help-10

[honest flicker]

50% because there are 4 possible ways for the exam to turn out, and 2 out of the 4 is getting exactly one right

[civic zealot]

yes

[honest flicker]

WOOOOOO

[timid silo]

Would you be able to answer the following:
What are the chances you guess two answers right after rolling the dice three times

[honest flicker]

Nah

I'm out

How to clise

!close

!end

.close

[obtuse pebble]

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[obtuse pebble]

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[ancient needle]

hi can someone verify that i have the correct answers here?

[ancient needle]

the topic is key features of an absolute value function

ty 😊

[glossy basalt]

let's check

,w graph y=0.5abs(x+1)-1

[warm shale]

Results provided by WolframAlpha

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

Requested by biscuityxd

[glossy basalt]

graph good

you need to correct:
increasing interval
decreasing interval

[ancient needle]

hm what's wrong with that?

[glossy basalt]

oh wait

[ancient needle]

i wrote them in interval notation

[glossy basalt]

my bad

[ancient needle]

👍

[glossy basalt]

lol

all good

[ancient needle]

thank you sm!

i have another question if that's alright with u?

[glossy basalt]

do post

[ancient needle]

ok

so my teacher says that this is the positive interval for this function

instead of (negative infinity, positive infinity)

im not sure how (-4,0) separates the graph for us to use U here

could you explain why here? i kind of have trouble with understanding that

and i also have trouble understanding why we would use parentheses () instead of brackets [] for some problems regarding the vertex here

my teacher never explained the logic or reasoning for this

[glossy basalt]

it's just split the interval (-infty,infty) at x=-4

ohhhh that's why

[glossy basalt]

x in (a,b) means a<x<b
x in [a,b] means a≤x≤b

[ancient needle]

ah alright

[ancient needle]

so will this only work when the vertex is on the x axis?

or if a point is on an axis

[ancient needle]

like if this graph was shifted up we wouldnt use U

[glossy basalt]

well, Positive means number like 1,2,3 or ½ or pi or √2
but not 0

so, when the y value is 0, i.e. the point is on the x-axis, we need to exclude that point from "positive interval(s)"

[ancient needle]

ohh ok i get it

yeah because our teacher told us that positive interval expresses points above the line y = 0

which is the x-axis

[glossy basalt]

yep

[ancient needle]

i also have one final question here

[glossy basalt]

yea?

[ancient needle]

so our teacher tried showing us the reason for why an absolute value graph will move the opposite direction when you translate it left or right

he just made a table and drew some graphs

but i thought the reasoning would be that youre only substituting the amount you shift it by into h only, not -h

[glossy basalt]

it's hard to spot left or right eith abs value graphs

[ancient needle]

so if you wanted to move it left 4 units, it'd be: x-(-4) which is x+4

that's what i thought

[glossy basalt]

try reading graphs like y=x²

shift left by 1 unit would be
y=(x-(-1))²

and generally

y=f(x-h)

shift left is when h is negative, right when h is positive

your teacher might just want you to remember it's opposite sign (-) for movement along x-axis, and same sign (+) for movement along y-axis

[ancient needle]

yeah

ok thank you so much! this helped me sm ❤️

.close

[obtuse pebble]

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[quick arch]

Hello I really need help with this question

[nocturne minnow]

Why did you close your previous channel?

[quick arch]

I kept waiting and no one answered

[nocturne minnow]

You waited 11 minutes... You can wait longer, you don't need to bump your question to the top

[urban patrol]

why dont you look up a video on this topic

its very simple

[quick arch]

I did but they are very different examples

and I'm not really understanding it

.close

[obtuse pebble]

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[jagged hawk]

Not sure what I should do

[glossy basalt]

did you try finding the height of the coorespdoning base AB of triangle ABC?

[jagged hawk]

?

[glossy basalt]

?

[jagged hawk]

what is corresponding base

[glossy basalt]

like height of the triangle with base AB

[jagged hawk]

isn’t that k/sintheta

[jagged hawk]

r u talking abt AC or BC

[glossy basalt]

nah, k/sin(theta) is just AC

[glossy basalt]

I'm talking about an imaginary line

[jagged hawk]

Ohh

wait like this

[glossy basalt]

nah

[jagged hawk]

Then where

Oh wait

ic

[jagged hawk]

how would u find that

[glossy basalt]

of course using beta

can you see the angle which is 180°-beta?

use that

to find the height

[jagged hawk]

Ohhh

and use AC ?

[glossy basalt]

yep!

[jagged hawk]

ok is it this

[glossy basalt]

yes and you can use CE to find AC

[jagged hawk]

Didn’t we already find AC ?

[glossy basalt]

ouch

typo

BC

hehe, sorry

[jagged hawk]

oh yea it’s fine

This is what I got for BC

[spice sleet]

Am I able to send my math question here ?

[jagged hawk]

Send in empty channel

[jagged hawk]

what do I do next

NVM

I SOLVED IT!!

Ty

.close

[obtuse pebble]

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[obtuse pebble]

@uneven night Has your question been resolved?

[uneven night]

.close

[obtuse pebble]

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[leaden dust]

help

[leaden dust]

i understand this step until check mark

okay same base 3 negative nine and 3 to power 2 right

so if its the same base and ur diving u had to subtract

right?>

so wouldnt it be

same base 3^(-9+2) so equal 3^-7

minus nine plus 2 gonna equal negative 7

so how he get 11

how

[shut lagoon]

You didn't subtract though

[leaden dust]

right but for the exponent rules

if u had dision

u need to subract

[shut lagoon]

Yes

But you added them

[leaden dust]

right so if u add them minus nine plus 2 is gonna equal you 3 base power negative 7

so how he get negative 11

how

[polar fossil]

why are you adding them

[shut lagoon]

-9-2

Not -9 + 2

[polar fossil]

top - bottom

[leaden dust]

wtf

https://media.discordapp.net/attachments/1125307329814986752/1128066974354767953/IMG_4869.png?width=266&height=577

i still dont get it lol

can u re explain it officer?

[polar fossil]

um i think the negative signs might be confusing you?

if you had like $\frac{5^{11}}{5^3}$ what would that be?

[royal basin]

"officer?" what do we look like, cops?

[warm shale]

hailey

[leaden dust]

that would be same base but then addition rite

5 to the power of 14

[zenith spade]

what

[polar fossil]

,tex .exp rules

[leaden dust]

5 base power of 14

[warm shale]

hailey

[polar fossil]

look at Quotient Rule

[zenith spade]

You literally said this at the start

This is correct

[royal basin]

incorrect. but also, use the symbol ^ for exponents.

5^11/5^3 is not equal to 5^14.

[leaden dust]

roasted 🔥

lol

give me a second to think

one sec

🤔

[leaden dust]

same base exponent 11 minus 3 so same base ( 5) exponent 8?

right?

[polar fossil]

yes that's correct

[leaden dust]

OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOH

[royal basin]

this is not a roast.

[polar fossil]

i think you just had your wires crossed

[royal basin]

having your mistakes pointed out to you is not a roast.

[leaden dust]

I GET IT now ngl

feel mad stupid rn

🤣

[polar fossil]

okay, so let's return to the original problem

of $\frac{3^{-9}}{3^2}$

[warm shale]

hailey

[leaden dust]

same base 3, base 3 power of minus 9 minus 2 (--) make negative 11 exponent and base 3

[polar fossil]

yeah so 3^-11

i'd recommend holding onto that image i posted

the one with the rules

you may have a similar chart in your book somewhere

[royal basin]

also you should still use the symbol ^.

it's most likely shift+6 on your keyboard if you are on pc.

[leaden dust]

bet

[leaden dust]

yep i get it, actually i know the rule too but for some reason my brain had a stroke tryna solve and read that problem lol ye but thnx for the clarification

/close

/closeticket

[polar fossil]

.close

[obtuse pebble]

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[stuck herald]

not able to get the answer for this

i have equated them but can't find k

[flat sparrow]

In an undirected random graph of 8 vertices, the probability of an edge being present between a pair of vertices in 1/2. What is the expected number of unordered cycles of length 4?

Actually there was a similar question for cycle length of 3.
It's answer was 8C3 × (1/2)^3.

Based on that for 4 length cycle I thought it would be 8C4 × (1/2)^4. But I think this is wrong because there are also structures with 4 vertices and 4 edges which doesn't forms a cycle.

[polar fossil]

hi, I think you got unlucky and tom posted before you. You should move your question into an available help channel

[polar fossil]

can you show your work?

[stuck herald]

yeah

[polar fossil]

[stuck herald]

oh it should be zero

[polar fossil]

yep

[stuck herald]

my bad

[zenith spade]

f(x) = f(-x) implies the function is even

So yeah, fun fact

[stuck herald]

yes right

[zenith spade]

And a polynomial can only be even if all the degrees of x are even

So that’s another way you could have concluded k is zero

[stuck herald]

true

[stuck herald]

thanks!

.close

[obtuse pebble]

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[surreal carbon]

Hey need some help to move on from here

[haughty coyote]

Do it again

(the IBP, that is)

Then see what a second IBP gives you

[surreal carbon]

but will it not just keep repeating itself?

[haughty coyote]

Not if you notice something

[surreal carbon]

ahh minus * minus makes positive saw that

[haughty coyote]

Then notice that ||you get an equation in the integral you want||

[obtuse pebble]

@surreal carbon Has your question been resolved?

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@bright plaza Has your question been resolved?

[harsh remnant]

Which quadrants give a negative value for tangent?

And what value theta does return -√3?

or √3 in general

[obtuse pebble]

@bright plaza Has your question been resolved?

[obtuse pebble]

@bright plaza Has your question been resolved?

[obtuse pebble]

@bright plaza Has your question been resolved?

[gilded topaz]

@bright plaza you are on the right track, two of the four you circled work, try to find which.

For a rigorous proof, you could let $\sin \theta=x$ and $\cos \theta = -\sqrt{1-x^2}$ and solve for $x.$

[warm shale]

lpieleanu

[obtuse pebble]

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[untold warren]

I understand how (x-1)/(1-x)=-1 but how can that logic not be applied to (a-b)/(b-a)≠-1?

[zenith raft]

whaaat

[ruby path]

Can we have the original question

[civic zealot]

unless a=b that is also -1

[untold warren]

okay i knew it was something along the lines of that thank you

.close

[obtuse pebble]

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[slate hamlet]

This is the answer I get for this limit

However the ans says it does not exist

[frank monolith]

you forgot to replace the x with pi/3 - h of cos6x

[ripe knoll]

you cant partially put limits

you have a term with x in it

you need to convert all terms in h

[slate hamlet]

Gotcha

My bad

Thanks

,closed l

Wow

.close

[obtuse pebble]

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[pseudo void]

Which formula to use to solve this?

[frank monolith]

no formula, integrate it!

[slate hamlet]

I dont think they need to integrate it, they have a distance time relation

cant they just find distance travelled at 1s and 3s?

Well

Thats basically integrating it

[frank monolith]

also at t = 3. x = 0

[pseudo void]

Ok thanks

[pulsar quarry]

welcome

ques?

what

no

wheres the ques tho

[tardy epoch]

!help

[obtuse pebble]

Please read #❓how-to-get-help

[tardy epoch]

Open a new channel

[pulsar quarry]

wait

why should he?

if the person is already done with his doubt

[civic zealot]

It's the rules, read #❓how-to-get-help

[pulsar quarry]

ik

[pseudo void]

.close

[obtuse pebble]

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[inland thicket]

Does anyone know what ! means?

[kind hawk]

factorial

[inland thicket]

[kind hawk]

n! = n*(n-1)*(n-2)*...*3*2*1

[inland thicket]

hmm

i got same result without ! stress

[kind hawk]

yes 2! is just 2*1=2

[inland thicket]

hmmmmmmm

so ! = *1

[kind hawk]

no

[inland thicket]

⚔️ Math War⚔️

[kind hawk]

3! = 3*2*1 = 6

[inland thicket]

woah

Woah

Woah

[kind hawk]

5! = 5*4*3*2*1=120

[inland thicket]

OH

https://tenor.com/view/evolution-ape-man-homo-sapiens-modern-man-gif-8726299

now im math pro

👍

[royal basin]

https://sr.wikipedia.org/wiki/Факторијел

[inland thicket]

.close

[obtuse pebble]

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[obtuse pebble]

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[pseudo void]

Hi i tried to intrigate from t 1 to 2 but the answer is not matching

[haughty coyote]

You're not supposed to integrate

[timid silo]

Just put in the values and then subtract

As the body is moving along a straight line

[hexed gull]

ys just insert the values

position(3s)-position(1s) = distance travelled

[true summit]

displacement

shouldnt it be displacement

the one you talking about

[timid silo]

No

I mean yes

[true summit]

AH

STRIAGHT LINE

FHNKDF

sorry

[timid silo]

But both are same, as particle/object is travelling in straight line

Yeah

@pseudo void

Got it?

[pseudo void]

Yea thanks

The answer is 2m

[obtuse pebble]

@pseudo void Has your question been resolved?

[timid silo]

even in a straight line, displacement and distance aren't always the same

you have to check when the velocity is 0

[timid silo]

? When you travel in a straight line in the same direction

in the same direction sure but velocity can still be positive or negative

Along a straight line means body keeps moving in same direction

no it doesnt

along a straight line means it moves in the x-axis only and not on any other axes

doesn't mean it's only positive x or negative x, it can be both

[obtuse pebble]

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[knotty matrix]

Dead

[royal basin]

i'd say not to call me bro but you're pretty overt in stating you are transphobic

[royal basin]

b& ?

[knotty matrix]

Yee

[royal basin]

ty

.close

[obtuse pebble]

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[pulsar quarry]

wait

why

[royal basin]

this person not only has a racist slur in his profile, TWICE, but is also bigoted enough to DIRECTLY put "anti lgbtq" in his profile.

@pulsar quarry

[obtuse pebble]

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[fathom flicker]

don't use the help channels to troll

.close

[obtuse pebble]

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[tardy epoch]

<@&268886789983436800>

[pulsar quarry]

no space btw

dont troll tho

[fathom flicker]

he clearly does not need to know how to reopen the channel yamdoot

[balmy mortar]

<@&1047243315935969371>

[hot hazel]

.close

[obtuse pebble]

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[storm bay]

how did they do this?

from left to right

I understand the denominator

but not the numerator

nvm I see it now lol

but I wonder how they see this

without knowing it beforehand

whats the strategy to factor like that

[tardy epoch]

3 * (s+2) = ?

[storm bay]

I see how its done

I just dont see how they figure it out in order to solve the task

when you start with the first part

how do you figure out the rest

in order to solve the laplace

feels like u must think so far ahead

[tardy epoch]

yes work backwards

common technique in math

[obtuse pebble]

@storm bay Has your question been resolved?

[obtuse pebble]

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[worn quail]

Hello everyone! I would be very grateful if someone could help me.
I am trying to make a formula to automatically calculate the value of "B" with the given examples.
We have "X" and "Y" position in the world. They both start from 0. We also have "A" and "B" numbers, they both start from 100 and they are related, when "A" grows it affects "B" and it shrinks. "A" corresponds to the "X" position, they are linked. "B" corresponds to the "Y" position, they are linked. Here are more examples of "X" and "Y" positions in the world and the correct values for "A" and "B" at these coordinates:

When "X" is 0 and "Y" is 0, then "A" is 100 and "B" is 100.
When "X" is 100 and "Y" is 0, then "A" is 200 and "B" is 100.
When "X" is 200 and "Y" is 0, then "A" is 300 and "B" is 100.
When "X" is 0 and "Y" is 100, then "A" is 100 and "B" is 166.6666.
When "X" is 100 and "Y" is 100, then "A" is 200 and "B" is 150.
When "X" is 200 and "Y" is 100, then "A" is 300 and "B" is 133.3333.

What will be the right formula to calculate any other values of "B" when we have any other positions of "X" and "Y". When searching for "B" the formula must include "A" (just a reminder they are related).

[obtuse pebble]

@worn quail Has your question been resolved?

[obtuse pebble]

@worn quail Has your question been resolved?

[worn quail]

<@&286206848099549185>

[sweet cobalt]

Well it's clear A = X + 100

Do you have any ideas about B, I'm a bit stumped atm

[worn quail]

Thank you for the reply. Yes A = X + 100

"B" is the problem here... I tried many ways, but without success so far

[sweet cobalt]

An interesting observation about the decimal parts, they appear to be multiples of eachother

[worn quail]

Three full days in a row sweating over this formula. I don't know if I should include more details about what this is, because it may become even more complicated.

[worn quail]

It's a two dimensional solution for 3d world (minimap) HUD system... There are 2 joints (bones) and they are connected. When joint A scale up it affects joint B. So at the beginning joint A and B are scale 100, but for example joint A become scale 200 and joint B also automatically become scale 200, because it is after it and they are connected. I need to scale down joint B to its original size and then apply to it the next number, which is the Z position of the player in the world (I transform it to Y). Scale 100 means 100%.

[obtuse pebble]

@worn quail Has your question been resolved?

[obtuse pebble]

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[pine badger]

i need help finding the distance between 2 points

[shadow tangle]

Looks good so far, are you having trouble proceeding from here?

[pine badger]

im answering a quiz right now and i keep getting the wrong answer

i assume its maybe because im substituting wrong

[shadow tangle]

Oh we can't help with quizzes

[pine badger]

oh nah i just need help with figuring out how to go from here

and also figuring out what my mistake was

that resulted in a wrong

[shadow tangle]

Nope, srry but asking for help on a quiz is cheating and that's not condoned

[pine badger]

unfortunate, but ty anyways

[shadow tangle]

Just look over your work carefully and I'm sure you'll get it 👍

[obtuse pebble]

@pine badger Has your question been resolved?

[shadow tangle]

@pine badger don't forget to close the channel when you are done.

[obtuse pebble]

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[tidal comet]

Can someone help me with this I’m stuck on the part let delta<=1

[tidal comet]

I have to prove this limit

[obtuse pebble]

@tidal comet Has your question been resolved?

[tidal comet]

<@&286206848099549185>

does anyone know if you have |-5x+5|<ε can it become -5|x-1|<ε

|x-1|<-ε/5?

.close

[obtuse pebble]

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[fathom flicker]

This is a system of 2 equations, but the first is second order and the second is first order

I should expect 3 arbitrary constants in my solution right?

[obtuse pebble]

@fathom flicker Has your question been resolved?

[fathom flicker]

,w y''+5/2 y'+y/2=-5

[warm shale]

Results provided by WolframAlpha

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Upgrade to WolframAlpha Pro!

Requested by austinu

[fathom flicker]

,w x''+x'/2-3/2 x=-5/2

[warm shale]

Results provided by WolframAlpha

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Requested by austinu

[gilded needle]

are these the supposed solutions?

or rather, equivalent set of equations?

[fathom flicker]

no sorry these are irrelevant

I am just working on some other thigns

[gilded needle]

ah good, i was gonna say, where is e^(4t) going to come from

[fathom flicker]

solving systems of differential equations by elimination by hand is the worst thing that this earth has ever invented and I would rather cut my hands off then do a 5 problem set of these god forsaken questions ever again

.close

[obtuse pebble]

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[chrome lintel]

i’d like to learn math from grade 8-12

[brave bramble]

Check out Khan Academy

[chrome lintel]

yippue

[obtuse pebble]

@chrome lintel Has your question been resolved?

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[obtuse pebble]

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[arctic fjord]

how many integer values ​​of m are there for the following equation to have a solution 2sin^4(x) +2cos^4(x)-3sin2x-m^2=0

[royal basin]

what's that file?

[polar fossil]

i think you might want to try again on that file upload

[royal basin]

what extension is .plist?

[polar fossil]

some mac thing but it was actually a jpg

[royal basin]

ok

[royal basin]

!status

[obtuse pebble]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[arctic fjord]

1,2

[royal basin]

wym "1,2"

did you begin or not?

[arctic fjord]

I need an idea for this problem

[royal basin]

"no, i did not begin"

ok, then here is your idea:

write 2(cos^4(x) + sin^4(x)) in a different way.

[arctic fjord]

How?

[royal basin]

you know that cos^2(x) + sin^2(x) = 1, yes?

[arctic fjord]

Yes

[royal basin]

think about how you could do something similar here.

[arctic fjord]

Is this the result?

@royal basin

[royal basin]

i can't open plist files.

[arctic fjord]

3/4 +1/4cos(4x)

:))

[royal basin]

i think you messed up somewhere

show me your work as a jpg or png or some other normal file format

[arctic fjord]

Ok after this step, what to do next

@royal basin

[timid silo]

is the answer 9?

[arctic fjord]

how do you do it?

[timid silo]

is it 9

[arctic fjord]

I need to know your way?

[timid silo]

i need to know if my answer is correct first

if 9 isnt the answer my way is wrong and its useless

[arctic fjord]

I don't know the answer and this is my homework

[royal basin]

we can't verify your answer without seeing your work

[royal basin]

this is not your work this is just your 'final answer' or whatever

which im suspicious of

[timid silo]

this is my work

[royal basin]

how did the third line happen?

[timid silo]

wait i forgot to add the +4sin^2xcos^2x in the second line

[arctic fjord]

This is the formula I have to remember without having to prove it

[timid silo]

i took the whole square

[arctic fjord]

@royal basin

[royal basin]

[warm blaze]

@unreal dew

my question is

draw a circle whose diameter is 10cm Find the radius

[royal basin]

@warm blaze get your own channel. read #❓how-to-get-help for instructions.

[timid silo]

did i make a mistake?

[royal basin]

no i was stupefied at OP

[arctic fjord]

why 3sin2x=4sin^2(x).cos^2(x)

[timid silo]

those are not equal

3sin2x is 3(2sinxcosx) which is 6sinxcosx

i added and subtracted 4sin^2xcos^2x to turn the 2sin^4x+2cos^4x into a whole square of (sqrt(2)sin^2x+sqrt(2)cos^2x)

which is further simplified into just 2

[royal basin]

alright so then why did you set the discriminant to zero

[timid silo]

i set it to >=0

since sinxcosx is always real

[royal basin]

m^2 <= 4.25 doesn't imply -4.25 <= m <= 4.25 btw

[timid silo]

it does

no no wait did you understand all the steps

he deleted the messages

bruh

ok

[worn quail]

Can someone help me please?

#help-10 message

[arctic fjord]

I don't understand this line

[timid silo]

i forgot to write +4sin^2xcos^2x in the second line

[arctic fjord]

no i mean the 3rd line

[timid silo]

do you see that 2sin^4x+2cos^4x+4sin^2xcos^2x can be written as [sqrt(2)*sin^2x]^2+[sqrt(2)*cos^2x]+2*[sqrt(2)sin^2x]*[sqrt(2)cos^2x]?

which is in the form of a^2+b^2+2ab?

which is (a+b)^2?

[arctic fjord]

Can you explain the 3rd line?

[timid silo]

$(\sqrt2sin^2x+\sqrt2cos^2x)^2-2[\sqrt2sin^2x][\sqrt2cos^2x]-6sinxcosx=m^2$

[warm shale]

dimpledoink

[timid silo]

you can simplify the whole square into just 2

that's what i did in the third line

[arctic fjord]

I think not the minus sign

[timid silo]

what

the minus sign is correct

[arctic fjord]

ok sorry

I haven't seen it yet, but there's one side in brackets

[timid silo]

$(\sqrt2sin^2x)^2+(\sqrt2cos^2x)^2+2[\sqrt2sin^2x][\sqrt2cos^2x]-2[\sqrt2sin^2x][\sqrt2cos^2x]-3sinxcosx=m^2$

[warm shale]

dimpledoink

[timid silo]

do you understand what i did here

[arctic fjord]

yes

[timid silo]

alright then do you see the first three terms are of this form

$a^2+b^2+2ab$

[warm shale]

dimpledoink

[arctic fjord]

I understood this part, what should I do next?

[timid silo]

take the first three terms into a whole square and simplify the thing

[arctic fjord]

I don't understand, can you explain in more detail?

[timid silo]

ok wait i think this will help you understand better

after this, you let (sinxcosx) be any variable of your choice
then you get a quadratic in that variable
then you find the discriminant and set the discriminant greater than or equal to 0 since the roots are real (the values for the variable, i.e., sinxcosx, will always be real as sinxcosx is always real and the condition for real roots is D>=0)

then the rest of the steps are the same

[arctic fjord]

ok I understood your transformation. What should we do next

[timid silo]

did you understand all of these steps

[arctic fjord]

No, but I understand the above transformation. Now what do we do?

[timid silo]

what part of this is confusing you

[arctic fjord]

It's too long and I don't want to understand. I need you to make it short and easy to understand

[worn quail]

Oh my god, then why you're here?

you got the help...

[arctic fjord]

I have 1 unresolved problem

[arctic fjord]

Wait why does D have such results

[timid silo]

i answered that question here

please read it

[arctic fjord]

It's too long and I don't want to understand. I need you to make it short and easy to understand

[timid silo]

the discriminant is greater than or equal to 0 since the roots of the quadratic equation are real

[arctic fjord]

ok i see what do you mean delta??

[timid silo]

delta?

no that's the discriminant of the quadratic equation

[arctic fjord]

yes delta=b^2-4ac

[timid silo]

oh wait its represented by delta yeah

yeah

here we were taught to use D and not delta

[arctic fjord]

quadratic equations have a solution if and only if delta is greater than or equal to 0

[timid silo]

have a real solution*

they can have imaginary roots if delta is less than 0

but here the solutions will be real only

[arctic fjord]

The last point seems wrong. You haven't square root on both sides

[timid silo]

oops

wait

yeah you're right

[arctic fjord]

Oke

[timid silo]

the square root of 4.25 comes to be approximately 2.06

so the answer will be 5

$-2.06\le(m)\le+2.06$

[warm shale]

dimpledoink

[arctic fjord]

That's right the problem has been solved thank @timid silo

@bot Closed

[timid silo]

type .close

[arctic fjord]

.close

[obtuse pebble]

Channel closed

Closed by @arctic fjord

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Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
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[worn quail]

I need help

[worn quail]

#help-10 message

[undone quartz]

we can start by making some patterns
X + 100 = A
Yk + 100 = B

K is some constant factor here which I think is somewhat related to a multiple of 3

33.33
50.00
66.67

[obtuse pebble]

@worn quail Has your question been resolved?

[undone quartz]

found a similarity

or this

1/3
3/6
6/9

this one is a more fitting sequence

@worn quail I think i have found the sequence

the constant factor is indeed a multiple of 3

[worn quail]

That's interesting, so how to find "B", what is the formula? I tried many ways, but without success

[undone quartz]

In the middle of writing it

 X  |  Y  |  A  |     B
 0  |  0  | 100 | 100.000000
100 |  0  | 200 | 100.000000
200 |  0  | 300 | 100.000000
 0  | 100 | 100 | 166.666667
100 | 100 | 200 | 150.000000
200 | 100 | 300 | 133.333334

A = 100 + X
B = 100 + (100 - Y * ((A/100) / (3*A/100)))

Can I get 1 more value in the sequence

need to confirm if it makes the triangular series or its a multiple of 3

[worn quail]

ok, one moment

[undone quartz]

like 1, 3, 6, 10, etc

[undone quartz]

let me guess

116.6667?

[worn quail]

B = (100 - Y * i/3i)
What is "i"?
I am confused how to implement this as a script in the engine. And where is "A" when searching for "B"?

[undone quartz]

in the middle of writing it ignore that

just need to confirm if the next value is 116.667

then consider it solved

[worn quail]

The next value after which one?

[undone quartz]

133.333

[worn quail]

I think it's 125

[undone quartz]

ahh Y gets to 200

[worn quail]

when X=250 and Y=100

[undone quartz]

write the data in a table form

 X  |  Y  |  A  |     B
 0  |  0  | 100 | 100.000000
100 |  0  | 200 | 100.000000
200 |  0  | 300 | 100.000000
 0  | 100 | 100 | 166.666667
100 | 100 | 200 | 150.000000
200 | 100 | 300 | 133.333334

A = 100 + X
B = 100 + (100 - Y * (t / (3*i)))
where t is the sum of series
i1 = 1
t = 1
i2 = 2
t = i1 + i2 = 1 + 2 = 3
i3 = 3
t = i1 + i2 + i3 = 1 + 2 + 3 = 6

Like this

[worn quail]

ok, but it will take some time

thank you for the help

[undone quartz]

this works for the given data

but need a bit more values to see where it fails

also missing something important here but I found triangular series pattern

[obtuse pebble]

@worn quail Has your question been resolved?

[worn quail]

` X   |  Y   |  A   |    B
 0   |  0   | 100  | 100.0000
100  |  0   | 200  | 100.0000
200  |  0   | 300  | 100.0000
300  |  0   | 400  | 100.0000
400  |  0   | 500  | 100.0000
500  |  0   | 600  | 100.0000
600  |  0   | 700  | 100.0000
700  |  0   | 800  | 100.0000
800  |  0   | 900  | 100.0000
900  |  0   | 1000 | 100.0000
1000 |  0   | 1100 | 100.0000

0   | 100  | 100  | 166.6666
 0   | 200  | 100  | 233.3333
 0   | 300  | 100  | 300
 0   | 400  | 100  | 366.6666
 0   | 500  | 100  | 433.3333
 0   | 600  | 100  | 500
 0   | 700  | 100  | 566.6666
 0   | 800  | 100  | 633.3333
 0   | 900  | 100  | 700
 0   | 1000 | 100  | 766.6666

100  | 100  | 200  | 150
100  | 200  | 200  | 200
100  | 300  | 200  | 250
100  | 400  | 200  | 300
100  | 500  | 200  | 350
100  | 600  | 200  | 400
100  | 700  | 200  | 450
100  | 800  | 200  | 500
100  | 900  | 200  | 550
100  | 1000 | 200  | 600

200  | 100  | 300  | 133.3333
200  | 200  | 300  | 166.6666
200  | 300  | 300  | 200
200  | 400  | 300  | 233.3333
200  | 500  | 300  | 266.6666
200  | 600  | 300  | 300
200  | 700  | 300  | 333.3333
200  | 800  | 300  | 366.6666
200  | 900  | 300  | 400
200  | 1000 | 300  | 433.3333

300  | 100  | 400  | 116.6666
300  | 200  | 400  | 133.3333
300  | 300  | 400  | 150
300  | 400  | 400  | 166.6666
300  | 500  | 400  | 183.3333
300  | 600  | 400  | 200
300  | 700  | 400  | 216.6666
300  | 800  | 400  | 233.3333
300  | 900  | 400  | 250
300  | 1000 | 400  | 266.6666`

[undone quartz]

you can see the pattern clearly now

2/3
1/3
0/3

look they got 116.666

like i predicted

it is making the triangular series

1/3
3/6
6/9
10/12
15/15
.
.
.

[worn quail]

I have no idea what that means

How to make the calculation automatically with formula?

[undone quartz]

keep adding the dots in the row

you will get this sequence

 1 = 1
 3 = 1 + 2
 6 = 1 + 2 + 3
10 = 1 + 2 + 3 + 4
15 = 1 + 2 + 3 + 4 + 5

[worn quail]

1/3 (2)
3/6 (3)
6/9 (3)
10/12 (2)
15/15 (0)

???

[undone quartz]

adding 3 in denominator

adding the running sequence in the numerator

[worn quail]

Is this NASA science? I have no clue how to use that

[undone quartz]

i = 1, N = 0, D = 3
N+i / D*i = 0+1 / 3*1 = 1 / 3

i = 2, N = 1, D = 3
N+i / D*i = 1+2 / 3*2 = 3 / 6

i = 3, N = 3, D = 3
N+i / D*i = 3+3 / 3*3 = 6 / 9

i = 4, N = 6, D = 3
N+i / D*i = 6+4 / 3*4 = 10 / 12

yea im not that good in explaining

but I have figured out the sequence

[worn quail]

Alright, and how to turn this into one line formula?

@undone quartz you are life saver

[undone quartz]

this formula depends on a loop

and also the sequences are changing a bit in each section

[worn quail]

I can't finish this task alone. Thank you again @undone quartz for the help, I really appreciate it!

[undone quartz]

i just noticed the pattern, the problem is still not solved

see if anyone else can continue from here

[worn quail]

well I guess there is no one else, I need a miracle now

<@&286206848099549185>

[dawn iris]

little me shall give it a try

[frozen thistle]

what i don't understand is why B's value doesn't drop below 100 even when A grows if Y=0

[worn quail]

A and B start from 100

the action command in the game engine want a number
100 means 100%

so 100 is the normal size

[flat mauve]

hi guys

[worn quail]

hello

[frozen thistle]

i think i found the answer

but i made multiple assumptions

[worn quail]

ok

[frozen thistle]

nvm it doesn't fulfill the condition where X=0 and B=166.666

[obtuse pebble]

@worn quail Has your question been resolved?

[dawn iris]

@worn quail All these values verify the formula:

*

[obtuse pebble]

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• Show your work, and if possible, explain where you are stuck.
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• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[obtuse pebble]

Channel closed

Closed due to the original message being deleted

[meager elm]

.close

[obtuse pebble]

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[royal basin]

!status

[obtuse pebble]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[hidden compass]

You mean expand?

[royal basin]

so you do not know the distributive property?

[hidden compass]

Don't you know how to expand 3•(2 + 5)?

[royal basin]

you will have to learn the distributive property. you won't be able to remain ignorant of it for long.

how did you do that if you don't now the distributive property?

[hidden compass]

Ok so it seems you know it

[royal basin]

[hidden compass]

Which indices??

[royal basin]

do it without worrying about what to do with the indices first.

[hidden compass]

There aren't any indices in your question

[royal basin]

z^2, not z2.

also if you don't see what to do with that

then for the time being, don't

write 8z * z^2 as 8z * z^2

and only AFTERWARDS worry about what to do with it

[hidden compass]

This is far too difficult for 5th grade in my opinion

8z³ + 16z

[royal basin]

hang on, 5th grade?

how old is 5th grade?

... that wasn't a yes/no question.

how old are you?

[hidden compass]

But yes z * z² = z³, yep

[royal basin]

you are too young to be on discord!!!

you have to be at least 13.

sorry, we're really strict about this stuff here.

the server could get in trouble.

[pulsar quarry]

how?

[polar fossil]

that's a good way to get your older sister banned

[obtuse musk]

that doesnt suffice

if its your sister

your guardian (i.e. probably a parent) needs full control of the account and be present at all times

so you will have to come back in 3 years

[obtuse musk]

servers have to enforce discord tos

[polar fossil]

kids don't know how to lie these days

[obtuse musk]

its technically fine with parental consent but unfortunately discord doesnt implement a good way for this

[obtuse musk]

the general idea is that guardians need full control and supervision of accounts

i dont think discord offers this (yet)

.close

[obtuse pebble]

Channel closed

Closed by @obtuse musk

Use .reopen if this was a mistake.

[pulsar quarry]

what?💀

[polar fossil]

this is a partnered server

[royal basin]

if we don't enforce discord's terms of service, we risk getting nuked

[pulsar quarry]

wtf

[obtuse pebble]

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[pulsar quarry]

its only discord

not any adult or some kind of scary shit app

[obtuse musk]

then complain with discord

[royal basin]

they are a company and they have their terms of service, this is not something we have the power to change.

[obtuse musk]

this isnt the place to discuss this, you have to follow tos, thats it

.close

[obtuse pebble]

Channel closed

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[obtuse pebble]

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[timid silo]

If a function is convex on [a,b] then is integrable on [a,b] right?

[compact shadow]

Yes

[timid silo]

Because convex [a,b] implies continuous on (a,b) and in the worst case f is not continuous in a and b but we have a finite number of discontinuities so by lebesgue integrability we have integrable on [a,b]

[compact shadow]

Because being convex -> being continuous

Exactly

As long as the set of not continuous points is of measure 0

[timid silo]

Yeah cuz in some problem they said f integrable on [a,b] and convex on [a,b] and I was what?

[compact shadow]

😂

[timid silo]

.close

[obtuse pebble]

Channel closed

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[distant dagger]

3(2z+1)=35

[distant dagger]

i dont know how to start

[crimson spoke]

okay. have you tried basic algebra before?

[distant dagger]

i thought the first thing to do was to distribute the 3 to the 2z and 1 first

but i think thats wrong

[crimson spoke]

hm. you can do it like that too

if you distribute it it would be 6z + 3 = 35

how will you proceed now?

[distant dagger]

subtract 3 from both sides

[crimson spoke]

yup

that gets us to 6z = 32

now?

[distant dagger]

then divide 6 from both sides

[crimson spoke]

yup

so z = 32/6

[distant dagger]

ohh ok

that makes sense

bc i thought the answer would be a decimal

so in cases like this if you were to end up getting a decimal as an answer would the answer just be a fraction?

[crimson spoke]

you can leave it as a fraction or convert to decimal

[distant dagger]

got it

thanks

.close

[obtuse pebble]

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[obtuse pebble]

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[gilded topaz]

I've graphed it in desmos but I couldn't draw any conclusions from that.

[obtuse pebble]

@gilded topaz Has your question been resolved?

[dawn iris]

@worn quail I sent you the formula

[gilded topaz]

<@&286206848099549185>

[obtuse pebble]

@gilded topaz Has your question been resolved?

[obtuse pebble]

Channel closed

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[hybrid shoal]

it is A or B good? and why?

[hybrid shoal]

my professor wrote A but i think it is wrong

[shut lagoon]

They're the same

Just multiply numerator and denominator by -1

[hybrid shoal]

1/2 -1 = 1/2
1-1/2 = -1/2

they arent the same(? or it does?

[shut lagoon]

Yeah but your numerator is flipped as well

The -1 cancels out

Just do it take A and multiply numerator and denominator by -1

[hybrid shoal]

i get that they are the same but dunno why :V

i read what u wrote but dont get it :V

[shut lagoon]

Well you're right that 1/2-1=-1/2 and 1-1/2=1/2

But we also have that 1- (1/2)^30 = -((1/2)^30 -1)

So whichever you choose, dividing them just cancels out the -1 if there is one

1-(something) = -((something)-1)

[hybrid shoal]

oooh i think i get it

then its the same that

its more easy to see it that way

its like one is 1 and the other is -(-1)

right?

[shut lagoon]

Yeah essentially

[hybrid shoal]

THANK U

.close

[obtuse pebble]

Channel closed

Closed by @hybrid shoal

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[shut lagoon]

No worries

[obtuse pebble]

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[novel pewter]

hi how do you start with this

alg 2 btw

[gilded needle]

do you have any thoughts about the four options? can you rule any of them out?

[novel pewter]

I dont think B and C are correct

am I right or no?

[gilded needle]

what's your reasoning?

[novel pewter]

because if its infinity I dont think they wouldnt use cubic root or 2^

[gilded needle]

infinity isn't really involved here

it's asking which function's range consists of all numbers greater than or equal to 0

[0,infinity) is just a succinct way of saying that

the open paren ) at the end of [0,infinity) means that infinity is not included in the interval

[novel pewter]

oh I see

so how can i know which can be represented by the interval

[gilded needle]

well one way to rule a function out is if it can have negative values

because then its range wouldn't be [0,infinity) - that set doesn't include any negative numbers

so which of the options can be negative?

[novel pewter]

how can i check that

[gilded needle]

well try the first one, g(x) = x... are there are values of x you can plug in that would cause g(x) to be negative?

[novel pewter]

no I dont think

[gilded needle]

what is g(-1)?

if g(x) = x

[novel pewter]

g(-1) would be equal to -1

is that wym?

[gilded needle]

yes

so in fact g(x) = x can have negative values

so its range can't be [0,infinity)

[novel pewter]

I see

right

[gilded needle]

you can rule out one of the other answers the same way

do you see which one?

[novel pewter]

g(x) = |x|?

[gilded needle]

can that one have negative values?

[novel pewter]

the vertical lines mean absolute value right?

yes I think it can have negative numbers

[gilded needle]

absolute value is never negative actually

[novel pewter]

oh

I didnt know that

thanks for telling me

[hidden compass]

Do you know what the definition of |x| is?

|x| = x if x ≥ 0, right?

[novel pewter]

that X is that absolute value?

[hidden compass]

?? x is just x

[novel pewter]

oh ok

[hidden compass]

The absolute value is |...|

Those vertical bars delimiting the x indicate that we are taking (applying) the absolute value function

[novel pewter]

yea

[hidden compass]

Alright

[hidden compass]

Do yuo agree with this sentence? @novel pewter

[novel pewter]

Im not sure

[hidden compass]

Do you know anything about the absoulte value function? Maybe its graph?

[novel pewter]

yea

it is graph

[hidden compass]

Alright, can you show it?

[novel pewter]

isnt it like a V chaped graph

?

shaped

wait are u asking if I have a graph

[hidden compass]

Yes it is V-shaped, but can you draw it on a piece of paper? Or if you like with a computer?
No, I'm asking you to draw it

[novel pewter]

Oh okay

can I get an example from the internet

[hidden compass]

Ok if you want you can (but it's better if you know how to draw it on your own)

[novel pewter]

I do its just that I dont have a paper

this?

[hidden compass]

Ah ok don't worry, then you can use online plotters (such as GeoGebra, Desmos...)

[hidden compass]

Yes, now can you draw the line y = x over that graph?

Have you ever used Desmos or GeoGebra? @novel pewter

[novel pewter]

Yes

i just finished a lesson on desmos

I

[hidden compass]

Nice

[novel pewter]

how do i draw y = x on the graph btw

[hidden compass]

Use Desmos

And first draw y = abs(x)

[novel pewter]

I think i figured it out

is it C?

[hidden compass]

Are you talking about answer C here?

[novel pewter]

yes

[hidden compass]

Then no, it is not the correct answer

[novel pewter]

oh okay

[hidden compass]

Graph those 4 functions in Desmos

[novel pewter]

how do i open a graph in desmos

I just have assigned lessons when iopen it

[hidden compass]

Search Desmos in Internet, it's very simple

<@&268886789983436800>

[novel pewter]

whos this

[hidden compass]

Someone who is going to be kicked soon

[novel pewter]

I see

[hidden compass]

https://www.desmos.com/calculator

[hidden compass]

However it's here @novel pewter

[novel pewter]

thats

[hidden compass]

Yes

[novel pewter]

C

[hidden compass]

Do you see that the function approaches 0 but never touches the x-axis?

[novel pewter]

yea

and then goes for infinity

right?

[hidden compass]

So the range of y = 2^x is **(**0, +inf) and not **[**0, +inf)

[novel pewter]

right

so thats the one correct?

[hidden compass]

No as we said before

[novel pewter]

oh right nvm

[hidden compass]

That's why I asked you the definition of the function |x|

[novel pewter]

this ones it

starts from 0

then infinity

right?

[hidden compass]

Yes, exactly D is the correct answer

Because |0| = 0, so 0 belongs to the range

[novel pewter]

I got 2 more questions I need to solve can u still help

?

[novel pewter]

right

[hidden compass]

Let's just finish quickly with the absolute value definition, then I help you with the other questions

[novel pewter]

Okay

[hidden compass]

Now, on this plot graph also the function y = x

[novel pewter]

mhm

[hidden compass]

Write this y = {x > 0 : x , -x}

[novel pewter]

on desmos?

[hidden compass]

Yep

Of course 😅

[novel pewter]

its the same basically

[hidden compass]

Why did you delete the |x| ?

[novel pewter]

I did?

[hidden compass]

Yes

[novel pewter]

oh

u wanted me to make a new line

I see

one sec

[hidden compass]

Yes, sorry if I didn't specify

[novel pewter]

np

[hidden compass]

Don't worry

You should see that the two functions overlap perfectly

[novel pewter]

yes

I see

I see okay

very nice

should we move on?

[hidden compass]

This is better @novel pewter

[novel pewter]

ah okay

[hidden compass]

It's something you surely have to understand very well, you will use it a lot probably from now on

[novel pewter]

yea

[hidden compass]

But yes, let's go on with the other two exercises

[hidden compass]

What do you think the domain is?

[novel pewter]

like how big the graph is?

something like that or am i wrong

wrong

[hidden compass]

That's not something mathematically reasonable