help-0

[alpine sable]

nope

I need help

[limpid spade]

what

[alpine sable]

it's not 670 boxes.

On a math quiz

[limpid spade]

what's the answer then

[alpine sable]

55

[limpid spade]

[alpine sable]

apparently you can turn them around or something

[devout tundra]

First one is 2 people with both

9 teachers with birds and 14 with gerbil, 2 with both

That problem took too many brain cells

[barren ginkgo]

awesome thank you so much

[devout tundra]

Second one too hard

[rich haven]

hey can anyone help i already got 1 of the angles but dont know any other

[flint steeple]

I think DAG is equal too

Because, I assume ∆FBA=∆ADE
∆FBA is like ∆BCF rotated 90° clockwise, so DGA is 90°

[scenic kestrel]

You can only prove that by proving that GEA is also equal, because then DAG + GAE would be 90°, as would AED + GAE (because GEA = GAE because they're in the "same triangle").

So, AED shares its two lines with GEA, so it's the same, and because AGE is 90° (that can be proved because AE = BF), GEA + GAE has to be 90°, or, what's equivalent, AED + GAE = 90° = DAG + GAE, so DAG = AED.

[royal glacier]

can anyone help me

[scenic kestrel]

The mass seems to be irrelevant.

Isn't this technically a differential equation? It's posed weirdly, but you can solve it if you take it to be y' = a - k y^2.

Don't quote me on that, because it's 1:40 here and I'm pretty tired, but, if it is, it should be something like: v = (a0)v - k (1/3) v^3

[royal glacier]

do i substitude the v in the equation for acceleration

[scenic kestrel]

First of all, is this a calculus class?

[royal glacier]

its dynamics

[scenic kestrel]

Have you learned calculus?

[royal glacier]

yes

[scenic kestrel]

Well, then wait a moment as I correct the equation.

[royal glacier]

i meant would you substitute v = (a0)v - k (1/3) v^3 into a = a - k v^2.

im tired aswell but its due for tomorrow

[scenic kestrel]

You would substitute it if it was the right equation, so I'm going to double check because I'm pretty sure I went wrong somewhere.

[royal glacier]

a0 is 2

its given in the question

so is k

[modest parcel]

hey can someone pls help me with this problem

i have no idea where to start

i feel like it depends on A being the right subset

<@&286206848099549185>

[charred flint]

@modest parcel yea you just need to find 1 example that works

maybe try a well known 2^c set for B, and just take out c elements to make A

that way 2^c - (2^c - c) = c

[modest parcel]

okay is my logic correct that

if A is a subset such that it has all sets except for R

it should work

or is taht wrong

[charred flint]

I don't think this is relevant to the question O_o

[modest parcel]

oof

i mean ye it doesn't matter

well known 2^c set?

@charred flint aren't you dividing the cardinalities not subtracting them

[charred flint]

nah that symbol is set subtraction

|A\B| = |A| - |B|

[modest parcel]

@charred flint ah got it ty i see

@charred flint can u say |P(R) - R| = 2^c - c

[night sinew]

oh sorry

[modest parcel]

@charred flint can i make A be the subset |P(R) / R|

and then have |B| = |P(R)|

then |B/A| = |R| = c?

[charred flint]

yea

[modest parcel]

@charred flint tysm

[nocturne jay]

Hey

May someone please help me out?

[wide talon]

whatsup?

[nocturne jay]

I need help with this questions

Question*

[wary stream]

Did you get 188? How did you calculate that?

[oak chasm]

@nocturne jay What are the surface areas of the two parts? What's the surface area of the rectangle where they meet? What's the surface area of the two parts minus twice the surface area of the rectangle where they meet?

[wary stream]

@oak chasm What's the highest math you've completed?

[oak chasm]

Abstract algebra.

But then of the lower level courses, I only really did calculus 1 and 2, linear algebra, discrete math, and first-order logic.

[alpine sable]

help lol

[oak chasm]

@alpine sable Sorry, Biskit still has time before their 15 minute @Helpers call, so not enough time has gone by.

Try #help-6 if you hurry.

[alpine sable]

(12 x 2 x 4) + (2x3 x 2) - (2 x 2) + (7 x 2 x 4) + (2x2)

[wary stream]

@oak chasm If you have some time, can I dm you? I took a linear algebra exam a few hours, and if it's possible could you check my work on some of the questions, specifically some conceptual questions

[oak chasm]

@wary stream I only really remember the basics, like vector space axioms.

[wary stream]

It was about eigenvalue and SVD decomposition

[oak chasm]

Oh, I don't know those, sorry.

[modest parcel]

@oak chasm how would u go about proving that the set of all bijections from Z+to Z+ is uncountable

im not rly sure how to come up with a set containing all bijections

[oak chasm]

@nocturne jay You can call @Helpers now if you want.

[alpine sable]

<@&286206848099549185>

[glass lichen]

#❓how-to-get-help

[alpine sable]

sorry for the lack of context

i've tried the question a bunch of times and honestly, i just don't know where to start

[charred flint]

(a+b)/2 is the midpoint* of AB

[glass lichen]

No, you pinged right away

[charred flint]

they asked the same thing a while ago :v

[alpine sable]

oh sorry i misinterpreted the rules lol

my bad

won't happen again

@charred flint are you willing to help?

[charred flint]

yea

can you see how to get a vector for the medians

[alpine sable]

holdo n

ill draw a diagram real quick

so i can visualise better

[charred flint]

oops I'm gonna be busy

try this https://www.youtube.com/watch?v=1otVf_HXLN8

[alpine sable]

o okay

[alpine sable]

• The thickness of the asphalt layer should be 20 cm to 25 cm
• The base layer corresponds to 2/7 of the total volume of the materials
• The foundation layer is at least 80 cm thick.
• The inclination of segments AB and BC is 2%

I dont know if this a multi answer or i have to pin point for the exact answer

[woeful pulsar]

idk what is the entire question?

probably not just this picture?

[alpine sable]

the other question is just about the volume and the price for each layer

this is the only picture

[woeful pulsar]

wait this question only provides the picture?

how do you know what to find out?

where did the text come from?

[alpine sable]

This is the full version it’s in french

[woeful pulsar]

Looks like you have to do calculations for a 1km road?

So what you need seems to be
a diagram?
equations/inequalities/graphs?
coordinates of A and H?
cost of 1km road?

[alpine sable]

I’m trying to figure out the coordinates of A H G and I think i know what to do after that but I don’t know how to find those coordinates

[woeful pulsar]

okay so we need to use the information in the question

"The foundation layer is at least 80 cm thick", therefore?

remember a coordinate requires the x-coordinate and y-coordinate

so you can figure them out

[alpine sable]

I know the minimum is 80 cm so am I suppose to use a random number above 80 or is there an equation that I am suppose to do

[woeful pulsar]

I think you can use use 80

because you want the minimum cost

[alpine sable]

right

and for the 2% incline for AB is a = 1.02x?

because 1 = 100%

[late rapids]

Dumb question; to find charge, it's capacitance*voltage right?

Because this is saying that it's wrong

[sly mantle]

,calc .77e-6*1.5

[ocean seal]

Result:

1.155e-6

[late rapids]

It's telling me it's wrong

[wary stream]

Is that the entire question?

[late rapids]

Should I just assume that the homework program is wrong

[late rapids]

Yes

[wary stream]

Cause it says plates, so it doesn't mention area or anything like that?

[late rapids]

No. That's the full question and there aren't any other parts to it

[wary stream]

Could it be because of sig figs?

[late rapids]

I could try tweaking it. But the hw program haven't cared in the past

[spare sage]

capacitance is charge/voltage right

[late rapids]

Ya. Since I'm looking for charge, it should just be multiplying voltage on both sides.

[spare sage]

they want it in microcoulombs i think

you put it in coulombs

[late rapids]

I'm a big dummmy

Thank you!

[spare sage]

np

[woeful pulsar]

you need to do y=1.02x+c for some constant c

y=mx+c

[spare sage]

ok so if you draw a triangle between point A (the first hiker), point B (the second hiker) and point C (the landmark) what do you notice

can you figure out any angles or lengths?

[tranquil cove]

guys can someone hlep me with a practice quiz for math plzzzzzzz

[oak chasm]

@alpine sable Did you draw a diagram?

OK, draw one and label the sides and angles you know.

[limber lynx]

i know why this is true but i have no idea how to put it into words

im supposed to do a proof by cases

[crude tendon]

It's okay.

[limber lynx]

?

[rigid smelt]

this is like the product property of absolute values

you just have to seperate by cases

and apply the case into the equation

[dry plover]

how do i solve this?

[wary stream]

Do you know what perimeter is?

[dry plover]

yes

[viscid blaze]

Just add the side

And equate it to 76

[wary stream]

So the sum of the sides equals the total given

[dry plover]

thanks

[wary stream]

You don't tell people the answers. They have to learn the process

[viscid blaze]

My bad

[dry plover]

I hope it’s right and I can’t put my answer in rn

cause I’m on the toliet

[wary stream]

Go ahead and delete these so @dry plover will learn how to solve it

[viscid blaze]

Thanks for Lemme me know

I'm new in this server

[wary stream]

This too

If you're new, check out #❓how-to-get-help @viscid blaze

So you can be familiar with how things are done, if you want help or give help

[wary maple]

R^2 * theta/2

It should be 7pi cm^2

[modern plinth]

could someone help me w this real quick

[woeful pulsar]

do you know how to evaluate the inner product of vectors?

[modern plinth]

ye

[woeful pulsar]

can you evaluate the inner product of those vectors?

[modern plinth]

well

you just edited what you said

lol

[woeful pulsar]

yeah

[modern plinth]

but yea

[woeful pulsar]

I tend to edit if it's quite fast

inner product/dot product, same thing really

• up to basis

[modern plinth]

so its

$(sqrt{a},sqrt{b])^2$

hang it

[woeful pulsar]

no, remember it's a inner product of u and v

[modern plinth]

its been a while

yeah but isn't that the inner product

u*v

[woeful pulsar]

can you simplify the expression?

remember v is like u but backwards

[modern plinth]

the expression I got?

[woeful pulsar]

not really

not sure how you got that

[modern plinth]

i did u*v

[woeful pulsar]

yeah, shouldn't you get an expression a and b from that?

not some (... , ...)^2?

[coarse hatch]

Plz help me with the following...

[woeful pulsar]

might want to use a less occupied channel, the previous message was 3 minutes ago

[coarse hatch]

Ok got it,I am new so currently exploring

Plz suggest a channel

[modern plinth]

one sec

[woeful pulsar]

find one where the previous message is as old as possible

like #help-7｜zen1thxyz where it looks solved

[modern plinth]

i still get the same thing

[woeful pulsar]

how did you even get it in the first place

like you know u and v are definitely not the same vector

[modern plinth]

so it should be that then?

[woeful pulsar]

yeah

you need to multiply the corresponding coordinate

[modern plinth]

yea sorry for the stupid question

ty

[calm grove]

K=7/4 ?

[coarse hatch]

How, I'm getting 140

Plz send sol

@woeful pulsar Thanks for guiding me

[woeful pulsar]

don't just give answers

[woeful pulsar]

can you find the value of P?

[coarse hatch]

Yes

[calm grove]

What's the value of p for you

[coarse hatch]

But it would be better to share whole answer...

[lone heart]

From

#❓how-to-get-help

Rule 7

When asking for help, do not insist on getting just the answer; we are here to help you learn, not cheat. Likewise, if you are providing help to others, try your best to explain and elaborate instead of simply giving away the answer.

[calm grove]

[coarse hatch]

@calm grove p is 7

[calm grove]

Yes right

[coarse hatch]

Now I substituted

The value

[calm grove]

Now what was the condition for equal roots
Use that for second eqn

[coarse hatch]

B2-4ac=0

[calm grove]

Yes

[coarse hatch]

Wait

Can I substitute Value of p in eq 2

[calm grove]

Yes you can

[coarse hatch]

Then mid term split

[calm grove]

No need to split mid term you know the value of b and a and c in second eqn

Use that

[calm grove]

You yourself said it

[coarse hatch]

Ok got it, I think I might have done calc error

Thanks

[calm grove]

[hushed dune]

hi guys. can someone help me with this one. AgccE EEbws (.) OEEfd mAwEhE OOAEx EOUnw AEUOA lypxs AAEOg cvxzE AOlAc AEqpc Avzxx tylpA AAlcb OOOOl ghqxA byAAA. can someone convert this into numbers?

[woeful pulsar]

you'll also need to share the encoding method

or the decoding method

right now it could convert to 0 and we would be none the wiser

[hushed dune]

idk the encoding method of that T-T.

[woeful pulsar]

idk I'm suspecting base85

since you have been using groups of 5

but is there any additional context?

[hushed dune]

nope

that's all

[woeful pulsar]

where did you find those letters?

who gave you those letterse?

[hushed dune]

It's a puzzle game.

[woeful pulsar]

from?

what sort of numbers are you looking for?

[hushed dune]

Longitude

[woeful pulsar]

oh

no wonder

[hushed dune]

It's a game.

yup

[woeful pulsar]

that's a lot of information

[hushed dune]

hehe

can i dm you?

[woeful pulsar]

Longitude lol

so now we know the dot refers to decimal point

[hushed dune]

yup

[woeful pulsar]

I have a feeling each group of 5 corresponds to one digit

something which I would have only known if it was a longitude

wait is it just more morse

@hushed dune might want to use this channel lol

[woeful pulsar]

looks off-topic

please move your off-topic stuff out of this channel

this question is for asking for help on math

,w current date

[ocean seal]

Results provided by WolframAlpha

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

Requested by Element118#2437

[woeful pulsar]

whoa nice

<@&268886789983436800>

[brave arch]

is the channel open for help?

[woeful pulsar]

yeah it's free

[sly mantle]

ty

[brave arch]

Ok so im working on a game and I want to be able to calculate probabilities based on the games parameters. I wrote a more generic problem statement that summarizes the problem but I'm not really sure where to start

[woeful pulsar]

oh martingales and stuff

not really tho

but yeah this is calculatable

[brave arch]

I wasn't a math major so I only took up through calc 2 in college

[woeful pulsar]

are k and l integers?

[brave arch]

yes

[woeful pulsar]

then a, b doesn't really matter

the player wins with 1/(b-a+1) probability

right?

[brave arch]

yea

[woeful pulsar]

what sort of values a, b, p, w, n are you looking at? Any particular range you are looking at?

do you want exact values or fast approximations?

[brave arch]

approximations is fine but the range will be [1, 100], w will be in the range of 1 million - 2 billion, n can really be anything but probably wont normally exceed 100 - 200

[woeful pulsar]

w doesn't matter tho

because the problem is scaled up correspondingly

[brave arch]

oh right

[woeful pulsar]

yeah exact values are probably possible within one second

are you trying to write a program to calculate this probability?

[brave arch]

eventually yes, my main goal is to be able to tweak p so that I can control the house odds

[woeful pulsar]

erm

isn't it sufficient for the expected value for one game to be <0

[brave arch]

wdym

[woeful pulsar]

okay, do you know what expected value is?

expected value is like "what you get on average when you play the game once"

[brave arch]

yea pretty much 0

but over a long period of time (larger values of n), if P was super high then the house would lose more than they gain no?

[woeful pulsar]

it's not 0

I think we should try to calculate it properly

so 1/(b-a+1) of the time, we win p, but (b-a)/(b-a+1) of the time, we lose 1

[clear pivot]

Hello, May I know that anyone of you good in descriptive statistics topic?

[brave arch]

win p*w, lose w

but yea that makes sense

[woeful pulsar]

so we have to make a weighted average and add them

I'm just going to let M = b-a+1

then the expected value of the game is $\frac{p}{M}+\frac{-1(M-1)}{M}$

[ocean seal]

Element118

[woeful pulsar]

which is $\frac{p-(M-1)}{M}$

[ocean seal]

Element118

[woeful pulsar]

for the house to win in the long run, this value needs to be negative

[brave arch]

alright, and then how does n factor into this

[woeful pulsar]

n does nothing

because we are looking at 1 game

that's how games are typically analysed

however if you still want to calculate for your original question, there are algorithms

[brave arch]

ah ok I guess my issue is that I'm having trouble meaningfully interpreting the expected value. I've plugged in some of my sample parameters and got -.79

[woeful pulsar]

yeah a negative expected value means the player is expected to lose a lot

for example you can calculate it roulette

[dapper bronze]

For rectangular hyperbola, y= 1/x

If its like -2/3x+4

Does 3 infront of x change the asymtote..?

[woeful pulsar]

wait is this -2/(3x+4)?

or is it -(2/3)x+4?

[brave arch]

thanks for the help. I did some reading and it makes sense now

[dapper bronze]

@woeful pulsar its these

[woeful pulsar]

you need to use parentheses

()

brackets

don't forget your brackets

like, everywhere you need to group stuff together

[woeful pulsar]

for example
d: y=-2/(3x+1)
h: y=3/(3x+4)-1

do you mean, the horizontal or vertical asymptote?

[harsh acorn]

i wrote $$\prod_2\sum{9}\frac{5}{n*(n+1)}$$

how can i write up PI

[woeful pulsar]

_{n=2}^4, \times

for example

\sum ?

[ocean seal]

Hyl1s

[harsh acorn]

wait a min

[woeful pulsar]

but the main idea here is to use telescoping sums

to do so try doing partial fraction on 5/(n(n+1))

[harsh acorn]

$\prod _{n=1}^9\left(\frac{5}{n\left(n+1\right)}\right)$

[ocean seal]

Hyl1s

[harsh acorn]

i stuck here

[harsh acorn]

like $$\frac{5}{n}-\frac{5}{n+1}$$ ?

[woeful pulsar]

not that, make sure you find the right coefficients

[woeful pulsar]

it's a sum, not a product

[harsh acorn]

oh my bad

[ocean seal]

Hyl1s

[harsh acorn]

what should i do after that

[woeful pulsar]

look at your sum now

a lot of terms should cancel

figure out which ones cancel

[harsh acorn]

so answer is 5-(5/10)?

bcs middle ones cancel

and it equals to 4.5

[quick surge]

i need to find the volume

[hollow fable]

Oke

So u have 2 geometrical figures

[quick surge]

yes

how do i find

the triangle prism

[hollow fable]

Well

[quick surge]

i know that

[hollow fable]

Its a triangle

[quick surge]

Volume = base of area x lenght

[quick surge]

isnt it a prism?

[hollow fable]

I mean the base

Is a triangle

[quick surge]

theres no base of area

me brain hurt

[hollow fable]

So u have that the area of a triangle is $A= 0.5 \times b \times h$

[ocean seal]

NotTheImpostor

[hollow fable]

Wait lemme explain

[quick surge]

yea i know that

but i dont know how to find rthe base

area

[hollow fable]

So the volume of a triangle prism is $V= A_{\text{triangle}} \times h$

[ocean seal]

NotTheImpostor

[hollow fable]

H is the length

Of the prism

[quick surge]

so its 1000cm^3

the volume of it

[hollow fable]

H is 40m

[quick surge]

yes

[hollow fable]

A is 25

[quick surge]

v = 25 x 40

[hollow fable]

Oh

Ya

[quick surge]

so the rectangular

i just

[hollow fable]

Yup

[quick surge]

20 x 10 x 40

thats it?

lol

[hollow fable]

Yea haha

[harsh acorn]

are u guys done

[hollow fable]

Correct

[harsh acorn]

i struggle to find pattern here

$$\frac{1}{4(???)}$$

[ocean seal]

Hyl1s

[hollow fable]

I mean

Differences

24-12 is 12

40 - 24 is 16

12 16 20 24 28 32

...

[woeful pulsar]

so it's a quadratic

2 * 6, 3 * 8, 4 * 10... hmm

[harsh acorn]

well i did find the answer wihout pattern but i am interested what was that

[woeful pulsar]

what was what?

it's a pretty similar pattern

[harsh acorn]

i mean we can write equation as sigma (xxx)

[woeful pulsar]

similar to this

try dividing the dernominators by 2

[harsh acorn]

idk i didnt find it

btw is the answer $$\frac{25}{112}$

[ocean seal]

Hyl1s
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[jade birch]

Remediation test @tough vessel

What's the exam about

<@&268886789983436800>

[sly mantle]

👢

[fading zephyr]

thanks

[coral shell]

Find the maximum and minimum value of (A = 2x + y) given that (x^2 + y^2 - 2x - 4y \le 0)

[ocean seal]

Luminal

[coral shell]

Can anyone help me with this?

[silent arch]

Circle equation can be written as (x-1)²+(y-2)²-5 ≤ 0

Then write x in terms of y and put that in the A = 2x+y

Then differentiate A with respect to x and equate to 0. you will get value of x and put this value in A to get max and min values.

[coral shell]

I see now, thanks!

[harsh acorn]

can someone explain me this please

[strong furnace]

write the general term for the sequence and you can reduce it to f(n+1)-f(n) after that use telescopic sums

[silent arch]

It's limited terms only so you can add them directly .... 5/21 = a/b

[harsh acorn]

which one should i do now im confused

[harsh acorn]

can I write general term like $\frac{1}{n(n+2n)}

oh no i cant

my bad

[strong furnace]

notice how every denominator is an Arithmetic progression?

[harsh acorn]

yes i notice it

but dominator's digits are rising

idk how to show that

i can write first term as maybe 1/(n+2n)

second is 1/(n+2n+3n)

3rd 1/(n+2n+3n+4n)

and keep going like that

[strong furnace]

you can use the formula for sum of AP for each one

[silent arch]

Take 1/3 common from every term and then use the series

[strong furnace]

or better yet skip that by taking 3 common and using the sum of natural numbers which comes from the sum of AP but it is expected that you remember them

[harsh acorn]

idk what is sum of AP

[strong furnace]

why are you attempting problems that require AP if you have not learned about AP?

[silent arch]

,help exactly

[ocean seal]

Command exactly not found!
Use the ,list command without arguments to see a list of commands.

May 8, 2021, 10:47 AM

[strong furnace]

I mean this solution uses a property of sums that can be used to get the sum of AP

[harsh acorn]

idk this is 8th grade past paper and i need to practice

[silent arch]

,list

[harsh acorn]

and there are this question

[buoyant vale]

I don't understand the third line

Surely x/x is 1

[alpine sable]

you are unsure how they went from $2\log_2(x)-\frac12 \log_2(x)=3$ to $\ \frac32 \log_2(x)=3$?

[ocean seal]

Al𝟛dium

[alpine sable]

2-1/2 = 4/2-1/2=3/2

[uncut bough]

infinity

[harsh acorn]

haha.

[uncut bough]

oh range

[harsh acorn]

$$\sqrt{30+12\sqrt{6}}$$

[ocean seal]

Hyl1s

[harsh acorn]

how can i simlify this

[woeful pulsar]

I don't see any clear way to

[limpid spade]

same

what about

[strong furnace]

can you show the actual problem?

[limpid spade]

dunno if that's a more simple version

[quartz tusk]

hey so i have a problem :

say , a+b =c . where c is a multiple of say 5.

if 'b' is not a multiple of 5 then can we say that 'a' will also not be a multiple of 5 ?

[limpid spade]

yes

no

0+5=5

if a or b is zero then the other can be a multiple

[quartz tusk]

b is not multiple of 5

[limpid spade]

what

what u mean by multiple of 5

[quartz tusk]

i said if 'b' is not mulitple of then 'a' is not a mulple of 5 too . but you took b as 5 in you eg.

[quartz tusk]

not divisible by 5

[limpid spade]

true because 5+5=10, 10+10=20, etc

these are not multiples

[quartz tusk]

they are indeed a multiple of 5 !!

[limpid spade]

?

they are divisable by 5 so they're not multiple

you said a multiple of 5 is if it's not divisable by 5

[quartz tusk]

oh no no

so multiple of 5 are such as , 10 ( 52) , 15 ( 53) like that

[quartz tusk]

notice they are also divisible by 5.

[limpid spade]

1+4=5,0+5=5,2+3=5,3+2=5,4+1=5

both a and b need to be mutlipels of 5 to get an answer that's a multiple of 5

[quartz tusk]

yeah you re right.

[strong furnace]

idk what they want from you but the thing under the radical can be written as 6*(sqrt(25)+sqrt(24)) if that helps

[harsh acorn]

can u help me for this too?

i think it looks like $$(x-y-z)^2$$

[ocean seal]

Hyl1s

[quartz tusk]

hey its actually easy

just ry to reduce it in the form of (a+b)^2

i cant tell you answer but it reduces.

[harsh acorn]

,w simplify (\sqrt{30+12\sqrt{6}})

[ocean seal]

Results provided by WolframAlpha

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

Requested by Hyl1s#3863

[harsh acorn]

wait

what

[quartz tusk]

yeah .

[harsh acorn]

you mean $\sqrt{30+12\sqrt{6}}=x$

[ocean seal]

Hyl1s

[harsh acorn]

$$30+12\sqrt{6}=x^2$$

and

[ocean seal]

Hyl1s

[harsh acorn]

$$(30+12\sqrt{6})^2=x^4$$

i think i did wrong lol

[ocean seal]

Hyl1s

[harsh acorn]

,w simplify \sqrt{(30+12\sqrt{6})^2}

no i cant do this ofc

,w simpify (sqrt{30+12\sqrt{6}})^2

[ocean seal]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by Hyl1s#3863

[indigo jetty]

i'll share something here for your interest:

[harsh acorn]

,w \sqrt{\frac{36+\sqrt{36^2-16\sqrt{6}^2}}{2} - \sqrt{\frac{36-\sqrt{36^2-16\sqrt{6}}{2}

[ocean seal]

Wolfram Alpha doesn't understand your query!
Perhaps try rephrasing your question?
Click here to refine your query online

Requested by Hyl1s#3863

[harsh acorn]

,w simplify \sqrt{\frac{36+\sqrt{36^2-16\sqrt{6}^2}}{2}

$\sqrt{\frac{36+\sqrt{36^2-\left(16\sqrt{6}\right)}^2}{2}}-\sqrt{\frac{36-\sqrt{36^2-\left(16\sqrt{6}\right)}^2}{2}}$

[ocean seal]

Hyl1s

[harsh acorn]

,w simplify sqrt{\frac{36+\sqrt{36^2-\left(16\sqrt{6}\right)}^2}{2}}-\sqrt{\frac{36-\sqrt{36^2-\left(16\sqrt{6}\right)}^2}{2}}

whut

better go to bot channel lol

[harsh acorn]

oooh your formula can be right but in my problem X < Y so it cant be used

thats why it gave error :d

[harsh acorn]

idk how to do that

when i try i cant simplify it

can u help me more please?

[quartz tusk]

yeah sure

but ry hard next time

[indigo jetty]

the other way is to assume $30+12\sqrt6 = a^2+2ab+b^2$

[ocean seal]

Ken G

[indigo jetty]

then deduce that $a^2+b^2 = 30$ and $2ab = 12\sqrt6$

[ocean seal]

Ken G

[indigo jetty]

of course it may not hold all the time

if it does not hold, then it means the expression cannot be simplified

[quartz tusk]

@harsh acorn

so remember this for next time.

whenever someone says to simplify someting under root

look for the possibilities of making it a square byt framing them under identities.

[harsh acorn]

actually i tried it to square but not that way
i assume they equal to x and i square each side

but did not work ofc

good to know that thing too

[quartz tusk]

like i did . in general case as we have only two identities mentioning square i.e (a+b)^2 and (a-2)^2 they will always reduce in them

it will come of with practice but you should try hard next time.

[harsh acorn]

thx mate :p

is the answer -20?

i mean x's value is -20

[wary maple]

X=-20

Double differentiation is positive

[harsh acorn]

yep thats right anyway it asks for value

so it is 901

[wary maple]

Denominator will achieve lowest value at x=-20

Yes

[harsh acorn]

for the greatest value $x^2+40x+401=1$

[ocean seal]

Hyl1s

[harsh acorn]

so it is solution right?

[wary maple]

Yes

[harsh acorn]

thanks

[wary maple]

Not the solution provided by @ocean seal

You can't directly equate it to 1

[harsh acorn]

why tho

[glass lichen]

If you want to maximize the value of a fraction, you need to maximize the numerator and minimize the denominator

901 is constant so you want to find the minimum value the denominator takes on

[harsh acorn]

dominator cant be negative or 0 so it must be 1

oor 0<?

[glass lichen]

You just want the minimum positive value

which in this case is 1 since the vertex of the parabola is at (-20,1)

[harsh acorn]

oooh i get it

btw the minium value of sinx+cosx is -squareroot of 2 right?

[glass lichen]

I believe so, yes

cause you have constructive interference at the pi/4 values

[harsh acorn]

$$17x+x=180,17x=170$$
$$\frac{(n-2)180}{n}=170$$
$$n=16$$

[ocean seal]

Hyl1s

[harsh acorn]

am I right?

[gleaming sluice]

i got n = 36

we know that LHS : 17* (360/n) [this is exterior angle]
is equal to
RHS : ((n-2)*180)/n [this is the interior angle]

[harsh acorn]

oooh i did basic error again

how can I solve this?

[floral anchor]

you can use the formula

inradius=area/semipeimeter

perimeter *

[half cobalt]

Does factorisation can accept multiples answers? for exemple factoring 2x^2y^3 - 4xy^5+8x^3y^3 I get 2xy(xy^2 - 2y^4 + 4x^2y^2). But a factoring calculator I found online gives me a different answer, so how should I proceed?

[alpine sable]

Is the channel occupied?

[modern pine]

@half cobalt u have done it right .the factorisation also u can take out one more y^2 from the bracket .

[half cobalt]

so 2xy^2(xy - 2y^3 + 4x^2y) ?

[modern pine]

Na na

Take one more y out

I mean take a y² out

[harsh acorn]

$$y_1=\frac{2}{3}x+4$$
$$y_2=\frac{2}{3}x+\frac{8}{3}$$

[ocean seal]

Hyl1s

[harsh acorn]

Idk next part

ik they are parallel

[glass lichen]

and the shortest distance will be perpendicular

[harsh acorn]

yep ik that too

but how can I find magnitude

[glass lichen]

Find the point of intersection of a perpendicular line and each line you want

then distance formula

[harsh acorn]

Perpendicular slope's product was -1 right?

[glass lichen]

negative recripocal

[harsh acorn]

so $$y_{perp.} = \frac {-3}{2}x+4$$
$$D=\sqrt{(x_1+x_2)^2+(y_1+y_2)^2}$$

btw perpen.'s function's "b" can be anything right?

does not matter as I know

[glass lichen]

Yes, but it has to be a perpendicular line

a constant function isnt perpendicular as you've written

[ocean seal]

Hyl1s

[harsh acorn]

forgot x

my bad

[glass lichen]

right so then solve for the intersection of y_p and y_1

then y_p with y_2

you get 2 points in which the shortest distance between the lines is between them

[harsh acorn]

kk thx for help

[alpine sable]

what does this mean?

[alpine sable]

<@&286206848099549185>

[ivory pier]

Hey, I have just installed manim and I want to run 3b1b animation

How do I do that?

P.S. Already downloaded all the scenes

<@&286206848099549185>

[ashen wave]

Can anyone help me understand what categorical data and quantitative data is

[ivory pier]

I am still here

[ivory pier]

.

))

[robust shadow]

@ashen wave Categorical data is used to represent groups eg. the colour red and the colour yellow. Quantitative data would be used to represent the number of people that are a certain height, age or weight etc

[civic crypt]

what is manim? What is 3b1b?

#computing-software perhaps also post here

[ashen wave]

Oh alright thanks!

[civic crypt]

Seems to me these 2 are the same?

I dont see the difference. Are quantitative like continuous?

[slate marsh]

Hey guys, anyone familiar with the Chinese Remainder Theorem ?

<@&286206848099549185>

[alpine sable]

Hey ed, you familiar with the reading the rules theorem ?

also no I am not

We have 100 cubes and every side is in one of the colours - red , green, blue. Let 80 cubes have at least 1 red side and 85 have at least one blue side , what is the minimum amount of cubes that have red and blue side?

should be somthing like this |R|=80 , |B|=85 , then | R intersect B | >= 65

but why is it 65?

[final viper]

acc to your ques

there must be 20 cubes which don't have red side

so it might be possible that all those 20 cubes come into the category of blue

which is 85

[atomic acorn]

use the formula here

aub will be 100

which is total

[alpine sable]

ohh

[final viper]

👀

you need atleast 3 values

to apply this formula

[alpine sable]

true

[final viper]

so if we just subtract 20 from 85

we are going to get the minimum possible number of cubes

with blue red both

its a theoretical answer

[alpine sable]

mhm i see your logic oreo

[final viper]

lets try to apply some maths here 🤔

[final viper]

ah yes this works

given,
union = 100
n(red) = 80

n(blue) = 85

so

100 = 85 + 80 - intersect

[atomic acorn]

yea

[final viper]

=> intersect = 165 - 100 = 65

damn

[ocean hearth]

パリのビーナー

パリのビーナー

パリのビーナー

[unkempt plover]

finde the area of parallelogram if sides are 48cm and 30cm and 1 diagonal is 30
can someone help me, i dont know what formula do i need to use

<@&286206848099549185>

[solar pebble]

@unkempt plover try to draw it first

[glossy current]

That's easy

They give you a 30 cm diagonal while sides are 30 cm

[solar pebble]

@glossy current that doesn't help

[glossy current]

use Pythagorean to find the red one, which is also the height

[unkempt plover]

but how did u get 24

[limpid spade]

48/2

[solar pebble]

oh nvm

[glossy current]

Because ACD is an isosceles triangle

[solar pebble]

I had a brainfart

I hate geometry lmao

[unkempt plover]

i know that its 48/2

[glossy current]

isosceles triangle is also

I mean

Median is also the height

in an isosceles triangle

@unkempt plover u got it?

[unkempt plover]

yes yes

[glossy current]

english isn't my first language so I have to google the term :c

[unkempt plover]

same

[dusk smelt]

since both sides of the triangle have the same length

the height will intersect the base at the center

so 48/2

[unkempt plover]

ok

i didnt even think about it

[wary maple]

@kamal did u get your answer of F'(0) one

[junior ferry]

Can anyone help me with this question thanks?

[dusk smelt]

i guess you could differentiate that equation and show that the thickness is inversely propertional to the square of the existing ice

[civic crypt]

I think better would be to write the differential equation frist @junior ferry

[junior ferry]

so would it be dx/dt = k/x^2

because its increasing so K must be positive multiplied by 1/x^2 as it is inversly proportional

[dusk smelt]

yeah

[junior ferry]

isnt inverse proportinal -1/x^2 though?

or do we make it positive because its increasing

[dusk smelt]

no

[civic crypt]

I'm not sure if k is 1 immediately

x = f(t)
dx/dt = 1/x^2

[dusk smelt]

inverse means in the denominator

[junior ferry]

ohh

ok i think i understand it now. So then I would integrate it to make the equation?

[civic crypt]

You would solve this differential equation.
In this case
x^2 dx = [k]dt - where I'm not completely sure if k is a parameter or just 1.

This is integrated:
x^3/3 = [k]*t + C

You have 2 conditions. t=0 => x=1cm and t=20 => x=2cm

[junior ferry]

Ohh so i can use those conditions to find the value of c and K

[civic crypt]

t=0 => 1/3 = 0 + C => C=1/3
t=20 => 8/3 = k*20 + 1/3

k=7/60

[junior ferry]

ah and then I can get to the formula given with that information by rearranging

thank you!

[civic crypt]

To me, the killing spot was to realize that inverse proportional contains the parameter of proportionality k

I would have put 1/x^2, without k, and would got stuck.

[junior ferry]

Yeh the wording is often tricky in these type of questions

designed to confuse people like me xD

[alpine sable]

Quickie

If my friend makes 200 off one thing, and 20 off another, and needs to make 1000, how much will that be?

200x + 20y = 1000

[gray gorge]

That's one equation with two unknowns

Many different solutions

Is there any more info?

[alpine sable]

Hmmm, where can I find all possible solutions?

No. Just a irl friend needs to make 1000 in a month.

Helping him calculate how much he'll have to do.

[gray gorge]

Well, it corresponds to the line y = (1000 - 200x)/20 if you rewrite it

Or y = 50 - 10x if you simplify it

[fathom rain]

I need to write an expression for the area to the figure n

I have no idea how to do it

[proud ibex]

what is figure n

[fathom rain]

figure n is the figure number

the first one is figure 1 second one is figure 2 and so on

figure n is the unknown figure number

[proud ibex]

can you see a pattern for the length of each figure?

[fathom rain]

well yeah both lengths increase by one for every figure

[proud ibex]

yep. so can you say something about the length of figure n?

[fathom rain]

well its two lenghts idk how to put it

if it was only the longer side it would just be n+2

but idk about two different lengths

[small swift]

Does this diverge by the cmparison test w/ 1/x^1 ?

[ashen wave]

can anyone quiz me? Like give me examples of categorical data or quantitative data and you tell me if my answer is right or wrong?

[fathom rain]

can yall go to another questions channel

[proud ibex]

so lets call the shorter one the width and longer one length

you said length of figure n is n+2

[fathom rain]

yeah

[proud ibex]

can we also do it for the width?

[fathom rain]

yeah that would just be n then right

[proud ibex]

yep

[fathom rain]

ooooh shit

n(n+2)

that right?

[proud ibex]

there ya go

[fathom rain]

damn easier than i thought thanks for the help!

[proud ibex]

np :)

[alpine sable]

So I gotta find the mean average of X

apparently i gotta use this formula

how do i do that?

[lethal ore]

Here x1 x2 x3 and so on, are the numbers in the upper rows
And p1 p2 p3 and so on, are the numbers in the lower rows

[alpine sable]

(0 * 0,25) + (2 * 0,15) + (4 * 0,30) + (6 * 0,20) + (8 * 0,10) = 3,5

I tried it

But I got 3,5 and I don't understand what 3,5 is

something is wrong i can feel it

[lethal ore]

Care to watch a video about it?

I've one

[alpine sable]

if it isn't too long

[lethal ore]

https://youtu.be/j__Kredt7vY

Totally worth it

[alpine sable]

What I did before was that right?

[ashen wave]

Can anyone explain this to me? It said that there are 3 variables and 2 quantitatives

[strong furnace]

it was

[exotic geyser]

Which is better pure or applied maths

In terms of job opportunities

[digital gulch]

applied really

pure is more for if you want to stay in academia

[alpine sable]

What did I do wrong here?

[rich basin]

-2y - y is not -y

[lethal ore]

A faster approach would be to just add those two equations "@alpine sable"

[tacit jasper]

Can someone help me solve this? i've been trying for hours

[tacit jasper]

?

[quasi scarab]

?

[woven dock]

One can find a unique parabola passing through 3 different non-colinear points.

Here's a site for you in case you're wondering how.
https://www.futurelearn.com/info/courses/maths-linear-quadratic/0/steps/12130

Good luck!

[spark shadow]

Help please

<@&286206848099549185>

Oh ok I am sorry , I posted in #precalculus about an hour ago.

[strong furnace]

,rotate

[strong furnace]

they want you to find the trivial root -1 and then go from there for the given 3 degree polynomial , since you have to solve for the inequality P(x)>0

[strong furnace]

for the first square there is a sequence for corners

5=2^2+1 7=3^2-2 19=4^2+3 21=5^2-4

[upper mesa]

@alpine sable whats ur question?

ok let me try

hang on

can u double check if the equations are copied correctly?

why not

and 77 min is nothing

https://tenor.com/view/rookie-numbers-matthew-mc-conaughey-wolf-of-wall-street-gif-6096185

reason why I ask is because there is no solution

so I think maybe there's typo

with equations

I'm 99.99% sure there is no solution

Don't take my words for it

that's what symbollab says

lol

So yeah I'm very sure

[dawn cave]

who can solving this question

[upper mesa]

what if u just show me the question

and cut you out as a middleman

so there's less room for error

no question, no answer

I love logic

@dawn cave what are u stuck with?

[dawn cave]

I don't understand f:A-->B what's this @upper mesa

[upper mesa]

if f(A) yields B

Like f(x) = Y

[alpine sable]

I have a quick simple question is this channel open

[toxic dust]

Whats the qustion?

[alpine sable]

What number when you take 70 percent of it gives you 150?

[toxic dust]

Do u have little more context

[alpine sable]

Well heres what i mean

On roblox you get 70 percent of what they pay

I wanna make a shirt

Where i get 150 rbx lol

So i divide ig

So like 215?

About?

Is that right

Since it comes to a decimal

So i will have to sell it for more

[toxic dust]

yeah

[empty shore]

i know that LHS = 3sec^2x(tan^3x)^2

but im not sure how that = to rhs

[stark lantern]

(tan^3(x))^2? how did you get that?

[empty shore]

chain rule as it lhs can be rewritten as (tanx)^3

i replaced the tehta with x

easier to type

[stark lantern]

Yes, so it should be 3tan^2(x) times derivative of tan(x)

not sure why you've cubed it

[empty shore]

yeah

bring a 3 out the front

and tan(x) differentiated is just sec^2x

[muted raft]

$\tan(\theta)^2 + 1 = \sec\qty(\theta)^2$

[ocean seal]

zslya

[empty shore]

pog

ok ty

[muted raft]

you're welcome.

[empty shore]

i just missed an identity

ty

[muted raft]

just remember your identities.

[strong girder]

Waiit

[muted raft]

you won't have integer solutions

ugly fractions yes

,w 784a+28b+c=743
3481a+59b+c=28599
7921a+89b+c=38648

[ocean seal]

Results provided by WolframAlpha

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

Requested by zslya#7821

[full wasp]

that is some chunky math

[ocean seal]

Results provided by WolframAlpha

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

Requested by blue guardian3.14#3722

[rain birch]

can someone explain how to solve 2016 pumac b/4: https://artofproblemsolving.com/community/c140h1624757p10182677

I don't follow the arguments presented in the solutions there

[stark lantern]

Do you agree that suppose we had an x such that x = f(x), the given condition would be satisfied?

[fallow pagoda]

"johnathan is twice as old as darren. darren is 3 times as old as bettina. the sum of their ages is 120 years. form and equation and find the ages of each person."
would the equation be (d = darren) :: d +d/2 +3d =120?

because either that equation is wrong or i cant even sovle that equation correct

OHHHH or would be equation be d+2d+d/3=120

nvm

[muted raft]

uh you sure? lol @fallow pagoda

your last eq is however correct

[alpine sable]

can anyone help me?

[glossy current]

you can't do anything I think

[alpine sable]

i didnt get it bro

[glossy current]

Cause you just write the square root over them and that's it

$help

@ocean seal help

[ocean seal]

A brief description and guide on how to use me was sent to your DMs!
Please use ,list to see a list of all my commands, and ,help cmd to get detailed help on a command!

[gray isle]

consider factorisation and (a+b)^2

[alpine sable]

oh thank darkness

got my awnser

[glossy current]

It looks like a solution for that function when it = 0 more then simplify it hmm

[alpine sable]

hmm

[glossy current]

,ask simplify √(2x+1+2√(x^2+x-2))

[ocean seal]

Results provided by WolframAlpha

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

Requested by Darkness#5004

[glossy current]

Hmm make sense

[alpine sable]

yep

[marble prism]

Hello
I want to post questions
How to use bot

[jaunty plover]

@marble prism #resources at the end, and they recently added #latex-help

[glossy current]

Isn't that the definition of lcm for that case

I can tell you there's prime in the multiplication

and there are infinite primes

With prime number, the lcm of them with another prime is the multiplication between them

It is

Yes by factorize

yes

With prime

[acoustic river]

is f(x)=x^3+5x^2 - 2/x a polynomial

[woeful pulsar]

it's not well defined

[woeful pulsar]

what's the definition of polynomial you learnt

does it look like a polynomial with your definition

[glossy current]

2/x makes it not

[obsidian path]

My professor gave me this homework and actually I was playing in the class. So can anyone help me with them?

[full wasp]

bro why werent u paying attention then

[obsidian path]

Cause I wanted to play

[full wasp]

well cant argue with that

[obsidian path]

So tell me the answers fast af

[full wasp]

nah these questions are kinda cracked

[obsidian path]

🙁

[full wasp]

like these aint easy
at least for me they arent

[south fox]

How do you answer this?

[vivid kayak]

oh sorry

[south fox]

np

[vivid kayak]

But ill help

[south fox]

that would be great!

[vale wigeon]

@alpine sable channel busy please move

[fading zephyr]

if you factor out a 2, you get 2(8x^3 - 1). the term in parentheses is a difference of cubes

[vivid kayak]

2(8x^3-1)

then

2(2x-1)(2x-1)^2

and therefore

2(2x-1)(4x^2+2x+1)

[south fox]

Ohhhhhh i see its a difference of cubes

[vivid kayak]

no wait

[south fox]

but how again is 1 a cube?

oh

[fading zephyr]

this is wrong

1 is a cube because 1^3 = 1

[south fox]

ah

[vivid kayak]

A population is normally distributed with a known standard deviation, σ = 14 units. A random sample of size 49 is obtained from this population. The mean of this sample is 45.
What is the lower limit of the 95% confidence interval for the population mean μ? (1 dp)

What is the upper limit of the 95% confidence interval for the population mean μ? (1 dp)

[fading zephyr]

@tight meadow please use an empty channel

you... click on another questions channel

[vivid kayak]

so far im using an excel function for this

but that isn't working anymore

[tight meadow]

already done that, the same thing was said to me

[fading zephyr]

because you didn't use an empty one, presumably

[vivid kayak]

well here you need to kinda hope someone answers your question

[vale stump]

could someone verify i solved these correctly

[queen merlin]

hi

[buoyant edge]

@queen merlin have you attempted the question yet

[limpid urchin]

Can someone show me how Cos^2theta(1+1/sin^2theta)
= (cos^2theta(sin^2theta+1))/sin^2theta