help-28

[fresh junco]

but im still not sure which option is "NOT CORRECT"

[hot lily]

Ok, now lets see if the correlation coefficient is -1 (testing option D)

[fresh junco]

okay (sorry since im noob at stats)

[glossy valve]

King Leo

[fresh junco]

i tried this answer and it says incorrect

[hot lily]

We didnt see if that option is correct/incorrect yet 😦

[fresh junco]

i answered it before

i got 0 points for that lol

I was thinking of "A. The two variables are linearly correlated."

somehow thats wrong too

downward trend cant really show if the variables are correlated

[hot lily]

Yes, because [this line](#help-28 message) appears to be a good fit to relate y and x

[fresh junco]

true so option A and D are wrong

[hot lily]

It doesnt matter whether the trend is downward/upward, we only care if the change in x appears to have a meaningful change in y

[fresh junco]

ok ill add it to my notes

thanks

"B. The correlation coefficient is negative.
C. The correlation coefficient is larger than -1."

[hot lily]

The correlation coefficient is negative.
We already established that theres a downward trend, so what does that tell you

[fresh junco]

B is a correct statement

not the "NOT CORRECT" one

cuz -2

[hot lily]

B is a true statement

[fresh junco]

yeah so cant pick B either because we have to pick a statement that isnt true

[hot lily]

Not that. The slope of the line is not necessarily the correlation coefficient, because the correlation coefficient must on the interval [-1, 1]

[fresh junco]

my bad for misunderstanding

correlation coefficient seems around -1 to 1 from the graph but cant find exact value

is it option C?

@hot lily

[hot lily]

So heres the thing

Ill tell you right now that $-1 < r < 0$

[glossy valve]

King Leo

[hot lily]

That much ik for sure

Which means the correlation coefficient > -1

[fresh junco]

so
C. The correlation coefficient is larger than -1 is also a true statement

[hot lily]

Yes

But it might be intended to be interpreted as "the correlation coefficient is farther away from 0 than -1" (this statement is false, making it the correct answer)

But im not 100% sure

[fresh junco]

it could be even im confused because option A was wrong
D was also wrong
we just got B as true and C seems true too but kinda unsure

i only have one try left
i tried to ask my friend and we are stuck on the same question with only last try lol

@hot lilyThanks for the help though

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[idle radish]

why is this wrong

[robust slate]

You wrote brackets, but there’s a hole at (5,4)

Meaning that the endpoints of 5 and 4 aren’t actually included

[idle radish]

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[mossy citrus]

Hi. I want to ask what type of question this is and what the usual process of answering it looks like. This is ap stats unit 5.

[mossy citrus]

It’s question C- I’ve done it earlier this month but unfortunately forgot how .. all the needed info is in the questions above

n=9000

mean = 500

standard deviation =90

a-answer is .133

[grim skiff]

Fyi you left your name in the image, idk if you want to remove and resend it so your name isn't there

[mossy citrus]

its fine i dont mind

<@&286206848099549185>

[grim skiff]

You're having trouble with c?

[mossy citrus]

yes

[grim skiff]

Do you recall the z score formula?

[mossy citrus]

i do its stat- parameter over standard deviation of stat right?

[grim skiff]

Those are different terms but it's this

That formula

[mossy citrus]

yes exactly

[grim skiff]

So the problem asks what score does Megan need to be in the top 1%, so you need to use the z score table to find the z value for that

[mossy citrus]

would my raw score be .99 ?

[grim skiff]

Nope, that's what you are looking for

Do you recall that the z score table translates into a percentage?

[mossy citrus]

yes

[grim skiff]

So to be in the top 1%, that means she needs to do better than 99%, correct?

[mossy citrus]

yes

[grim skiff]

So then you would need to use the z score table to find the value that translates closest to 99%

[mossy citrus]

can i find it on the calc as well?

im struggling with this table

i havent really used it to much

[grim skiff]

I don't think a calculator has z score on it

Do you have an image of the table you use?

[mossy citrus]

would .2 work?

ill send a picture

[grim skiff]

That's not the z score table

It looks something like this

[mossy citrus]

oh yea sorry i sent the wrong one

yes ok

so it would be .23

[grim skiff]

Not exactly

Do you understand how to interpret it?

[mossy citrus]

yea it would be 2.3 on the left and then the upper would be the next place soo i think its 2.33

[grim skiff]

2.33 relates to what percentage?

[mossy citrus]

the .9901

[grim skiff]

So 99.01%, yes that's technically the 99% that the question is asking for but technically 99.01% > 99%

So you want to choose the next smaller one

[mossy citrus]

ohhhhh oh okay okay

ahh okay

2.32

[grim skiff]

Yes

[mossy citrus]

okay so i would now plug that in and do algebra?

[grim skiff]

Now using the z score formula, that I sent above, you have z, mean, and SD, correct?

[mossy citrus]

yes

[grim skiff]

So yes you plug that in and do algebra to find the score that she needs

[mossy citrus]

i havent done algebra in a while, its reverse pemdas right?

[grim skiff]

Yes

[mossy citrus]

umm i dont think i did this correct, ultimately it would be 2.23 + 500 times 90?

[grim skiff]

What is the equation you have?

[mossy citrus]

x- 500/90=2.23

[grim skiff]

So you are right that you need to do reverse pemdas but you have a fraction, the numerator has like imaginary parentheses so it would be (x - 500)/90 = 2.32

[mossy citrus]

ohhhhhh

ohh so i got 708.8

that would be the score she needs to get the scholarship right?

[grim skiff]

That's the score she needs to be in the top 1%

Oh I reread the problem, yeah top 1% for the scholarship

[mossy citrus]

omg okay i get it now. so when i see a similar problem i can follow that process??

[grim skiff]

Yeah pretty much

[mossy citrus]

thanks so much for the help! i super appreciate it

[grim skiff]

No problem

[mossy citrus]

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[stoic ibex]

How can I solve x and y

[slow field]

Do you know the Pythagorean Theorem?

[stoic ibex]

yes

[slow field]

Alright, can you try and use it here?

[hybrid nymph]

what is the question ?

[slow field]

#help-28 message

[hybrid nymph]

alr

[slow field]

Is that even necessary?

[hybrid nymph]

ALr

Ill call this squared triangle is ABC

AD = AF = 6

AD squared to AF

=>ADEF is Square

AD = AF = DE = EF = 6

[slow field]

What are y'all doing?

[hybrid nymph]

using pythagoras theorem

[slow field]

How is this applying the Pythagoras Theorem-

[hybrid nymph]

i just caculated

CE = 10.81665

I MEAN APPORX

pythagoras theorem

[slow field]

(6 + x)² + (6 + y)² = 20².
36 + x² + 36 + y² = 400.
x² + y² = 400 - 2(36).
x² + y² = 400 - 72.
x² + y² = 328.

[hybrid nymph]

bro AB is y + 6

y is unknown

we need to find

delete up there

i just saw

AC < CB

BRO AC = Y+6

[slow field]

That's impossible.

[hybrid nymph]

CD < 14

[hybrid nymph]

Hypotenuse always is longest

note

[slow field]

My point. CB is the hypotenuse.

[hybrid nymph]

so CB is the longest

we dont have CD or CE yet

[slow field]

One sec, did I-
Oh. <, not >.

Please.

[hybrid nymph]

our goal is to find FB and CD

[slow field]

Just use the Pythagoras Theorem on ΔABC and solve for x and y.

[hybrid nymph]

i just said

AD = DE = AF = EF = 6

cuase ADEF is square

AD = AF = 6 and AD is square with AF

EB > 6

y < CE

x < EB

okay let me think more

[slow field]

What-

[hybrid nymph]

CD < 14
√(6^2+x^2 ) = EB
√(6^2+y^2 )=CE

Alr

let me think and i go for lunch for a while

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[cobalt atlas]

Can someone check this

[steel solar]

first step, you're subtracting, not adding 3/(5x-2)

and sry i left earlier, i ate and then accidentally took a nap 😭

[cobalt atlas]

nah ur good bro i figured it out 🤣

[cobalt atlas]

yeah i saw someone doing it like this in a vid so i assumed it was the same

but now that i remembered he was subtracting so

[steel solar]

yes

first thing to change

also, whenever you find a potential solution, plug it back into the equation to see if it is correct

[hollow herald]

You have successfully proved 1 + 1 = 0

Let me confirm. Is your question $\frac{2}{x+1} + \frac{3}{5x - 2} = 0$

[cobalt atlas]

yes

[hollow herald]

Then plugging x = 1 gives you what here

[cobalt atlas]

do u mean like this 2/1+1 + 3/5(1)-2 ?

and if so why 1 ?

[hollow herald]

because you solved and got x = 1 as your solution

So x = 1, must satisfy the question

Did you not?

[cobalt atlas]

no i did but i thought one of you said it was wrong so i crossed it all out

ill just recopy it

[steel solar]

u fixed signage issue right

[cobalt atlas]

not really sure how to do that

i am pretty new to this whole math thing just started after a gap year so treat me like an idiot

[steel solar]

$\frac{2}{x+1}=\frac{-3}{5x+2}$

[glossy valve]

;(

[hollow herald]

cross multiply, what'd you get?

[cobalt atlas]

give me a sec

[cobalt atlas]

Not sure I did this right but here it is

[hollow herald]

:p not sure if you should be calling yourself an idiot

You did pretty alright

,w 2/(x + 1) + 3/(5x + 2) = 0

[glossy valve]

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[cobalt atlas]

niceee

lets goo

[cobalt atlas]

my professor apparently gives the most homework out of any math professor on the campus from the reviews on ratemyprofessor so i guess ill be able to practice a lot of questions which i heard makes you better so even if i fail i still should get better in the end

you'll for sure see me in here a lot

[hollow herald]

Alr

[cobalt atlas]

thanks

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[woeful pasture]

this is not possible, right?

[olive olive]

it is

[woeful pasture]

could u shade where the area in between is

so i could set up an integral

[olive olive]

hold up

doing desmos magic right now

[woeful pasture]

okie

[olive olive]

i think

[woeful pasture]

then why is it 0 to pi

and not the region

[olive olive]

wait am i tripping

[twin wolf]

what about the left area

where 1/x > sinx

[olive olive]

it's infinity?

i think

because of 1/0

[woeful pasture]

im not sure

[woeful pasture]

thats what im thinking

[twin wolf]

does the left side count as the area if so it would diverge then?

[woeful pasture]

what do u think i should answer?

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@woeful pasture Has your question been resolved?

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@woeful pasture Has your question been resolved?

[nocturne shard]

it asks the area between y=1/x and y=sin(x) in 0 < x < pi

the bounds aren't necessarily 0 and pi so you dont need to include the left areas

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[woven ermine]

Any idea how to do

I got 15 but answer is 490

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@woven ermine Has your question been resolved?

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@woven ermine Has your question been resolved?

[wise tartan]

I got the answer

You gotta consider the individual values of f(n) for all n first

!status

[full forum]

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

[wise tartan]

i can respond any more

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@woven ermine Has your question been resolved?

[woven ermine]

I got 5 and 13

As what being able to divide

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[bleak delta]

last exercise for the day that i need help on

[bleak delta]

how do i figure out Sn

[steel solar]

$\sum_{k=0}^{n}\binom{k}{n}^2$

[bleak delta]

sure

i know that

but then what

[glossy valve]

;(

[leaden ermine]

Isn't this undefined?

[steel solar]

rewrite the sum backwards and apply $\binom{n}{k}=\binom{n}{n-k}$

[glossy valve]

;(

[steel solar]

how so

[bleak delta]

oooooooh

thats pretty cool

[steel solar]

try it, im not 100% sure if it works cause its not the same form as the one i was working on earlier

let me pull it up, though

[bleak delta]

but wait how does it work

[leaden ermine]

If I recall the thing above has to be greater or equal than below

[bleak delta]

i dont see the logic actually

[bleak delta]

no

its actually the opposite

the thing below has to greater or egal than the one on top

it depends on the notations though

[gentle salmon]

Because choosing r is equivalent to choosing n-r since if we have n=10 and r=3, then choosing 3 is equivalent to choosing 7 since you are just choosing which 3 you aren't going to choose

[bleak delta]

i know

i was saying that in this exercise i dont understand what the logic of doing that is

[steel solar]

hmm well there is no nice coefficient here

so this method doesn't work

[bleak delta]

ye

[leaden ermine]

,w 2 choose 4

[glossy valve]

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[bleak delta]

idk, i was thinking of doing some system

[bleak delta]

that notation is not the same as the one in the pic

[leaden ermine]

how is c_n^k defined

[bleak delta]

brother

[gentle salmon]

yeah idk why it's like switched

[bleak delta]

just write it backwards so that it matches your notation system

[gentle salmon]

kCn is crazy notation ngl😭

[bleak delta]

its just the notations we use

i didnt choose it myself

[bleak delta]

this guy seems to be familiar with the notation though so

[leaden ermine]

nice word pun

[bleak delta]

i dont think im crazy

[steel solar]

methinks

$\binom{n}{k}=\frac{n!}{k!(n-k)!}$

[glossy valve]

;(

[bleak delta]

good job

[leaden ermine]

no

[bleak delta]

or not

[steel solar]

yes $n\ge k$ for $\binom{n}{k}$ to be nonzero

[glossy valve]

;(

[leaden ermine]

this demands n >= k

so you need to adjust it your notation

[bleak delta]

thats fine, i dont understand what ure stuck on

[leaden ermine]

i am not stuck, you opened a help channel lol

[bleak delta]

well yea, and you seem to not understand the notations ussed

[gentle salmon]

🍿

[leaden ermine]

you didnt answer how it's defined dude

[bleak delta]

anyway, now that we got that out of the way

[steel solar]

ok guys

[bleak delta]

figure it out yourself

[bleak delta]

any ideas?

[leaden ermine]

i wont waste my time on you bruv

[bleak delta]

ight

[steel solar]

apparently you need the hypergeometric function...

[bleak delta]

i dont think so

they do have a solution at the end of the book

[steel solar]

this is the sum right?

[bleak delta]

seems like they pulled it out of their asses

[steel solar]

surely they meant something else

[bleak delta]

yeye

[steel solar]

can u show it

[bleak delta]

i guess, i dont really understand your notation but i think its right

[bleak delta]

sure

its 1.359

in the third and 4th line the translation is: we will equal x^n's coeficient from the LHS of C 2n ^n with the coeficient of x^n from the RHS

and in the 5th line its just the equations

[steel solar]

ah, binomial expansion.

[bleak delta]

well yea

thats usually how you do these

im 100% sure that theres an easier way tho

[steel solar]

wait, thats not how binomial coefficients work.

[bleak delta]

because how can you even come up with that

[steel solar]

$(x+y)^n=\sum_{k=0}^n\binom{n}{k}x^k\cdot y^{n-k}$

[glossy valve]

;(

[steel solar]

wtf are they talking about

[bleak delta]

yea

[steel solar]

dude

[bleak delta]

thats exactly what they did

[steel solar]

plug in k=0

is it 0Cn??

[bleak delta]

yea

[steel solar]

...

[bleak delta]

and then x^0 is 1 and 1 to the ^n = 1 so

thats correct

i hate the fact that we use these notations

just dont mind their solution

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[bleak delta]

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[atomic tartan]

dont know how to do this problem

[atomic tartan]

trying to find x

[keen vector]

find the sidelength of square

what ru given

[atomic tartan]

thats it northing else

its a regular nonagon

help

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[storm hinge]

i dont know how to set this up

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@storm hinge Has your question been resolved?

[narrow path]

Im very confused cause dont you need a big R

[storm hinge]

ya i dont know

[storm hinge]

<@&286206848099549185>

[leaden ermine]

What you wanna do is set up a circle equation for example x^2 + y^2 = R^2, you can actually consider just y = sqrt(R^2-x^2)

Then your integral bounds would be from r to R basically

and you would need to add a factor 2 because the height is h/2

that would be my approach

[storm hinge]

so would this be for just the shape on the left? assuming that the lest shape has a smaller radius and there for is "r" not "R"?

also im going to have to go in 16 min

so i might just have to come back to this question later tonight

[leaden ermine]

i didnt understand what you asked

[storm hinge]

so since there are two different shapes, the right shape and the left shape, I'm assuming that they will have different equations to find the volume. So im basically asking if y = sqrt(R^2-x^2) is for the right shape or left shape

[leaden ermine]

sqrt(R^2-x^2) is the upper half of the circle basically

what you are doing is actually calculating half the volume because you are rotating a quarter circle around the y-axis which makes it basically a semi sphere

but because of symmetry you can just double the volume

[storm hinge]

okay so it works for both

[leaden ermine]

the only thing that is bothering is the in terms of h

[storm hinge]

ya but wouldnt the radius just be h/2?

since its just half of h

[leaden ermine]

r and h are in a sense related if you consider r^2+(h/2)^2 = R^2 and solve for r so
h = 2sqrt(R^2-r^2)

that way you get corresponding height in terms of radius

wait actually we want the other way ops

r = sqrt(R^2-(h/2)^2)

get the corresponding radius in terms of height

[storm hinge]

ahhh sry i have to go, but i appreciate ur help and ill be back to figure this out later!

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[dense nova]

This is trigonometry I’m trying to figure out this question I don’t know which equation would be used to solve it.

[steel solar]

do you know about circular sectors?

[dense nova]

Not at all it’s all new to me

[spiral vigil]

hmmm

how long would the crust be if he just cut the pizza in half?

or better yet, how much crust is there right now

around the whole pizza

[dense nova]

Yea he already purchased the pizza that has the 12 cm but he wanna make it 18cm long

[spiral vigil]

he wants to make what 18cm

[steel solar]

that statement doesn't add up.

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[cobalt atlas]

Would the open circles be correct here

[cobalt atlas]

cause i don't know what x is

actually in the video i am watching the guy has x > or equal to -2 and he plugs in -2 for x do i do the same here or ?

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[blazing umbra]

24. If 9 men and 5 women randomly queue up at a ticket office, find probability 
    (c) among all the women, only 2 women stand next to each other.

[blazing umbra]

I know the total way is 14!

I try to use the required ways is 2!*(1+9)!*9P3 but it’s wrong

the correct answer is 60/143

<@&286206848099549185>

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[wary kindle]

what how do we do this

[spiral vigil]

well start by using the hint ig

[wary kindle]

is there a specific property where xy = xTy ?

i did use the hint but dont know what to do next

[sacred sparrow]

could you show where you are

[wary kindle]

ok sure

[sacred sparrow]

I presume you are here?

in case you weren't sure of this property anymore:

[wary kindle]

i was tryna manipulate like this

[sacred sparrow]

ah you're doing the proof backwards

I'd do it forwards

is easier

so we're currently here and want to slowly get rid of the Q

[wary kindle]

i thought xy = xTy ?
are we allowed to do QxQy = (Qx)T(Qy)?

i thought the hint was for xy ?

[sacred sparrow]

sure

the hint is just the general version

x and y can be any vectors

[wary kindle]

OUHHH thats where I got confused ye

i see

lemme try

[wary kindle]

boom easy

also I have a question tho

xy = xTy
is that a property?

i have never seen that one before

[sacred sparrow]

yop excellent

but write x dot y in the end

otherwise nobody knows you mean the scalar product

likewise at the start

multiplication and dot product are different operators

[wary kindle]

ye i just got confused about the property

cuz it wasnt mentioned in my course notes before

is that a rule?

oh yea i see now

thank you

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[hot star]

I need help on part b

how do I simulate 100000 games?

[peak knot]

I think there's a function on calculators that would be useful here but I can't remember it

[hot star]

i don't need that

I need to know how to do it

[peak knot]

Oh you don't mean run a simulation, I see

I'm like 40% sure I can remember this and help you but do you know if it's asking the likelihood you get $11000 or more or win at least 1112 out of the 10000 games?

[hot star]

to "win" 1000

so total at the end should be >11000

[peak knot]

Ok

You could find the mean and standard deviation

And then calculate the z-score of winning 11000 dollars I think

I guess that would be around 5790 wins

I'm too tired, idk if I'm doing this right, gn

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[feral urchin]

how are we supposed to know whether the payment is made before or after interest is applied?

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[plush birch]

I've been racking my brain on a small problem... but I don't get the difference. In the first case, we don't apply the -2 exponent to the base 3 but in the second case, we do apply the exponent 2 to the base 3... There is probably some sort of rules missing from by textbook which is essentially just a few pages of my pdf.

The only difference I see is that in case 1, the base is alone, no variable, except in the power and the exponent is negative.

I must be missing some exponent rule or something

[plush birch]

I get that 3 and 3 divide to 1 so we can simply the fraction inside the parentheses, but I tried getting gpt to solve the first case if the base was 4 over 5 and we still don't distribute the exponent

[quasi furnace]

ok basically

when something is powered

its own power is multiplied by that power

in the case of the first example

ok where tf is this upside down sign

oh found it

(3^-m)^-2 is just 3^(-m x -2)

so in the second case

its just (3^1)^2 which is equal to 3^(1 x 2)

thats why

you get that or?

[plush birch]

yeah I think so, if the power is 1, then you can go 1 x 2 so 3^2 in the second case, which we simplify to 9 but in the first case we can't simplify -m x -2

jeez, latex would be useful here

[quasi furnace]

basically

the exponent IS applied to the base 3 in both scenarios

its just that its multiplying 2 different powers so the result is different

[plush birch]

yeah, got it

[quasi furnace]

👍

[plush birch]

thx

[quasi furnace]

np

[plush birch]

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[swift bridge]

Why do we fix epsilon fo be < min(x, 1/4xn)? Specifically why do we need the minimum and why is there an x? Isn’t it sufficient to have e < 1/4xn?

[swift bridge]

Also not quite sure how Archimedes principle is being applied here. Because I thought it says for all x in R there exists n in N such that 1/n < x…..

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[lapis flower]

I think i did something wrong

[hot lily]

You need te multiply 2y by dy/dx at the end

[lapis flower]

Wat

Oh the last one

[hot lily]

Chain rule after power rule

[lapis flower]

I got dy/dx = 6😭

I don't think that's right

I think its supposed to be 9

[hot lily]

Can you show your work

[lapis flower]

Oh I forgot to add the 6

NVM

TY

[lapis flower]

OK I FIXED IT

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[hot lily]

Did you just not add 6

[hot lily]

Oh alr

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[lapis flower]

I messed up

Idk where

[hot lily]

Same :(

[worn matrix]

what does the question say?

the working seems fine but i don't know why you even did that

[fallow thunder]

Bro I need to learn hamurabi code to understand that handwriting 💀

[ivory cairn]

that's the right slope. but the whole question looks like it's asking for an equation of a line. You just found a slope.

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[lapis flower]

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[lapis flower]

No the slope is 9 I think

On the answer key

[ivory cairn]

,w derivative sqrt(xy) = 12y-x

[glossy valve]

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[ivory cairn]

,w calc (2sqrt(9)+1)/(24sqrt(9)-9)

[glossy valve]

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[ivory cairn]

so, 1/9 is correct.

[lapis flower]

Oh will it equal 1/9

Omg did I get that

Omg

[ivory cairn]

,calc 7/63

[glossy valve]

Result:

0.11111111111111

[ivory cairn]

=1/9

[lapis flower]

OHHH

TY

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[valid rune]

If someone could explain this and how they got the answer it would be a lot of help. Thanks

[tight glen]

Have you tried anything?

[viral jasper]

This will be your exposed surface

so you need the area of that circular portion

[valid rune]

I’m just trying to figure out if it’s wanting an equation or if they’re is smt im missing entirely in regards to #’s

[valid rune]

So then I would be trying to find the SA using the formula to find a circles are?

Area

[viral jasper]

you will not need any numbers

It says to find the solution in terms of R, H, and h

so it'll be an expression (or equation if you do A=blahblah)

[valid rune]

So I tried piR^2 because that would be the area formula but wouldn’t you have to divide it by h?

[tight glen]

R is not the radius of the exposed circle

It’s the radius of the base of the container the water was in

Also what’s your reasoning behind dividing by h?

[valid rune]

I was assuming that if I divided by h it would make it work. More of a guess

[tight glen]

Okay let’s start off by letting the radius of the exposed surface area be ‘r’

[valid rune]

Okay

[tight glen]

This is what I mean

Now what is the area of the exposed region in terms of ‘r’ ?

[valid rune]

It would be pi r^2? Because that’s the area formula right?

[tight glen]

Yes good

Now we need to express ‘r’ in terms of variables we’ve already been given in the question

That is, R, H, h

[valid rune]

Ok how would you figure that part out?

[tight glen]

Here’s a hint

It might not come across as entirely obvious at first, especially if haven’t seen something like this used in problems

[valid rune]

Would it involve square rooting the bigger one?

[tight glen]

Any guesses now?

[tight glen]

No why would you do that?

[valid rune]

Well since it’s a smaller version I thought maybe that would contribute?

[tight glen]

Here’s another hint:
||Think in terms of similarity of triangles||

[valid rune]

It’s like r=R and h=H

[tight glen]

r is not equal to R. And h is not equal to H

That’s is not similarity

That’s congruence

[valid rune]

I meant it more as in r is to R as h is to H

Would it be Rh/H

[tight glen]

Yes

[tight glen]

Very important to express yourself as such

[valid rune]

My bad I wrote it better on paper and didn’t translate it over

[tight glen]

You can now just plug that

[valid rune]

Into the area formula right?

[tight glen]

Yes

[valid rune]

Pi(Rh/H)^]

^2

Not the bracket

Thank you

[tight glen]

Should be correct

[tight glen]

[valid rune]

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[cold crow]

hi

[cold crow]

i need help please

[leaden ermine]

don't reopen channels for no reason

[cold crow]

i closed the other one

[cold crow]

ok so basically

i tried simplifying the roots

like root 15 and root 20

and got lost from there

[grand hatch]

Continue

[cold crow]

ok

[grand hatch]

Proceed

[cold crow]

but do you make the root 4 into 2?

and then multiply it with 21

[grand hatch]

What does the word "simplify" mean to you exactly?

[cold crow]

in this case, dividing the numbers as small as they get?

making the numbers smaller

simpler?

[grand hatch]

So what do you think the appropriate course of action must be regarding this question

[cold crow]

i would've thought yes but apparently not

i was thinking to make it 2 and then multiply it by 21

so there's only one root one bottom

[grand hatch]

Where are you making the inference to not do that from?

[cold crow]

nevermind

i multiplied 21 by the 2 i got from root 4

[grand hatch]

Indeed you have

[cold crow]

yes and now do i multiply the root 5 by root 3

[grand hatch]

I would not recommend this

Please complete the natural steps first

[cold crow]

dont u usually see if 28 goes into 42 or something?

its been some time since ive done this topic

[grand hatch]

There is a very obvious cancellation you are refusing to perform

[cold crow]

o

[grand hatch]

There are furthermore cancellations possible

[cold crow]

42/28?

[grand hatch]

Indeed

[cold crow]

that would give 1.5 no?

huh?

[grand hatch]

Yes

[cold crow]

oh ok

so you would just write 1.5 root 3

[grand hatch]

42/28 is not what is written

[cold crow]

or u could put it as 3/2 root 3

[grand hatch]

Its 28/42

[cold crow]

oh

[grand hatch]

Please read the image you have sent

[cold crow]

28/42

yeah ur right

[grand hatch]

What does this fraction simplify to

[cold crow]

2/3

[grand hatch]

Indeed

[cold crow]

could u just leave it as a fraction?

in non calc

[grand hatch]

The world is your oyster

[cold crow]

i meant like sometimes they dont give u full marks for leaving as a fraction in non calc tests

but i just wanted to ask to make sure

[grand hatch]

I am not sure what your teachers award marks for and what they dont

[cold crow]

yep

[cold crow]

i meant like the exam boards

but ok

so answer would be 2/3 root 3

[real barn]

i think that's dumb

[cold crow]

yeah

[real barn]

i believe students should actually be taught to LEAVE IT in the form of a fraction and not divide with a calculator in decimals

because most of complex math will not involve numbers (or well, rarely)

[cold crow]

@grand hatch yea i got it right

i think they disappeared

[real barn]

because that's basically like saying sin(pi/3) = 1.73/2 = 0.866 (which is correct)

and i believe in situations like those

students should leave it as a fraction of sqrt(3)/2

[cold crow]

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[merry eagle]

Is the alternating series test still applicable here: $(-1)^n\cdot\frac{(-1)^n}{\sqrt{n}}$

[glossy valve]

Polar

[merry eagle]

if not what else can I use to test whether the series converges or diverges?

I tried using the ratio test but it was indecisive

[clear pumice]

i mean say a = -1
a^n * a^n is either 1*1 or -1 * -1

a^(n + n)
n is always even

[merry eagle]

so AST isnt applicable here

what other test could i use then?

the ratio test was indecisive

[clear pumice]

(tbh i dont really know the methods just implying from the given series)

no matter what n is the numerator/top is always 1

in this case

[merry eagle]

Ok well thank you for the help

I appreciate it

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[vestal moat]

What happened ?

[dense barn]

My last was deleted I can see it so I opened new

But I can't figure to solve this

[vestal moat]

Ok so what's the volume of a cone ?

[dense barn]

,1/3 πrh

, 1/3 πrh

[vestal moat]

Cool, now you got 2 cones, let's name the volumes Vs (small cone) and Vb (big cone)

[dense barn]

The cone of 21 and 6

[vestal moat]

There are 2 cones they said not just one

[vestal moat]

.rotate

[dense barn]

Yes but one cone with 21 and other with 6

[vestal moat]

No

[dense barn]

Then what?

[vestal moat]

If you take your cylindrical tube, there is one cone to the right and one cone to the left

Ok ?

[vestal moat]

rotate please

[ancient folio]

;rotate

[dense barn]

,rotate

[vestal moat]

No that's wrong

Look at the cone on the right

[dense barn]

Ok

[vestal moat]

What's the radius of its base

?

[dense barn]

It would be 3

[vestal moat]

Ok so that's your r

do you know its height ? (for the small one)

[dense barn]

No but assume h

[vestal moat]

ok call it hs for small

now calculate its volume as a function of hs

leave the hs within your formula

[vestal moat]

Ok now you’ve done Vs

Do the same with Vb

[vestal moat]

What did you take for r ?

[dense barn]

21/2

[vestal moat]

Why ? What’s the radius of the base for the big cone ?

[dense barn]

Bro right cone has 6 and top cone has 21

[vestal moat]

There’s no top cone there’s just right and left, they’re sharing a summit

[dense barn]

Ok now I understand let me redo it

[vestal moat]

Ok now how can you find h1 and h2 ?

[dense barn]

How to start?

[vestal moat]

You found h1 = 2h2

[dense barn]

H1 + h2 = 21

[vestal moat]

https://tenor.com/view/yas-queen-finger-snap-gif-9873002

[dense barn]

I got the answer

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[midnight lotus]

quick qiuestion

[midnight lotus]

are there any functions that are both odd and even

[grim skiff]

There's only one, and that's f(x) = 0

[vestal moat]

Any function can be uniquely split into even ( f(x)+ f(-x))/2 and odd (f(x)-f(-x))/2.

This decomposition being unique. An odd and even function would be 0

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[midnight lotus]

also, is vertical asymptote is just whenever u divide by 0?

[clear pumice]

pretty much, unless you have 0/0, which makes it indeterminate (could be any value, would have to take a limit)

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[midnight lotus]

(could be any value, would have to take a limit. what do u mean by this @clear pumice

[clear pumice]

well if you think about it 0/0 can be any value since 0*(any number) = 0

i probably should've rephrased but when you get 0/0 that means that there is a hole in the graph (since you can't divide by zero). this hole is usually from terms that cancel each other out on the top and bottom eg. (x-2)/(x-2) results in line y = 1 (since (x-2) factors cancel out) with a hole at x = 2.

[midnight lotus]

if u factored and canceled out terms in a fraction in ur example, u wouldnt be left with 0/0 tho

how does 0/0 come from factoring @clear pumice

[clear pumice]

because in the original equation the value doesn't exist

therefore it shouldn't exist even after you cancel it

the value you get after cancelling it at the point is what the value would be if there was no hole

but you have to follow the original equation otherwise it would be wrong

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[hot star]

i need help

[hot star]

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[muted vigil]

How are lines 6 and 8 true?

never mind

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[grizzled dirge]

Hello

Why is it divide bt 22

[brittle reef]

For the $n^{\text{th}}$ week, the number of lily pads increases by $2^n~22$.$\\$

We are required to find the time in which the lily pads grow to 400. So, we can solve for n in the following equation$\\$
$2^n~22=400\\
or, n=\log_2{\frac{400}{22}}$

[glossy valve]

GoldBarley

[grizzled dirge]

mmm

[brittle reef]

Is there a confusion?

[grizzled dirge]

I see

Thanks

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[brittle reef]

You're welcome

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[pale nova]

My problem is to solve x^4 - 2x^3 + 3x^2 -2x -3 = 0

[pale nova]

Things I've tried so far:

1. has no rational roots

2. I notice it looks kinda of like a reciprocal equation, but substituting z = x + x^-1 did not work

[next gale]

hint: it factors into two quadratics

[pale nova]

Yeah I defnitley get that since no rational roots

ok, ill think harder

[next gale]

assume it factors into $(x^2 + ax + b)(x^2 + cx + d)$

[glossy valve]

Deftioon

[next gale]

expand, match coefficients, equate and solve a system of equations

[pale nova]

Nice idea. Could this replace ferrari's method / memorizing the quartic equation. Like if polynomial has rational roots -> reduce to cubic. If it doesn't, use this method?

Nevermind I'm stupid, this obviously always works

Got just checking it right now

[next gale]

well, yes, every quartic can be expressed as a product of two quadratics but this definitely does not work for the general case

[pale nova]

(x^2 - x + 3)(x^2 -x -1) is the answer lets go

why doesn't it work for the general case?

[next gale]

not every quartic can be factorized so easily

the general approach is to depress it

and solve the depressed equation

[pale nova]

I guess it worked out because guess integer solutions for your system of equations made it easy to solve

thanks alot

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[void nova]

If you'd like I did in a slightly weirder and different way, but I think it is still valid

I first factored it like this:
x²(x² - 2x + 1 - 1) + 3x² - 2x - 3 = 0
x²[(x - 1)² - 1] + 3x² - 2x - 3 = 0
x²(x - 1)² - x² + 3x² - 2x - 3 = 0
[x(x - 1)]² + 2x² - 2x - 3 = 0
[x(x - 1)]² + 2(x² - x - 3/2) = 0
[x(x - 1)]² + 2(x² - x + 1/4 -1/4- 3/2) = 0
[x(x - 1)]² + 2[(x - 1/2)² - 7/4] = 0

Now I rewrite x(x - 1) as (x-1/2+1/2)•(x-1/2-1/2) so that it is equal to (x-1/2)² - 1/4

[(x - 1/2)² - 1/4]² + 2(x - 1/2)² - 7/2 = 0

Let's now make a sub, I chose
t = (x - 1/2)², for instance

Thus we have
(t - 1/4)² + 2t -7/2 = 0
t² + 3/2 t -55/16 = 0

∆ = 9/4 + 55/4 = 16
t_1,2 = ( -3/2 ± 4 ) / 2
==> t = 5/4 or -11/4

But t was (x - 1/2)², so we get to
(x - 1/2)² = 5/4, hence
x = 1/2 ± √5/2

[pale nova]

.reopen

[void nova]

(I specify that's not gpt, even if it seems lol)

[full forum]

✅

[pale nova]

lmao

thank you for writing down you approach. I see how it is more versatile but also more tricky. TBH I've never seen the factorization technique e.g. (x-1) = (x + 1/2 + 1/2). You must have a really great mind to see x(x-1) and think, oh obviously a difference of squares.

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[marsh wedge]

idk where pi/2 comes from. Do you have a graph or anything maybe?

[honest hill]

!nogpt

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[honest hill]

or is this not chatgpt

[marsh wedge]

its deepseek

so ai yeah

[honest hill]

....

[marsh wedge]

okay but where can i see pi/2? :3

-pi/2

[honest hill]

$-i=e^{\frac{-\pi}{2}i}$

[glossy valve]

Bonk

[steel solar]

-pi/2 is the angle that -i makes.

[marsh wedge]

so its a rule that -i is -pi/2 ?

[steel solar]

No, it is not equal, rather when you graph it it will have a counterclockwise angle of -pi/2 radians.

[pale nova]

se how on the chart -i alligns with theta = - pi /2

you should review that chart / eulers formula

[honest hill]

do you know eulers formula? $e^{ix}=\cos(x)+i\sin(x)$?

[glossy valve]

Bonk

[marsh wedge]

yes i know this

[honest hill]

if you fill in x=-pi/2 you get -i

[marsh wedge]

oh okay, but im not allowed to use a callculator

[honest hill]

so?

you can calculate this by hand

cos(-pi/2)

and sin(-pi/2)

[marsh wedge]

thats -i then yeah

[honest hill]

if you dont know this, you should review the unit circle again

[pale nova]

you should memorize cosine/sine of 30/60/90 at least.

[honest hill]

pi/2,pi/3,pi/4,pi/6 is all the ones you should know

including all the reflections

,tex .unit circle

[glossy valve]

Bonk

[marsh wedge]

oh yeah this is helpfull

but wait

if i havecos(pi/10) + i * sind(pi/10)
I can calculate the degree with pi/10 * 180/pi right?

but how can i get from degree to the pi number

[honest hill]

what?

[marsh wedge]

or these numbers

[honest hill]

only use radians

much simpler

,w cos(pi/10)

[glossy valve]

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[marsh wedge]

radians = the pi number?

[honest hill]

the pi number??

what

[marsh wedge]

Pi/10

[honest hill]

2pi radians is a whole circle

[marsh wedge]

how do calculate the exact result by hand?

cause I need to know that

[honest hill]

you dont

then use a calculator

[marsh wedge]

So i have to recognize everything?

[marsh wedge]

from this circle

because these are probably common values?

[honest hill]

all of these you should know

without having to look up

[marsh wedge]

alr tyy!

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[naive monolith]

<@&268886789983436800>

[honest hill]

<@&268886789983436800> here too

[tribal wadi]

<@&268886789983436800>

[sacred sparrow]

stemmcomunity xd

[naive monolith]

man, in every channel actually

[honest hill]

mods quick pls, theyre everywhere

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[sacred sparrow]

didn't know link spam is allowed

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[slate violet]

Should be 2^3 - 0^3 for n = 1

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@fluid prism Has your question been resolved?

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[glossy valve]

938c2cc0dcc05f2b68c4287040cfcf71

[torpid perch]

M_B'B(f) . (v)_B' = (f(v))_B

-v1 + 2v2 + v3 = (-1,2,1)_B

[sacred sparrow]

Not exactly sure what the question asks

Select one (such that?)

@torpid perch

[torpid perch]

is asking which v makes f(v) = (-1,2,1)_B

[sacred sparrow]

but why select one if multiple work

I mean you could just pick b)

since it's obviously true

[torpid perch]

?

[torpid perch]

wdym

[sacred sparrow]

if we pick b)

then f(v) = f(-v1+2v2+v3)

is true

[torpid perch]

f(v) is not v

f(v) ≠ v

ahh

[sacred sparrow]

so I guess just pick b)?

but yeah if you want to compare:
a) false
b) true
c) true
d) false

[torpid perch]

I mean is asking for which one is ALL v such that f(v) = that

so should be a line of solutions

[sacred sparrow]

"For which v is for all v such that f(v) = ..."?

doesn't seem to make much sense to me

It's like "Pick x such that for all x e R that statement is true"

[torpid perch]

dont focus on the alternatives tho

[sacred sparrow]

maybe a translation detail is missing