help-13

[potent sluice]

nah this is all

that might be why im confused

.close

[cedar kiln]

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[quiet hazel]

Roll a six-sided die, if I get a larger number than the opponent, I get $1. What's the expected winning?

[quiet hazel]

so i know i have 6 possible options i could get if i roll a 6 sided dies

the 6 possible options i can get are D1 - D6

P(D1) = 0/6

P(D2) = 1/6

P(D3) = 2/6

P(D4) = 3/6

P(D5) = 4/6

P(D6) = 5/6

i would need to discrete random variable to get the expected winning right?

<@&286206848099549185>

[dense wing]

so 1) What is Dx suppose to be?

cause the probability you roll a 1 isn't 0

[quiet hazel]

did you read the problem

[dense wing]

Yes

Hence why I'm asking you what your notation means

Cause you don't care about what you roll specifically

[quiet hazel]

if i roll a 1 no matter what the other person rolls i wont win $1

[dense wing]

You only care that it's larger than your opponent

[quiet hazel]

theres no number in a die 1 is larger than

thats why i said 0

[dense wing]

Ok so you still did something wrong

cause your probabilities don't add up to 1

[quiet hazel]

im not suppose to divide it by 6 right?

[dense wing]

Write out the entire 6x6 sample space

and find P(You win) and P(You lose)

[quiet hazel]

its asking for how much money am i expecting to win

[dense wing]

Im aware.

If you recall the definition of expectation, you'd know you need the pmf

[quiet hazel]

so discrete random variable?

[dense wing]

Yes it'll be discrete

since you either win or lose

specifically bernoulli but I disgress

[quiet hazel]

i got $2.50

[dense wing]

$E[X]=(1)P(W)+(0)P(L)$ where X is the rv, W is the event you win, L is the event you lose

[wraith dagger]

Mosh

[dense wing]

so $E[X]=P(W)$

[wraith dagger]

Mosh

[quiet hazel]

we multiply the chance it takes to roll and the chance we have to win with the number we are in

so for example

if we roll D6

chance to roll is 1/6

chance to win is 5/6

there are 5 numbers 6 is greater than

but if the opponent roles a 6

we lose since 6 isnt greater than 6

[dense wing]

The sample space isn't what you individually roll

it's the collection of both roll pairs

there are 36 possible outcomes

and (insert number here) of them, you win

the rest you lose

The probability you win is, like we saw last time, $P(W)=\frac{|W|}{|\Omega|}$

[wraith dagger]

Mosh

[dense wing]

number of outcomes you win / total number of outcomes

I don't care how you get |W|, so long as it's the correct number

[quiet hazel]

ok so we have 36 outcomes

[dense wing]

Yes

[quiet hazel]

between me and my opponent

[dense wing]

Yes.

2 standard dice rolled = 36 outcomes

[quiet hazel]

the number of outcomes i win is 15/6

P(D1) = 0/6
P(D2) = 1/6
P(D3) = 2/6
P(D4) = 3/6
P(D5) = 4/6
P(D6) = 5/6

based on this^

[dense wing]

15/36

cause we literally just agreed the size of the sample space was 36 not 6

[quiet hazel]

yeah

[dense wing]

Don't "yeah" when you also said P(W)>1

[quiet hazel]

i did?

[dense wing]

.

15/6>1

in fact greater than 2

[quiet hazel]

we just add the 0 + 1 + 2 + 3 + 4 + 5 and divide it all by 36 right?

[dense wing]

Yes, that is another way to do it

[quiet hazel]

whats the other way?

[dense wing]

but anyway, so you have the expected winning is 15/36

[quiet hazel]

thats dollars right?

15/36 dollars

or percent

its percent

[dense wing]

15/36 dollars

cause expected winning is in dollars

[quiet hazel]

yeah

okay makes sense

this was okay

[quiet hazel]

this is bernoulli distribution?

[dense wing]

If X is the rv you win, then yes X ~ bernoulli(15/36)

[quiet hazel]

what equation is that though?

[dense wing]

wdym

[quiet hazel]

how did you come up with that?

[dense wing]

come up with what?

[quiet hazel]

this equation

P(W)

[dense wing]

Definition of expectation

oh that one

The literally definition of probability

you were told this last night iirc.

[quiet hazel]

oh

is that a real equation?

[dense wing]

.....

[quiet hazel]

oh no its made up to fit the context of the problem

[dense wing]

Im not even going to attempt to understand what you just said

it's the definition of probability

end of

[quiet hazel]

the percentage of winning is the number of outcomes of winning over the total outcomes

which is common sense

[dense wing]

yes

[quiet hazel]

you probably just made up those symbols

[dense wing]

Well duh

However everything was defined either today or yesterday.

[quiet hazel]

if i leave the answer like this, is this wrong?

[dense wing]

????????????????

[quiet hazel]

for bernoulli

nvm

[dense wing]

The answer is 15/36...............

cause..

[quiet hazel]

ik

[dense wing]

You dont

you dont know

cause you just asked that

[quiet hazel]

ok nvm you dont understand me but ik now

ty

why does the answer have to be less than1?

its not like its a percentage

obv percentage cant be greater than 1

[dense wing]

cause you're expected to lose

[quiet hazel]

oh snap

[dense wing]

P(W)=15/36<18/36=1/2

[quiet hazel]

it cant be greater than 1 since thats the most money i can get if i win

makes sense

[dense wing]

If it were a completely fair game, you'd expect to win half the time

thus expect on each go to win 50 cents

[quiet hazel]

yeah

[dense wing]

since you're at a disadvantage, you expect to make less

[quiet hazel]

yup

[dense wing]

,calc 15/36

[wraith dagger]

Result:

0.41666666666667

[quiet hazel]

im expected to lose since thats the total outcomes i win is less than the total outcomes

[dense wing]

right idea, wrong phrasing.

[quiet hazel]

the total outcome i win is 15

[dense wing]

The number of times you win is less than half the number of outcomes

[quiet hazel]

yeah

so thats why it cant be greater than 1

if i play this game

its not worth playing cause ill lose the majority of the time

[dense wing]

yes

[quiet hazel]

since the number of times i win less than the total outcomes of both die

[dense wing]

welcome to the world of casinos

[quiet hazel]

so ill be losing money playing this game

ahhhh

this was a fun problem

i overcomplicated things at the beginning

ty

[cedar kiln]

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[austere moat]

How to get derivative of x^lnx

[split mirage]

We can start by writing this as $(e^{\ln x})^{\ln x} = e^{(\ln x)^2}$.

[wraith dagger]

PhenomPlasma

[austere moat]

Why?

[split mirage]

Having x both as the base and the exponent is hard to work with.

So we rewrite the base as an exponent.

[austere moat]

Ohh okok

[split mirage]

We can always write $x = e^{\ln x}$.

[wraith dagger]

PhenomPlasma

[split mirage]

From here, you can just differentiate using the chain rule.

[austere moat]

Derivative of e^(lnx)²?

[split mirage]

Yep.

[austere moat]

Ok noted

Thanks

[split mirage]

👍

[austere moat]

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[cedar kiln]

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[crimson sedge]

8aii. How do I eliminate the R?

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

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[dry monolith]

The base one b1=1.6m ,base two b2= 4m , height h=2m.
anyone know how to solve this?

[reef venture]

area of trapezium?

[dry monolith]

yeah

[reef venture]

what is the question

alright

use the formula

[dry monolith]

what's the formula

that's what I am trying to figure

[reef venture]

1/2(b1 + b2)h

[dry monolith]

???

[dry monolith]

ohhh

thanks a lot

[reef venture]

[dry monolith]

so it's 1 times 5.6

yeah ok

i am pretty dumb sometimes lol

[cedar kiln]

@dry monolith Has your question been resolved?

[cedar kiln]

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[languid narwhal]

<@&286206848099549185>

[reef venture]

Please wait before pinging helpers

[languid narwhal]

ok

[reef venture]

and the first thing you should send here is the question

[languid narwhal]

okey

oh yea and also how long do i have to wait for thoo- (im in a rush a bit)

[reef venture]

send your question

[languid narwhal]

what is the length of the bases of the trapizoid? (-3,3) (4,1) (-3,-2) (4,-2)

[reef venture]

try to plot it, and find the parallel sides those are the bases

then find their lengths using the distance formula

[languid narwhal]

ok

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[crimson sedge]

can anyone help me with a series of questions?

[crimson sedge]

nvm

.close

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[glass blade]

Sure give

[cedar kiln]

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[wraith dagger]

adam03

[silver fable]

.close

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[covert island]

I was hoping someone can review this with me really quick since Im having a bunch of problems

but my question mainly goes into how do you tell

what points are the local min/max

and which points are the absoloute min max

.close

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[coarse hearth]

can someone explain how x+2>0

[cedar kiln]

@coarse hearth Has your question been resolved?

[coarse hearth]

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[warm vector]

How would I sketch this function?

[tropic oxide]

you would take the portion of the graph of y=x^2 that lies to the right of the line x=1, and the potion of the graph of y=3x-2 that lies to the left of the line x=1.

[warm vector]

But why does the graph like ..’break’ at the points (1,1)?

[tropic oxide]

what's q?

[crimson sedge]

Because the person who made this question defined the function to "break"....?

[warm vector]

Oh sorry it’s 1

[tropic oxide]

are you asking why there is a sharp bend at the point (1,1)?

there's no discontinuity there.

[warm vector]

Ye

[tropic oxide]

look at the slopes of secant lines through a point on the graph close to (1,1) on the left and on the right

[warm vector]

Like there’s half a parabola and have the other equation of the line joint together

[tropic oxide]

on the left you will get that the slopes of these secant lines will approach (or in fact be equal to, in this case) 3
but on the right you will get that the slopes approach 2 and not 3

there is a mismatch

that's what it looks like on a graph

[warm vector]

How do we know the points are 1,1

[crimson sedge]

f(x)= x^2 for x>=1

[warm vector]

Ok

[crimson sedge]

Therefore f(1)= 1^2= 1

[warm vector]

Ohhh ok I see

[tropic oxide]

mentions the point (1,1)
"how do we know the point is (1,1)"

by the way, we're talking about ONE point here, not two

[warm vector]

Yep

[tropic oxide]

so why say points, plural, when there's only one?

[warm vector]

Oops a mistake

[tropic oxide]

in any case

have i answered your question as to why there is a sharp bend at x=1?

[warm vector]

Yes

[tropic oxide]

or i guess more like a corner

okay

do you have anything else left to ask?

[warm vector]

Nope I’m fine

Thanks

[crimson sedge]

There's no rule f(x) should really be defined as a single equation, always

[warm vector]

Oh ya

[crimson sedge]

and sometimes it's counterintuitive to make it in a single equation, either

[warm vector]

Ok I see

[crimson sedge]

Take( sinx+|sinx|)/2, for example

[tropic oxide]

if theres nothing else to ask about the original problem then this channel is best off closed

so that jun can post about different problems in a new channel

.close

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[dreamy lily]

help

[dreamy lily]

I need to find the circumcenter of this triangle

I already found the midpoints, slope, perpendicular slopes, and right bisector of AB, BC, AC

Now heres the thing, i found the coordinate points of the circumcenter,(-1/7, 16/7)

I'm stuck on question 5 which asks, "5) Verify that the circumcenter you determined in #4) is equidistant (i.e. the same distance) to each vertex of the triangle. Show your calculations below."

how do i calculate the distance of each vertex from the circumcenter?

<@&286206848099549185>

[peak relic]

Please do not ping moderators for help with a math problem, only ping mods if you have a server issue / rule violation you need us to address.

[dreamy lily]

oh, im sorry i thought they were helpers aswell

<@&286206848099549185>

do i use this formula?

[magic laurel]

Ye, it’s that formula, basically just Pythagoras to find the length

[dreamy lily]

i did this but none of them are equidistant

[magic laurel]

The point may be wrong then, have you done it like:

This where it’s the difference between them

[dreamy lily]

where did 27/7 come from?

[magic laurel]

Wait no that should be 34/7

Didn’t use my calculator

[dreamy lily]

5.1 units

[magic laurel]

Are they not all same?

Because that is the formula

[dreamy lily]

can you try doing the vertex b?

im also seeing if its the same

i got 2.9 units

[magic laurel]

I got 5.15 for them all

[dreamy lily]

how?

[dreamy lily]

for vertex b, isnt -3/1x7=21/1

how'd you get 36/7?

[magic laurel]

Because I did the difference between 5 and -1/7 which is 36/7

[dreamy lily]

oh ok

and for (-3,-2) where did 30/7 come from

[magic laurel]

Difference between the y values, -2 and 16/7

[dreamy lily]

so if i wanted to show my work would i start off like this

[magic laurel]

Ye, that’s perfect

[dreamy lily]

for all of them?

[magic laurel]

Ye I think so

[cedar kiln]

@dreamy lily Has your question been resolved?

[cedar kiln]

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[tiny marten]

any ideas on this?

i used x=3/4 tan(u)

and I reached the integral of sin^2/cos^3

is that right?

[cedar kiln]

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[lime kelp]

does anyone mind helping explain how to prove this for my Algebra course? the solution given isn't really all that useful to help me understand the concept. I get that you have to prove the axioms of a ring but I'm not quite sure how with the Z mod n group. Thank you!

[cedar kiln]

@lime kelp Has your question been resolved?

[cedar kiln]

@lime kelp Has your question been resolved?

[upper abyss]

Since there's no context here I do have to ask - do you know what Zn is, and how addition and multiplication works on it?

If the answer to that is yes, then which axioms are giving you trouble? We can focus on those.

[lime kelp]

i'm really strugging with my algebra rn, but iirc the set Z/n is the remainders of the real numbers modulo n which is n-1 basically. Then the addition and multiplication is the respective modulus n of the results? I'm just not really sure how to formulate an answer for an exam, because for the most part it's our answers have just said bookwork or trivial but obviously that wouldn't be accepted in an exam?

[upper abyss]

So the answer is yes. Which axioms were giving you trouble?

Do you know what the additive identity is, for example?

@lime kelp

[lime kelp]

yeah so the additive identity in this case would be 0?

sorry, i'm just quite bad at proofs and not entirely sure what is sufficient. so for like proving the associativity of the binary operation *, i did the following

but i just feel like it's a lot of waffle

[cedar kiln]

@lime kelp Has your question been resolved?

[upper abyss]

Let's say that
a(bc) = (ab)c (mod n)

That means, by definition,
a(bc) - (ab)c = kn for some k

But now we're working in the integers, where we know multiplication is associative. So the left is just 0, and k = 0 exists. Therefore, the original statement is proven.

@lime kelp

Note that this isn't a subgroup of Z so associativity isn't immediately inherited.

I think you might be missing a definition of the modulo n thing? You'll need to mention it somewhere

[cedar kiln]

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[wanton glacier]

how do I find a?

tried plugging in 1, 2, 3, 4, and 5 and they're all zeroes

which means (x-1)(x-2)(x-3)(x-4)(x-5) are factors

[dense wing]

vieta's results..?

[wanton glacier]

$(x-1)(x-2)(x-3)(x-4)(x-5)=(x-a)((x+1)-a)((x+2)-a)((x+3)-a)((x+4)-a)$

[wraith dagger]

hyperlix26

[wanton glacier]

how can I apply it?

[dense wing]

you can easily find the sum of the roots 1 at a time

cause you have an almost fully factored form

[wanton glacier]

almost?

[dense wing]

(x+1)-a isn't a factor

[wanton glacier]

(x-1)(x-2)(x-3)(x-4)(x-5) is not fully factored?

[wanton glacier]

oh that one

[dense wing]

(x+1-a) is a factor

to which the root is a-1

[wanton glacier]

I simply need to add all the roots? 5 + 4 + 3 +2 + 1 = 15

[dense wing]

those arent the roots

the roots are in terms of a.

[wanton glacier]

hmm

[dense wing]

write out all the roots from the factored form.

[wanton glacier]

wait a sec, how are they not roots?

if (x-1) is a factor

[dense wing]

cause the roots are clearly dependent on a

[wanton glacier]

that means 1 is a root right?

[dense wing]

yes

you never have (x-1) anywhere as a factor

[wanton glacier]

this? @dense wing

[dense wing]

yeah that's nonsense

hence why I never replied to it

[wanton glacier]

why is that nonsense?

[dense wing]

doesn't help you find a

unless you like pain staking trial and error

[wanton glacier]

hmmm

[dense wing]

.

[wanton glacier]

you mean this? (x-a)((x+1)-a)((x+2)-a)((x+3)-a)((x+4)-a)?

[dense wing]

yes.

[wanton glacier]

ok

@dense wing

[dense wing]

yes.

now set up an equation for a using roots 1 at a time.

[wanton glacier]

what

does that mean

[dense wing]

$\alpha+\beta+\gamma+\delta+\varepsilon=\frac{-b}{a}$

[wraith dagger]

Mosh

[dense wing]

LHS are the roots one at a time

[dense wing]

yes.

and you know what -b/a is

[wanton glacier]

ok

[wanton glacier]

yes

[dense wing]

so you have a linear equation in a.

note that -b/a a isnt the same as the variable a.

[wanton glacier]

ok

[dense wing]

ok

[wanton glacier]

-b/a = 15

[dense wing]

yes.

[wanton glacier]

a is one?

[dense wing]

shouldnt be

$5a-10=15$

[wraith dagger]

Mosh

[wanton glacier]

oh found my mistake

rip

[dense wing]

...

[wanton glacier]

ok it's 5

[dense wing]

yes.

[wanton glacier]

alright cool

wayy better than what I did here

[dense wing]

yep

[wanton glacier]

,w (1 - a) (2 - a) (3 - a) (4 - a) (5 - a) = 0

@dense wing you said those weren't the roots

[dense wing]

No, cause I was referring to the original factored form

[wanton glacier]

hmmm

[wraith dagger]

Results provided by WolframAlpha

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

Requested by hyperlix26#0041

[wanton glacier]

wait a sec

they're asking for the value of $a(a-1)(a-2)(a-3)(a-4)$

[wraith dagger]

hyperlix26

[wanton glacier]

does that mean I could've just answered it immediately just by looking at this equation? @dense wing

[dense wing]

if that was the original question, then you could have just used roots 5 at a time, yes

this is why you ask the entire question verbatim right off the bat

[wanton glacier]

smh

seems like another case of https://xyproblem.info/

.close

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[dense wing]

yeah, it was

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[crimson sedge]

$A \cap B \subseteq A \Rightarrow A \cap B \in P(A) \Rightarrow P(A \cap B) \subseteq P(A) \Rightarrow P(A \cap B) \subseteq P(A) \cup P(B)$

[wraith dagger]

mahmooz

[crimson sedge]

is this series of consequences correct?

specifically, is this true: $A \cap B \in P(A) \Rightarrow P(A \cap B) \subseteq P(A)$

[wraith dagger]

mahmooz

[mighty drift]

yes, A ^ B is a subset of A, so a subset of A ^ B is a subset of A because being a subset is a transitive relationship

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[regal torrent]

Guys I need help with breaking down how Taylor's series works, so I'm reading this paper about magnetic levitation and after the author makes a model of a non-linear system, he uses the taylor series to basically linearise it

[regal torrent]

But what I don't get is from what I usually see from Taylor's series expansion, how do they end up getting the above image as an answer?

This is the full image

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[limpid grail]

Can anyone help me understand how to complete this table

[lost lance]

Frequency density x class width = frequency

[limpid grail]

Thats the issue I don't know freq density

which has thrown me off

[lost lance]

You count the boxes and you find a scale I’m pretty sure

[limpid grail]

tried it but it doesn't add up

[lost lance]

So for 5-8 you have a class width of 3 but a frequency of 12

So you use the formula to rearrange for frequency density

You have the bar for that part so the number of boxes equates to that frequency density then you can get a scale

I can reword that if you want

[limpid grail]

wait so whats freq density for 5-8

[lost lance]

Should be 4

[limpid grail]

That explanation is good , I can take a look

thanks I think i've got it now @lost lance

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[lost lance]

👍

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[elder lily]

ive been doing this for the past fifteen minutes i dont know what im doing wrong please help me

[elder lily]

.close

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[harsh relic]

just plug in -2 into x then calculate the value of y

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[knotty comet]

lg 0, 1 + lg 100 − lg 10^3 + 10^lg(2)

[knotty comet]

I did lg0.1 * 100 = lg 10

lg 10 / 1000

=

lg 1/100

or 0.01

then 10^ log x = x

so 2

and then i took 0.01 * 2

= 0.02

but its wrong

[cedar kiln]

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[crimson sedge]

Who can help

[dense wing]

answer is 7, glad I could help you with your well worded math question

• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.

[crimson sedge]

Oi this is sick

You guys changed it

The server

Can’t lie this is 10x better

Haven’t been here in time

Will send question now sis✨😛

[dense wing]

ok...

[crimson sedge]

Taking ages sorry queen🙈

[dense wing]

why are you being cringe?

[crimson sedge]

Dunno mate

Anyway

[dense wing]

Also I don't use she/her pronouns.

[crimson sedge]

Okay slay✨🙈💯

[dense wing]

Ok, gl.

[crimson sedge]

Anyway

Bruh how matched me with this drag queen

I’ve got the basics of the question but the mark scheme is #useless

[dense wing]

#❓how-to-get-help

[cedar kiln]

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[violet rapids]

so i'm thinking

$y = \frac{-b}{a}x+b$

[wraith dagger]

sills

[dense wing]

that's the equation of the line, yes

[violet rapids]

now what i should do is find that in terms of x and integrate from 0, b?

[leaden snow]

draw it in 3d

[dense wing]

yes, x=f(y) will be the diameter of the slices

[violet rapids]

so

$V=\frac{1}{2} \pi \int_0^b (\frac{-a(y-b)}{b})^2 \dd y$

[wraith dagger]

sills

[dense wing]

missing factor of 1/4 from squaring I think

you have the diameter which is f(y)

you want radius which is f(y)/2

[violet rapids]

ah

[dense wing]

$\dd{V}=A(y)\dd{y}=\frac{\pi r(y)^2}{2}\dd{y}=\frac{\pi f(y)^2}{8}\dd{y}$

[wraith dagger]

Mosh

[dense wing]

so $V=\int\dd{V}=\int_0^b\frac{\pi}{8}[f(y)]^2\dd{y}$

[wraith dagger]

Mosh

[dense wing]

so you can hopefully gut check that, cause 8*3 will give the /24 you want

[violet rapids]

how do i bridge the gap from this to $\frac{a^2b \pi}{24}$

[wraith dagger]

sills

[leaden snow]

integrate and see?

[dense wing]

do the integral lol

f(y) is the equation of the slanted line when you have x=

[violet rapids]

do i just do FTC?

F(b)-F(a)

[dense wing]

yes.

[violet rapids]

[dense wing]

what?

it's just a polynomial integrand

[leaden snow]

if you pull out the constant factors a^2 and 1/b^2 it will look less intimidating

[violet rapids]

$\frac{y^3}{3}-by^2+b^2y\Big|_0^b$

[wraith dagger]

sills

[violet rapids]

ok that was fun while it lasted!

tysm

.close

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[cedar kiln]

@odd rock Has your question been resolved?

[cedar kiln]

@odd rock Has your question been resolved?

[calm sierra]

.close

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[random oyster]

Hello.

[random oyster]

The surface area of a cube is changing at a rate of 8cm^2/s. How fast is the volume changing when the surface area is 60cm^2?

I did A = 6a^2

60 = 12a

a = 1/5

V=a^3

V=3a^2

V = 3(1/5)^2 x 8 i got 24/25

but the book says

[dense wing]

yeah you forgot chain rule

$A=6a^2\implies \dv{A}{t}=12a\dv{a}{t}$

[random oyster]

for which step(s)

[wraith dagger]

Mosh

[random oyster]

yeah i did that

60 = 12a

?

[dense wing]

you didnt

[random oyster]

I did A = 6a^2
60 = 12a

[dense wing]

where's the da/dt

you're not told it's 1

[random oyster]

ah

so da/dt is 8

[dense wing]

no

[random oyster]

?

[dense wing]

dA/dt is 8

what's a if the SA is 60cm^2?

[random oyster]

ah

1/5

?

[dense wing]

60=6a^2

what's a?

[random oyster]

ohh

so u dont derive it yet

[dense wing]

I asked for a given SA, yes

so you use the SA formula.

and differentiate*

[random oyster]

a = root 10

?

[dense wing]

you're not deriving anything

yes

so what's da/dt?

[random oyster]

ah

root 10

[dense wing]

60=12a*da/dt

[random oyster]

60 = 12 a(root10)

then i solve for da/dt

or a

[dense wing]

...

you know what a is

we just found that it was sqrt(10)

[random oyster]

60 = 12 (root10) da/dt

solve for da/dt

?

[dense wing]

yes.

[random oyster]

ah I see..

so da/dt

is 60/ 12 root 10

[dense wing]

which simplified is?

[random oyster]

5 root 10

OH

I SEE

ah makes sense lmao

[dense wing]

5/sqrt(10), which is sqrt(10)/2

[random oyster]

yeye

can u help me with another one

A box with a square based and no top must have a volume of 10,000 cm^3. If the smallest dimension in any direction is 5cm, then determine the dimensions of the box that minimize the amount of material used.

[random oyster]

also

whats the point of saying SA of cube is changing at a rate of 8cm

if its never used?

[dense wing]

it is used...?

Oh you solved 60=12a da/dt

missed that, 60 should be 8

[random oyster]

ah.

[dense wing]

since $\dv{A}{t}=8$

[random oyster]

so use the same fromula

[wraith dagger]

Mosh

[random oyster]

A = 6a^2

[dense wing]

yes

[random oyster]

differentiate it

then A becomes 8

okok!

[dense wing]

you know $A=60, \dv{A}{t}=8$

[wraith dagger]

Mosh

[random oyster]

ah I see

[random oyster]

can u help with this?

[dense wing]

(at some moment in time T)

Not really rn

[random oyster]

uhh

anyone else?

[cedar kiln]

@random oyster Has your question been resolved?

[random oyster]

nah fam

[cedar kiln]

@random oyster Has your question been resolved?

[cedar kiln]

@random oyster Has your question been resolved?

[random oyster]

No

A box with a square based and no top must have a volume of 10,000 cm^3. If the smallest dimension in any direction is 5cm, then determine the dimensions of the box that minimize the amount of material used.

[little wolf]

wdym by smallest dimension in any direction is 5?

[radiant topaz]

5cm is any of l,b,w

One of them is 5cm is what it is saying

5lw=1000 and to find min(2(5l+5w+lw))

[cedar kiln]

@random oyster Has your question been resolved?

[cedar kiln]

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[ripe hamlet]

It's an equilateral triangle.
How to prove ∠Q1 = ∠Q2 = 60
And ∠B1 = ∠B2 = 30

[quartz vale]

the sides are tangential to the circles

so the line joining Q and B bisect the angle of the triangle

which is an equilateral triangle

[ripe hamlet]

Is this a proven theorem?

[quartz vale]

it is, yes

you could prove it yourself using congruency of triangles

based on the more fundamental theorem that the tangent is perpendicular to the radius

which you know, in this case anyways, as it is already given

which was also the basis for concluding that it was a tangent ig

[ripe hamlet]

So is the radius of the circle enclosed in a bisector triangle as well?

[quartz vale]

wdym?

[ripe hamlet]

Is the radius of the circle in the triangle bisector? (BQ)

[quartz vale]

i dont see how that matter, but yes

[ripe hamlet]

How can I prove it?

[quartz vale]

the triangle is a right angle

the radii are equal (which are two corresponding sides)

there is one common side

do you see it?

[ripe hamlet]

I can only say that BQ=BQ and both have 90 angles

[quartz vale]

the radii are also equal

but yeah you need to mark a point

in case you cant, you can just assume the theorem to be true (since it is, well, a theorem) and prove your angle measures

[ripe hamlet]

We can say QN=QF, BQ=BQ and BN=BF

.close

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[steady plover]

how do you find TN if VY = 9?

[steady plover]

we've just tackled the midpoint theorem (m=b1+b2/2). can this theorem be applied to this?

[wispy talon]

Is T the midpoint of XV?

Is any other info given or it's just this figure?

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[autumn carbon]

what does πx mean? does it mean x times by π?

[autumn carbon]

oh, so i was right? just thumb this message if i was right

ok

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[autumn carbon]

thank you

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[bold lotus]

what is a method to compute say:
the number of outcomes where the sum of two six sided die is equal to 7

without having to list out every outcome that meets these requirements

[marble bone]

I mean we roll the die once we get let's say a
And roll again we get b
Now how many pairs of a and b exists where a+b=7

?

And also a<=6 and b<=6

[bold lotus]

yes im asking how you can calculate it without this method

say you had 500 sided dice and trying to get them to sum to 357

[marble bone]

I see

I just want to say

Can I write the question as

a+b=7 given a and b is less or equal to 6

Now find the number of pairs

Without brute force

[bold lotus]

how would you find it without brute force?

[marble bone]

Umm simple

a+b=7

Thus

b=7-a

as a is an integer value

Such that

0<a<7

Thus there are 6 possible values for a

That leaves us with our 6 possible pairs

Without using brute

Force

[bold lotus]

*2 since pairs?

[marble bone]

No

Just a sec

(1, 7-1)
(2, 7-2)
(3, 7-3)
(4, 7-4)
.....

Would also include the inverses

So we don't need to multiply by 2

[bold lotus]

hmm

ah yeah

i get it

so the question i proposed has 352 possible pairs?

b=353-a
0<a<501
0<b<501

a [1, 352]

@marble bone how would you do such a thing with 3 numbers

a + b + c = 7

let a + b = d
d + c = 7

idk

[marble bone]

I see

Interesting

[bold lotus]

what

[marble bone]

I am giving it a thought

Just a sec

[bold lotus]

oh oki

[wispy talon]

I can share the formula but I can't remember the proof for this atm

Is that fine?

[bold lotus]

yeah

do you know what the formula is called?

[wispy talon]

Do you know the stars and bars problem and inclusion exclusion principle?

[bold lotus]

i do not

[wispy talon]

Just search "number of integer solutions for a linear equation"

[wispy talon]

There isn't a name per se, it just uses combinatorics

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[real dock]

Confused on this question

[neon oxide]

what do you have so far/what have you tried

[real dock]

I thought since AC is 26 and dc is 8 it would be 20 again

But it’s either 19.5 or 18.5

@neon oxide

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[real dock]

.close

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[candid hedge]

Hello, I've been wondering about what the procedure would be to extract the underlying density function from empirical density function. I have the following epdf. Would it be more appropriate to filter it with something like Savitzky-Golay filter or is there another better way ?

[candid hedge]

I also have the ecdf

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@candid hedge Has your question been resolved?

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@candid hedge Has your question been resolved?

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@candid hedge Has your question been resolved?

[dire geode]

.close

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[vague coyote]

I am given this, but I am confused on what it means by the sequence of partial sums of the sequence S_n

[vague coyote]

If I have this example, what would be the partial sums of the sequence S_n?

[still barn]

each S_n is a partial sum, the collection S_1, S_2, ... is a sequence of partial sums

[red jewel]

<@&286206848099549185>

[cedar kiln]

@vague coyote Has your question been resolved?

[upper garnet]

take an available channel and dont ping helpers

[vague coyote]

a follow up question, I can use the tests to find if a series converge or diverge. If it converges, then I would need to find a partial sum formula for the series to find out what it converges at infinity right

[still barn]

The definition is mostly making rigorous the meaning of what an infinite sum is, i.e., it is a limit of a sequence of partial sums

If you can write that all down and find a limit yes, but usually infinite sums are extremely difficult to calculate unless you can algebraically manipulate it into something well-known

[vague coyote]

got it, ty

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[split crypt]

Hello. On the 2nd question of my homework, it wants me to calculate line segment length(XM) using only the information provided, and the fact that it is an incenter, and I need help, since I do not know how to do it.

[cedar kiln]

@split crypt Has your question been resolved?

[split crypt]

<@&286206848099549185>

Is anyone going to help me answer the question?

[wise trench]

Is there a better image

[split crypt]

thats the image in the homework

[wise trench]

oh ok

[split crypt]

I'm just having trouble with finding length of line segment XM, so I do not need help on the angle measurements

[wise trench]

it says X is an incenter

[split crypt]

yes

[wise trench]

and that BX = 6

wouldnt that just mean

MX is also 6

[split crypt]

is it just really badly drawn to scale

[wise trench]

well maybe

it says X is the center of the triangle

and BX and MX both create right angles

so their lengths are equal no?

[split crypt]

probably

yeah

im just dumb

Thank you

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[ocean ingot]

Hi, I’m struggling with this

[ocean ingot]

Question d ii

[ocean ingot]

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[median steppe]

is anyone familiar with probability theory? basic combinations/permutations

[bold vine]

[median steppe]

sorry one second

say we have 5 red balls, 3 white balls, 2 blue balls.

if we want to find the possibilities both ordered and unordered, we would use combinations and permutations correct?

i.e. 10!/(10-3)! and 10!/[(10-3)!*3!]

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[thorn crescent]

could someone help me with these, any of these . doesnt have to be all

[dusty hazel]

Is this an exam?

[thorn crescent]

worksheet

it’s graded for accuracy tho and i don’t wanna bring my grade lower

[dusty hazel]

What have you tried?

[thorn crescent]

I don’t really understand it

[dusty hazel]

Do you know what cos or sin is?

[thorn crescent]

yes i do , like i know the formulas and all but working it out is what frustrates me

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[dim island]

I need help with this synthetic division problem.

It’s 2x^4-x^3+21x^2-9x+27 divided by 3i

I understand how to synthetic division. The complex numbers are just confusing me

<@&286206848099549185>

[upper abyss]

Divided by 3i? Or divided by x - 3i?

[dim island]

Oh x-3i

[upper abyss]

Anyway your start looks good

Adding those gives
-1 + 6i

[dim island]

Ok. Would 6i-1 times 3i be 18i^2 -1

[upper abyss]

No. Distributive property still works even if there's an i

Would be 18i² - 3i

[dim island]

Oh okay so then I would 21 to that

Add*

[upper abyss]

Should write this correctly so that it's clear why I use distributive property:
3i(-1 + 6i)
= -3i + 18i²

[dim island]

Oh ok

[upper abyss]

Now, i² should ring a bell

No problem. So i is defined such that:
i² = -1

[dim island]

Oh yeah

[upper abyss]

So we actually have:
-3i - 18

Then yeah, add 21, multiply by 3i, ect.

[dim island]

So I would get -3i+3

Then -9i^2 + 9i which would be 9i+9?

The 9 would cancel out and give me 9i when adding.

Then 3i times 9i would give be -27

Which means a remainder of 0

Thank you!

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[visual hill]

https://prnt.sc/-oPG4UEQhfpr

[visual hill]

i got the bottom looking like something towards an end goal but it just doesnt seem to compute in my head

i started with bottom

s^2+4-4+8=(s+4)^2+2^2

then i split it into two fractions 8s/(s+4)^2+2^2 and -10/(2+4)^2+2^2

then i use my laplace transform table https://prnt.sc/10b8a--fDm3e

but i cant seem to get them right

[obsidian coral]

$$s^2+4-4+8 \neq (s+4)^2+2^2$$

[wraith dagger]

dldh06

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[visual hill]

sorry (s+2)^2

[visual hill]

i got that one but now im onto this one and i have forgotten how to do partial fractin expansion https://prnt.sc/Dq-6LiEJqI45

[obsidian coral]

If you don't recall PFD, then you should look up resources on that

[visual hill]

yea calculus take up my brain

laplace transforms can suck a big one

[obsidian coral]

Laplace Transforms are useful, if you plan on doing engineering

[visual hill]

yea but when i do an interview and ask if they can even do them and they say no thats what computers are for it gets harder lol

[obsidian coral]

Because that's true, that is what computers are for. LaPlace is taught to get the concept across but a lot of times, it takes too long to do by hand

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[scenic halo]

https://gyazo.com/024a48206c35c3b058eb8f30cfc7f491

[scenic halo]

how do i do this

please help

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[stuck stream]

hello

[stuck stream]

how do you evaluate this limit?

i subtituted 0 now i got log _{0.6666}5

[inland quartz]

Don't see a further way

[stuck stream]

its one horizontal line when i plugged it in

is that normal?

ok

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[stuck stream]

ok

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[silent ledge]

pLease someone tell me, is calculus exact or approximate?

[marble bone]

I think approximate value coz yk

U can never find the exact dx

But sometimes it's exact

[bold hinge]

Calculus produces exact results

[marble bone]

How can u justify it?

[silent ledge]

how exact tho? like we see 0.000001 is not equal to 0 but we say its done its solved

[marble bone]

Exactly

dx^2 isn't 0

We approximate it

[bold hinge]

Thats the whole point behind limits

The "error" goes to 0

[marble bone]

Hold on just a sec

U mean let's say I am talking the limit defnition of a derivative

Then

Let's say f(x) = x^2

When I tried to compute it

I always pick

That

h^2=0

Otherways

We wouldn't be able to solve it

[bold hinge]

Tell me what the defn of the derivative is

[marble bone]

As h approaches 0 what does (f(x+h) - f(x)) / h approaches

[bold hinge]

Right

[marble bone]

So ya have u tried solving that limit