help-23

[robust stream]

right

what is f between 1 and 3

yes

np

dont swap x swap f(x) to be clear

but yes

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[lofty elbow]

Could someone please explain why 160.6 is the mean - 1 standard dev and 175 cm is 2 standard devs above the mean??

[lofty elbow]

this is from the 2021 advanced math hsc paper btw

[rigid inlet]

do you know the empirical rule for the normal distribution?

[lofty elbow]

i have the formula sheet with me, im confused because 68, 95 and 99.7 are not mentioned

[rigid inlet]

perhaps that's something they just expect you to know

and/or memorize

[lofty elbow]

its given to us on the formula sheet, im more confused as to why 16% is considered to be the mean - 1 standard deviation?

ill send solution

[rigid inlet]

it comes from the empirical rule, which is why I wanted to know if you knew it

do you know what that 68 represents?

[lofty elbow]

68 is the z score between 1 and -1 right?

[rigid inlet]

0.68 is the probability of falling in the range [mu-sigma, mu+sigma]

a z-score is a value, it's not a probability

now, seeing as the normal distribution is symmetric about the mean, what would you say is the probability of falling in the range [mu-sigma, mu]?

[lofty elbow]

what are you referring to for 'mu'?

[rigid inlet]

$\mu$

[flat frigate]

Steakanator

[lofty elbow]

oh ty, so do you mean the 'mean' - '1 standard deviation'?

[rigid inlet]

yeah, I'm just using the greek letters since it's more concise

[lofty elbow]

34%?

[rigid inlet]

indeed

and lastly, what is the probability of falling in the range (-infinity, mu-sigma]?

[lofty elbow]

16?

[rigid inlet]

16%

[lofty elbow]

oh my god

[rigid inlet]

so the probability of being less than mu-sigma is 16%, and the probability of being less than 160.6 is 16%

it must follow that 160.6 = mu-sigma, yes?

[lofty elbow]

i think im starting to see it now

but yes i see that it must follow that

[rigid inlet]

great

[lofty elbow]

thankyou thats a huge help that was throwing me off a lot

[rigid inlet]

if you can apply similar logic to the other one, you can extract the mean and std dev

[lofty elbow]

will do

[rigid inlet]

and then everything else should fall into place

(i hope)

[lofty elbow]

one last question, is there a reason why the 16% is on the left and the 97.5 on the right?

[rigid inlet]

left and right of what?

[lofty elbow]

wait nevermind i am stupid

i simply did not read properly

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[dusty cave]

Hello folks, I am trying a geometry problem. In this I want to calculate the arc angle.

[elfin tusk]

id say need more info

[dusty cave]

Like...

[lean otter]

radius

[dusty cave]

Oh... I forgot I have those 2 points coordinates

X1 y1 and x2 y2

Are known points

But we don't know the radius

[teal skiff]

how is that 90 deg

it's literally on a curve

[elfin tusk]

you still dont have enough info

[dusty cave]

Ah, well it's not completely a curve but close to curve so it's kinda blocky curve. I am writing a program and I have normal to that point or can say vector

[dusty cave]

What else should I have ....

[elfin tusk]

oh you have the points

i thought they were unknown

[dusty cave]

They are known but I don't have the exact value for now so wrote x and y😅

But they are known

What I thought was to calculate the intersecting point of those 2 normals

Which would be the center of arc and then I will have the radius

And it would be easy afterwards

[elfin tusk]

well have you tried that

[dusty cave]

But finding intersecting point of those normals is what I couldn't able to😅

[dusty cave]

Somewhat

But my math has become little dull

[elfin tusk]

What id do is find distance between points

[dusty cave]

And then...

[elfin tusk]

wait do you have radius at all

since you have those points

[dusty cave]

No, i don't have radius. those points are on Cartesian corrdinates

Sorry for my poor drawing😅

So, I have points x and y values

But because I don't have arc center value

I can't calculate radius

We need to find that center first

[graceful sorrel]

wait wha

90?

[elfin tusk]

ok i just thought about it and i dont think you have enough info

[dusty cave]

Yeah, they are normals

[graceful sorrel]

huh?

[elfin tusk]

its a circle

[graceful sorrel]

yeye i know

[elfin tusk]

that points the origin

[graceful sorrel]

but

[elfin tusk]

makes a normal

you need radius

[graceful sorrel]

can someone really explain to me how it would be a 90?

thanks

[elfin tusk]

google it

[dusty cave]

Think of it as blocky line

[graceful sorrel]

i did

but

[elfin tusk]

its a circle fact everyone should know

[graceful sorrel]

it should look like this no?

its not 90 DIRECTLY ON THE CIRCLE

[elfin tusk]

the tangent just isnt drawn on

[dusty cave]

So we can't calculate from intersection of normals?

[graceful sorrel]

?

[elfin tusk]

no

[dusty cave]

I mean calculate center

[elfin tusk]

not enough info at all

[dusty cave]

@graceful sorrel well, consider it 90 and that curve as flat on that point.... because I programming everything is approximate 😅
And I am using this calculation there

[dusty cave]

Can you elaborate on that

[elfin tusk]

whats the context here ?

the most you could do is use the law of cosines

but youd need radius

[dusty cave]

If I calculate the center of arc then we can get the radius .... right?

[elfin tusk]

if u have the centre then it would be very easy yes

but from the info you have you cannot

[dusty cave]

So you mean to say we can't find the normals intersection point

[elfin tusk]

we dont have enough info

whats the context here anyway

you mentioned a programming challenge, and it being a blocky curve

[dusty cave]

Welll, I am developing a game

I have set of points from which I create a catmull rom spline

Now, I want to find arc angle every 0.2 m

For that spline

[graceful sorrel]

oh got it

i got mad confused lol

sorry

[dusty cave]

Don't you think those normals are unique and we can make line equation for them

[elfin tusk]

no

[dusty cave]

Np, happens😅

[elfin tusk]

you dont have enough info

[graceful sorrel]

but yes he said it

[elfin tusk]

i have said it 5 times

[dusty cave]

I am just thinking why?😅

[graceful sorrel]

you know what @elfin tusk

[elfin tusk]

what @graceful sorrel

[graceful sorrel]

i think whats missing is the angle

right?

[dusty cave]

We need to find that

[elfin tusk]

he needs anything

[graceful sorrel]

for to find the angle

[elfin tusk]

radius angle centre

any of them

[graceful sorrel]

@dusty cave

since its a game

just give it an angle for free thing

but if its a sphere

[elfin tusk]

well its a spline

[graceful sorrel]

make a centre man

[dusty cave]

Yeah, I am also thinking that but then my game physics would break😅
It's a cycling game, I create roads from GPS coordinates

So I cannot assume every turn as same

[elfin tusk]

can you just approximate it geometric in the game

[dusty cave]

Yeah, splines are also just approximations 😅

[elfin tusk]

hey approximations make the world go round

woo

[dusty cave]

Anyways, thanks guys... i will try to find some other way🙂

[graceful sorrel]

bro

the map is a sphere yeah?

[dusty cave]

Nope

[graceful sorrel]

a plane right?

plain

jesus christ

you could just have it be like a straight distance

or based on the rotation of the wheels

its much more easy to code than that i think

[dusty cave]

I didn't made the physics part

😅

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[junior fulcrum]

I've been using a website to help me understand circle equations. I've understood it until the final part circled. How exactly do they get the equation to that point from the line above?

[tough obsidian]

(a-b) ^2

[thin bridge]

that was the result of the idea in the previous steps

[tough obsidian]

Is a^2 - 2 × a × b + b^2

[thin bridge]

(-2/2)^2 = (-1)^2
was the value that completed the square for x^2 - 2x

this should help

$\cts$

[flat frigate]

ℝamonov

[junior fulcrum]

so where exactly does the number without the x go?

oh nevermind

ok I'm pretty sure I understand It now. Thank you!

.close

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[woeful elm]

hey! its not like much help but i need someone to clarify this because i can't seem to find it anywhere

so i have square inequality, but all it matters is the result of this and if i get something like

xe(–infinity;4)u(4;infinity)
i heard i just can write it like that:
xeR\{4}
is this true?

[tough obsidian]

R - {4} yes

[woeful elm]

so both – and \ is correct or just the –?

[thin bridge]

both are acceptable

[woeful elm]

alright, thanks!

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[peak badge]

Guys what is the method called when he multiplys opposite squares?

[peak badge]

Can you please mention me if u have an answer?

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@peak badge Has your question been resolved?

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@peak badge Has your question been resolved?

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[tender totem]

a bit confused by the explanation on quadratic residues here:
let k=1, then assuming p=4k+3, we have p=7.
assume x=5. 5^2 = 4 (mod 7). by the conditions below, i believe that it suggests 5 = 4^(1+1) = 16 (mod7), even though is is not true. any idea how this works?

[tender totem]

link is here: https://mathworld.wolfram.com/QuadraticResidue.html

<@&286206848099549185>

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@tender totem Has your question been resolved?

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@tender totem Has your question been resolved?

[quasi bison]

the equation x^2 = 4 mod 7 has two solutions: one of them is given by the formula and it's 4^(1+1) = 16 = 2, and the other is its additive inverse (5)

[tender totem]

oh, that makes sense. cuz they would become the same after squaring. thanks for clarifying

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[lean otter]

ignore my working but helppp

[lean otter]

why

your working is so far correct

you should proceed

[safe radish]

@lean otter Has your question been resolved?

[lean otter]

I’m just confused on where to go

the question in general seems very daunting

log a to the base b = c

is the same as a =b^c

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[autumn creek]

write in polar form:

[autumn creek]

my try:

where do i go from the last step or does that count as polar form

[compact ferry]

use the argument and modulus rules to determine the answer nicely

because this is a mess

im not saying its wrong but you can do it more easily

[autumn creek]

can you show me how?

[compact ferry]

to find out how to write it in complex form you just need to find the modulus and argument

[compact ferry]

so determine the modulus of and argument of this

[autumn creek]

the argument would be arctan(sqrt(3) - 2) which i cant do by hand

,0

[compact ferry]

you can

well

wait

[autumn creek]

(1 − i)^3 ( √ 3 + i) / 4i ⇔
(1-3i-3+i)(√3 + i) / 4i ⇔
(-2-2i)(√3 + i) / 4i ⇔
2(-1-i)(√3 + i) / 4i ⇔
(-1-i)(√3 + i) / 2i ⇔
(-√3-i-√3 x i+1) / 2i ⇔
(-√3-i-√3 x i+1) x -2i / (2i x -2i)⇔
(2i√3 - 2 - 2√3+-2i) / 4 ⇔
(- 2 - 2√3)/4 + (2i√3-2i) / 4 ⇔
-(1+√3)/2 + (√3-1)i / 2

Polar form:
r =√( (-(1+√3)/2)2 +((√3-1) / 2)2) = √2
tanv = (√3-1) / -(1+√3) ⇔ v = arctan(√3-2) <-- this i cant do by hand

[wind stream]

why is it a trouble for you to express it as is

by that i meant just as arctangent itself

also, you took lightly of my warning earlier, the argument of z is not simply arctan(sqrt(3)-2)

[compact ferry]

yeah the exponent form wont be "nice"

[wind stream]

technically there is an exact evaluation to arctan(sqrt(3)-2) in radians

but it's not really troublesome to express it like this either

[autumn creek]

can you explain this since i thought i got it but apperntly not

[compact ferry]

there is?

[autumn creek]

also does the last line here count as polar form?

[wind stream]

so basically, arctangent will only output the angles in (-pi/2, pi/2) this does not cover every angle in a circle

[worn dock]

I need help

[wind stream]

now, note that z is in the third quadrant

this means that your argument is actually more than pi/2 radians, in the counterclock-wise direction

but arctan(sqrt(3)-2) will never give you such an angle

[wind stream]

yes, it should be 5pi/12

have you reviewed the definition for principal argument?

this should be mentioned there

[autumn creek]

i did look for it, just wasnt able to comprehend a lot

any case i think i get it now

[wind stream]

sure

this is basically what you should be doing

where z here can be represented as z=x+yi

x, y in R

[autumn creek]

would it make sense to use cosine and sine then?

[wind stream]

right, for your method above, not quite

you can expressed it like that, but it will not help

perhaps it would be better to look at multiplication geometrically

(also not to mention, your argument of z1 is wrong too)

[autumn creek]

oh yea XD

[wind stream]

oh and with your method above, you would actually be able to find exactly in terms of radians what your argument is

but with the cost of time

[autumn creek]

thanks a lot for the help again

[wind stream]

np

[autumn creek]

i got lots of that lol

[wind stream]

again, just be careful with the arguments stuff, it's hard to swallow at first, it's not very similar to the argument that you knew in polar coordinates

[autumn creek]

yea it is a bit confusing but ill take my time to get it right

thx again

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[lean otter]

Hi hello. Got this question but I can't figure out how to solve it. Sorry if it's annoying:

Given a polynomial P(x), knowing that P(1) = 3 and P(3) = 33 write the polynonial.

[compact ferry]

do you know anything else about the polynomial?

[lofty latch]

is that it? any information on the highest degree?

[lean otter]

It has to be a 1st degree polynomial, ye?

Well, no info about the deg.

That's what confuses me.

[compact ferry]

weird lol

[lofty latch]

well

[lean otter]

It talks about a very generic polynomial.

[compact ferry]

could you send a picture of the question

[lofty latch]

"generic"

[tall bough]

lol

[lean otter]

No pic. That's it.

Just text.

It's something a dude told me. So I have no actual picture.

[tall bough]

bruh

[lean otter]

But I can't imagine it being over degree 1.

[lofty latch]

just ignore him lmao

[lean otter]

Lmao.

Maybe that dawg wanted me to mourn because of unknown degree. 😔

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[ornate acorn]

Need help with part b. I have no clue what each element would mean in terms of communication through the network

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[pale dock]

x can be anything right?

[red glen]

yes

[pale dock]

Ty

!close

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[pale dock]

?close

oh kk

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[safe radish]

@final quail Has your question been resolved?

[final quail]

<@&286206848099549185>

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@final quail Has your question been resolved?

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@final quail Has your question been resolved?

[final quail]

.close

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[rare grove]

who to open a math help

[signal ocean]

how do i put tan(pie/17)+i in the trigonemetric form

[rare grove]

i need help no cap

<@&286206848099549185>

[bright nacelle]

sum of all interior angles must be 360

[nova creek]

!15m

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[rare grove]

yes but x value

[bright nacelle]

just add all and equate to 360, then solve for x

[signal ocean]

write 90+x+2x+3x=360

[bright nacelle]

angle b is 90

[signal ocean]

360*

[rare grove]

didnt work

[signal ocean]

lemme see

[rare grove]

okay

[bright nacelle]

what did you answer?

[bright nacelle]

you have to solve the equation

[signal ocean]

x(1+2+3)=360-90

6x=270

x=270/6

[bright nacelle]

*6x=270

[signal ocean]

XD yea mb

[bright nacelle]

x=45

[rare grove]

W

damn question b now

[bright nacelle]

they would be parallel only when angle A = angle B

In this case angle A is 2x = 2x45 = 90

angle B = 90

so they are equal

hence the sides will be parallel

[rare grove]

w IT WORKED

https://tenor.com/view/doggo-dog-thx-thank-u-thank-you-gif-19863377

[floral epoch]

Hi

[rare grove]

.close

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[obtuse plover]

Do u know the formula for area of circle

@lean otter

[lean otter]

A = π r²

[obtuse plover]

Yes

[lean otter]

@obtuse plover

Don’t know where to go from here

First time doing py stuff on circles

[obtuse plover]

So pi * (radius^2)

How can we find the radius from the diameter we are given

[lean otter]

No clue

[obtuse plover]

So the diameter is double the radius

So if the diameter is 14 mm, what’s the radius

[lean otter]

7

@obtuse plover

[obtuse plover]

Yes 7mm

So plug that into our formula

[lean otter]

Pi* (49) ?

[obtuse plover]

Yes, that’s ur answer

49pi mm^2

See, very simple

[lean otter]

So 49 is the answer? @obtuse plover

[obtuse plover]

No

[obtuse plover]

What did u write here

That’s ur answer

[lean otter]

Ohhh I get it. Thanks @obtuse plover

.close

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[hallow sedge]

can someone help me figure out what im doing wrong?

[hallow sedge]

i found the antiderivative for height, but im having trouble with the constant

[obtuse plover]

once u get the antiderivative + C, plug in 0 for t, and set it equal to 25

then solve for C

[hallow sedge]

im an idiot thank you

[obtuse plover]

np

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[ionic juniper]

https://gyazo.com/0bf8a82c62d20916f98c8b7667148643

[ionic juniper]

how is question 10 true

[halcyon carbon]

Why would it not be true

[cedar rivet]

10 should be true

since the limit is approching the value of f(0) from both sides

[ionic juniper]

oh

oops

[cedar rivet]

lool

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[lean otter]

how does x = 0 here. aren’t you supposed to set both the top and bottom to 0

[lean otter]

the bottom would be x = plus or minus 3 too, so wouldn’t the answer be x= 3, -3, 0?

[civic mist]

Division by zero is undefined

[lean otter]

im not dividing by 0

it’ll be (9-x^2)^2= 0

[civic mist]

So you're saying the denominator will be 0?

[ebon rock]

which is equal to 18x/0?

[crisp linden]

I presume you want to solve this equation for x. So a fraction is equal to 0 iff the numerator is equal to zero and the denominator is not equal to 0.

If they are both equal to 0, the value of the fraction is indeterminate.

[lean otter]

So .. hm

I am trying to find the critical #'s, so it has to be equal to 0 in this case

[lean otter]

when your equate things to 0, the denominator does not matter

because 0 is not a multiplicative inverse

if you multiply both sides with (9-x^2)^2 which is your denominator it still would be 0

so realistically, only your numerator matters here

18x = 0 is obviously only equal to 0 when x = 0

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[lean otter]

It’s asking to evaluate the derivative?

[lean otter]

H

Is this the right idea

Or would I have to do the logarithmic differentiation?

I feel like this is wrong tho

There’s no way it’s that easy

[pure agate]

,rotate

[lean otter]

I have to solve for dy/dx right?

To be able to evaluate the derivative

Cuz the question is asking EVALUATE THE DERIVATIVE

Rip

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[lean otter]

can anyone help me, i did a and b

[lusty widget]

aye aye

wassup

eh

alr

just do

long division

and get ur quad factor

and factorise

[lean otter]

Umm which part you talking about

?

for d?

[lusty widget]

c

which will help

to find d

[lean otter]

ohh okay

one min lemme try

[lean otter]

i got (x - 5) (2x - 1) (x+6) (x - 2)

so would the zeros be x=5 x=1/2 x=-6 x=2

?

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[solemn vault]

Well

That's a cyclic quadrilateral

And a property of cyclic quadrilateral is that its opposite side add up to 180°

[short sky]

wait so the whole thing adds up to 360?

[solemn vault]

Yep

[quasi bison]

opposite angles add up to 180°

also the sum of all angles is 360° regardless of whether or not your quadrilateral is cyclic

[short sky]

so u mean like HP = 180

[quasi bison]

no

that was a swing and a massive miss from you

[short sky]

dang

[quasi bison]

opposite ANGLES add up to 180°

the sum of either pair of opposite angles is 180°

angle P + angle H = 180°

[short sky]

I have to solve for X in this case btw right?

[solemn vault]

Ye

[quasi bison]

yes

[short sky]

alr

I'm still kinda confused on how to find x

[solemn vault]

So

You're given angle E and angle O and they're opp

Angles

[short sky]

so they add up to 180

[solemn vault]

So there sum must equal to 180

Yes

2x+15+3x-10=180

Now solve for x

[short sky]

alr lemme try

is x 35?

[solemn vault]

Let me see

,w 2x+15+3x-10=180

Yep

So

[short sky]

ayy

[solemn vault]

Now pluck back into the eqn and you'll get your angles

[short sky]

yeah I get it now thanks

[solemn vault]

Ok

[short sky]

can u help w another one?

I don't get this

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[lean otter]

hi im stuck at the complex partial decomp

so im not allowed to use residue to solve this

i got the decomp if the top is 1

dont remember what i should do next

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@lean otter Has your question been resolved?

[lean otter]

<@&286206848099549185>

<@&286206848099549185>

lol someone pls im losing my mind i cant do fkn hs math concepts and its cock blockign me from finish these questions

.close

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[lean otter]

w/e

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[stuck wren]

why is this incorrect

[quasi bison]

cos(πθ) would have period equal to 2, not pi as it really is

[stuck wren]

wdym

isnt my arguement suppose to be the period

[quasi bison]

i mean exactly what i said, and no, the argument is not supposed to be the period. that would exclude theta from it...

it's cos(2pi/period * theta)

(up to vertical adjustments which you did get right)

[stuck wren]

isn't the 2pi over the theta only for graphs that have radian measures

@quasi bison

[quasi bison]

this one does seem to be in radians though

also 2pi/pi is just 2

[stuck wren]

i see

[stuck wren]

is verticle adjustments always the Y= x

?

[quasi bison]

.....

i have no idea what you mean

[stuck wren]

by x i just meant a number

that is right

like is it the mid line

[quasi bison]

...

when i said vertical adjustments, i meant both the amplitude and the midline.

[stuck wren]

❤️ preciate it twin

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[craggy trout]

[165^{\circ} * \frac{\pi}{180} = \frac{165\pi}{180} = \frac{33\pi}{35}]

[craggy trout]

Can this be simplified any further?

[flat frigate]

dopediscorduser

[mortal sandal]

180/5 = 36

not 35

[craggy trout]

Ah yeah you're right

[\frac{11\pi}{12}]

?

[flat frigate]

dopediscorduser

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[mortal sandal]

Yeah

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[shell elm]

i’m not sure if i’m supposed to manipulate the arithmetic sequence formula or something else to get the number of chairs :’)

[shell elm]

<@&286206848099549185>

.close

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[slender reef]

sin(6.28 rad)

[slender reef]

how would i solve this

[quasi bison]

do you mean 6.2800 radians exactly or do you mean 2pi

[slender reef]

no no

my bad

i didnt realize what it was asking

i didnt realize it was just 2pi lol

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[opaque sorrel]

@toxic stratus can i get help with qn 30 pls

[quasi bison]

these are easy if you know the defn of linear independence.

do you know the definition of linear independence?

[opaque sorrel]

hi

yes

[quasi bison]

right

are you allergic to big sigma notation?

[opaque sorrel]

gimme a moment

no XD

[quasi bison]

ok then you may have a somewhat easier time writing this out

[opaque sorrel]

hmm

gimme a moment ill brb

Im bacc

Hmm

[toxic stratus]

hi

[opaque sorrel]

Oh hi

Two math gods replying me back to back

[toxic stratus]

im in a class rn

[opaque sorrel]

Amazing

Oh

Can i think of P as a constant

Somehwat

[quasi bison]

no

P is P

[opaque sorrel]

Oh

[quasi bison]

you can and should remember that the map x ↦ Px is linear, and what that means

[opaque sorrel]

Linear relations are preserved by elementray row operations

Is that right Xd

[quasi bison]

no, bad.

[opaque sorrel]

Oh wait

Linear relations on columns

[quasi bison]

still bad.

you do not need to think about rows or columns or any of the nitty-gritty numerical details here.

when i said the map $x \mapsto Px$ is linear, what i meant is that, as a map, it preserves addition and scaling. i.e. $P(x + y) = Px + Py$ and $P(\alpha x) = \alpha Px$ for all vectors $x, y$ and scalars $\alpha$.

[flat frigate]

Ann

[opaque sorrel]

Ohh

Okay so i shall use that property

[toxic stratus]

try contrapositive?

[opaque sorrel]

oh

OH

imma do both ways

[quasi bison]

no need

you don't need contrapositive for (a) nor for (b)(i)

you can do a direct proof and imo you should do a direct proof and not saddle yourself with the labor of going through a contrapositive proof that will sound clunky and shoehorned and unexciting

[opaque sorrel]

okay i shall do that

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[vapid knoll]

A right angled isosceles triangle has the area of 4 square units. Determine the exact perimeter of the triangle.

[vapid knoll]

Someone help please!!!!

Area = 4

[halcyon carbon]

CB = CA

Area is 1/2 CA * CB

[vapid knoll]

yes

But how to get exact numbers

4 = (CA * CB)/2

[halcyon carbon]

Call CA=CB=x

[vapid knoll]

8 = CA * CB

[halcyon carbon]

x^2 = 8

x=2sqrt(2)

[vapid knoll]

Why

how did you get x^2

[halcyon carbon]

Here

[vapid knoll]

yes

Wouldnt that mean X^2 = Square root of CA + CB

[halcyon carbon]

?

[vapid knoll]

I am lost here

[halcyon carbon]

I just replaced CA and CB with x

[vapid knoll]

oh yea

I see

[vapid knoll]

alright i see what you mean

what should I do next?

[halcyon carbon]

Find AB

Pythagorean

[vapid knoll]

Square root of X^2 + X^2 = AB

[halcyon carbon]

Ye

[vapid knoll]

Square root of 8 + 8 = AB

right

which is

10.8284271247

🙂

thank you

👍

.close

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[halcyon carbon]

How did you get that

[safe radish]

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[lean otter]

If there are 20 people, what is the probability, that they were born in 12 out of the 12 months?

[grave flint]

what have you tried?

[tall bough]

Probability that the 20 were born on December?

[grave flint]

i think at least one birthday in every 12 months

[tiny wraith]

assuming each of the months contains the same amount of days btw?

[grave flint]

its probably just assume 1/12 chance for each month

[foggy salmon]

every 4 years lol

[raw fox]

you were born on leap year?

[grave flint]

kind of an L ngl

[grave flint]

leap day**

[raw fox]

yeah

same

[grave flint]

no

[raw fox]

refining body layer

[raw fox]

Same as in same bda

y

Leap year bdays suck ass

[grave flint]

o

[raw fox]

dont be born on leap day

Hold the baby

[lean otter]

If there are 20 people, what is the probability, that they were born in 12 out of the 12 months?

So that there is no month in which no one was born.

• assuming each of the months contains the same amount of days and that all months are equally likely

[foggy salmon]

trollin the child

[buoyant shadow]

this is just buns and raisins again

[grave flint]

cake is tastier

[safe radish]

@lean otter Has your question been resolved?

[buoyant shadow]

,w StirlingS2(20,12) * 12! / 12^20

[flat frigate]

Results provided by WolframAlpha

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

Requested by frownyfrog#3707

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[timid goblet]

Hey

[timid goblet]

Teacher gave us the answers but I don’t understand how to solve it

Second one was 0 I think

[prisma acorn]

can you explain how you got that

[timid goblet]

Teacher gave us the answers

[prisma acorn]

the one with 0?

[prisma acorn]

or just the first one?

[safe radish]

@timid goblet Has your question been resolved?

[timid goblet]

For both

[olive fossil]

your teacher's answer for the second question is wrong, 0 is the value you get for h(g(-8)) not g(h(-8))
||g(h(-8)=g(1/2(8)-2))||,this is||=g(2)=1/2(2)+8=9||(dont click it unless you really need help)
for q1 -7 is correct

just sub it in

[timid goblet]

Dam nah my teachers wrong 💀💀💀💀

[olive fossil]

it is an understandable mistake to make

since looking at g(h(-8)) you might think you apply g first then h but thats wrong

[timid goblet]

O

I think I’m starting to remember

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[placid cove]

Negate the following statements and re-express the result in equivalent positive form: I have already tasted all the items in the food menu.

[placid cove]

can you help me guys on this?

[sharp crane]

whats the negation of "all"?

[fresh stream]

I am yet to not taste all of the items on the menu

[placid cove]

i do not understand the re-express the result in equivalent positive form

[fresh stream]

what i wrote

[placid cove]

can you check my answer in negation: There is one item in the food menu, i have not tasted

[placid cove]

and you mean this is the equivalent positive form?

[placid cove]

this is my answer

[sharp crane]

It should be there is at least one item on the food menu that I have not already tasted

[crisp linden]

To verify that, you could e.g. assume you have not tasted 2 items

[crisp linden]

Your statement would be false, but the original statement with all is also false.

[placid cove]

“I am still about to taste all the items in the food menu”

is this possible?

because the re-expres the result in equivalent positive is included in the question

and this "I'm just about to attempt to taste every thing on the menu."

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[fresh stream]

can someone help me understand this
i dont get what the +0c means with respect to the new i coordinate x value

[safe radish]

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[lean otter]

Can I say that any straight line is part of an infinite radius circumference?

[still charm]

🤯

Not really

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@lean otter Has your question been resolved?

[buoyant shadow]

why part

they should coincide all the way lol

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[safe radish]

@marsh patio Has your question been resolved?

[stray socket]

Translate it

[marsh patio]

ok

1. In the squared plane, in the dotted plane, then in the non-squared plane (use a ruler and a square):
   a) Construct a representative of the vector
   
   u of direction (BC), of direction B to C and of length 2 BC .
   b) Construct a representative of the vector
   
   v of the same direction and of the same length as 
   w , but of
   contrary.

2. a) In each frame, construct a representative of the vector 
   u+
   
   v.
   b) In each frame, construct a representative of the vector 
   u+
   
   v+
   
   w.

[stray socket]

You just connect the vectors tip-to-tail and then connect from the beginning point to the end point

[safe radish]

@marsh patio Has your question been resolved?

[safe radish]

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• Show your work, and if possible, explain where you are stuck.
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[final flax]

I need help on this please

In how many ways can a committee with nine members form a subcommittee with at least one person on it?

potential answer= 511

[jaunty belfry]

find the number of ways you can get a subcommittee of 1 member, then 2, up till 8

so that is 9C1 + 9C2 ... + 9C8

[final flax]

i got 511

[jaunty belfry]

nope

A good formula to remember

I think it's 510

[final flax]

is it 511

[jaunty belfry]

the sum nC0 + nC1 + nC2 ... + nCn = 2^n

[final flax]

ok

[jaunty belfry]

here we don't have everything but 9C0 and 9C9, both of which are 1

so 2^9 - 1 -1 = 512 - 2 = 510

[final flax]

ok thanks

can you help me on a couple more questions please

[jaunty belfry]

sure, go ahead. have a bit of time

[final flax]

I was unsure about this one

[jaunty belfry]

ok, idk what that symbol between A and B is

[final flax]

me neither

[jaunty belfry]

is that al the question is?

or is there more

and did you try coppasting the question into a search engine

[final flax]

no

ok skip that question

Eight children are to be selected from a group of 15 children. In how many ways could this be done if either Danylo or Shuying must be included but not both?

@jaunty belfry are you there

[jaunty belfry]

yup

[final flax]

thanks

[jaunty belfry]

so

you fix either Danylo or Shuying

[final flax]

yes

[jaunty belfry]

one in the team, other out

[final flax]

yes

[jaunty belfry]

so you still require 7 members

and you have 13 children left

[final flax]

i got 2c1 x 14c7

[jaunty belfry]

13C7

not 14C7

[final flax]

ok

[jaunty belfry]

because you are accounting for Dan and Shu already

[final flax]

alright perfect

I got 130

@jaunty belfry are u still here

[jaunty belfry]

it's right there

it's 9

I think you misttok intersevtion as union

[final flax]

Rightttt

ok I got it thanks

can I post more questions

How many different sums of money can you make with three coins of different denominations?

[jaunty belfry]

same as this question

except here you have 0 and all coins as well

[final flax]

ok

[jaunty belfry]

so the formula I told you

[final flax]

ok

[jaunty belfry]

there are some nuances here though

if you had denonations 1 2 and 3

then 1+2 would be same as just having 3

[final flax]

right

which means itll be 3

[jaunty belfry]

so it would be 7, or 8 different values, depending on whether the 2 smaller denominations add up to the larger one

[final flax]

2^3

[jaunty belfry]

yup
2^3
or 2^3 - 1 if the lower two add up to the largest one

[final flax]

ok thanks

A lottery ticket has six numbers selected from the numbers 1 through 49, without regard to order. How many combinations of six numbers are possible?

[jaunty belfry]

have to go now

[final flax]

can you please help me with a couple more

@jaunty belfry

just 10 mins

I have learned alot from you today

.close

[safe radish]

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Closed by @final flax

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Remember:
• Ask your math question in a clear, concise manner.
• Show your work, and if possible, explain where you are stuck.
• After 15 minutes, feel free to ping <@&286206848099549185>.
• Type the command .close to free the channel when you're done.
• Be polite and have a nice day!

Read #❓how-to-get-help for further information on how to ask a good question, and about conduct in the question channels.

[rapid raptor]

how do I ask for help?

[sonic spruce]

show your progress if youve made any?

[rapid raptor]

I have not made any

All I know

is you have to make those 2 damn equations

and see if its

substitution or the other thing

[halcyon carbon]

In this kind of question always clearly define a variable(s)

[rapid raptor]

Would the variables be anna and lincoln?

[halcyon carbon]

Their age rather but yes

[rapid raptor]

aight

[halcyon carbon]

You also have to consider which time period we want to define these at

[rapid raptor]

Wdym by that?

[halcyon carbon]

Well do you want to define their age now?

Or 6 years later

Or 22 years

[rapid raptor]

Want to know their age now.

[halcyon carbon]

Right so let’s say x is Anna age now and y is Lincoln’s age also now

[rapid raptor]

Im just confused on how I set up the equations.

hmm

so

x = 2.2 + 6

?

[halcyon carbon]

Not quite

Okay let’s do this step by ste

[rapid raptor]

alright

[halcyon carbon]

Base on this, what are their ages 6 years from now in terms of x?

Just their ages

[rapid raptor]

Unknown?

[halcyon carbon]

Sure unknown but we can express it in terms of x

[rapid raptor]

indeed

oooh

so

x - 6?

wait

that makes no sense

[halcyon carbon]

Exactly

Makes no sense

Let’s look at an example

Say you’re now 5 years old

How old will you be in 6 years?

[rapid raptor]

11

[halcyon carbon]

Yes

So it’s current age +6

x+6 for Anna

y+6 for Lincoln

Agreed?

[rapid raptor]

Ohhhh

Agreed

So

x = 2.2

x + 2.2*

[halcyon carbon]

Wait wait

Step by step

We’re told that Anna is 2.2 times as old as Lincoln

[rapid raptor]

In 6 yrs

[halcyon carbon]

Yes

[rapid raptor]

would it

be

[halcyon carbon]

So Anna age after 6 years is 2.2 times Lincoln’s age after 6 years

[rapid raptor]

x = 2.2 = 6

• 6

lemme actually write this down

Im confusing myself

[rapid raptor]

would it

be

uhh

multiplication since

is says

2.2 times?

[halcyon carbon]

Yes

[rapid raptor]

x = 2.2 x 6

[halcyon carbon]

Now recall the expressions for their ages after 6 years

x+6 and y+6

[rapid raptor]

oh

wait

so do u plug in?

[halcyon carbon]

What exactly do you mean by plug in

[rapid raptor]

so we know what x is now

and we know x is = to anna

so wouldnt we

do

2.2 x 6 + 6

but

that wouldnt make any damn

sense

if were salving for age

since age cant be a point

idk

at this point

[halcyon carbon]

Let me write the expression for you

Maybe you would understand why after you see it

[rapid raptor]

alr

[halcyon carbon]

$x+6 = 2.2 \times (y+6)$

[flat frigate]

Pure

[rapid raptor]

omfg

yes

that makes sense nopw

[halcyon carbon]

[rapid raptor]

god damn it

Ima go

write it in my notebook rq

[halcyon carbon]

Aight

[rapid raptor]

wait

so now

we would distrbute the 2.2(y+6)

than solve for x?

but

no

[halcyon carbon]

Well we need another equation

[rapid raptor]

cuz we have 2 variables

agreed

lets see

[halcyon carbon]

Let’s find the other one first

[rapid raptor]

y = 3/5 + 22

eh naw

that doesent sound right

[halcyon carbon]

You need both x and y in your equation

Okay so firstly

What are their ages 22 years later?

[rapid raptor]

3/5?