the result

1.12500000028 and 0.1127 are quite different

that not what i have expected, it should be close to 1.125

[cursive badger]

... but 1.125000000000028 is close to 1.125?

[cinder sundial]

god i think i found the problem

[cinder sundial]

yes they are

[cursive badger]

it's a rounding error because you didn't divide by a specific enough number

[cinder sundial]

yes, i type 0.266 instead of 0.02666

theres a huge diffrent between them

[cursive badger]

well, doing this fixed TWO errors

one error was the factor of ten. Of course, that changed your answer by approximately a factor of ten, even disregarding or counting fixing your other mistake

the second error you fixed was using four sig figs instead of three sig figs

which made your answer significantly (pardon the pun) more precise

ideally you would never convert to decimals, since the fractions are not approximations, but the decimals sometimes are (as in the case of 2/75)

make sense? @cinder sundial

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[prime flax]

Snowy’s snowboard Co manufactures snowboards. The company uses the function
𝑃(𝑤) = 324𝑥 − 54𝑥^2
to model its profit, where P(x) is the profit in thousands of
dollars and x is the number of snowboards sold, in thousands.
a) How many snowboards must be sold for the company to break even?
𝑏) How many snowboards must be sold for the company to be profitable?

[prime flax]

is someone able to help me please

how to solve this using completeing the sqaure

or solve my factoring

grade 10 math

[buoyant kayak]

set equal to zero and solve

they would "break even" at a profit of 0

[prime flax]

i set it to eqaul zero and got a answer but hen i plug it back in both sides are not equivalent

i got -54(x-3)^2+486

i don'nt know how to start the second part either

what does it mean??

[buoyant kayak]

how did you get this

don't give people answers

[alpine sable]

Oh I see, sorry

[prime flax]

I don't get it, i solved it by completing the sqaure

[buoyant kayak]

that's not the route you'd want to take with this

[prime flax]

then what do i do solve by facotring?

[buoyant kayak]

yes

[prime flax]

i tried that im unable to get two numbers

[buoyant kayak]

there's a pretty large common multiple that can simplify it quite a bit

a hint in the x^2 term's coefficient

[prime flax]

gcf would be -54x?

[buoyant kayak]

yes

[prime flax]

i have 6,0 right now -54x (x+6)

would that be the final answer or si there a way i could have simplified it further

but this is for the break even only right

[buoyant kayak]

should be x-6 since you factored out a negative

[prime flax]

sorry wrong sign

i meant -

[buoyant kayak]

your question asks how many snowboards must be sold for the company to break even

you got solutions x=0 and x=6

so what is your answer?

[prime flax]

6

but do we have to show (x-0) in the eqaurion as well??

[buoyant kayak]

note that you solved for x in thousands of snowboards

[prime flax]

6 thousand skateboards must be sold for the company to break even

[buoyant kayak]

and what do you mean by this?

[prime flax]

wait but how do we show that 0 is another break even point, i mean it is obvious but i dont think we would count it

[buoyant kayak]

that would not be an answer

[prime flax]

oh oky

*okay

[buoyant kayak]

you can just throw that away due to logic

[prime flax]

also for the second part of the question what does that mean

[buoyant kayak]

obviously the company is not gonna break even if they haven't sold anything yet

well, for a company to be profitable, profits must be greater than zero

[prime flax]

do we complete the sqaure for that?

[buoyant kayak]

no need

[prime flax]

but what exactly is b asking

about profitibale

wouldnt it be 6 as well??

or do we find the maximum revenue

i think its the same question

because 0 and 6 are the break even points and b) is asking which one will make a profit

but im not sure

[alpine sable]

I think it means "How many minimum number of boards should be sold so it generates profit?"

[prime flax]

wouldn't it be maximum number

or are th emaximum and minimum the same in this case

[buoyant kayak]

P(x) needs to be greater than zero for the company to be profitable

[prime flax]

so does that mean we alread have the answer or do we have ot find the maximum value

by ocmpleting the sqaure

i dont udnerstnd that part

[buoyant kayak]

you almost already have the answer

just gotta find where P(x) > 0

[prime flax]

i got 3000 as my answers earlier

by completing the sqaure

[buoyant kayak]

you don't need to complete the square

you already have zeroes

set up a sign chart and find where P(x) > 0

[prime flax]

so the axis of symettry??

[buoyant kayak]

no?

[prime flax]

whats a sign chart?

[buoyant kayak]

a chart of signs

[prime flax]

??, im lost

[buoyant kayak]

you want to find where P(x) > 0, that's where the company is profitable

[prime flax]

ive never done that before

[buoyant kayak]

P(x) can only change from positive to negative if it crosses the x axis

correct?

[prime flax]

yes

[buoyant kayak]

and the zeroes describe where the function crosses the x axis

you found those zeroes

x = 0 and x = 6

excuse the awful handwriting i'm not good with a mouse

these are the intervals in which you can generalize the sign of the function

since it can only change from positive to negative when it crosses a zero

so take a test point... anywhere within those intervals

plug it in

see if your value is negative or positive

move on to next interval

[prime flax]

i've nevrr learned this before im not sure

is there any other way i can solve this

because completing the sqaure is the only other way i learned in class

[buoyant kayak]

completing the square only solves quadratics

you need to find where P(x) > 0

you're just solving an inequality

[prime flax]

im confused just leave it, 3000 is the only answer i can think of because its the maximum value

[buoyant kayak]

that's not right

[prime flax]

idk what to do because the other stuff is grade 11

and if i do that on a test, my teachers gonna say i didn't do it right

[buoyant kayak]

solving inequalities is like grade 7

[prime flax]

ive never done that idk im tired

its okay

thankyou for helping tho

.close

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[wispy sorrel]

why does this return a complex number?

[alpine sable]

isn't sin(5) a negative?

[wispy sorrel]

that doesn't justify returning a complex number

[buoyant kayak]

the decimal exponent ends up as an even root

[wispy sorrel]

ah ok thanks

.close

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[jaunty crane]

help pls

[alpine sable]

How much of this have you solved?

[jaunty crane]

nothing

[alpine sable]

If you assume the area of the shaded portion as B, the portion left of that as A and the right portion as C then you would realise you have to find area B.

But you only know formulas to find areas of (A and B)Area of sector, (B and C)Area of other sector and (A+B+C)Area of Rhombus

How can you add or subtract these areas to find area of B?

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@jaunty crane Has your question been resolved?

[jaunty crane]

https://media.discordapp.net/attachments/818047052079431702/913395376139149342/ezgif.com-gif-maker.gif

why so hard

[alpine sable]

Let me rephrase
You can find A+B, you can find B+C, you can find A+B+C. How can you add or subtract these to only get B

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[tight locust]

is this for real? it's literally just -((A+B+C) - (A+B) - (B+C))

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[junior stirrup]

guys

[junior stirrup]

how to convert degrees to revolution

helpp

[brazen forge]

360 degrees is one revolution

[junior stirrup]

so how many revolutions is 830°

[brazen forge]

830°/360°

So just 2 complete revolutions + 110°

[junior stirrup]

oh ok thx

does the reference angle mean the quadrants?

[thorny panther]

reference angle does not mean quadrants

[junior stirrup]

so how do i get the referecne angle

ok nvm i found this

help

can radians be negative

[vale wigeon]

can feet be negative?

radians are just a unit of measurement. more specifically a unit of measurement for angles.

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[cinder sundial]

ay

[tiny minnow]

what?

[cinder sundial]

its solved

.close

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[gritty veldt]

Not homework, just pondering:

if I have an infinitely long chain graph, is that equivalent to the natural number?

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[vale wigeon]

what is a chain graph and what do you mean by equivalence in this context?

[gritty veldt]

huh, maybe it is not called chain graph.

but what I meant was something like this (without the direction)

equivalence is... IDK really,
I just started reading about analysis, the textbook was saying something like, all natural number sets, even if written using different scripts, are all equivalent with one another, so they are the same thing.
that's my understanding of equivalence