help-0

[quasi tangle]

it's paid one time only?

[tacit arch]

i take it back, my interpretation must be wrong

this is almost right

nevermind i'm probably wrong again. hope someone else can help

[quasi tangle]

Yeah ok, thanks for the help at least

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[quasi tangle]

.reopne

.reopen

[lone heart]

✅

[lone heart]

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[rigid orchid]

2x=E(x)

Someone can help me with this

!!!

[zenith sparrow]

What are you asking

[rigid orchid]

I found the response 0,-1/2

E is the integer part ig

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[alpine sable]

how do i do this please ( red is the answer )

[alpine sable]

just put 12345

??

[covert agate]

$(1 + 4)(1 - 1), (2 + 4)(2 - 1), ...$

lol

[ocean seal]

Chromium

[alpine sable]

ok thanks

this was wierd

i got exams tommorow

.close

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[stable panther]

Hey can someone help me with this radical equation?

[stable panther]

i tried it a few times and im getting wrong answers

[glad sluice]

try squaring both sides

[stable panther]

alright so this is how i do it?

[gray isle]

no

[stable panther]

oh wait

i skipped a few parts

i think this should be it

[gray isle]

i can see what you tried to do,
but you didn't do it and/or write it properly

that would be an acceptable first step

[stable panther]

alright then

[gray isle]

that's also fine now

[stable panther]

the next part is where stuff goes wrong i think

[gray isle]

is still ok

[stable panther]

alright so adding all like terms

[gray isle]

keep going

[stable panther]

putting everything to the right, subtract x and 5 from the left and right side

[gray isle]

still currently ok

[stable panther]

putting the radical to the left side to isolate it

[gray isle]

keep going

[stable panther]

alright, squaring both sides

[gray isle]

keep going

[stable panther]

minus 1000 from both sides leads to
100x = -100

[gray isle]

and finally...the last step?

[stable panther]

divide both sides by 100 and x = -1

[gray isle]

yes

[stable panther]

i see what went wrong before, i forgot to square the 10 too

[gray isle]

efficiency can be improved a bit in the last few steps

instead of squaring both sides directly you could first divide both sides by 10 to get:
$$\sqrt{x+10} = 3$$

[ocean seal]

ℝamonov

[stable panther]

ah, i see so just square both sides too

then minus ten from both sides

[gray isle]

even if you did do that and reached $100(x+10) = 900$,you could've then divided both sides by 100 first instead of distributing to get
$$x+10 = 9$$

[ocean seal]

ℝamonov

[stable panther]

i see, always look for more efficient ways

[stable panther]

alright one more question, since im not really confident in foiling radicals

everything except for the x cancels out?

[gray isle]

vague wording

what do you think the final result will be

[stable panther]

well i guess you can write this squared

negatives cancels out, the surd cancels out too, i think

[gray isle]

so what do you have

at the end

[stable panther]

X

[ripe rain]

I like how useful @gray isle helped to you

XD

[gray isle]

yes, the final result will be x

you can consider the commutative property of multiplication to get:
$$\underbrace{-1 \cdot -1}{1} \cdot \underbrace{\sqrt{x} \cdot \sqrt{x}}{x \text{ by definition}}$$

[ocean seal]

ℝamonov

[stable panther]

yea, i would have been stuck for a quite a bit of time if it wasnt for ramonov

[gray isle]

i didn't do that much

[stable panther]

i think its you confirming my steps being right, then myself explaining

yea, the squaring both sides confused me

ill just divide both sides first next time

but thanks man

.close

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[alpine sable]

The notes to the drawings are in German.

This question is related to probability.

You have a dice with the letter A on one side, the letter B on 2 sides, and the letter 3 on three sides. You throw three times. What is the probability of rolling three different letters?

The above diagram is from my lecturer and I don't quite understand how I can put everything together in my head. Without the probabilities (i.e. just with letters which have an equal chance of being drawn) I would have thought the answer would be 6/27 = 2/9. 6 here would be 3! (permutation with no repetitions) and 27 would essentially just be 3 ^ 3 (so 3 possibilities in each round - A, B, or C - for 3 rounds). I'm unsure how to factor in the probabilities

[alpine sable]

sorry the notes also relate to another question (I am concerned with question b )

just to be clear, the answer should be 1/6

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[alpine sable]

<@&286206848099549185>

I'm being stupid

it comes out as the same thing#

so if they were equal probability

((1/3)^3) * (3!) = 6 /27

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[alpine sable]

help pls

[gray isle]

what have you tried?

[alpine sable]

umm

idk

[gray isle]

try something

[alpine sable]

nah cant get a hint

[gray isle]

this is a question about angles

[alpine sable]

yeah

hold up

its a square

which adds up to 360

90 each side

so the one next to x is 90 right

90+32 is 122

180-122 = 58

x is 58

58+32=90

[tacit arch]

Does x look like it's 58degrees

[alpine sable]

180-90=90

[tacit arch]

The angles you're calculating are for a triangle

[alpine sable]

yeah im tryna calculate x y and z

i jiust said there is a square which each corner is 90 whic hgave me the clue

[tacit arch]

Then why are you saying they're angles in a square

[alpine sable]

am i correct though?

[gray isle]

rewrite your updated work

and justify each step

[alpine sable]

.close

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[tacit arch]

"Too much work to explain to these discord plebs" --nobu, probably

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[proper ibex]

Hello I’m a student working on histograms. I would like to know if the Chart is correct so far?

[proper ibex]

<@&286206848099549185>

If so I might need help figuring out the relative frequency and midpoint

.close

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[spring harbor]

I don’t understand most of these symbols, but I’m trying to isolate a particular part of this paper that shows the highlighted section. Can someone find that part in this short paper and explain just that part to me http://static.aligulac.com/method.pdf

[spring harbor]

<@&286206848099549185>

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@spring harbor Has your question been resolved?

[spring harbor]

Anyone?

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@spring harbor Has your question been resolved?

[spring harbor]

What are the chances I close this one and ask in other channel and get an answer?

[gaunt glacier]

I mean… the paper you linked doesn’t even contain the section you screenshotted as far as I can see

Oh I see you’re not saying it does. You’re just saying it relates to the highlighted section. Let me look

Okay @spring harbor you there?

Each player is modeled as having four ratings:

1. General skill level
2. Skill against Terran
3. Skill against Protoss
4. Skill against Zerg

The latter three are the “matchup ratings” mentioned in the highlighted section

In the math, these last three are normalized, in the sense that they add up to zero

If a player had positive matchup ratings against all three races, then that really just means their general skill level (1) should be increased. By analogy, imagine you rate 100 women, all blondes or brunettes, on attractiveness from -5 to 5 (instead of 1 to 10). Let’s say your average score for blondes was 4.0 Oh, so you have a bias for blondes! Not so fast. If your average score for Brunettes is 4.4 then you actually have a negative bias for blondes. In that case I say “look… you just think all women are attractive.” Your general rating for women is (4.4+4.0)/2 = 4.2, and your matchup ratings are 4.4-4.2 = 0.2 and 4.0-4.2 = -0.2 for brunettes and blondes respectively. Notice these add up to 0. This is what it means for them to be normalized

Thus, rating categories 2,3,4 represent the “bias” in your skill against each race

While rating category 1 represents the average of your skill against the three races — hence “general rating”

When it says the rating adjustments are not independent of each other, it means for example that when it reads data that says the player does worse against zerg, that influences mostly their Zerg skill rating, but it also influences their general skill rating, since every bad performance, against any race, is also a reflection of general skill

@spring harbor hope that helps

[spring harbor]

Yes

Ok I don’t really get it entirely

Doesn’t the average of them make the more than average parts equal the less than average parts

[gaunt glacier]

Yes I see how I made that unclear! The general skill rating is NOT the average of the three matchup ratings.

Let’s say you play against 10000 people. Your win/loss ratios are 0.80,0.67,0.89 against Terran, Zerg, Protoss

With me so far?

[spring harbor]

But this says it does equal the mean of the 3 matchups

Yes

[gaunt glacier]

I will first continue my message, and then respond to the great point that you just mentioned

So general win/loss, averaged across the races, is (0.8+0.67+0.89)/3 = 0.79

This corresponds to your general skill level

Note this is not the same formula they use. They don’t just use win/loss ratios. But the idea is the same

[spring harbor]

Yea I get it

[gaunt glacier]

Then your matchup ratings are the deviations from the average: 0.80-0.79, 0.67-0.79, and 0.89-0.79 for Terran, Zerg, Protoss respectively. I.e. they’re 0.01, -0.12, and 0.1. These don’t quite add to zero only because I rounded earlier

Now to the point you made before

When it says “the matchup ratings must have mean equal to the general rating” it’s actually lying to you a bit

When it says that’s it’s referring to the numbers 0.8, 0.67, 0.89

Before they were normalized by subtracting the average

This equation here says that the (normalized) matchup ratings sum to zero, which of course means their average is zero

Does that make sense?

[spring harbor]

Yes

But I’m still uncertain how changing one, I.e, blonde changes the other (brunette)

Like what if you play more games the 0.8 and 0.89 stay the same but you get better in one and bring it to 0.75

How would that affect the score for the 0.8 and 0.89 matchup

[gaunt glacier]

That’s a great question. Let me see the math

[spring harbor]

Because I’ve said it doesn’t and a friend said it does according to the image I shared here

I’ve personally noticed that the rating of other matchups are independent but the text implies otherwise

[gaunt glacier]

Okay so here’s the answer.

The raw skill levels against the races (0.80, 0.67, 0.89) are completely independent of each other, as you would hope.

The normalized skill differences, call them t,z,p must add to 0. So if you win a bunch of games against Terran, t increases. So for t,z,p to still add to 0, z,p must decrease. This is because t,z,p are relative skills. It doesn’t mean anything to be relatively good against terrain, unless you’re comparatively bad against zerg and Protoss.

“But what about independence??” You ask. “Isn’t the paper making a mistake here?”

There is no mistake. The paper is not implying that winning against Terran makes you worse against Zerg.

What you have to understand is that the absolute Zerg performance is equal to your general performance PLUS your Zerg performance. So when you win all those Terran games, your relative/normalized Zerg score goes down, but your general skill goes up.

So to apply all of this, if you lose a bunch of Terran games, this will not influence the model’s prediction for the chance that you win a Zerg game.

@spring harbor hope that makes sense

Conceptually, there is no reason to have a general skill rating, when you could just have skill ratings for each race. The general skill rating is redundant.

Mathematically and algorithmically, having a general skill rating just amounts to shifting the origin of your coordinate system to lie on the mean of the data. This allows the skill levels of Terran, Zerg, Protoss to be analyzed as deviations away from your average performance, and makes the math work easier. The “relative skills” are then the coordinates against each race relative to this new origin. These are only for the math to be easier. But ultimately the performance against each race is handled independently

[spring harbor]

That makes sense

But I can’t help but feel the wording is not accurate

From their side

And sorry for the late response I had to take a fluid mechanics exam at 3

The issue I have is that at the bottom of the screenshot (posted again for reference) it says if you underperform against other races your Terran rating will decrease

And this is what I thought about it to try to make them both true

“If you lose a bunch against z and p, but win a bunch against T in the same time frame (usually a tournament or if you play 2 in a day) your T rating will not raise as much as it should only given the data for T, Not that it will decrease absolutely, but that it will decrease relatively to what the original increase would be”

And if that’s not accurate then I think there’s something wrong from either you or aligulacs wording maybe

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[cinder sundial]

Given that a,b,c is real number, log(a)=1.1, log(b)=2.2, log(c)=3.3
choose the correct options
1.a+c=2b
2.1<a<10
3.1000<c<2000
4.b=2a
5.a,b,c is geometric progression

[cinder sundial]

First I assume a=2,b=4,c=8

So loga=0.301, logb=0.602, logc=0.903

1.a+c=2b
=>log(a+c)=log(2b)
=>log(10)=/=log(8)

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[alpine sable]

Hello how I do this

Do I just find derivative and set it equal to zero?

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[loud grove]

Ya, you would get the max point I think

You can't get the min point of that graph from 0 to 1 with that though since it isn't a stationary point

But you can tell that as x increases, the y value decreases

After the max point

So basically the min point would be the greatest x value within that domain

[alpine sable]

okay

ty

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[west hill]

Find the cost of the polishing a circular table top of diameter 4 m, if the rate of polishing it is
₹25 per m2

. [use π=3.14]

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[alpine sable]

help me this geometry homework

[west hill]

.reopen

[alpine sable]

.reopen

so.........

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[raven rover]

Start by drawing a diagram

[alpine sable]

how?

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[void niche]

with a piece of paper and a pencil

what do you mean how?

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[upper echo]

Is the formula for uncertainty |xmax-xmin|/2 or (xmax-xmin)/2?

e.g.
y=0.016x-0.02
y=0.015x-0.01
y=0.014x+0.24

would the uncertainty of the y-int be:
a. (0.24--0.02)/2 =0.13
or
b. (0.24-0.01)/2=0.115?

[upper echo]

2021 data test says b, however 2022 data test says a

@ me if got answer

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[tender crystal]

. How many 5-card poker hands are possible with a 52-card deck?

[delicate walrus]

Convert 0.4 into a simple fraction

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[alpine sable]

h

[edgy cape]

I got the first differential equation but idk how that becomes the second for the final answer?

also why does h=20m when t→ ∞

[hasty elk]

notice how the denominator changes?

it's got a e^(t/5)+1 at the top, and a 1+e^(-t/5) at the bottom

so you can try dividing both numerator and denominator by e^(t/5)

[edgy cape]

doesn't that make it 1? because t/5-t/5 =0 and e^0 =1

[hasty elk]

sure, you're dividing both numerator and denominator by the same thing, and this doesn't change the fraction

[edgy cape]

But that's still a different answer to the final answer

[edgy cape]

Wait no I was wrong, but I don't know what actually happens when you divide everything by (e^t/5)/ (e^t/5)

I keep getting 1 but that's definitely wrong

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[edgy cape]

i don't get it

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[strong hornet]

why is s_n and t_n defined like that?

[strong hornet]

the small span theorem just means the theorem on uniform continuity

i don't get why for sn it's $if x_{k-1} <x \leq x_k$ while for tn it's $x_{k-1} \leq x <x_k$

[ocean seal]

sean

[strong hornet]

as in

why is x_k included for s_n while x_k-1 is included for t_n

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[frail grove]

Evaluate the lim[ln(x^2+2x+2)] /x as x approaches +infinity

[vale sapphire]

What facts do you know about limits involving logarithms ?

[frail grove]

Limits of x.ln(x) as x approaches 0
lnx/x as x approaches +infinity
And limits of composite functions

<@&286206848099549185>

[vale sapphire]

I see

Okay, here's a question of gut feeling

when x gets very large, what is x²+2x+2 approximately equal to?

[frail grove]

Infinity?

[vale sapphire]

when x gets large, not infinite

I'm not asking about the limit, just an expression that's close enough to the actual value of x²+2x+2

An equivalent, in other words

(hint : what is the fastest between x², x and a constant?)

[frail grove]

Wdym what is the fastest?

[vale sapphire]

What grows the fastest

[frail grove]

Oh x^2

[vale sapphire]

Yeah

So would you agree that the other two terms become quickly negligible in comparison?

[frail grove]

Yeah

[vale sapphire]

We'll see how to make this formal in just an instant, but can you solve the problem if you replace x²+2x+2 by x²?

[frail grove]

Yup it's 2*0=0

[vale sapphire]

Correct

Now, this is an extremely common trick with polynomials, and sums of functions growing at different rates in general

[frail grove]

But i need to prove it though

[vale sapphire]

You can factor the largest term from the polynomial

so, x²+2x+2=x²(1+2/x+2/x²)

We have x² times a term that tends to 1 as x→∞

Well, we can turn that product into a sum with the logarithm

Hence, ln(x²+2x+2) = ln(x²(1+2/x+2/x²)) = ln(x²)+ln(1+2/x+2/x²)

Divide by x, and this time you'll have no trouble

Keep this in mind whenever you stumble upon any limit problem with polynomials

You can factor the term of highest degree and be left with something more easily workable

[frail grove]

Which property did u use here

[vale sapphire]

ln(ab)=ln(a)+ln(b)

edited to show the intermediate step

[frail grove]

Oh ok tysm u really are a good tutor 😅❤️🙏

[vale sapphire]

yw

[frail grove]

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[ancient halo]

err, this might seem very dumb but
but here's my question

-Change the following statements using expressions into statements in ordinary language.
(For example, Given Salim scores r runs in a cricket match, Nalin scores (r + 15) runs. In ordinary language – Nalin scores 15 runs more than Salim.
(a) A notebook costs ₹p. A book costs ₹3p.
(b) Tony puts q marbles on the table. He has 8q marbles in his box.
(c) Our class has n students. The school has 20n students.
(d) Jaggu is 2 years old. His uncle is 42 years old and his aunt is (4z – 3) years old.
(e) In an arrangement of dots there are r rows. Each row contains 5 dots.

[ancient halo]

(btw, im just not that good at understanding algebra)

[lethal dock]

a) a book costs 3 times more than a notebook.
b) Tony has 8 times more marbles in his box than on the table.
c) The school had 20 times more students than our class.
d) Question seems wrong, recheck if u entered this correctly....
e) 5×r = 5r = total dots -> The arrangement of dots contains 5 times the ammount of rows number of dots.

[lone heart]

@ancient halo Has your question been resolved?

[alpine sable]

try not to give direct answers

[lethal dock]

Oh ok

[lethal dock]

I see next I will

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[ancient halo]

thx

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[median mist]

how could we do b, do i just need to plug the 2 into the differentiated function or is there more to it?

[median mist]

I did A, for b will we just have to substitute 2 in the x for the dy/dx function

[alpine sable]

3x²+k

thats what u got

right

@median mist

ill just continue

12+k=0

so k=-12

f(x)=x³-12x

x=2

8-24=-16

[median mist]

ahhh

got it

ty

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[tepid mantle]

hi

[tepid mantle]

can anyone help me in a algebra

question

[little drum]

[tepid mantle]

yah so

3x+4y-11-2x+4y

whats the answer for this

tell this

anyone

help

[tepid mantle]

lhlo

@little drum

[little drum]

is that a simplification question?

[gray isle]

no, there is no z term in that expression

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[frail ruin]

1. The diagram below shows some string without open ends which cross n times. Explain how the number of strings can be determined. [Hint: Try to draw some cases for concrete values ​​of n.] (Picture 1)

2. (continued) Let us now select a random crossing and redo it as in the picture below. How will this change affect the number of strings? (Picture 2)

[frail ruin]

please help me here

[lone heart]

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@frail ruin Has your question been resolved?

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[buoyant kayak]

i'm sure google knows

https://www.youtube.com/watch?v=eI33kckOLLs

first video result on google

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[alpine sable]

how come ratio test doesn't work here

[vale sapphire]

It does

[marsh rapids]

it does

[alpine sable]

no i get some insane number

sigh

[knotty spire]

just at a quick glance, the last finished fraction you wrote should go to 0 as n to infty

[marsh rapids]

(3n+4)/(3n+1) -> 1 so you're "left" with -1 / (n+1) -> 0

[knotty spire]

you have n^1 at the top

n^2 at the bottom

[alpine sable]

oh wow

I didn't know you could divide your fraction up like that

[marsh rapids]

limit of product = product of limits. If well defined that is

[alpine sable]

yeah I guess that makes sense in terms of the limit

right

can ias k another question?

[marsh rapids]

you can

[alpine sable]

are these correct?

[marsh rapids]

For 23 it's faster to say that the terms don't go to 0 (because you can say it's obvious as it increases starting from n = 9 and is positive)

[alpine sable]

what about q24?

[marsh rapids]

sounds good

[alpine sable]

for this one im getting minus -1/11

[marsh rapids]

finding the value ?

[alpine sable]

root test

[marsh rapids]

reassuring

so nth root of nth term -> -1/11 is what you get ?

[alpine sable]

yessir

[marsh rapids]

the signs are already looking fishy, are you simply looking at absolute convergence ?

[alpine sable]

oh my God

I forgot about the absolute value

ok yeah so it's 1/11

and it converges since it's less than 1

[marsh rapids]

yes

[alpine sable]

thanks

I have about 3 more qs

can i go ahead?

[marsh rapids]

damn

I might have to go before the end but post it

[alpine sable]

alternating series test

[marsh rapids]

How did you show it was decreasing ?

[alpine sable]

i just did n+1 and compared

[marsh rapids]

is it that obvious ?

[alpine sable]

hmmmmmm

no

[marsh rapids]

no

[alpine sable]

so take 1st deriv instead?

oh wait

[marsh rapids]

you can try that

[alpine sable]

ill just rearrange the inequality

[marsh rapids]

you can do that

it's not painless but it's doable

[marsh rapids]

not that I actually went through it, but I see how it's done

[alpine sable]

oh what the hell

LOL

what is that monstrosity

[marsh rapids]

that first rearrangement doesn't look any more obvious

maybe bring it back to some simple polynomials ?

so there's no sqrt anymore

[marsh rapids]

see what I mean ?

[alpine sable]

so square the whole thing?

this is new to me

[marsh rapids]

you can

[marsh rapids]

bring it back to something not new

that's the way

make the unfamiliar familiar until you're familiar with it

[alpine sable]

woot it works

[marsh rapids]

you just did an example

that's no proof

[alpine sable]

[marsh rapids]

Same as the start. You also did an example. That's why I asked what your proof was. Because you showed none

[alpine sable]

I dno what that means

how do I even come up with one?

that n+1 is all we did in class

[marsh rapids]

actually do math

[alpine sable]

I'm doing math

LOL!!

[marsh rapids]

do math for any n

that last fraction was almost where I went

Except you're not supposed to plug in numbers and check the value. That proves it for n=4, not for any n

[alpine sable]

ok then what if I divided both sies by n

and compare the ratio with 1

[marsh rapids]

good luck with that

nvm it actually works

if you know how to do it

though it's just my method with a little extra complexity, ngl

[alpine sable]

What's your method

why u gotta do such a tease man

[marsh rapids]

just compare 2 degree 3 polynomials

get rid of the fraction instead of adding more stuff to it

who likes fractions when they can avoid them

[alpine sable]

oh

hm I see

@marsh rapidsCould I ask 1 last question pls

[marsh rapids]

You see how to do that at least ?

[alpine sable]

no

but I get what you're driving at

[marsh rapids]

then try it

[alpine sable]

doesn't change anything u get n^3 on both sides

[marsh rapids]

then remove them

[alpine sable]

how

[marsh rapids]

-n^3

[alpine sable]

uh

ok

then we'll be left with n^2

[marsh rapids]

so what can you say ?

[alpine sable]

they're the same?

are u saying AST can't be used here?

[marsh rapids]

So ?

it can

we're just proving it decreases for the AST

You're trying to compare 2 polynomials. Just expand and see which one is greater

[alpine sable]

nah I can't. I'm running out of time sorry

gotta do integrals

and go to lab in like 20 mins

[marsh rapids]

noon break in the US ?

[alpine sable]

wut?

no it's 1:56pm

[marsh rapids]

better

[alpine sable]

and I still have like 50 practice questions to do

got an exam tmrw

[marsh rapids]

to send or for practice ?

Cause if you want to do them all I feel like you should have started another day

[alpine sable]

practice

[alpine sable]

no I did.

I've done like uhh

150 so far

lol

im so bad at this

[marsh rapids]

in how many days ?

[alpine sable]

past 2 weeks

[marsh rapids]

that's a ton of exercises

[alpine sable]

ok maybe 50 more is an exaggeration

I only have like 30 left

[marsh rapids]

we get like 10 or 15 practice questions a week (or 50 if any exercice is counted)

though some of them can easily take a few hours

[alpine sable]

and uhh it's not 150 for series alone

integrals + series

This is my last one

oh nvm

ill try the LCT

[marsh rapids]

ratio test is trivial

gotta go eat though, so goodbye

[alpine sable]

bye. thanks for your help

[marsh rapids]

trivial because it's between 1/e^n and 3/e^n

[alpine sable]

wut

this series converges by Limit Comparison Test

.close

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@hidden hawk Has your question been resolved?

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[ocean seal]

DarQ

[lone island]

oh yeah

it is $\langle f, g \rangle = \int_0^\pi f(x) \cdot g(x) dx$

[ocean seal]

DarQ

[lone island]

and C[0, pi] is the set of continuous functions on [0, pi]

[vale sapphire]

No, they're flat out orthogonal

Oh wait, let me actually read the question, that might help

[lone island]

yeah, you right

I flipped

[vale sapphire]

Wait, is that true?

I thought all of them would be orthogonal

Let me work this out

It's between 0 and π and not 0 and 2π

That threw me for a loop

I proved all of these were mutually orthogonal of the inner product was over [0,2π] in a test recently, that's why i was confused

[lone island]

ye

k, thanks guys

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[safe mountain]

if i have (16^n)^-1/2

[safe mountain]

can i make that 16^n = 2^3n

or is it equal to 2^(n +3)

[vague coral]

$(16^n)^{-\frac{1}{2}}$

[ocean seal]

Herels

[vague coral]

this ?

[safe mountain]

yep0

i want the base to become 2

[echo socket]

16^n = 2^(4n)

[vague coral]

16^1/2 = sqrt(16) = 2²

[safe mountain]

so why isnt it 2^ (n + 4)

because if we * by another 2 for example

the power would add

not *

[echo socket]

Because 16^n = (2^4)^n = 2^(4*n)

[safe mountain]

oh your allowed to seperate like htat ?

[echo socket]

Yeah, because 16 = 2^4

[safe mountain]

okay thats cool

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[untold aspen]

can anyone help me?

i found b which was 0

but cant find a

[sterile ravine]

if you have b you can replace f(x) with the values

but how did you find b?

@untold aspen

[untold aspen]

i found the dervivative

and set it equal to 0

[sterile ravine]

yes

[untold aspen]

but now im stuck witgh finding the a

[sterile ravine]

f(2)=-1

and replace x with 2

[sterile ravine]

it's correct and you have the point (2, -1) is belonging to the graph

simplifying f(2)=-1 you will find 2a+b=2

[untold aspen]

where did u get the 2a+b=2 from>

?

[sterile ravine]

from f(2)=-1

=> (a*2+b)/[(2-1)(2-4)]=-1

because the point (2, -1) is belonging to the graph @untold aspen

[untold aspen]

oh yeah ur right

then what would I do next then?

afteer that

[sterile ravine]

you will get 2a+b=2 => 2a=2 because b=0=>a=1

@untold aspen

[untold aspen]

ohhh

tysmmm

so u basically used the point into the function

and then let b=0

right

[sterile ravine]

yes

[untold aspen]

why wouldnt u plug it into the dervived one

is it bc the dervived one only helps with the slope?

[sterile ravine]

I used on derivate one too

and I found the same result

I did f'(2)=0

[untold aspen]

i see

bc the slope is 0

right

[sterile ravine]

YES

[untold aspen]

tyyy

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[fringe condor]

I have a probability question and I think I am overcomplicating it.

[fringe condor]

Specifically, question c.)

Here are my thoughts so far (would really like to learn the right approach):

So - I can't quite figure out how to add 2/3 and 1/2 probabilities to then multiply against the 38.4%

Is this permutation overthinking it?

P(A or B) = P(A) + P(B) - P(A and B)

I can't quite see how to calculate for P(A and B) to remove it from the equation.

The flip side, potentially is a Binomial Experiment?

(P(x) = \binom{n}{k}p^x q^{n-x})

[ocean seal]

MrMadium

[fringe condor]

(P(x) = \binom{3}{2}\frac{2}{3}^2 \frac{1}{3}^{1})

[ocean seal]

MrMadium

[fringe condor]

?

Then the result of P(x) is multiplied with the 38.4% already calculated about 2 people landing anywhere on the line.

<@&286206848099549185>

Thoughts? Feelings?

I suppose the only other thought would be if this is right, considering the nature of no replacement.

But that is somewhat already taken care of by the Binomial as we include the rate of failure as well, doesn't it?

[lone heart]

@fringe condor Has your question been resolved?

[fringe condor]

<@&286206848099549185>

[lone heart]

@fringe condor Has your question been resolved?

[fringe condor]

<@&286206848099549185>

[lone heart]

@fringe condor Has your question been resolved?

[lone heart]

@fringe condor Has your question been resolved?

[fringe condor]

<@&286206848099549185>

[silver adder]

Its a puzzling question, but i think the answer is just P(Jenny landing)*P(either of the others landing)

[silver adder]

P(A and B) = P(A)*P(B)

[fringe condor]

Oh of course. Talk about not seeing the forest through the trees.

[silver adder]

Haha i like that idiom

So whats P(either of the others landing) ?

Its NOT the same as P(A or B)

[fringe condor]

I don't think we have that information.

Here is what we have thus far:

Each jumper has a probability of getting anywhere on the line = 0.8
Landing within AB of line = 0.5, Landing within BC of line 0.5

What I have calculated so far:
Probability of any two out of the 3 manage to land somewhere on the line = 0.384

Jenny is one of the jumpers, what is the probability of Jenny is one of only two that get on the line?
(For this, so far, I've done the Binomial as posted above = 0.4444 and then multiplied that with the chance of 2 getting anywhere on the line. 0.444 * 0.384 = 0.170666)

Final question:
What is the probability that two jumpers manage to land somewhere on the line, given that Jenny is one of them? (I've read that as a Bayes Theorem and used the spec from above).

This is the one that is the pincher.

Jenny is one of the jumpers, what is the probability of Jenny is one of only two that get on the line?
(For this, so far, I've done the Binomial as posted above = 0.4444 and then multiplied that with the chance of 2 getting anywhere on the line. 0.444 * 0.384 = 0.170666)

I think using Binomial takes into account the 2/3 and 1/2. However, now that I can see the forest through the trees, it could be:
2/3 + 1/2 - (2/3*1/2) * 0.384

Which is 0.83333

[silver adder]

seems too complicated for me

[silver adder]

we have the info

P(either A or B) = P(A or B not both) = P(A or B) - P(A and B)

[fringe condor]

P(A and B) - P(A or B) is the top one.

Which makes sense, it takes into account 2/3 + 1/2 sample space.

[silver adder]

x = P(person landing) = 0.8, the answer should be x(x + x - x^2 - x^2) = 2(x^2-x^3) = 0.256

[fringe condor]

But does that take into account that the third person must not land on the line?

I feel like we need to be taking that into account, no?

Wait - I'm going to read your equation another 15 times.

[silver adder]

It does

P(A or B) = 2x-x^2, P(A and B) = x^2, P(A or B not both) = P(A or B) - P(A and B) = 2x-x^2 - x^2

@fringe condor draw a venn diagram

[fringe condor]

Sorry @silver adder - had a job to get done.

Thank you so much for your help, I really appreciate it.

It's really been bugging me about how to best think through the problem and come to a conclusion.

[silver adder]

yeah?

me too

[silver adder]

but surely this is the answer

you get the same if you consider P(2 people make it and jenny makes it)

2 out of the 3 ways they can make it, jenny makes it

then its 2/3 P(2 people make it) = 2/3 (3x^2 - 3x^3) = 2(x^2-x^3)

you might need to draw the venn diagram to see this is true

[lunar spoke]

.close

[lone heart]

@fringe condor Has your question been resolved?

[lone heart]

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[alpine sable]

Would someone either prove or point me to a proof of the following please? $$ \lim_{n \to 0} (1 + n)^{\frac{1}n} = e $$

[ocean seal]

leadersheir

[lone heart]

@alpine sable Has your question been resolved?

[vague coral]

(1+n)^{1/n} = exp((1/n)ln(1+n))

[alpine sable]

that's.. not entirely clear

[rustic jungle]

Can't you just say something like $$n = 1/(1/n)$$ so $$ \lim_{n \to 0} (1 + 1/(1/n)^{\frac{1}n} = e $$

[ocean seal]

centuryegg

[alpine sable]

are you alluding to (1 + 1/n)^n = e?

[rustic jungle]

Yeah i think that good right?

[alpine sable]

but in that case, n goes to infinity not 0

[rustic jungle]

Oh that's true

Nvm

[alpine sable]

the limit is $\lim_{n \to \infty} \left(1 + \frac{1}n \right) = e$

[crude wren]

leader

[ocean seal]

leadersheir

[crude wren]

check mine and help me'

u are smart

[alpine sable]

pardon?

[crude wren]

check shetiscool because i need help

[alpine sable]

i believe the answer to your question would depend on the game logic.. it's not purely mathematical

[crude wren]

its minecraft

ok

[alpine sable]

expand using the binomial theorem, factor out terms similar to the following $\frac{1}n\left(\frac{1}n - 1\right) = \frac{1}{n^2}\left(1 -n\right)$ and substitute

[ocean seal]

leadersheir

[lone heart]

@alpine sable Has your question been resolved?

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[alpine sable]

yes i bloody answered my own question

[lone heart]

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[olive garden]

Anyone wanna help me do a basic maths question? My dumbass is too stupid to understand it lmao

[stoic ember]

sure dude

[olive garden]

I don't understand how tf this works out 😂

[stoic ember]

so

you try to divide 2 by 5

but it doesnt work out

so we add a 0 to 2

to make it 20

now we divide 20 by 5

20 / 5 = 4

but then we have to remember that we added a 0

so for every 0 we added to the 2 we have move the answer back 1 place

meaning 4 becomes 0.4

[olive garden]

Uhhh oki, I think I understand

Lol

[stoic ember]

try 2 / 25

[olive garden]

I'm stuck round here

[stoic ember]

firstly thats 25/2

not 2 / 25

[olive garden]

Oop..

[stoic ember]

but we can do this one quick

so you multiply 2 and 12

2 x 12 = 24

then you subtract that from 25

25 - 24

[olive garden]

1

[stoic ember]

now you divide 1 by 2

so 1 / 2

[olive garden]

0.5

[stoic ember]

and add that to 12

[olive garden]

12.5

[stoic ember]

now multiply 2 and 12.5

and subtract that from 25

[olive garden]

2x12.5 ?

[stoic ember]

yes

[olive garden]

25 - 25 =0

[stoic ember]

that means we're done

so 25 / 2 = 12.5

you can do 2 / 25 now if you want or we can stop here

[olive garden]

Ima try 2 / 25

0.0

[stoic ember]

you sure the answer is 0?

[olive garden]

25 doesn't go into 20

[stoic ember]

so we add another 0

[olive garden]

200

[stoic ember]

and now 25 goes into 200

[olive garden]

8

[stoic ember]

but we added 2 zeros

so we have to move the 8 back 2 times

[olive garden]

0.08?

[stoic ember]

yes

[olive garden]

Ah that makes sense

Sorry for boring you with my stupidity 😂

[stoic ember]

nah man

[olive garden]

I got an exam on the 9th

[stoic ember]

just practice a few more and you'll be good

[olive garden]

I was gonna open 1 of these and try do a practice test, but idk what software to use lmao

[lone heart]

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[fallow charm]

What is the value of x?

[visual vine]

@fallow charm can you see that it's just $x^{\frac{1}{2}} = \frac{1}{2}$?

[ocean seal]

Souradip Das

[fallow charm]

Why so

?

[visual vine]

Because this is an infinite series

And if you consider this way.
It's just $x^{(x^x...)} = \frac{1}{2}$, and the thing in the bracket is also $\frac{1}{2}$, from the question itself.

[ocean seal]

Souradip Das

[fallow charm]

How would that work?

[lone heart]

@fallow charm Has your question been resolved?

[fallow charm]

x^x^x.... (series repeats x times) = 0.5

0.25^(0.25*0.25) = 0.9170040432

[lone heart]

@fallow charm Has your question been resolved?

[pale kestrel]

call that thing S = x^x^x^...

notice S = x^S

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[dire cradle]

Can someone please explain to me how to work out which one is an open subset of A?

[pale kestrel]

define open subset

[dire cradle]

An open subset is for every $x\in [a, b]$ there exists $\epsilon > 0$ such that $(x-\epsilon, x+\epsilon)$ is a subset of $[a, b]$.

[ocean seal]

lgargaro

[dire cradle]

I have written all the possible answers out in set notation

[pale kestrel]

I mean

define

'An open subset of A'

It is currently unclear to me

a subset of A that is open in R? And no it isnt

[dire cradle]

but all of the possibilities contain an end point except c, but that contains points which aren’t in A

This is for topology

So I believe an open subset shouldn’t contain the boundary

[pale kestrel]

I can't help until you clear this up

In particular you should look up what an open set in the subspace metric is

It is not what you wrote above

[dire cradle]

Okay, i’ll have a look

I may have misunderstood the definition but i have read it so many times it’s starting to get more confusing as time goes on 😩

[pale kestrel]

Define for yourself the subspace metric

Then note with that definition what the open sets within that metric is

Then convince yourself the open sets within a subspace metric may not be considered open in the original metric

[oak perch]

He seems don’t know how subset become a topological space…

[dire cradle]

I think, maybe, this theorem might work

[oak perch]

Yeah so for example (2,3] is open in [1,3]

[dire cradle]

that’s still confusing though because how is the 3 included?

[oak perch]

Do it by definition

Not by your imagination

[dire cradle]

If you need an open set to intersect with A, then with the example you have just given [1, 3] intersected with (2, 3) (an open set) is just (2, 3) itself, is it not?

[oak perch]

(2,4) intersection [1,3]

[dire cradle]

Ohh okay, so from my example, I can take any open subset of the Reals?

and use that to find an open subset for A?

[oak perch]

Your example? Where?

X a topological space, A is a subset of X, B is a subset of A. B is an open subset of A iff B is intersection of U and A for some open subset U of X

[dire cradle]

The first photo i sent in

from my laptop screen

[dire cradle]

here

[oak perch]

Yeah there exists exact one open subset among those 4

You can write that one as U intersect A for some open subset U of R

[near lagoon]

It is a theorem that for a topology given by a metric the subspace topology coincides with the topology given by the subspace metric, namely Theorem 1 in Igargaro's notes

[dire cradle]

Thank you everyone, you have given me a lot to think about !

[dire cradle]

Hopefully i can work it out now with this

muchas gracias 🙏 😊

One last thing @oak perch, is U allowed to be a union of open subsets?

actually never mind…

I suppose it wouldn’t matter too much

[oak perch]

Any union of open subsets is open

Finite intersection of open subsets is open

[dire cradle]

okay, thank you kindly 🙏

[lone heart]

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[burnt flume]

hi! sorry, I'm wondering if anyone could explain a concept to me? that is, finding other angles with the same trig ratios- for example, finding an angle with the same trig ratio of sine 38. I get that the second angle would be in quadrant 2 so that it's positive, but I don't know how to go further.

[umbral prism]

Need help with something simple pls dm

[lone heart]

@burnt flume Has your question been resolved?

[burnt flume]

<@&286206848099549185>

[static grail]

I'm having trouble understanding what you mean

are you tryiing to find the value of sin(38)?

or finding a different trig function that would give the same output

[burnt flume]

a different trig function that would give the same output

[static grail]

oh

So

[sage bronze]

sin (180-x)=sin (x)

[static grail]

Have you seen the double-angle identities?

not double

cofactor

what ami saying

lmfao

[burnt flume]

no it's okay! and no I don't think so, it's not in the notes my teacher gave us

[static grail]

cofunction

I keep saying it wrong

[burnt flume]

OH NVM

[static grail]

where pi/2 is 90 degrees

[burnt flume]

yeah I know those!

[static grail]

ok yeah

use those

so sin(38)=cos(52)

[burnt flume]

ohh

oh my gosh I get it now thank you so much!!

.close

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@barren bough Has your question been resolved?

[barren bough]

<@&286206848099549185> ?

[lone heart]

Channel closed

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[barren bough]

.close

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[fallen kayak]

Hello can I get some help on my math homework?

[fallen kayak]

<@&286206848099549185>

I am not fammiliar with discord

[wary stream]

You have to wait at least 15 minutes before pinging helpers

[fallen kayak]

sorry, but can you help me?

[wary stream]

Nope

[fallen kayak]

very well then..... .... fucking jackass

[wary stream]

I'm just passing by, reading the channels, and noticed you pinged helpers before waiting, so I mentioned, but I'm busy

[long sleet]

Need help on question 11, 12 and 13

Got the rest

[fallen kayak]

I am using this server

[long sleet]

Sorry

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@fallen kayak Has your question been resolved?

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@fallen kayak Has your question been resolved?

[hardy gulch]

( y \propto z x^2 t^{-1} \sqrt{w} \implies y = kzx^2t^{-1} \sqrt{w} ) where (k) is a constant to be found

[ocean seal]

ricey

[hardy gulch]

after you find k you will have the information to solve the problem

[lone heart]

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[lunar elk]

can someone explain this to me?

I'm learning of to use a ti84 calculator

[lone heart]

@lunar elk Has your question been resolved?

[lunar elk]

.close

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@hazy knoll Has your question been resolved?

[hazy knoll]

<@&286206848099549185>

[noble sinew]

if you take the sum of (m_i-mean) it will be equal to 0

[hazy knoll]

Can you explain that to a stupid person

Clearly I dont understand what you're typing

[noble sinew]

if 150 was the true mean the sum would be equal to 0

[hazy knoll]

Ok I don't know what to do with that information

you're saying the true mean is 32?

[noble sinew]

no

if mean was 149 then because we are 1 off on every single term in the sum

and there are 52 terms

how much are we off?

[hazy knoll]

52?

[noble sinew]

yes

[hazy knoll]

why does this work

How does that make every term in the sum 1 off

[noble sinew]

on avg they are one off

its just definition of mean

[hazy knoll]

k

so on average we're off by 52 on each term

how can I use this in my question

[noble sinew]

where did that come from?

[hazy knoll]

thought thats what we just found out

[noble sinew]

not what I said was it?

[hazy knoll]

Im confused

can you write that sentence in the context of my problem

[noble sinew]

I am?

if mean was 149 then the sum would be equal to -52 like we just agreed

[hazy knoll]

ok

but I don't know what to do next

I don't know the mean

so I cant use that

[noble sinew]

if sum was equal to -104 how many are we off on each term on avg?

[hazy knoll]

2?

[noble sinew]

yes

how did you figure that out?

[hazy knoll]

-52 was 1 off as theres 52 terms

so 104/52 = 2

[noble sinew]

okay division