help-0

[glass lichen]

x=-2 and x=-5 have hollow circles

[candid thistle]

Oh right

That as well

[stoic cloud]

@glass lichen i thought () are only used if it is infinite

[glass lichen]

no...

[candid thistle]

() is for </>

[glass lichen]

() means not included

[candid thistle]

and [] for <=, >=

[glass lichen]

[] means included

the function isnt defined at x=-2, so you cant include -2 in the set of allowed x values

[stoic cloud]

oh yeah

[glass lichen]

likewise for -5

[candid thistle]

What are hollowed out bubbles supposed to represent?

[glass lichen]

a point not included

[candid thistle]

I was asking them about it ;-;

But I think they got it either way

¯_(ツ)_/¯

How can I find the inradius of an isosceles triangle?

[stoic cloud]

so it would be (-2,-5) for domain right? @glass lichen

[candid thistle]

I can start off by splitting it into two right triangles

[glass lichen]

yes

[stoic cloud]

yes

[candid thistle]

And getting the altitude afterwards, by using pythag

[glass lichen]

actually no

[stoic cloud]

me?

[glass lichen]

yeah

[candid thistle]

you include smaller num first

[glass lichen]

(-5,-2)

[candid thistle]

-2 > -5

[glass lichen]

you go left to right

[candid thistle]

Did you get it, Just_Roberto?

[stoic cloud]

ye

[candid thistle]

You can then simply do the same for range

[glass lichen]

if we're being nitpicky, technically it should be $x\in (-5,-2)$ but again, that's being pedantic

[ocean seal]

Mosh

[candid thistle]

Lol I don't like doing stuff like that

its good enough like this but yea

I hate it when a problem has a million math symbols, even if ik most of em

[stoic cloud]

For the range of this would it be [5, -inf)? or do i have that backwards again?

[candid thistle]

Backwards

is -inf > or < -5

[stoic cloud]

so bottom to top for range just like left to right for domain?

[glass lichen]

yes

[candid thistle]

yes

[stoic cloud]

ah yes

[glass lichen]

negative to positive in both cases

[stoic cloud]

(-inf, 5] right

[glass lichen]

for the range?

[stoic cloud]

ye

[glass lichen]

no

range is y values

[candid thistle]

I need help with this; I need to find the inradius of the incircle of this triangle. After sketching up a deathly hollows style diagram idk what to do :/

[stoic cloud]

is it only for parabolas that the range can look like, (inf, inf)?

[candid thistle]

I connected the points where the circle is tangent to the triangle, don't know what to do next though.

[candid thistle]

Domain*

But yes

and it can be for other cases as wel;

x = y, y = some constant, etc.

Wait I can just find the area of the triangle, which is just 60, then usign the fact that inradius * semiperimeter = area of the triangle, i can try to solve this

[glass lichen]

no

(inf, inf) isnt a thing

[candid thistle]

I got it, anyways have to go

[glass lichen]

(-inf,inf) just means the whole R line, ie any value you can put in or get

[stoic cloud]

ye

[glass lichen]

but yeah.. not only parabolas have domain R.. any polynomial will have a domain R provided it's not manually restricted

[alpine sable]

Can you guys solve it?

[stoic cloud]

hold up, so it would be (-inf,2] if im correct? for range

@glass lichen ?

[glass lichen]

it's a filled circle at (5,2)

or looks like one at least

[compact sundial]

If its filled it has square brackets

[stoic cloud]

ye so (-inf,2]

ah yes eyes starting to pick up on it a bit more

only use x line values for domain

only use y values for range

right?

[glass lichen]

yes

[stoic cloud]

ah yes

[glass lichen]

since domain is the set of x values, and range is the set of y values

[stoic cloud]

thank u for helping

[full lantern]

looks like chat needs another person to ask a question 😄

is there a way to count using stars and bars method

so that each 'bin' is ordered in a certain way

for example n balls in k bins but we want the bins to be arranged so that its in increasing order

[bitter sage]

can anyone help me with this

[open rampart]

Can someone help me figure out this sequence?

[wise sigil]

@open rampart Looks roughly exponential, yeah? Try computing the ratios of successive terms

[open rampart]

I don't really know what that means

[stoic cloud]

range for this is (4,4) right?

[open rampart]

;((

[open rampart]

I think it'd be (-4,4) (?

[stoic cloud]

oh yeah

whoops

[gray isle]

what were the exact instructions that came with that sequence of numbers

[open rampart]

Find out the sort of formula(? It's not really an exercise so there are no instructions

[gray isle]

wdym by not really an excercise

anyway like seoin said, this sequence is very close to exponential

[open rampart]

It was given by my teacher however it is kind of a challenge and the only instructions were to figure out the formula

[gray isle]

like seoin mentioned, consider first determining the ratio between consecutive terms

fk

accidentally add an extra word in there (edited)

[open rampart]

I'm unfamiliar with the terminology, you mean how far one is from another?

[gray isle]

Not quite

$\frac{t_n}{t_{n-1}}$

[ocean seal]

ℝamonov

[gray isle]

(for appropriate values of n)

[open rampart]

Idk how to do that sorry :((

[gray isle]

then you are really lacking the knowledge to so this type of question

[open rampart]

I think I am

[placid zinc]

Domain is all of the potential x-values you can plug in
Range is all of the potential y-values you can get out

[stoic cloud]

Bruh

just state ur question if someone wanna help they help

[rough hemlock]

52√3 - 2√3 = 4√3``` is this correct? i've never done operations on root numbers before except for multiplication

[placid zinc]

What's 52x - 2x?

[errant jacinth]

50x

similar terms

[placid zinc]

Was asking ballad lol

[errant jacinth]

whats ballad

LMAO

[placid zinc]

Fair I wasn't clear

[errant jacinth]

oh

i see

now

LMAO my bad

[placid zinc]

@rough hemlock
Question is relevant I swear
What's 52x - 2x?

[errant jacinth]

yeahh

i do have a question of my own though

[gaunt magnet]

ahahaaaaaaa

[errant jacinth]

lmao

[gaunt magnet]

https://tenor.com/view/cat-leaving-leave-oops-bye-gif-17519616

[errant jacinth]

need help with the second limit

do not understand it

[gaunt magnet]

<@&286206848099549185> he needs help

[gray isle]

do you understand what $\lim_{x \to -4^-}$ is asking for?

[errant jacinth]

so heres the thing right

wait

isnt it -4

-4 -

yeah its lim > -4 -

[gray isle]

sry missed a - sign

[ocean seal]

ℝamonov

[errant jacinth]

wouldnt that mean approaching x = -4 from the left to the right

[gray isle]

poor wording

just approaching -4 from the left is fine

[rough hemlock]

50x*? lets continue in #help-9

[gray isle]

to evaluate the limit algebraically, you could consider -4^- as a value slightly less than -4

[errant jacinth]

sorry i do not understand

so would i be going left to right?

aka moving to the right

[gray isle]

plugging that in you'd get
$\frac{-4-1}{-4^- + 4} = \frac{-5}{0^-}$

[ocean seal]

ℝamonov

[gray isle]

adding 4 to something slightly less than -4, you'd get something slightly less than 0 denoted with 0- (which is negative)

from this you can determine the sign of the infinity you're approaching

[errant jacinth]

so you are saying that

if we did -3 for example it would make the denominator 1

and onwards

[small flint]

wait, is it not a matter of a simple formula?

[sly mantle]

@small flint keep copypasta out of here

[small flint]

what grade are you?

ah

ok then

[gray isle]

the limit for x→-3 is simpler as you don't have stuff that may involve division by 0

[errant jacinth]

im still not understanding, sorry. From what direction would I go?

[gray isle]

just approaching -4 from the left is fine

[errant jacinth]

ok so its like the first black arrow i drew but we would start with that other red arrow in the second quadarant

[errant jacinth]

ah ok

i see now.

Thanks!

[small flint]

2560 is 128 % of the original price, so (2560/128)* 100, right?@icy lantern

[candid wedge]

I need help with d and e

[surreal meadow]

do you know the laws of exponents?

is this homework?

then what is it?

what's byjus?

can you simplify the left side?

what

for x?

yes

[tired hamlet]

how would I start setting this question up?

[surreal meadow]

draw a picture

[tired hamlet]

and then? still confused lol

[surreal meadow]

can i see the picture

[surreal meadow]

the x marks the side lengths of those squares

make sure you understand that

now i'm assuming you know what a derivative is

if so, you'll want to find the volume of the box as a function of x, call it V(x)

and then you'll want to maximize that function with calculus

if any of that was unclear or you need help modeling the volume lmk

[gritty veldt]

What have you tried?

[surreal meadow]

do you know the fundamental theorem of calculus?

it is not

do you know the fundamental theorem of calculus?

so this should look familiar

the top is part 1, which is what we want to use

so what is f(t) here

so if f(t) = cos(e^t)

what is f(x)

yes

[gaunt dirge]

Hello, I have a question

I'm trying to create a video game, and I need help with a 3D geometry problem regarding cylinders and rectangular prisms.

[low topaz]

How can i represent a hundred million nines

[gaunt dirge]

:/

[surreal meadow]

100,000,000 * 9

[surreal meadow]

care to elaborate?

[gaunt dirge]

I would like to create a cylinder with a fixed upright orientation (its height would be infinite, i'm only worried about its length and width)

but

the length and width of this cylinder should encompass a prism of variable dimensions as small as possible

the cylinder would be unchanging

but like

[tired hamlet]

could I get some help with modeling the volume?

[gaunt dirge]

no matter what orientation this finite prism is, it should be encompassed by this fixed cylinder

it's kind of hard for me to explain

im sorry, haha

[surreal meadow]

yeah i'm not quite understanding

so the prism changes in size

but the cylinder doesn't

and you want the cylinder to encompass the prism

[gaunt dirge]

well, no

so the prism has the capability to be any size you want, but it doesn't change on the fly

yes

[low topaz]

How can i represent a number with 100 Digits and all of the digits are 9

[gaunt dirge]

i want the cylinder to encompass the prism as small as possible, while not changing at all, even if the prism its encompassing rotates

golly that's such a mouthful

hmmm

let me find a way for me to make this easy to understand

[surreal meadow]

$10^{100} -1$

[ocean seal]

maximo

[gaunt dirge]

so imagine you take a prism

and rotate it in every possible way you can

and imagine it rotates so fast, that it looks like a sphere

are you with me @surreal meadow?

[surreal meadow]

what point does it rotate about?

[gaunt dirge]

its center

[surreal meadow]

sure

[gaunt dirge]

and then

you want to circumscribe a cylinder onto the sphere

[surreal meadow]

you just need a cylinder with diameter = prism's diagonal

[gaunt dirge]

i guess i should ask how to calculate a prism's diagonal

[surreal meadow]

pythagoras

[gaunt dirge]

oh okay

[full lantern]

hey could anyone help out with this

#help-0 message

[gaunt dirge]

yeah i kinda feel silly LOL

sorry

[full lantern]

o crap am i intruding

sorry sorry

[gaunt dirge]

its okay, im done

👋

[full lantern]

o nice

[surreal meadow]

another way would be $\floor{9.\overline{9}\cdot 10^{99}}$

[ocean seal]

maximo

[surreal meadow]

there's tons of ways really

[stone crystal]

these channels finna blow up in about a month

[surreal meadow]

wdym

[stone crystal]

we are all going back to school

[surreal meadow]

yeah that's true haha

[full lantern]

😢

[stone crystal]

starting calc II in college fr year

hard asf so yall better help me lol

[gaunt dirge]

this one made me laugh

0.9 repeating = 1

[surreal meadow]

yeah but then we floor it to remove the decimals

[gaunt dirge]

thats so over-the-top

LOL

[full lantern]

does anyone know how to go about this 😅

[surreal meadow]

yep

[vestal oriole]

max and min turning point?

[ionic jewel]

derivative

[vestal oriole]

do I differentiate twice?

dy/dx = 12 - 6x

[devout bronze]

just diff once

solve for when its zero

or u could just use the max/min value of a general quadratic

[solar cradle]

also check your derivative

[full lantern]

[vestal oriole]

12-6x = 0

x=2

now what

[solar cradle]

well first off dy/dx is not 12 - 6x

[vestal oriole]

12-3ˆ2

12x-3xˆ2

then?

[devout bronze]

when u solve for dy/dx = 0 ur finding values of x where the rate of change is zero, so the graph of y i stationary. The min/max points have to be stationary since they are points where the graph turns around, so ur basically finding values of x that correspond to min/max points

just plug that value of x back into y

[vestal oriole]

oh

so its

6(2)ˆ2 - (2)ˆ3 - 10

[alpine sable]

Hey can someone give me a hand with my ap stat hw? I missed the day my teacher went over this topic

[placid zinc]

[alpine sable]

I have no clue what to put for what type of relative frequency is this

[west solstice]

,rcw

[alpine sable]

I don’t know what that is😭

[west solstice]

i rotated the image for you

[alpine sable]

OH thank you

[alpine sable]

if the global minimum is B

what would point C be classified as then?

anyone able to help?

[spare fern]

End point

[pastel forge]

Hey guys I recently got confused on a such dumb question
21-8×2+12÷3

If I solve this by bodmas rule then the answer is 1 and if I rearrange it then answer is 9. Which is correct and why explain in detail

[spare fern]

Wdym by rearrange it??

[ionic jewel]

which is 9

not sure what rule you are using to get 1

[pastel forge]

BODMAS

[pastel forge]

If I rearrange it in third step that is
21-16+4

[spare fern]

That is still 9

[ionic jewel]

yes thats right

thats 9

ah i see

you have to go left to right @pastel forge

when doing addition/subtraction, and when doing multiplication/division

so it has to be (21-16)+4

[pastel forge]

But what about BODMAS

That is thought in lower classes

[ionic jewel]

what about it?

are you using that to say you do the addition before subtraction?

[pastel forge]

BODMAS stands for Bracket, of , divide , multiple, add, subtraction

[ionic jewel]

BODMAS (or PEMDAS for Americans) is a tool to help you remember, it doesn't follow the order exactly, the proper order is

1. Brackets
2. order/exponents/whatever
3. multiplication AND division going left to right
4. addition AND subtraction going left to right

[pastel forge]

Ohk

But it was rearrange in some or the other way

[ionic jewel]

I'm not sure what you mean

[pastel forge]

Heell

[vale wigeon]

addition and subtraction are on the same level.

your issue is that you take BODMAS literally and parse 21 - 16 + 4 as 21 - (16 + 4)

which is incorrect

[pastel forge]

How it is incorrect

[vale wigeon]

addition and subtraction are on the same level

addition doesn't take precedence over subtraction

when you have a bunch of additions and subtractions together like this you just do it left to right

[west solstice]

not true

[vale wigeon]

BODMAS requires you to add first and then subtract.

[west solstice]

Addition and Subtraction are equal operations, you perform them from left to right in that order

[vale wigeon]

this is exactly what i said was not true

[west solstice]

BODMAS = PEMDAS?

[vale wigeon]

this is exactly why BODMAS/PEMDAS/whatever are bad acronyms

[gray isle]

this is why GEMA is superior and you should just consider "subtraction" as the addition of negative numbers

[pastel forge]

But in this case I rearrange it some or other way

[vale wigeon]

@alpine sable you were taught that a - b + c parses as a - (b+c) and not as (a-b)+c?

[ionic jewel]

whats GEMA?

[vale wigeon]

Grouping, Exponents, Multiplication, Addition

[gray isle]

grouping
exponents
multiplication
addition

[ionic jewel]

well soecifically whats the g

ah thanks

[vale wigeon]

grouping symbols

[pastel forge]

Now I think I was taught a bit wrong in my lower classes

[west solstice]

werent we all?

[pastel forge]

Ohk thanks for clearing my doubt

[vale wigeon]

this includes parentheses and other bracket-like symbols, such as:

• fraction lines
• absolute value bars
• radical symbols

this involves rearrangement, which is needlessly error-prone

[gray isle]

you can if you want

but it isn't necessary

its an application of the commutative property and in some cases may help with simplification depending on whether you have numerical values

[rancid narwhal]

are my maths correct?

pls also check my diagram

[placid zinc]

Any thoughts on the problem so far?

[clear vessel]

How do I solve 10^a/5^b = 2^6 * 5^2

$10^a/5^b = 2^6 * 5^2$

[ocean seal]

qWeb

[ionic jewel]

unless theres more contraints i imagine there infinite solutions

[clear vessel]

integers

[ionic jewel]

10 = 2*5
2^a * 5^(a-b)
a = 6, b = 4

,w 10^a/5^b = 2^6 * 5^2 over the integers

[ocean seal]

Results provided by WolframAlpha

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

Requested by 兔子#6562

[clear vessel]

how do I express (√72 )/ 64 in the form a√b

[gray isle]

technically it is already in that form.
but i'm guessing they want you to simplify as much as possible

do you know how to simplify square roots in general?

[clear vessel]

I do, but it requests a and b to be integers

@gray isle

[gray isle]

don't think it can be done if both a and b are integers

[ionic jewel]

they are already integers

oh wait nvm i forgot how fractions work

[clear vessel]

exactly I am confused

I think it meant for √72 to be the denominator

[gray isle]

do you have the exact original question qweb?

[vital tree]

Is this still in use?

[clear vessel]

yes

write each of the following in the form a√b where a and b are integers and b is as small as possible

a) (√72) / 64

[gray isle]

do you have the exact image of the expression

or can you definitively confirm that
$$\frac{\sqrt{72}}{64}$$
is exactly what is printed on the page

[ocean seal]

ℝamonov

[clear vessel]

100%

lol

[ionic jewel]

best you can get is (3 sqrt(2))/(32)

[gray isle]

yes

keep meme questions out of here pls

[ivory otter]

bit confused here, idk why

the hypotenus is the opposite ?

for A

[alpine sable]

sin with respect to which angle is asked ?

hypotenuse is the side opposite to the right angle

[ivory otter]

like i was asked this question

how do i know if they are asking for a right angled triangle

or not

[gray isle]

you don't

and you shouldn't assume that any triangle in a question will be right angled

[ivory otter]

damn

so how can i know then

[alpine sable]

well the one way i can think of is to check if they are pythogorean triplets,

anyways i am not familiar with what they mean by "Solve \triangle ABC"

[gray isle]

and as such you should start with a scalene triangle

using an appropriate scale from the values given.

and determine unknowns using stuff like sine law

solving a triangle pretty much means to determine all sides and angles in that triangle

[alpine sable]

i see

[ivory otter]

but i dont get it

how am i supposed to come to the conclusion

if its right angled or not

[gray isle]

wdym

[ivory otter]

You said i shouldnt assume its right angled

[gray isle]

yes

[ivory otter]

so how can i know

if it is or isnt

[gray isle]

you start with a triangle without any outstanding properties

[ivory otter]

ok, i end up solving it, then what?

[gray isle]

and through applying trigonometric properties and rules
you can determine if your triangle has any special properties

[ivory otter]

aaaaaaah

yes yes makes sense

wow i never thought about it lol

[gray isle]

i.e. by solving the triangle you'll have determined all sides and angles

[ivory otter]

ye if one angle is 90

then its obv right angled

[gray isle]

and if you end up with an angle that is exactly 90° you have a right triangle

[ivory otter]

ye nice, thank you!

[vital tree]

Can someone help

[ionic jewel]

do you know the chain rule

[vital tree]

yes

I'm getting lost trying to find dA/dx

[ionic jewel]

ah i see

it's not a very nice calculation, but product, then power, then chain (with a power inside of it)

[vital tree]

I've got -x^2/sqrt(100-x^2) + sqrt(100-x^2)

[alpine sable]

It should be -x/sqrt(100-x^2)+sqrt(100-x^2)

[alpine sable]

Sorry you are right

[vital tree]

Can anyone help with this

[radiant coyote]

i need help

general terms of series and sequence

[alpine sable]

$\sum^8_{n=4}=-n+5$ is nonsense

[ocean seal]

Al𝟛dium

[alpine sable]

did you mean $\sum^8_{n=4}(-n+5)$?

[ocean seal]

Al𝟛dium

[alpine sable]

\sum

@radiant coyote what is your goal you are trying to archieve with that?

[radiant coyote]

uh its for my seat work

and im trying to learn it basing on the solution

[alpine sable]

okay, choose one channel to stay in, don't multipost, i'm seeing you in #q-3 as well.

please read #❓how-to-get-help as well

[radiant coyote]

im sorry

[ivory thicket]

is this taken?

Am I doing this correctly

[ivory thicket]

<@&286206848099549185>

[vale wigeon]

yes looks ok

[ivory thicket]

okay tysm, also do you know where the prime factorisation button is on a calculator

[gray isle]

dislike that : (-16+9)
in the middle of part a) though

[ivory thicket]

thats just to explain to me what im doing in that step to get ot the next line

[alpine sable]

@fading citrus I would like to be a Helper.

[gray isle]

i see what you're trying to do there, but its better to just leave it out in this case

[ivory thicket]

is this u

[gray isle]

especially since : may be used for division
if you really want to show that step in your work like that,
you're better off typing another line

[alpine sable]

Yes.

[ivory thicket]

I meant it is temporary

[gray isle]

don't think most calculators have prime factorisation

[ivory thicket]

is there a way to do it in ur head

eg. adding all the digits together

[alpine sable]

What Prime Factorization?

[ivory thicket]

like 133

cause I need to simplyfy the surds

[gray isle]

you could use division algorithms

[ivory thicket]

root(133) 1 + 3 + 3 = 7, 7 is prime thus it cant be divided? right

[gray isle]

knowing multiplication rules helps

[alpine sable]

Exactly

y

[ivory thicket]

ok

tysm

[gray isle]

ugh. that justification is a bit dodgy

[alpine sable]

@heavy otter I would like to volunteer as an helper.

[alpine sable]

Dodgy but right.

[gray isle]

in this specific example it happens to be true

[ivory thicket]

it works for all the numbers I can think of

[gray isle]

but what about something like sqrt(16)
1 + 6 = 7 is prime,
are you implying that sqrt(16) can't be simplified because 1+6 = 7 is prime?

[ivory thicket]

oh not 155

okay ill just but a calculator with a fact button lol

[gray isle]

ti84 seems to have a primefact function

[ivory thicket]

Im on my 5th calculator this year

[gray isle]

otherwise you could systematically search for prime factors if they exist

[ivory thicket]

I keep losing them

[gray isle]

knowing basic divisibility rules helps a lot

[alpine sable]

I can factor numbers up to 3 or 6030 as my form of "counting sheep" when I want to relax and sleep. It's not hard. Obviously, you only need to check primes up to the square root of the number in question. 2, 3, 5 and 11 are easy to check. Beyond that, my main trick is to quickly reduce a divisibility check to a check on a smaller number. For example, if I want to know whether 2747 is divisible by 7, that's true if and only if 2040 is, which is divisible by 7 if 204 is, which is divisible by 7 if 102 is, which is divisible by 7 iff 51 is, and it isn't. Alternatively, 2747 is divisible by 7 iff 2800-2747 = 53 is, which it isn't.
To check 13, I might subtract off 2600 to get 147, then also 130 to get 17. Or I might have started by adding 13 to get 2760 and hence 276, then subtracted 260 or 26.

To check 17 subtract it once to get 2730 and hence 273. Then add it to get 290 and hence 29.

To check 19 subtract 1900 to get 847, then 38 to get 805. Divide by 5 to get 161, add 19, and we've pretty much gotten to "no".

For 23 add it to 2747 to get 2770 and 277, then substract 230 to get 47.

2900 - 2747 = 153, which can only be divisible by 29 if it equals 29 x 7 (because else the last digit wouldn't be 3), which it doesn't.

Similarly, 31 doesn't divide 353.

2747 - 37 = 2710, and now there's a special trick, because 37 divides 111. 271 - 111 = 136. 136 - 37 = 99, which 37 obviously doesn't divide.

At 41 I'll just do a size check. 41 x 57 is too small, and 57 isn't prime anyway. 41 * 77 also couldn't work. So it's 41 x 67 or bust. That's 2400 + 280 + 60 + 7 ... and we have a winner! 2747 = 41 x 67. Checking the multiplication, (40+1) x (70-3) = 2800 + 70 - 120 - 3, which indeed works out to 2747.

@ivory thicket Did you understand?

or are you still reading?

[ivory thicket]

I understand you put effor into that but my brain is too little for this, ima just hope that on the exam we get given surds I know the prime factors of (4s 16s 36s times tables will come in handy)

there is a coeffecient of 1 there so this works right

[gray isle]

yes

[vernal igloo]

why does substitution work in system of equations? Like.. it makes sense visually, the point where they intersect is the solution for both of them, but for some reason, I can't grasp as to why solving by substitution works

[glass lichen]

the same reason visually

there's a point on each line with the same x and y value

[vernal igloo]

but, why can you just solve for.. let's say x in one of the equations and substitute it in the other equation? is it because they are or must be the same number in the end?

like, it kind of makes sense, but i can't for some reason grasp it

[glass lichen]

cause the x values are equal

the x in eqn 1 is the x in eqn 2 at the POI

[alpine sable]

or just study quadratic eqns

[ivory thicket]

does e) make sense

@alpine sable

[alpine sable]

No

[ivory thicket]

solve e) 0 = 9𝑥² - 16

I got 𝑥 : ± 4/3

ok ty

[vernal igloo]

right, so that's why you can substitute in the other equation, it's because they're the same x in both equations

[ivory thicket]

well we are learning to solve quadratic equations, so it would make sense following our methods, but solving algebracically makes sense

[twilit dune]

algebraically?

[ivory thicket]

moving the 16 over etc

[twilit dune]

how can you solve a quadratic equation nonalgebraically

[ivory thicket]

i meant like completing the square, factoring, that formula, here i used difference of 2 square rule

[twilit dune]

that's algebra...

also what is the difference of 2 square rule?

[ivory thicket]

algebracially, when I use it, means, without a predetermined mehtod, but instead using raw algebra moving the equation from one side to the other

[twilit dune]

raw algebra?

[ivory thicket]

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

[twilit dune]

oh that

[ivory thicket]

ooh whats that

[twilit dune]

yeah multionimal theorem

don;t know it

anyway

the proof for why these methods work relies on algebra, so therefore you are still doing algebra

[ivory thicket]

this method makes ssense though right

[twilit dune]

what method

[alpine sable]

(3x+4)(3x-4)

Use Identities.

[ivory thicket]

what

[alpine sable]

Identify it yourself

[ivory thicket]

whats that mean

I got the answer ? and that step you said

[alpine sable]

Sorry posted it 15 mins ago

Bad Internet

[ivory thicket]

lol k

[alpine sable]

1
Use the quadratic formula
𝑥

−
𝑏
±
𝑏
2
−
4
𝑎
𝑐
√
2
𝑎
x=\frac{-{\color{#e8710a}{b}} \pm \sqrt{{\color{#e8710a}{b}}^{2}-4{\color{#c92786}{a}}{\color{#129eaf}{c}}}}{2{\color{#c92786}{a}}}
x=2a−b±b2−4ac​​
Once in standard form, identify a, b and c from the original equation and plug them into the quadratic formula.
9
𝑥
2
−
1
6

0
9x^{2}-16=0
9x2−16=0
𝑎

9
a={\color{#c92786}{9}}
a=9
𝑏

0
b={\color{#e8710a}{0}}
b=0
𝑐

−
1
6
c={\color{#129eaf}{-16}}
c=−16
𝑥

−
0
±
0
2
−
4
⋅
9
(
−
1
6
)
√
2
⋅
9
x=\frac{-{\color{#e8710a}{0}} \pm \sqrt{{\color{#e8710a}{0}}^{2}-4 \cdot {\color{#c92786}{9}}({\color{#129eaf}{-16}})}}{2 \cdot {\color{#c92786}{9}}}
x=2⋅9−0±02−4⋅9(−16)​​
2
Simplify
Evaluate the exponent
Multiply the numbers
Add the numbers
Evaluate the square root
Multiply the numbers
𝑥

0
±
2
4
1
8
x=\frac{0 \pm 24}{18}
x=180±24​
3
Separate the equations
To solve for the unknown variable, separate into two equations: one with a plus and the other with a minus.
𝑥

0
+
2
4
1
8
x=\frac{0+24}{18}
x=180+24​
𝑥

0
−
2
4
1
8
x=\frac{0-24}{18}
x=180−24​
4
Solve
Rearrange and isolate the variable to find each solution
𝑥

4
3
x=\frac{4}{3}
x=34​
𝑥

−
4
3
x=-\frac{4}{3}
x=−34​
Solution
𝑥

4
3
𝑥

−
4
3

[twilit dune]

wtf

[ivory thicket]

our class hasnt learnt it yet

well, i do know it

[twilit dune]

your class hasn't learnt the quadratic formula yet?

[ivory thicket]

its -b root(b^2 - 4ac)/2a right? im not good at memory

[twilit dune]

er use latex if you know how to

[alpine sable]

Well, I have learned it in KinderGarden.

[twilit dune]

nice

[alpine sable]

Are mods asleep

?

[ivory thicket]

im in year 10 okay lol

[alpine sable]

I asked for helper.

[twilit dune]

wait what?!

[ivory thicket]

yea

[twilit dune]

my country doesn't even have math competition stuff

not even in the IMO lol

[ivory thicket]

Im always the top of my class in maths, but not good enough to do competitions for it (I won a few gold metals when I was younger but I gave up lol)

[alpine sable]

Just search my name on google

[twilit dune]

YOU ARE AT THE TOP!?!?!

which country is this

[ivory thicket]

im not even at the top, im like massivley above the rest

Australia

[twilit dune]

and also you are measuring years since like grade 1 right?

[ivory thicket]

others in my class are still trying to figure out why the equation = 0.

[twilit dune]

no trying to be condescending, i'm just perplexed :p

[alpine sable]

I am a canadian and education is very-I literally mean very important

Transferred.

[ivory thicket]

prep yr 1, yr 2... yr 6 (HIGH school starts yr 7.) ... yr. 10

[twilit dune]

ok so yr 1,2 are just kindergarten?

what age is year 1?

[ivory thicket]

no kindy is before prep

[ivory thicket]

5/6 depending on if born before /after june

[twilit dune]

well alright

anyway did you get the help you wanted?

[ivory thicket]

yes tysm good night

[twilit dune]

cheers!

[burnt meadow]

Can someone help me with this question?

[twilit dune]

oh

ok so the surface area equation is $S=4{\pi}r^2$ right?

[ocean seal]

alshfik

[burnt meadow]

yep

[twilit dune]

so yo just need to multiply the raidus here by 0.955 then

do you agree with this step?

[burnt meadow]

multiply what?

the SA?

[twilit dune]

the radius

the radius is r

[burnt meadow]

ah yeah

[twilit dune]

and then the equation becomes $S=4{\pi}(r*0.955)^2$

[ocean seal]

alshfik

[burnt meadow]

but its decreasing over time no?

[twilit dune]

im confused about the question though

is the answer supossed to be a function? a ratio?

[burnt meadow]

its supposed to be a ratio

as its decreasing by 4.5%

over time

how much does the SA decrease by

overtime

as a percentage

[twilit dune]

ok so we don't need to worry about the "over time" part if its not a function

[burnt meadow]

uh ok

[twilit dune]

we just need to know that there is a sphere, and a sphere with a radius 4.5% smaller

4.5% smaller just translates to multiply by 0.955

we get $S=4{\pi}(r*0.955)^2$

[ocean seal]

alshfik

[burnt meadow]

ok

[twilit dune]

then we can use the exponent for both r and 0.955

[burnt meadow]

uh huh

[twilit dune]

$S=4{\pi}r^2(0.912025)$

[ocean seal]

alshfik

[twilit dune]

dividing this by the original surface area of a sphere function we get 0.912025

so given the radius of a sphere, if it shrinks by 4.5%, the surface area decreases by 8.7975%

[burnt meadow]

ahhh ok

tyty

[misty holly]

10 [𝑛 = 0.88 … ] Multiply 10
10 𝑛 = 8.88 …
− 𝑛 = 0.88 … Subtract 𝑛 = 0.88 from 10 𝑛 = 8.88 …

9 𝑛 = 8 Divide by 9

---

9 9

𝑛 =8
-
9

uhm, i just wanna confirm something, so, can someone explain this a bit?

9 𝑛

9

btw, the two nines here are with a slash in the middle

[vale wigeon]

9n/9 = 8/9

just to type that equation of yours into a more plaintext-friendly format

you're confused about something to with the fraction 9n/9?

[misty holly]

uhh no, i sometimes get lost when solving with this algorithm, bcuz it is poorly explained in my opinion, so, i was wondering if anyone here could explain this a bit more detailed

[vale wigeon]

the reason we subtract 10n - n is to cancel out the repeating part so we have a whole number (or terminating decimal) on the right-hand side

[misty holly]

so, all in all, we multiply n by 10, subtract n from product....actually, the part where i'm confused with is "Divide by 9" why do we still have to divide when we could just write 9 as denominator right away?

[vale wigeon]

..."write 9 as denominator" and "divide by 9" are the same thing

[glacial kernel]

i need help

[vale wigeon]

@glacial kernel

channel busy please move

[glacial kernel]

ok

[misty holly]

well, is what i posted the full algo? or am i missing something? besides from the simplifying part

[vale wigeon]

@alpine sable channel busy please move

[vale wigeon]

it pretty much is the full algorithm yes

[misty holly]

9 𝑛

9
with a slash in the middle

why do we have to write this?

[vale wigeon]

what do you mean

i have no idea what you're talking about right now

[misty holly]

wait, brb

why do we have to write this and not just 8/9 directly?

[alpine sable]

When do you use index numbers and when do you use the formula difference / initial value * 100

what is the difference

[crude wave]

anyone know how to do vectors

[small flint]

hey

help

please

4. A sprint cyclist starts from rest and accelerates at 1 m/s from rest and accelerates at 1m/s2 for 20 seconds. He then travels at a constant speed for 1 minute and finally decelerates at 2 m/s2 until he stops. Find his maximum speed in km/h and the total distance covered in metres. (20)

how does he speed up

sorry witch one is the acceleration.

@everyone

[mossy stream]

He speeds up at a constant acceleration then maintains said acceleration and finally slows down. It wants the max speed which can be found at the very end of his period of acceleration. Since it’s 1 m/s^2 for 20 seconds it’s easy to find (just multiply them together)

This problem seems like more of an exercise in unit conversation because it gives you the problem in meters and seconds and wants the answer in km/h

[alpine sable]

Don't know the first step

[golden arch]

a²-b² = (a-b)(a+b) maybe?

[golden arch]

What would be the easiest way to calculate A² and A³

[inland shale]

can u help with this

[alpine sable]

I guess just multiply? Not sure how diagonalisation would work here.

[alpine sable]

Do you know what pythagoras’ theorem is?

[inland shale]

yes

i do

but i dont know how to solve it

like what numbers u plugin

.

[halcyon geode]

Dude, don't spam 7 channels

[inland shale]

ok

sorry

i just wanted to know how to solve the question

[sage bronze]

as it is a isosceles triangle

the height (h) bisects the base

so base=4

and hypotenuse is given 5

now you can solve for h

[ancient saddle]

Hello, I guess this is a rotation matrix in 2D. Applying once this rotation matrix, you get a φ degrees or rad rotation. If you apply it one more time (A^2), then you get anoher rotation of φ degrees or rad. The total effect is a rotation of 2φ

[ancient saddle]

then, for A^2 you can just plug 2φ in this matrix, and so on for higher powers

[inland shale]

it is 3

right

but it says to round to nearest tenth

so my answer must be wrong

@sage bronze

[sage bronze]

Its right

3 should be the correct answer

[sage bronze]

Not really no

[inland shale]

ok

i got it

[sage bronze]

Alright

[inland shale]

this was my last question

i dont not know what to do since they are including 2 shpheres

what would i do @sage bronze

[sage bronze]

Do you know

The formula for the volume of

[inland shale]

sphere

[sage bronze]

A cylinder

[inland shale]

yes

[inland shale]

mhm

that too

[sage bronze]

Ok

[inland shale]

pie r2h

[sage bronze]

Ok

So apply that here

[inland shale]

so what numbers would i plugin

[sage bronze]

U know r and you have the height for the big can

Find the volume

[inland shale]

yes

so then what do i do for the small can

?

[sage bronze]

Then it is given that only 1/4 can is filled

So volume of the liquid will be?

@inland shale

[inland shale]

um

i only know the volume for the clinder

but not the sphere

so do i solve for the sphere

[sage bronze]

No one has asked

For volume of a sphere

[inland shale]

oh yea

[inland shale]

wait

i think i got it

i think i solve for cylinder

and then i multiply by 1.4

correct

[sage bronze]

Yes

U get the volume of the second smaller can

From there its just simple algebra

[inland shale]

yea

thank you man

[sage bronze]

Ur welcome

[inland shale]

ok

i got 320

after solving the volume of the cylinder

and multiplying by 1/4

so should that be my answer

@sage bronze

[sage bronze]

Wait

[inland shale]

ok

[sage bronze]

320 wont be the answer

[inland shale]

ok

i did that after solving for the clinder nd multiplying by 1/4

[inland shale]

so should i multiply that by the volume of sphere

@sage bronze

[sage bronze]

Where is the sphere coming from

Again

[inland shale]

not sphere sorry

the smaller can

[sage bronze]

There are no spheres

[inland shale]

the smaller can

[sage bronze]

Ok

U will get

[inland shale]

would that be right?

[sage bronze]

6420pi/4 = volume of the smaller can

Shit

[inland shale]

im just asking

[sage bronze]

64x20xpi/4

Then

[inland shale]

do i multiply my value of the volume of the cylinder that was multiplied by 1/4

to the smaller can

?

to get my answer

[jade canyon]

～

[sage bronze]

I dont understand what u mean

By that

Lemme write it out

[inland shale]

scratch that

just tell me what to do

after i multiplied my cylinder 1/4

[sage bronze]

Ok

[inland shale]

cause i got 320

thats my answer

know what do i do

*now

[sage bronze]

320 pi is the volume of the smaller can

Now

Radius of the smaller can is 5 cm

[inland shale]

ok

[sage bronze]

Volume will be pi r^2 h

That is pi x 25 x h

[inland shale]

bro

[sage bronze]

Do u understand this

[inland shale]

how do i get the height of the smaller can

it doesnt tell me

[sage bronze]

Ill get to it

Now

[inland shale]

ok

[sage bronze]

U know that 320 pi is the volume of the smaller can from the calculations above

[inland shale]

yes

i know that

[sage bronze]

Therefore

$320 \pi = 25\pi \times h$

[ocean seal]

HELLOBELLO

[sage bronze]

Now solve for h

Thats it

[inland shale]

ok

thanks

its 64/5

[sage bronze]

Ur welcome

[inland shale]

thats the answer

[sage bronze]

Yeah

[arctic wren]

I'm studying Taylor polynomials and i don't get why df(X) = f'(X0)*dX

[alpine sable]

I am so lost with factoring quadratics that have a>1

there are so few resources online that explain it

[alpine sable]

Drow Ranger.

[ionic jewel]

AC method or just quadratic equation

[alpine sable]

yep I'm watching the ac method

there's almost never any explanation as to why steps are done

just "hey do this"

[ionic jewel]

the proof isn't trivial at your level of math iirc

ur just gonna have to trust it

[alpine sable]

why don't they just teach it in ways that students can understand?

instead of just "trust me"

surely the first mathematitican who discovered it had to actually understand the underlying mechanisms

he didn't have the rules

[ionic jewel]

wait do you not understand how to apply it, or not understand why it works?

[alpine sable]

so like this for example

the dude gave zero explanation as to where that -1 came from

just wrote it as if I knew where it came from

[ionic jewel]

have you considered not being toxic

[alpine sable]

you're right someone who's watching a math tutorial doesn't yet understand the concept they're watching a tutorial on

crazy idea

[ionic jewel]

i saw your conversation in the other channels

[alpine sable]

I get what a lcm is

no I started learning what quadratics are like 4 days ago

[jolly stone]

what don't you get on that part?

[alpine sable]

it's all just numbers and formulas to me for the most part

[jolly stone]

on why it has -1?

[alpine sable]

<@&268886789983436800>

[sly mantle]

@upper ice knock off the condescension

[jolly stone]

you see the term 6x^2 - 3x + 8x - 4 right? we will try to factor first two terms and last two terms

[alpine sable]

you're an idiot if you think that would help in any way

you don't though, you're just an asshole.

That ain’t pressure that’s just insults

[sly mantle]

insults are never justified. keep it up & you're out

[jolly stone]

just ignore it, i studied quadratic equations back in elementary school and i dont even brag lol i wanna help you as fast as possible here so please cooperate with me first then deal with that later

[alpine sable]

Yeah

[jolly stone]

what are the first two term's common factor? and the last two terms?

[sly mantle]

we can also do without the incessant pings

[alpine sable]

exactly it’s quite annoying about how they do that in most videos but here’s why the AC method works:

[sly mantle]

you're on thin ice. continuing to be abrasive doesn't help your case

[alpine sable]

so a quadratic equation is of the form (ax-b)(cx-d)

then when you multiply out the terms you get acx^2-bcx-dax-bd

[rose geode]

is this channel full

[alpine sable]

It’s currently busy but soon it won’t I hope

[rose geode]

is is it full you not

is it full or not damn auto correct

[alpine sable]

i don’t think right now the person who posed the question is active, so feel free to ask

[rose geode]

ok

i’m kinda lost

that’s the problem i don’t know what to do the teacher did not explain how to do them

[jolly stone]

what have you learned so far?

we can scope the required knowledge to solve this

tbh that's a pretty weird question lol

[rose geode]

don’t have a text book it is through a online academy and i can’t just ask a teacher question any time

[jolly stone]

what grade are you? no need to answer if it's personal

[rose geode]

i just need to finish this class so i can go back to school i will be in 11th

[jolly stone]

have you learned of law of sines yet?

[alpine sable]

<@&268886789983436800> I don't know why NFX is still allowed here. He has repeatedly made it clear that he's only on this server to boost his ego by giving condescending remarks to people with genuine questions

[rose geode]

nope this is geometry

[alpine sable]

He makes this a toxic learning environment

[jolly stone]

yeah it's geometry, i was asking if you've ever learned that yet

[rose geode]

no i haven’t

[jolly stone]

hmm

still have no idea to solve that when you can't use law of sines

[rose geode]

The way my school system words inside to pre-algebra, algebra one, geometry, and then I will take algebra two

[ionic jewel]

+1

[jolly stone]

just in case, check glossary if your textbook (online?) has law of sines

[alpine sable]

that can’t possibly be a genuine question

[jolly stone]

if yes, it might be needed to solve that

[night geyser]

apparently not

bye friend

[rose geode]

I don’t have a text book this Academy is retarded

[jolly stone]

damn finally i was so annoyed lol

thank you

[alpine sable]

GJ mods

[jolly stone]

eh? and what do you use to learn this?

no materials at all, just classes?

[rose geode]

we whack a 5-10 minute video of the teacher talking then they give me questions that’s why i need to just get back into real school

watch

[jolly stone]

thats one problem but how do you even review materials?

[alpine sable]

oh just use the triangle inequality

are you aware of it?

[rose geode]

I have struggled in geometry all year because of the stupid academy so I don’t really know I am taking again when I go back to real school

[alpine sable]

Someone help

[alpine sable]

Ah man that feels bad. Anyway, I’ll explain it with a picture

[alpine sable]

Channel’s busy

[jolly stone]

so also not law of cosine also?

damn that is bad

i mean the school's education system

[rose geode]

@jolly stone i don’t know what that is

[jolly stone]

tbh i'm still trying to solve that, given no knowledge beyond grade 10

[rose geode]

that is why i need to be back in a class room i have always been advanced in math till now

[alpine sable]

Look at the top picture

[alpine sable]

Yeah I had that same phase during the first wave of COVID

Basically, the length of the third side of any triangle is less than the sum of the two other sides.

And the length of any third side of a triangle is greater than the difference between the two other sides.

[rose geode]

ok got the first part

@alpine sable @jolly stone thx guys you saved me kinda

i got the full thing right

[jolly stone]

what was the last one? i'm a bit curious

[shut elk]

canine just fyi, you shouldn't use this for help with marked exams, not saying you were

just in the event that u were

[alpine sable]

Nice GJ

[jolly stone]

and i gotta say frankly, x = 2.0000001 probably isn't possible

[rose geode]

i’m not on an exam i’m at home going through a online academy @shut elk

[jolly stone]

what's the answer for second part x < ?

[alpine sable]

that is true because it would mean that the hypotenuse is less than one of the two other sides.

[rose geode]

i got 7 and it said correct idk how but this academy mis called acellus

is not mis

[jolly stone]

do they have solution?

[rose geode]

when i answer all it says is☑️or❌

[jolly stone]

that's alright

[alpine sable]

hm that sounds a bit off to me.

Oh actually never mind I misread it.

[rose geode]

well thx @alpine sable @jolly stone have a good day

[jolly stone]

no problem! i still have problems with that problem lol

it felt extremely off lol

[alpine sable]

you too, well it’s night for me lol

[rose geode]

lol is 3:45 PM

[jolly stone]

not sure if it's even worth asking but basically

[elder cloud]

what’s 2+2?

[jolly stone]

let y be the common side between 2 triangles

[rose geode]

4

[elder cloud]

damn

i got Abraham Lincoln

[jolly stone]

we can choose y as large as possible, to achieve that 5x-10 just slightly approaches 25, but less than 25

so that means 5x-10 < 25, then x < 7

[rose geode]

yea

[elder cloud]

i think you’re wrong tho

[jolly stone]

because the angle of left side is 85, less than 90, 5x-10 must be less than 25

[rose geode]

yes you correct

[elder cloud]

i knew it

[rose geode]

not you dumb ass @elder cloud

[elder cloud]

why you gotta do me like that 😔

[alpine sable]

bro don’t insult people like that

[jolly stone]

i still have no idea how to achieve x > 2

[rose geode]

sorry @alpine sable

[alpine sable]

i guess 5x-10 = 0 where x = 2, so x>2

[elder cloud]

you a real one 😔😎

[jolly stone]

can't say x > 2 just because 5x-10 > 0, because it's pretty much impossible to construct a very small length given that configuration

[rose geode]

@elder cloud i’m in here bc i actually needed help so that is why you kinda got on my nerves

[elder cloud]

💀 you could have ignored me yk

[sly mantle]

@elder cloud stop trolling

[elder cloud]

ight mb mb

[jolly stone]

there exists a minimum of 5x-10, but the number's not gonna be pretty

[elder cloud]

i do got a question tho

[sly mantle]

ask in an unoccupied channel

[elder cloud]

whats 41+93x281-x

[alpine sable]

I have a question

well you can’t ask it if it’s a test.

Listen to me

[sly mantle]

are you actually 8?

[alpine sable]

I have a question

can’t have discord then

[sly mantle]

b&

[alpine sable]

I have a question

[alpine sable]

alright go on

[elder cloud]

bruh no one answered mine

[alpine sable]

Are you smart enough??

To answer my question

[alpine sable]

it was unclear because first you used x for multiplication I assume and then as a variable and it wasn’t an equality it was an expression

[alpine sable]

Hopefully

Okay

[elder cloud]

ohhh okay okay ty so much

[alpine sable]

Listen here

Find The min and max values of |z|

Alright let me work it out on paper and I’ll get back to you

Ok

Don't take too much time

Sure

[jolly stone]

i just did the math, the minimum of 5x-10 is actually 25*sin(85deg) ~ 24.905

so obviously their solution is wrong

[elder cloud]

@ripe bolt

oh shoot

[ripe bolt]

hi

[elder cloud]

yes hi

[ripe bolt]

woah

math

how are yall so good at math

[alpine sable]

k so we write z of the form z = x+yi