help-10

[obtuse pebble]

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[obtuse pebble]

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[obtuse pebble]

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[livid merlin]

Can someone help me fully factor this, all I really know is that 3 is greatest common factor, dont know what to do from there

[sick wren]

Well what else can you factor from those 3 numbers?

Or, what is multiplied into all of these terms to be able to be distributed out?

[livid merlin]

isnt 3x the only number that really works for all those numbers though?

[tardy epoch]

Not the only, but it is the greatest

[livid merlin]

well 2 wouldnt work so I mean you could say 1

[tardy epoch]

The remainder after taking out 3x might be factorable

[heavy thicket]

3x is the GCF

[livid merlin]

oh good point

so if I factor out 3x Id have
3x(4x² - 20x + 25) right?

[sick wren]

Yes

[fierce lagoon]

Factor out 3x, like you did:

$$3x(4x^2 - 20x + 25)$$

[warm shale]

Umbraleviathan

[fierce lagoon]

You can factor out that quadratic further

It's a perfect square

It seems

[livid merlin]

should i factor out the standalone 25

[fierce lagoon]

No

You just gotta throw spaghetti at the wall now lol

List out factors of 25 and 4

[livid merlin]

doI have to factor out all the equation tho because since its 25 and not 25x wouldnt it not be possible to facotr the whole thing out?

[fierce lagoon]

I mean you could

If you want fractions

Well you can first find out if it is even factorable by checking its discriminant:

$$b^2 - 4ac$$
$$(-20)^2 - 4(25)(4) = 0$$

Since the discriminant is 0, there is a way to factor it as a perfect square, such that:

$$(ax+b)^2 = a^2x + 2abx + ab = 4x^2 - 20x + 25$$

[livid merlin]

uhh how do I do that?

[warm shale]

Umbraleviathan

[nocturne minnow]

Do you know how to factor in general?

[fierce lagoon]

Then you can just match terms

another way is to factor in general, but it can be overwhelming with leading coefficients that arent 1 or -1

and i always check if the quadratic is perfect square

Because then you kinda have to think of this:

And it sucks ass lol

[livid merlin]

wow

which of my values is a and b lol

and do i determine a and b values based off the original equation or when the 3 has been factored out?

[fierce lagoon]

well heres this

lemme copy and paste

and

uh

edit it

Well you can first find out if it is even factorable by checking its discriminant:

$$b^2 - 4ac$$
$$(-20)^2 - 4(25)(4) = 0$$

Since the discriminant is 0, there is a way to factor it as a perfect square, such that:

$$(ax+b)^2 = a^2x + 2abx + ab = 4x^2 - 20x + 25$$

So, start matching terms. If $a^2x + 2abx + b^2 = 4x^2 - 20x + 25$, then:

$$a^2 = 4$$
$$2ab = -10$$
$$b^2 = 25$$

[warm shale]

Umbraleviathan

[fierce lagoon]

@livid merlin i also fixed a typo lol

[livid merlin]

okay so which equation do i put those values into?

[fierce lagoon]

wdym which equation

this is all to factor $4x^2 - 20x + 25$ without having to throw spaghetti

[warm shale]

Umbraleviathan

[livid merlin]

so is 4x^2 - 20x + 25 the current factored form im honestly really confued rn lol

[nocturne minnow]

No

Do you know how to factor in general?

Because you can apply whatever factoring method you know

[heavy thicket]

Slide divide

[fierce lagoon]

no

[fierce lagoon]

this is all for 4x^2 - 20x + 25

[heavy thicket]

You can factor further by this method ^

[fierce lagoon]

$4x^2-20x+25$ is a pain to mentally factor out. You can first find out if it is even factorable by checking its discriminant:

$$b^2 - 4ac$$
$$(-20)^2 - 4(25)(4) = 0$$

Since the discriminant is 0, there is a way to factor it as a perfect square, such that:

$$(ax+b)^2 = a^2x + 2abx + ab = 4x^2 - 20x + 25$$

So, start matching terms. If ${\color{lime}{a^2}}x + {\color{cyan}{2ab}}x + {\color{orange}{b^2}} = {\color{lime}{4}}x^2 - {\color{cyan}{20}}x + {\color{orange}{25}}$, then:

$$a^2 = 4$$
$$2ab = -20$$
$$b^2 = 25$$

[warm shale]

Umbraleviathan

[fierce lagoon]

edited it, again

This is all to factor the quadratoc

[livid merlin]

Okay is there a c value im also supposed to have though?

[fierce lagoon]

wdym c value

no

$$(ax+b)^2 = a^2x + 2abx + ab = 4x^2 - 20x + 25$$

[warm shale]

Umbraleviathan

[fierce lagoon]

idk why you need a c

[nocturne minnow]

It's because this is a special quadratic

It's not going look like the usual form of $ax^2 + bx + c$

[warm shale]

dldh06

[livid merlin]

okay how would I start factoring the quadratic with this info tho that part confuses me

[fierce lagoon]

this is how you factor it

youre trying to find a and b for (ax+b)^2 = 4x^2 -20x + 25

[livid merlin]

$(ax+b)^2 = 4x^2 -20x + 25$

[warm shale]

Shreader87

[fierce lagoon]

the (ax+b)^2 is the factored form

[livid merlin]

(ax + b)^2 - 25 = 4x^2 - 20x

would I do it by fully doing this

[nocturne minnow]

No don't do that

[livid merlin]

oh

okay

[nocturne minnow]

Have you heard of the term perfect square quadratic?

[livid merlin]

no I havnt

[nocturne minnow]

So that's the method Umbraleviathan is showing you

But in general, do you know how to factor a quadratic?

[livid merlin]

Im not very good at factoring in general and Ive done factoring for non quadratic equations but I dont think Ive ever properly done it for an equation like this

[nocturne minnow]

https://www.youtube.com/watch?v=lQLTx33Plgo&ab_channel=BrianMcLogan
Here's a video on Umbraleviathan method

[fierce lagoon]

this is for leading coefficients

[nocturne minnow]

https://www.youtube.com/watch?v=4v-EQIxqpMQ&ab_channel=TheOrganicChemistryTutor
And factoring in general

[fierce lagoon]

but we have an easier case

[livid merlin]

so 2 and 5 can be multiplied to get 4 and 25

so Im assuming those both can be used to factor it

[fierce lagoon]

well, there's also -2 and -5

[fierce lagoon]

it just as to satisfy the last 3 things

[livid merlin]

I thought for function you cannout use -5 and square it

because it would be undifined

[fierce lagoon]

Not if the unknown variable is the one being squared

If the variable is being squared, you have to take negative and positive

(-5)^2 = 25

[livid merlin]

oh okay

how would I know if its negative or positive then

[nocturne minnow]

Am I being invisible to you? You can look at the videos I sent

[fierce lagoon]

for like, the 4th time:

$$a^2 = 4$$
$$2ab = -20$$
$$b^2 = 25$$

has to satisfy those

[livid merlin]

so it would just be 2 and 5 then

[nocturne minnow]

No

As mentioned, you can have -2 and -5

Because it needs to satisfy the second equation that Umbraleviathan stated

And as I stated, watch those videos I sent

It will help you

[warm shale]

Umbraleviathan

[livid merlin]

Im honestly in a really bad head space right now, im gonna re watch those videos properly sorry yall for being like a total dummy in this thread

[fierce lagoon]

here it is again if you need to see why i made a perfect square

$4x^2-20x+25$ is a pain to mentally factor out. You can first find out if it is even factorable by checking its discriminant:

$$b^2 - 4ac$$
$$(-20)^2 - 4(25)(4) = 0$$

Since the discriminant is 0, there is a way to factor it as a perfect square, such that:

$$(ax+b)^2 = a^2x + 2abx + ab = 4x^2 - 20x + 25$$

So, start matching terms. If ${\color{lime}{a^2}}x + {\color{cyan}{2ab}}x + {\color{orange}{b^2}} = {\color{lime}{4}}x^2 - {\color{cyan}{20}}x + {\color{orange}{25}}$, then:

$$a^2 = 4$$
$$2ab = -20$$
$$b^2 = 25$$

FUCK

[warm shale]

Umbraleviathan

[fierce lagoon]

you can refer to what i did to understand why i did what i did

[livid merlin]

Okay ive saved that msg and both the videos ima take a look at all that stuff properly sorry again for sorta wasting everyones time

thank you for the help tho anyway

[fierce lagoon]

np

i got nothing to do lol

other tha ngetting carpal tunnel from 20+ cps

[obtuse pebble]

@livid merlin Has your question been resolved?

[obtuse pebble]

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[inland hemlock]

I do not get second order partial derivatives.
My professor just pulls this out and my answers are all wrong.

[inland hemlock]

What am I doing wrong?

The explanation in my book kind of sucks.

Oh wait, I see what I'm doing wrong

The terms with only constants in them become 0

.close

[obtuse pebble]

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[distant schooner]

how do i find a?

[prime scarab]

,rotate

[distant schooner]

im not sure what a is actually

[prime scarab]

https://www.youtube.com/watch?v=W2IMWLX9n8M

[distant schooner]

alr got it

ty

.close

[obtuse pebble]

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[timid silo]

For this question, do I setup an equation? If so, I added all the values (x-2) + (2x) + (2x-7) This got me 5x-9

Then, I set it equal to 6

Then I solved for X

I got 3 as my answer

Am i overthinking it?

[next reef]

5x-9 is the total distance, not x.

[timid silo]

Yea

Could it be B then?

[next reef]

Average speed=Total Distance/Total time

Answer is 6.

[timid silo]

Oh

shit

i was overthinking it

[next reef]

(B)

[timid silo]

at first i was like i should just do 2 x 6

2 x 3

[next reef]

It happens

[timid silo]

yea

ty

wait

i dont think that formula works

because were solving for total distance

OH

lol

[timid silo]

average speed times total time = total distance

just divide

ty

.close

[obtuse pebble]

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[versed cave]

answers had no unit of measure 💀

[next reef]

should be 'miles'

[timid silo]

sat question man

[next reef]

sat seems to be very easy when compared to the indian admission exam!

[obtuse pebble]

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[lucid canyon]

hi guys

[next reef]

[versed cave]

@lucid canyon ???

[lucid canyon]

yes

[versed cave]

uhm.. do you have a question? ahah

[obtuse pebble]

@lucid canyon Has your question been resolved?

[obtuse pebble]

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[wanton tendon]

😭

happy birthday @lucid canyon

[obtuse pebble]

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[torn lotus]

I NEED HELP

[torn lotus]

Idk if statistics count as math

[royal basin]

statistics does count as math, and you should just post your question

[torn lotus]

How do I Plot this data into a scatter plot?

Without copying and pasting

[royal basin]

what file format is this and are you using R

[torn lotus]

How do u use r?

[royal basin]

that... does not answer my question

[placid nebula]

how do i do this

[royal basin]

@placid nebula stop posting in channels occupied by other people. #❓how-to-get-help

[torn lotus]

How do I find the file format?

[royal basin]

the file you've shown should be on your computer somewhere

and its file extension should be displayed

i think it might be a csv

i wanted to make sure

[torn lotus]

It’s not downloaded . So I really don’t know

[torn lotus]

Yes I think it is

It says census150.cvs at the top

[royal basin]

cvs?

or csv

[torn lotus]

I mean csv ***

[royal basin]

ok, and you still have not made it clear to me whether you are using R for this or not

[torn lotus]

What is r exactly?

[royal basin]

it's a programming language geared towards statistics and data analysis

[torn lotus]

It’s says I should use r.

[torn lotus]

Oh

How is it done?

[royal basin]

idk
google "R import data from csv"

[torn lotus]

So basically I need to create a scatter plot using the data of Age and Percent family income. There’s like 152 data so I’m guessing there has to be like a hack instead of copying and pasting each plot info excel right?

[torn lotus]

Oh ok

[royal basin]

excel can open CSVs too

[novel knoll]

Read.csv(…)

[torn lotus]

How???

[novel knoll]

But sounds like you haven’t paid any attention so far in your class if you don’t know that

[novel knoll]

And if you open the file on your pc it is downloaded

[royal basin]

google "how to open CSVs in excel"

[torn lotus]

My class just started like a few days ago.

[royal basin]

google is a powerful thing

[torn lotus]

Oh. Right 😂

[novel knoll]

And? Point still stands?

You didn’t even know what R is or any very common commands

[torn lotus]

Yea I don’t know

My professor hasn’t taught it yet.

So idk how she expects us to do this

How do I download a cvs file?

Nvm

[novel knoll]

.

[torn lotus]

Ignore that

WOW IT ALL TRANSFERRED INTO EXCEL SO QUICKLY

Thank u guys for helping my use my brain 💜💜💜

.close

[obtuse pebble]

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[lunar lagoon]

guys so now i get h=-3t^2+4t-6/5

and k as 4t^2+8t+3/5

now how do i find K

[obtuse pebble]

@lunar lagoon Has your question been resolved?

[obtuse pebble]

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[lunar lagoon]

.reopen

[obtuse pebble]

✅

[meager sapphire]

.close

[obtuse pebble]

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[meager sapphire]

it's and not abd

[proven zephyr]

uhh

[obtuse pebble]

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[dreamy current]

how can a non linear line be parallel to y=-8x

d/dx of y is -8x^-3

where do i go from there?

[royal basin]

the tangent is to be parallel to y=-8x.

[dreamy current]

i get it now, the wording is just confusing for me

thanks

.close

[obtuse pebble]

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[neon falcon]

How would I find the range of this?

[neon falcon]

never mind

i figured it out

.close

[obtuse pebble]

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[neon falcon]

Hello I just put this in a graphing calculator and I just want to make sure A is right

[quaint glen]

Yes, its a

[obtuse pebble]

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[drifting wraith]

because what if they are really bad

you would end up learning from very bad books

they mean what if people lied, can't trust people

well that's the same idea except you don't even have someone's word that they are best

idk, not obvious

there's no solution anyway

it's an easy trap with no easy countertrap

[obtuse pebble]

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[royal basin]

takes a lot of balls to ping mods individually lol

[main cedar]

u good bruv?

[upbeat plinth]

b&

.close

[obtuse pebble]

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[main cedar]

lol

[obtuse pebble]

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[radiant quail]

I have pretty fked space, i need help with algorithm on it

[radiant quail]

I created a hexagonal space, by transforming cartesian space

It looks like this

To move on it, i created a new plane

Here is how it looks like

I detect mouse clicks on that plane

How to find out, which tile i pressed?

That's how coordinates look like

My domain on x and y is
integers in [-6, 6]

[timid silo]

https://stackoverflow.com/questions/22180304/snap-to-closest-hexagon-centre-in-hex-based-grid

[radiant quail]

Looks good

Thank you

.close

[obtuse pebble]

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[timid silo]

nvm

i got it

.close

[obtuse pebble]

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[proper forum]

I don't quite understand how the underlined step is possible.. r & r will cancel out so LHS won't be equal to RHS anymore

[royal basin]

this is a typo

they meant r+1-1

[proper forum]

I see. Thank you for your assistance and time.

.close

[obtuse pebble]

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.reopen

[obtuse pebble]

✅

[proper forum]

A different query... how was the sum of n factorials calculated in the solution? (Final step) I am not aware of any formula for it (1!+2!.... n!)

[novel knoll]

Stuffs cancel doesn’t it?

T_1+T_2=(2!-1!)+(3!-2!)

Does anything cancel?

See a pattern?

[proper forum]

I see.. though is there a general formula for solving the summation of factorials?

I did search it up but the answers were fairly jargonistic.

[novel knoll]

Not anything pretty, no

[proper forum]

I see.. Thank you for your assistance and time.

.close

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[cunning citrus]

how do I prove this in a way that a 13-14 year old could understand

"prove that no straight line can be drawn within a triangle which is greater than the greatest side of the triangle"

[kind hawk]

well how much of proofs does that 13-14 year old understand

[rigid turtle]

the shortest path between two points line

[kind hawk]

I guess you could do it by repeatedly using the triangle inequality. might be messy but each individual step should be understandable

[cunning citrus]

yeah sure

wait

how could u use that

triangle inequality

[rigid turtle]

a+b>c

[cunning citrus]

ikbut how in the question

[rigid turtle]

tricky bc not straight line can be to infinity

[cerulean tulip]

Well first you could start with proving that if the longest lines endpoints must lie on the edges of the triangle

[cunning citrus]

so there could be 2 cases of the line in the triangle
1 that it's end points are corner and edge
2 edge to edge

[cerulean tulip]

Yes

[cunning citrus]

I got it for case 1

but not case 2

[kind hawk]

well first case is that the two endpoints are somewhere in the triangle. using triangle inequality you can show that the line between them is shorter than the line from at least one of them to an edge.
so next step is that one of the endpoints is an edge and the other is somewhere in the triangle. again using triangle inequality you can show that this is shorter than one of the sidelengths
and then you take the max of all sidelengths

[cunning citrus]

how about angle bea>eda so ba>ea

[kind hawk]

use triangle inequality on the triangle ABE

or one of the other triangles involving either E or D

[cunning citrus]

wait I got it

sorry

thanks for help

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[pulsar mulch]

So maths is all about numbers so I wanted to know how they worked. So I got an doubt. How can 1 come after 0.there are these decimals between 0 and one that are 0.1,0.2,0.
3,... and so on . So decimals are another form of fractions .fractions are another form of division. Divison is nothing but repeated subtractions. (Ex- multiplication is nothing but repeated additions )and subtraction is a degrade of value so on the number line how can 1 come after 0

[lofty jay]

what

[timid silo]

There are different sets of numbers

there are natural numbers (0,1,2,3,4,....)

there are integers (..-3,-2,-1,0,1,2,3....)

there are rational numbers, which are all the numbers which can be expressed as a fraction of two integers

the rest of the real numbers are called irrational numbers.

[pulsar mulch]

Can anyone please help with this🥺

[slim cove]

what exactly is your question?

I don't understand

[pulsar mulch]

I am saying that why does one come after 0

[slim cove]

because we define 1 as the natural number that comes after 0

1 is just the name for it

[novel knoll]

What else do you want there to come after 0?

[slim cove]

there are infinite real numbers between 0 and 1

but 1 is the first natural number after 0

[pulsar mulch]

Exactly that there are these decimals between 0 and one that are 0.1,0.2,0.
3,... and so on . So decimals are another form of fractions .fractions are another form of division. Divison is nothing but repeated subtractions. (Ex- multiplication is nothing but repeated additions )and subtraction is a degrade of value so on the number line how can 1 come after 0

[novel knoll]

Ah yes copy-pasting your rambling again

[novel knoll]

Did you actually read any of the answers above?

[slim cove]

yes but what is your question

[pulsar mulch]

Yes so when the value degrades shouldn't it hit 0 or a negative integer why is it one

[novel knoll]

What?

“The value degrades”?

Type a full sentence using proper English

So your question is understandable

[pulsar mulch]

So ok there are the decimals between 0 and 1 those are 0.1,0.2,0.3 ... and so on clear till here

So decimals are a form of division right so shouldn't the value degrade because of divison

[novel knoll]

Degrade?

You mean decrease?

[pulsar mulch]

Yes

[slim cove]

chill their first language might not be english

at least that's always the assumption I make online

[pulsar mulch]

I am so sorry I am a 7 grade kid from india so I can't house proper english

[novel knoll]

Neither is mine. But him copy-pasteing his ramble again is obv pointless

[novel knoll]

“The value”? What?

[slim cove]

wait 7th grade? I think the minimum age for discord is 13

[slim cove]

if you represent it as fractions then you get 0, 1/10, 2/10, 3/10, ..., up to 10/10 and then 10/10 = 1

idk if that answers your question

[pulsar mulch]

When I ask these questions in school the mock me so that's why I thought to ask here

[royal basin]

well your questions do not make much sense to us

0.1, 0.2, 0.3 and so on are between 0 and 1. their values are less than 1. is this something you are having trouble with?

[pulsar mulch]

Sorry for disturbing you guys 😢

[slim cove]

nah it's okay ask your question

we just don't understand what you are asking right now

[pulsar mulch]

So it's that is saw a video on ramanujan paradox so the sum of infinity is -1/2 so it might the same the decimals between 0 and 1

[slim cove]

Oh I see

[pulsar mulch]

The aim of infinity is -1/12

[slim cove]

the sum of 1+2+3+4+.. is not -1/12 (in the way that we usually mean "sum")

that's a common misconception caused by that one numberphile video

if you want to learn more here is a video explaining https://www.youtube.com/watch?v=YuIIjLr6vUA

[pulsar mulch]

Thank you very much you guys are the best

[slim cove]

no problem

[obtuse pebble]

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[pine sail]

Let $\sum_{k=1}^{360}{\frac{1}{k\sqrt{k+1} + (k+1)\sqrt{k}}}$ be the ratio of two relatively prime integers m and n. Then m + n + ?

[warm shale]

What the hell am I doing here?

[pine sail]

This should telescope, I just am not able to do that.

[kind hawk]

what do you mean with m+n+?

[pine sail]

Sorry.

It is just m + n

[kind hawk]

my first step would be to multiply numerator and denominator by $k\sqrt{k+1}-(k+1)\sqrt{k}$

[warm shale]

Denascite

[kind hawk]

have you tried that?

does that lead somewhere?

[pine sail]

I did do that, I was not able to rewrite the numerator because of the sqrt.

[kind hawk]

I would assume that you can probably cancel sum stuff

after you write it as the sum of two fractions

or in this case a difference

[pine sail]

Okay, so,

[warm shale]

What the hell am I doing here?

[kind hawk]

cancel the k^2

then just pull the fractions apart

and cancel everythign until you are left with 1/sqrt(something)

[pine sail]

Wait, what I got it already, I was cancelling the terms wrong and was ending up with a + before.

Now that I have corrected it, the terms cancel pretty nicely.

Thank you very much, it is doable from here.

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[tall arrow]

when in tests, i use Microsoft Word to solve equations in my maths test, but when i write equations and attempt solving them, they look quite dull

example of how i write equation in test:

Question A: 3/5 : 1/7 = 3/5 * 7 = 21/5

or in some cases

3/5 : 1/7
= 3/5 * 7
= 21/5

[tall arrow]

is this the way you're intended to solve equation in Word, or is there some better way of writing equation than the ones above?

[hexed agate]

Wait you guys don't write on paper?

[tall arrow]

in some cases we are required to use computers and not papers, yes

that's why I use Word to solve this, which i believe is strongly confusing to write and read

[kindred oasis]

You can use the equation tool in word, but it's pretty bad and it takes ages to write a whole solution to an equation

[timid silo]

learn latex

[kindred oasis]

Yeah that's what I would recommend

It's really easy

[tall arrow]

I've heard of LaTex, but I'm not sure whether my teacher would understand such commands shown on screen

[timid silo]

it compiles to readble

[pine sail]

Your teacher does not have to decipher those.

[tall arrow]

it may appear as if i was using LaTex as a calculator

[timid silo]

like $\frac{a}{b}$

[warm shale]

Bananach

[pine sail]

Do you have to post a file or what?

[tall arrow]

Yeah, that works, but when using LaTex, does the teacher see the LaTex code that I'm writing?

[timid silo]

if you want him to

you can just export them to pdf

and he will the see the human readable latex

[tall arrow]

I'll attempt messing around with latex in word and dicsuss with my teacher if it's suitable or not

it's probably a lot more simpler than writing the entire thing in form of a sentence

thanks a lot folks

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[hexed agate]

(2n + 3n^2 + n^3) / (n^3 - n)

Maybe it leads somewhere

Also it says k should be involved

(2n + 3n^2 + n^3) / (n^3 - n) multiplied by k maybe?

So

[nocturne minnow]

It also does say involve the last two parts

[hexed agate]

(kn^2 + 3kn + 2k)/(n^2-1)

?

[obtuse pebble]

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[timid silo]

what's the rule here?

[wanton tendon]

its just called the logarithm to exponential form rules

[timid silo]

thank you

[wanton tendon]

alg

[timid silo]

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[obtuse pebble]

@mystic torrent Has your question been resolved?

[obtuse pebble]

@mystic torrent Has your question been resolved?

[nocturne cloak]

Do you need help with all 4 parts?

[mystic torrent]

i think if i got help and an explanation for one part i can do the rest.

[nocturne cloak]

Ok I will take a look at part a

So you know about binomial distributions right?

[mystic torrent]

yes

[nocturne cloak]

and pdf vs cdf?

[mystic torrent]

i havent learned that specifically but its implied in some other problems

this is homework from the x bar

so i didnt think i would need to learn more to solve

[nocturne cloak]

Could you find the probability that 14 or fewer live past 90?

Because that is the complement of 15 or more living past 90 right

[mystic torrent]

I could find the complement and go from there. I used salt so it was a program that was given to me to use in the past. My teacher said that i needed the normal distribution table

[nocturne cloak]

The would be a binomial distribution, not a normal dist

[mystic torrent]

I thought it would be binomial too since it would be more accurate, im not sure why I got that wrong if I did use binomial

The answer that I typed in for A, B, and C were all calculated using binomial

[nocturne cloak]

What did you get for a

[mystic torrent]

0.9954

rounded to the 4th decimal

[nocturne cloak]

Wait that's what I got uh oh maybe I don't remember this as well as I thought

[mystic torrent]

Yea, im not sure what I did wrong too. Considering that binomial would be more accurate idk why i would have to use normal distribution lol

[nocturne cloak]

Oh wait yeah it helps to read

It wants you to use the normal distribution because it approximates the binomial distribution when you have a large number of trials

[mystic torrent]

oh, okay. i didnt think about that. I'll try and solve it and see if it still wrong

[nocturne cloak]

Oh right and presumably you're given the std dev formula

Because I don't remember that off the top of my head

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[smoky panther]

how do i answer this question?

[timid silo]

Is there any negative real number which is a power of 2?

[restive ridge]

that's wrong

there are solutions to those equations

[timid silo]

Complex

Not real

[restive ridge]

exactly

[smoky panther]

yea the question is asking to explain why

[smoky panther]

uhh no?

[timid silo]

It's asking to explain why there aren't

[timid silo]

So is there a solution to the first equation?

2 to the power of what = -8??

there is no real number which satisfies that

[smoky panther]

nothing

[timid silo]

So there is no solution to that

[smoky panther]

so all i have to write for the first question is that no negative real number can be to the power of 2?

[timid silo]

no, no negative real number is a power of two

[smoky panther]

okay i gotchu, the question says use math terms and different reasoning, but thats the only reason we have thought of

and i think thats the only actual reason there are no solutions

[smoky panther]

so is there anything else i should add to that question or just write this?

[austere heath]

that reasoning is solid

you can say that a positive number raised to any real-valued exponent will always be positive

[smoky panther]

i see

[smoky panther]

okay just a sec imma write that, do you think i should also use an example like this?

[austere heath]

well given your problem

you don't really need an example beacuse its not a generalised proof

its one problem asking whether $2^x=-8$ is possible

[warm shale]

ethan

[smoky panther]

ah i see

[austere heath]

so you can just say its not, and provide proper justification

and same for part b

[smoky panther]

what should i write for part b? no positive real number is a power of -2?

[austere heath]

part b is actually a little bit more concrete and easy to understand

[austere heath]

well what is $(-2)^2$

[warm shale]

ethan

[timid silo]

but (-2)^2 = 4

[smoky panther]

oh shoot that is right

[austere heath]

for part b, you can visualise it as such

$(-2)^x=8 -> (-1)^x(2)^x=8$

[warm shale]

ethan

[austere heath]

if that makes it easier to understand

[smoky panther]

yea

[austere heath]

and since $(-1)^x$ only alternates between -1 and 1

[warm shale]

ethan

[austere heath]

the only way you can get to 8 is $2^3$

[warm shale]

ethan

[austere heath]

but then it doesn't work because $(-1)^3$ is -1, not 1

[warm shale]

ethan

[austere heath]

therefore there is no solution

that's an answer specific to that exact problem

[smoky panther]

ohh i understand

[austere heath]

but you can also generalise it

up to you!

[smoky panther]

so how would i put it in a sentence. like "it is only possible to get 8 from 2^3, however -1^3 is equal to -1. therefore there is no solution"?

i assume there is a more simple wording i can use that im just not thinking of rn

[austere heath]

that maybe overcomplicates it a bit

uhh

you can say

you can say that (-2)^x separates into (-1)^x(2)^x, and that (-1)^x is an alternator so the value 8 relies on the term (2)^x. Then yes you can go into detail about having x=3 as your chosen value

[smoky panther]

perfect

thankyou sm!

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[manic matrix]

Have I been doing this correctly so far? I have done part a and b. Also how would I go about doing part c?

[obtuse pebble]

@manic matrix Has your question been resolved?

[manic matrix]

,rotate

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[wanton tendon]

Do you know the corresponding angle law

Nvm I mean

Because the 2 lines are parallel, 2x and 4x are on the same plane, so you can move 2x up to next to 4x. There, you can see that there is a total of 6x within a line of 180°

[obtuse hatch]

okay thx

[wanton tendon]

Did you get it?

[obtuse hatch]

yes

[wanton tendon]

what is it

[obtuse hatch]

30

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[wanton tendon]

👏

[obtuse pebble]

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[sweet flint]

What is the language of this finite state machine?

[restive ridge]

show work

[sweet flint]

Set of all words ending in (0 or 1)

Has zero non-accepting black hole state except for final state

The shortest accepted word is 1. (1)n and then have 1. Its regular expression is (01)∗1.

[sweet flint]

Had not finished typing sorry.

[elfin burrow]

seems like (011)* (00 | 010 | 1) (0 | 1)*

let me know if you can find something wrong with it

i can explain my reasoning

[sweet flint]

Looks good, thanks i was struggling to find some resources on Language of the finite state machine.

Thanks

[elfin burrow]

i'll send my work over because the way i got there is important to know

do you know the strategy where you delete one vertex at a time?

every vertex in between the start state and final state

i'll show you in like 5 mins brb

so i took the original automata and deleted each vertex between A and D, combining the edges as needed

and the final automata gives me that regex in red (should be pretty easy to see why)

[obtuse pebble]

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[torpid scroll]

I got a quick question guys can sin4x turn into 4sinxcosx? by the doublke angle identity? even if the angle is 4?

[high lily]

the double angle identity could be applicable
but that's NOT quite how it works

[torpid scroll]

oh

cause i believe the identity is sin2x is 2sinxcosx

right?

[high lily]

yes

[torpid scroll]

and I asked once here if cos4x

then it can equal cos^2 2x - sin^2 2X

[high lily]

that isn't true either

[torpid scroll]

waut

[torpid scroll]

how bout now

[high lily]

assuming you mean
cos(4x) = cos^2(2x) - sin^2(2x)
that would be valid

[torpid scroll]

yes

but back to my first question what would be right identtiy?

[high lily]

$\sin\br{\text{this}} = 2\sin\br{\frac{\text{this}}{2}}\cos\br{\frac{\text{this}}{2}}$

[warm shale]

ℝamonov

[torpid scroll]

about this one

thats not a double angle?

im kinda unfamiliar with that one

[high lily]

that's the double angle identity

you start with the sine of something

and express that with the sine and cos of half of that

[torpid scroll]

I thought it was only 2sinx cosx?

whats with the divide by 2?

[solar trellis]

Let x = this/2

[high lily]

this is double this/2

2x is double of x

[torpid scroll]

oh

oh so its written that way

[torpid scroll]

its just a little simplified when written like this?

[high lily]

that's the simplest case

[torpid scroll]

oh so if u plug in sin 6

[high lily]

i rewrote it so there's less room for misinterpretaion

[torpid scroll]

it would be 2sin 3x cos 3x

[high lily]

as it seemed that you thought
$$\sin(ax) \wthonk a\sin(x)\cos(x)$$

[warm shale]

ℝamonov

[high lily]

sin(6x) = 2sin(3x)cos(3x)

[torpid scroll]

I see now

alright thanks so much that cleared so much

.close

[obtuse pebble]

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[little shuttle]

From her raft, a 1.6 m tall sailor sees the top of a 64 m high cliff on the horizon. Give the maximum distance she would have to swim to reach the coast. Hint: Radius of the earth: 6378 km. Round your answer to the nearest meter.

[little shuttle]

this is somehow a right angle problem or possibly an arclength problem from what I can tell

[hexed agate]

Well draw the whole thing

[little shuttle]

we would first need to find the maximum distance the sailor can see

right?

[hexed agate]

I have no idea. I merely suggested you to draw

And see where it goes

[drifting wraith]

you need to find the arc i think yeah

whoops where's my center

[obtuse pebble]

@little shuttle Has your question been resolved?

[obtuse pebble]

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[fluid snow]

For this, there is a theorem that says $\angle ABC = \frac{arc(AC)}{2}$

[warm shale]

Kepe

[fluid snow]

What is implied with arc(AC)?

The measure of the angle of the arc?

[timid silo]

the measure of the arc

or the measure of the central angle of the arc

[fluid snow]

Alpha?

[timid silo]

Yes

[fluid snow]

Alr, thx

.close

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[late oar]

Ok

[obtuse pebble]

@late oar Has your question been resolved?

[fierce lagoon]

The most of all time

[obtuse pebble]

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[cinder obsidian]

Hello. I have a rather advanced Topology question related to topological data analysis. A major technique in TDA is persistence homology, and the resulting diagrams. My question is: Is it possible to take a point cloud, characterize it using persistence homology, and then reconstruct a point cloud from that diagram? it doesn't need to be the same point cloud, just one that is topologically isomorphic with the original. For context, I am working in inorganic materials discovery using generative machine learning models. I am using TDA as dimensionality reduction so that bulk structure can be learned by the model (which is usually limited to a few dozen nodes/atoms). It is my hope that generated materials, which will partially be in the form of persistence diagrams will be able to be fully reconstructed into the point cloud that represents the global atomic structure.

[fierce lagoon]

#diff-geo-diff-top #point-set-topology you'll get more help there

[cinder obsidian]

Thank you. Would it be ok to simply repost this in those channels, and should I post in one before the other?

[fierce lagoon]

I highly doubt people would answer in a help channel

Yeah just repost

But close this

[cinder obsidian]

.close

[obtuse pebble]

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[cinder obsidian]

One quick issue: I don't have permission to post in these channels. Is this simply a matter of being in the server for enough time?

[fierce lagoon]

#info

You gotta get a special role

[royal basin]

#get-advanced-access

[cinder obsidian]

Thanks. There's a lot going on with this server. It's very well organized but still a bit difficult to orient myself. Sorry for not looking there first, but I appreciate your help 🙂

[obtuse pebble]

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[timid silo]

I need help with this question

[novel knoll]

Start from inside and move out

What is f(5)?

[violet flame]

g(f(5))

so, it is g(3)

it is 1

[timid silo]

First evaluate f(5)
Then put the result of f(5) into g

[timid silo]

is f(5) 3?

[violet flame]

yh

given na

[dawn light]

I need help with this question

[timid silo]

uhh

im asking for help first

[dawn light]

oh sorry

[timid silo]

is the answer 12?

[violet flame]

how???

g([f(5)]

so it g of function if f

so, it is g(3)

=1

[timid silo]

im very confused

to what u did there

[violet flame]

it is function g of function f

g ( function f of 5)

function f of 5 is 3

so, g(3)

=1

[timid silo]

how is g(3) 1?

[violet flame]

it is given

[timid silo]

thats what i dont understand

[timid silo]

but next to 3 is 12

can u like circle it or sum

[timid silo]

okay looki

f of 5 is 3

but what did u do to get the next step

[violet flame]

g(3) is 1

[timid silo]

where tf does it say that

WAIT NVM

[violet flame]

the circle i put in img

[timid silo]

IM STUPID

so where it says x

u match with

the g(x)

[violet flame]

bingo

f(x)*

[timid silo]

thank you

lol

[obtuse pebble]

@timid silo Has your question been resolved?

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[fickle narwhal]

yes so I have many questions, have anyone come across this kind of maths before if so can anyone help me please thank you

[austere heath]

can you post a specific question

it looks like that's an entire practice exam

[void pelican]

also in the future we advise that you don't post entire files bc that can look sus

screenshots >>>> files

[austere heath]

^^^

[fickle narwhal]

oh okay thank you aha

tbh all of the questions im stuck on I have never learn this kind of maths before

this is only a mock paper so i just wanted to see if anyone came across this maths before

i need help finding sources to learn this kind of maths either by youtube videos or website, anything to do with this kind of math i would be very grateful

[warm canopy]

Some buzzwords for you: linear algebra, differentiation & partial differentiation, probability & statistics - the various spaces and distributions,

Try khan academy, will have some of that stuff on there

[fickle narwhal]

awesome thank you

[obtuse pebble]

@fickle narwhal Has your question been resolved?

[obtuse pebble]

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[obtuse pebble]

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[cunning citrus]

https://cdn.discordapp.com/attachments/269573202018041856/998274905999151104/image0.jpg how do I prove this

[austere heath]

can you post the triangle

[cunning citrus]

there was no triangle in the question so I made on my self

[austere heath]

hmm

show me the triangle that you made?

[cunning citrus]

It says x could be any point so I just did a random one

<@&286206848099549185>

[oblique sage]

Because a hypotenuse is the longest side of a triangle

Since it’s travelling vertical and horizontal distance while AX is only vertical

[cunning citrus]

x could be any point

[oblique sage]

Okay, but it’s assuming that at the point x, you draw a horizontal line to the hypotenuse to make a triangle

[cunning citrus]

yes

but it won’t be a hypotenuse if ax is not perpendicular to the base

[obtuse pebble]

@cunning citrus Has your question been resolved?

[cunning citrus]

I’m just gonna close since no one is answering

.close

[obtuse pebble]

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[obtuse pebble]

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[wet bear]

Solve $\int_0^x f(t);\dd t=f(x)-1$. \
\textit{Cursed ``solution" coming up.}\
We want $\int f=f-1$. Rewriting, $1=f-\int f=f(1-\int)$. Therefore,
[f=\frac{1}{1-\int}=1+\int+\iint+\iiint+\cdots]
by series expansion. Also, $\int$ can be evaluated as $\int1;\dd x=x$, and similarly $\iint=\int\left(\int\right)=\tfrac{x^2}2$ and so on.\
Putting this all together, we have that $f=1+x+\tfrac{x^2}2+\tfrac{x^3}6+\cdots$ so $f(x)=e^x$, which works.

[austere heath]

texit is down right now

do you have a screenshot?

[wet bear]

yeah sad

Nope

.close

[obtuse pebble]

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[austere heath]

feel free to ask again once its back up!

[obtuse pebble]

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[neon falcon]

Hello im confused on how to simplify this would I break it down to √9x^7*√2

[haughty coyote]

Except for 18 = 3^2 x 2, there isn't much that's objectively simpler besides getting that 3 out

[timid silo]

18 is 3sqrt(2)

[neon falcon]

so

ok

[timid silo]

you can write the expression as sqrt(18)sqrt(x⁷)

then sqrt(18) as 3sqrt(2)

then sqrtx⁷ as x²sqrt(x³)

which is x²sqrt(x³)

[neon falcon]

wait

what

[timid silo]

so you get 3x²sqrt(2x³)

[neon falcon]

but how

[timid silo]

sqrt(a) × sqrt(b) = sqrt(ab)

[neon falcon]

here's my choices

[timid silo]

huh?

i hope i havent made any mistakes

[boreal condor]

you can split x^7 into smaller powers

[timid silo]

yes

thats what i did

[heavy thicket]

Definitely not a

[boreal condor]

x^7=x^2 * x^2 * x^2 * x

[heavy thicket]

Not c either because the square root of 18 does not equal 3. Instead it equals 3 times the square root of 2

[timid silo]

which is also x³x⁴

let me retry

[boreal condor]

it's x * x^6

x^3 still can be simplified

[timid silo]

xsqrt(x)?

[boreal condor]

yes

[timid silo]

oh yeah

so its the second choice

[boreal condor]

√x^7=x^3√x

[timid silo]

today we learn

[neon falcon]

oh

alright

tysm

.close

[obtuse pebble]

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[little shuttle]

im a little bit fuzzy on how to graph the inverse funcs

like how to manipulate them

I know the baseline is -1

I think this is inverse csc

so a helper sin func

[heavy thicket]

Do you know what the period is?

[little shuttle]

2pi/x = pi/10?

sorry I dont know latex well

[heavy thicket]

Almost

How about this, take the distance from the vertex of one curve to the vertex of another curve

[little shuttle]

pi/10

[heavy thicket]

How is it pi/10

[little shuttle]

0

-pi/10

[heavy thicket]

That’s not the period

Lemme clarify

Take the distance from the vertex of one curve that goes down to the other vertex of a curve that goes down

That’s your period

[little shuttle]

pi/5

[heavy thicket]

There you go

Do you know what the phase shift is

[little shuttle]

left right

yeah

[heavy thicket]

What’s the amplitude

[heavy thicket]

I need an exact number

Lmao

[little shuttle]

0

[little shuttle]

idk

[heavy thicket]

The amplitude is the vertical distance from the midline to the vertex of one curve

[little shuttle]

1

[heavy thicket]

Good

[heavy thicket]

Hmmm. Try again

[little shuttle]

idk what the graph is supposed to look like

[heavy thicket]

Do you know the parent graph of csc

[little shuttle]

no

[heavy thicket]

Csc is the reciprocal of sin

[little shuttle]

sin also starts at zero

[heavy thicket]

If sin is 0 csc would be undefined

[little shuttle]

oh

[little shuttle]

-pi/20?

[heavy thicket]

Here’s what the parent graph looks like

[little shuttle]

is it shifted by -pi/20

[heavy thicket]

Lemme check

[little shuttle]

unfortunately we cant use graphing calcs in my class for tests, but I can for homework

[heavy thicket]

Shifted by pi/2

[little shuttle]

how am I going to find that?

[heavy thicket]

To the right

[heavy thicket]

On the parent graph the first curve from the y axis that points down has a vertex with an x value of -pi/2

Since the downward curve has a vertex with an x value of 0

It is shifted right pi/2

[little shuttle]

poggers, more memorization

but cool

so now we have

[heavy thicket]

Now put it all together

[little shuttle]

y=1csc(-pi/5(x-pi/2))-1

[heavy thicket]

The midline is -1

Other than that it looks good

Maybe you might need to simplify it

Lemme check real quick

[little shuttle]

not in this class

[heavy thicket]

Lemme check b4 you go on

That does not look right

[little shuttle]

what did we do wrong?

[heavy thicket]

Figuring it out

[obtuse pebble]

@little shuttle Has your question been resolved?

[heavy thicket]

Period is 2pi/b

New b value is 10

@little shuttle the correct equation is csc(10(x-(pi/4))-1

Had to do some desmos tweaking

[obtuse pebble]

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[obtuse pebble]

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[timid pollen]

I was given this question for a math review assignment. The answer has been provided and it is c. 13, but when I try the question myself I get a. 12. My process is as follows:

1. create an equation for interest: 900 (1.03^y) = 1300 (y is the number of years)
2. isolate y: I first adjusted the formula to be 1.03^y = 13/9. I then brought down the exponent using logs, and manipulated the equation until I got y = log(13/9)/log(1.03)
3. solve for y: I plug the equation into my calculator and get the answer y = 12.44044928 which rounds down to 12 years. According to the answer sheet, it should round up to 13 years.

I suspect this has something to do with the bi-weekly compounding, as I don't really know how interest works 😂, if someone could explain how I can get the right answer it would be much appreciated

[hot sonnet]

In 12 years, the amount will be less than $1300 because the time needed for that is 12.44... years. That's why you should round it up

[timid pollen]

oh my god

[hot sonnet]

I guess they should clarify that on the statement

[timid pollen]

wait wait hold on

but it says round to the nearest year

nearest is 12 years

[hot sonnet]

13 is the nearest year when the amount is $1300 already

I'm saying this based on my experience in this kind of questions, as I said they should clarify that

[timid pollen]

ohhhh that's not worded very well

[hot sonnet]

,w 900*(1+0.03/26)^(26y) = 1300 solve for y

[warm shale]

Results provided by WolframAlpha

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

Requested by leonardogtf#2239

[hot sonnet]

I get 12.2646

Rounding it up, it's still 13

[timid pollen]

I'm still kinda struggling to get that but I think I know what you mean

"after reaching $1300, how many years would have passed?"

[hot sonnet]

How many "whole years" I guess 🤔

[timid pollen]

,w 900*(1+0.03/26.07145)^(26.07145y) = 1300 solve for y

[warm shale]

Results provided by WolframAlpha

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

Requested by Neem#9810

[timid pollen]

ever so slightly more specific

[hot sonnet]

That's 12.2645 too

[timid pollen]

I see, well thanks then

.close

[obtuse pebble]

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[little shuttle]

I hate graphing

[obtuse pebble]

@little shuttle Has your question been resolved?

[timid pollen]

I can’t say I can solve this but do look at x=-1.5

On -tan(x•pi/3)+2, there would be a vertical asymptote there

[little shuttle]

thanks

.close

[obtuse pebble]

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[little shuttle]

.reopen