help-27

[rigid pewter]

you only actually have to plot for (a) i believe

[lost creek]

I wonder for the graph, can I ask it to plot the area for 0.5-P(178<x<185), like directly show it’s on the the green part

[lost creek]

Nah, in the template our lecturer gave, we’re suppose to plot all three diagrams, the last one which is (c) is a bit troublesome because I want to include the purple one to explain, include the green on, which I type manually( should be plotting using 0.5-P(178<x<185)

Anyway, do you think the plot I plot using python is similar to this using Desmos? Maybe I didn’t explain the mathematics by calculus and I use probability to explain, that’s why marks is deducted😅

[rigid pewter]

that would have to be why i guess😅

[lost creek]

Can I ask how to plot the green area using 0.5-P(178<x<185)?

[rigid pewter]

im not sure about that one

it doesn't really make sense to plot a mathematical equation

it's not directly represented as an area like the others

[lost creek]

Maybe that’s only need explanation

And maybe that’s why my lecturer told me no solutions is provided

Because different people interpret differently for this

Just answer will be the same

[rigid pewter]

i guess so🤷‍♀️

[lost creek]

Maybe I can just show the integration area for 0.5, then the purple area and green area and explain 😂 not sure the correct method, but I think that’s why no solutions given

Anyway, for labelling the math equation in figure, it’s impossible right?

[devout snow]

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[uncut ore]

<@&286206848099549185>

<@&286206848099549185>

[onyx lion]

brotha done tagged helpers twice in 5 minutes

[uncut ore]

U can help me with the problem so that I wont do it 3 times

<@&286206848099549185>

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[upbeat turret]

i need help with a combinations principle questionnnn i have the question of 8 horizontal lines and 3 vertical make 84 combinations of rectangles, its a nCr x nCr equation but the only nCr equation that i remember makes 84 is 9 and 3, not 8 and 3

[restive river]

In order to form a rectangle

you need 2 horizontal lines and 2 vertical lines

[upbeat turret]

no its 8C2 x 3C2?

[restive river]

yes

[upbeat turret]

oh shoot now i feel so dumb ok tyyy

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[velvet swan]

i need to find the general term for this succession and prove it

[velvet swan]

i started to make a conjecture that looks like it holds for the general term which i suppose is

$a_n = 1/2^n$

[woven radish]

beginner

[velvet swan]

i was suggested a couple of hours ago to use strong induction to prove this

since i'm not very familiar with the process i read about it and i think i proved it, i just need someone experienced to verify if it's correct

my god first picture is very small

ah nevermind, i was opening the thumbnail

@sullen island sorry for the ping but i think i solved the exercise you told me about a couple of hours ago with strong induction

check it if you don't mind

[sullen island]

ok I'll look at it

looks good @velvet swan

[velvet swan]

thanks for the help man 👍

by the way, this method of strong induction works for exercises where regular induction can be used as well?

from what i've read, strong induction works well for recursive things that are defined in terms of their predecessors

[sullen island]

strong and regular induction are equivalent, you can technically use one or the other as you wish

[sullen island]

how does that not apply to "regular" induction ?

[velvet swan]

i mean, intuitively i think they are the same, only that "regular" induction one first supposes that some predicate holds for some natural to then try to get to the "successor" predicate but this method of strong induction works when one supposes everything before a predicate for a natural number holds to then try to prove said predicate on n

regular induction works "forwards" and strong induction from back to front i guess?

[sullen island]

you're still going forwards with strong induction

but you're looking further back to do so

[devout snow]

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[velvet swan]

yeah i guess, i gotta digest this thing i suppose

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[gray sonnet]

Can anyone help me with Finding FH i forgot how to do geometry

[gray sonnet]

.close

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[wicked badger]

@gray sonnet is your problem solved?

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@wicked badger Has your question been resolved?

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[restive river]

The domain of $f(x)=\log(\sin{x}\cos{x})$ is

[woven radish]

yajat

[mystic locust]

all real numbers

(-inf,inf)

[devout snow]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[restive river]

bruh

dyssrupt

how that's even the answer i dont understand

[mystic locust]

i'm writing an explanation

[uncut ore]

incorrect

[restive river]

^

[uncut ore]

x = 0 is not valid as an example

[restive river]

^^^^

yea so let me tell what i did

[mystic locust]

x=0 is valid if the interval isn't 0 < x < 360

you have to define the interval

[uncut ore]

yes

u said its all real numbers

[violet escarp]

log takes any values except 0, look when sinxcosx turns to 0. it cant be that hard can it?

[mystic locust]

set sinxcosx=0

[violet escarp]

wait im trippin any values above 0

[uncut ore]

negatives are also not allowed

[red turret]

not any, non-zero positives only

[restive river]

i made two cases\
$\sin{x}>0$ and $\cos{x}>0$\
$\sin{x}<0$ and $\cos{x}<0$

[woven radish]

yajat

[restive river]

and then union of both the intervals

[uncut ore]

these ones are not valid

[restive river]

why?

[random temple]

if you want a shortcut remember that sin(2x)=2sin(x)cos(x)

[uncut ore]

caouse when multiplied u ll get a negative number

[restive river]

what how?

[uncut ore]

wait

my mistake

[restive river]

bruh dyssrupt r u gonna say anything or just gonna react 💀

[uncut ore]

its ok

[red turret]

my wifi

[restive river]

lmao

[uncut ore]

i read one sign < and other one >

[mystic locust]

ok break the function step by step -

domain of log (0,inf)
domain of sin all real numbers
domain of cos all real numbers

so set sin x cos x =0

x={0,90,180,270,360}

{x such that x does not equal 0,90,180,270,360}

[red turret]

but this ^^

just solve for sin(2x) > 0

[restive river]

lmao how sinx cosx =0?

[restive river]

yea ok let me try

[mystic locust]

wdym?

[restive river]

i'm getting $x\in (2n\pi,2n\pi+\pi/2)$

[woven radish]

yajat

[restive river]

but the answer is $x\in (n\pi,n\pi+\pi/2)$ smh

[woven radish]

yajat

[red turret]

the period of sin(2x) is pi

[restive river]

is it becomes zero then it will log(0) which is not defined

[restive river]

oh

LMAO

but how do i know that?

[mystic locust]

exactly! we need to find values that make the log 0 so we can exclude them from the domain

[restive river]

is there any way to calc that?

[red turret]

know what? the period?

[restive river]

yea

[restive river]

it's ok im fine with this method too

[red turret]

sin(ax) means the period is now 2pi/a

[restive river]

oh

[red turret]

similarly for other trigonometric functions

[restive river]

i didnt know that

is that the same for other

trig func also?

[red turret]

well

[restive river]

well

[red turret]

for tanx, period is pi

so tan(ax) -> pi/a

you can try plotting the graphs

and compare for a better understanding as to why that happens

fuck airtel

[restive river]

ohh ok

[restive river]

burh i dont know in which corner u sitting

it's not that bad

[red turret]

i mean their wifi

[restive river]

atleast it's better than bsnl

bsnl is so trash

[red turret]

its ass

true

[restive river]

i dont know why they still exist

[restive river]

oh

[red turret]

govt services

[restive river]

was about to say that 💀

bsnl is on its verge of ending 💀

[red turret]

its ancient

btw

[restive river]

LMAO true

[devout snow]

If you are done with this channel, please mark your problem as solved by typing .close

[restive river]

shut up

[red turret]

[restive river]

bruh

i know

.close

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[restive river]

thanks for the help

eveyrone

[devout snow]

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[devout snow]

@mortal tinsel Has your question been resolved?

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@mortal tinsel Has your question been resolved?

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[hardy badger]

hi im asking this question again, id like to know if im on the right track in solving this question?

[hardy badger]

i got the sin substitution from this table

[restive river]

What's ur question?

[restive river]

Is it integration?

Is the variable u or x

@hardy badger ?

[hardy badger]

here it is, my bad for the delay

i had started doing some subs

[restive river]

Sin inverse x and it's differentiation noice

Let t = arc sin x

dt= 1/(1-x²)½

[hardy badger]

ok so far im following

[restive river]

It will integrate to t²/2 form

Put the limits from 0 to π/6

U will get ur answer

[hardy badger]

wait hold on i started losing you a bit here

you saying the whole thing will integrade to t^2/2?

and the appearance of pi/6?

[restive river]

It's definite integration, ur substituting sin inverse x as t and x is varying from 0 to ½ ,so t will vary from 0 to π/6

pi ²/72

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[hardy badger]

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[honest thorn]

Idk how to simplify that

This is the answer:

[solar goblet]

seems wrong

[opal cloak]

yeah

[solar goblet]

,tex .diff rules

[opal cloak]

based of the denominator i can already tell u its wrong

[woven radish]

فطر

[solar goblet]

recheck your quotient rule

[honest thorn]

ok i did it now

but i still cant simlify it

[solar goblet]

show your work

[honest thorn]

$\frac{((e^x+e^{-x})^2 - (e^x-e^{-x})^2)}{(e^x+e^{-x})^2}$

[woven radish]

sxer

[solar goblet]

$a^2-b^2=(a+b)(a-b)$

[woven radish]

فطر

[honest thorn]

thanks

i got it

.close

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[solid heron]

can someone tell me why there are no solutions to this / how to we check if there are no solutions?

[sharp root]

well, anything congruent to 1 mod 40 can be written as 1+40a for some integer a

thus it can be written as 1+5*8a, so it can't be divisible by 5

[solid heron]

what cant be divisible by five?

[sharp root]

well, no number one more than a multiple of 5 can be divisible by 5

[solid heron]

is there a way to check from the equation?

[sharp root]

e.g. 6 isn't divisible by 5, 11 isn't divisible by 5, 16.. 21... etc.

wdym?

[solid heron]

or not equation but

can we not check from the congruence?

like gcd(40,5) and check to see if 1 is divisible by 5

huh nvm i think i just answered my own question lmfao

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[deft spruce]

hi, its a really dumb question but im bamboozled by the fact that x/√x = √x

[blissful herald]

lol its ok

so

lets take 4/2 for example

so simplify this

[deft spruce]

is it bc √x = x^1/2

[blissful herald]

you take 2

[deft spruce]

and 2/2 - 1/2 = 1/2 which is equal to √x

[blissful herald]

as a common multiple

[blissful herald]

yeah this works too

[deft spruce]

could you also explain what you were doing ?

[blissful herald]

yeah so as i was saying

4/2

what is the simplified answer of this

[deft spruce]

2

[blissful herald]

yes

to get 2

what you did was

you miltiplied 2 by 2

to get 4 in the numerator

[deft spruce]

yep

[blissful herald]

and 2 by 1

in the denominator

so similarly

for x/sqrt(x)

what do you get when you multiply sqrt(x) by itself

[deft spruce]

x

[blissful herald]

yes

and what do you multiply sqrt(x) with so you get sqrt(x)

[deft spruce]

1

[blissful herald]

there you go

[deft spruce]

alright

thank you so much

[blissful herald]

no problem

[deft spruce]

this makes much more sense

btw what grade are u in ?

[blissful herald]

uni

[deft spruce]

what are u studying ?

[blissful herald]

computer science

[deft spruce]

nicee

im debating between engineering an cs

[blissful herald]

what grade are you studying in

im assuming 11th or 12th

[deft spruce]

10

[blissful herald]

oh

between engineering and cs?

[deft spruce]

in my school i do precalc in 10th and calc in 11th/12th

[deft spruce]

yep

[blissful herald]

cs comes under engineering

[deft spruce]

mmh

do you like it ?

[blissful herald]

ig

@deft spruce close the channel

[deft spruce]

how ?

sorry its my first time

[blissful herald]

.close

[blissful herald]

its alright

[deft spruce]

.close

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[prime ridge]

A ballot box contains indistinguishable white, black and red balls. Two balls are drawn, each time with reentry, thus not changing the probabilities with each draw. The red balls are 6 in total. Knowing that the probability of drawing at least one white ball is 51% and the probability of drawing at least one black ball is 75%, determine the total number of balls in the ballot box.

[prime ridge]

I was doing some problems on probability and idk how to tackle this one

I translated it to english, hopefully it still makes sense

[sharp root]

I makes sense

[prime ridge]

I'm glad that you make sense

[sharp root]

The way I would start out is by making a system of equations with variables for the number of white, black, and total number of balls

[devout snow]

@prime ridge Has your question been resolved?

[prime ridge]

I just reread my textbook to make this. Is it right?

N for the total number of balls, W for white, B for black

<@&286206848099549185>

[limpid dove]

Meth

[prime ridge]

meth 👍

[limpid dove]

This seems correct

[prime ridge]

I did the equations separately and got this ^

i'm always making the silliest errors when calculating, so i hope you can briefly check it

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[urban aurora]

This is a common diagram used to show where the formula for a determinant comes from.

[urban aurora]

I have rotated this diagram, and I get a different formula for the area. What is happening here?

[stark sinew]

whats your different formula for the area?

[urban aurora]

(a+c)(b+d) - cd - ab
= ab + ad + bc + cd - cd - ab
= ad + bc

Obviously the formula should be ad - bc (Which you can easily obtain from the first diagram)

[stark sinew]

when you rotated it, your corners aren't described by the vectors (a,b) and (c,d) anymore. While (a,b) may describe the first corner, (c,d) sort of has nothing to do with anything anymore in your second figure

[urban aurora]

How so?
Lets give c and d some values like (c,d) = (-3,3)
That could describe the other corner right?

[stark sinew]

you need to pay attention in the first figure what c and d are. They are not the coordinates of the opposite corner. They are actually the coodinates of the change from the first to the second corner. So in fact that first corner in the bottom right has coordinates (a,b) but teh coordinates of the top right corner are (a+c, b+d)

[urban aurora]

I am a little confused by this

[stark sinew]

when you show the formula of a determinant, you're usually constructing a parallelogram whose sides are (a,b) and (c,d). Your new figure doesn't have that, so the formula doesn't mean anything per se. Yes its the area if you define those to be abcd but those abcd don't mean anything geometrically about the parallelogram

[urban aurora]

How could I represent the coordinates of the corners in the second diagram to get the correct formula of the determinant then?

[stark sinew]

good question 🙂 it's actually as simple as changing c to -c. Basically to get from the first corner (middle right) to the second corner (top corner), you go d up but c left so its actually -c

then if you do that I have a feeling you'll get the right answer

and you'll realize its more or less just applying the 90* rotation matrix on the matrix

[urban aurora]

(a+(-c))(b+d) - (-c)d - ab
= ab + ad - cb - cd + cd - ab
= ad-cb

Interesting... That is correct. I find that difficult to think about though because I feel as if I am calculating squares of negative area. For example the square with side lengths c and d I am now calculating by -cd...

[stark sinew]

negative areas are real! and your calculation shows you that they were needed to get the right result

if you've taken calculus its just the same thing as signed areas

[urban aurora]

Fair enough

Thank you

.close

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[grave salmon]

help

[unborn cedar]

how am i supposed to do this

[trail eagle]

You didn't subtract the terms correctly, if that's what you did.

[devout snow]

@unborn cedar Has your question been resolved?

[unborn cedar]

how should i

[devout snow]

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[unborn cedar]

.reopen

[devout snow]

✅

@unborn cedar Has your question been resolved?

[unborn cedar]

how should i

im unsure

[trail eagle]

2x^2 - x^2

5x - (-3x)

4 - 2

[unborn cedar]

oh

ok thanks

.close

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[fallen badger]

Hello, i need help understanding questions in an Intro to Mathematical stats course. Answers are given, i'd like to know how the answer is derived

[fallen badger]

working to the answer is also given, just need an explanation

[devout snow]

@fallen badger Has your question been resolved?

[fallen badger]

given this question

does this make sense?

[devout snow]

@fallen badger Has your question been resolved?

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[graceful cosmos]

(4x)^n = (4)^n (x)^n

?

[elfin atlas]

I think they want to know how to find out the Taylor series at a particular x*

[graceful cosmos]

Sorry, was talking about what you said after, didn't see the screenshot. I see now you want to use the series centered at 0, to get the series centered at 1/4

[elfin atlas]

there is a formula for that

[graceful cosmos]

I don't follow with what you're suggesting

[graceful cosmos]

But I feel this is non-trivial to do

For some functions, a good strategy is to shift it.

arctan(4x) centered at 0 is exactly the same as arctan(4(x - 1/4)) centered at 1/4

Problem is there's no nice algebraic simplification for that

[elfin atlas]

In this problem I wouldn't shift

[devout snow]

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[unborn cedar]

how did i multiply it wrong

[elfin atlas]

you did nothing wrong

[versed juniper]

you did do something wrong

thats not a polynomial in standard form

[elfin atlas]

ahh yeah

[unborn cedar]

ah shit fr

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[tepid oracle]

How can I answer these questions?

[devout snow]

@tepid oracle Has your question been resolved?

[sand dove]

can you see an easy one to one function for a?

[tepid oracle]

not really, only one that I can think of is maybe f(n) = n?

because (0,2) is always within [0,2]

actually, I think that is the answer

[sand dove]

it is

one of the answers, but definitely the easiest and the one I was looking for

[tepid oracle]

what about for b

[sand dove]

well for b

you would like f(n) = n again

but as you can see

[0,2] is too "large" to fit in (0,2)

so maybe if you scaled it a bit

so it can fit

[tepid oracle]

so I would want to find a way to make it smaller

[sand dove]

exactly

[sand dove]

can you find a smaller set [x,y] that fits in (0,2)?

[tepid oracle]

I'm thinking division, but then how would I handle the 0?

oh, since the problem was dealing with the real numbers even the smallest number after 0 and before 2 would fit, so [0.0001, 0.99]?

[sand dove]

sure, but it's not the most practical ones

I was thinking maybe [0.5,1.5]?

[tepid oracle]

[1/2, 3/2]?

[sand dove]

yes

[tepid oracle]

yeah same one haha

[sand dove]

ok

challenge :

there exists a linear function between [0,2] and [1/2,3/2] that perfectly matches every number one on one

find g(x) = ax+b that makes it match perfectly

(hint : what would g(0) and g(2) be?)

[tepid oracle]

so g(0) and g(2) would be 1/2 and 3/2, would be 1/2x + 1/2?

sorry, I blanked for a bit

ah I see, so the function was still simple, but not as simple as f(x) = x

and im pretty sure from the looks of it this would work for every smaller set of numbers within (0,2)?

I have a question also, would g also be a surjective function for the domain and codomain of question a?

[sand dove]

that's it yep

[sand dove]

So we didn't define a surjective function here, neither for a nor for b

for f in the question a, 0 and 2 have no inverse images...
for g in the question b that we just define, it's worse, any number between 0 and 1/2 and between 3/2 and 1 is left out of inverse images

[tepid oracle]

ah ok, I see what you mean now

alright, thanks so much, I get it now, going to practice some more of these

[tepid oracle]

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[static mason]

I am supposed to find the determinant of this matrix, but I am honestly unsure of where to even start. Any help would be appreciated

[static mason]

<@&286206848099549185>

[devout snow]

@static mason Has your question been resolved?

[devout snow]

@static mason Has your question been resolved?

[forest pelican]

Upper diagonal except that 10

So your answer is (10 * above partition) + (1 * below partition)

Below partition is 0, since that main diagonal ends in 0

Above partition is n!

Kinda

The last column is an issue

Draw some boxes

Take determinant along column 1

You get 10*(det removing first col and last row)

Of that new det you have to find, find it by the first row

Is 1*n!

So final answer is 10*n!

Hopefully

[static mason]

Thank you

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[thorn kestrel]

How to derivitive x²/ 4x+1

[thorn kestrel]

Can i send a picture here?

[tall knoll]

It's encouraged, even

[thorn kestrel]

Okiee wait ah

[viral rapids]

x²/(4x+1) or x²/(4x)+1

[thorn kestrel]

Is actually this one

Wait ah

[viral rapids]

set up quotient rule

[thorn kestrel]

So i need to bring that 4x+1 to up and it will be (4x+1)^-1 right? Then we can do product rule for it or what?

[scenic mirage]

No just use the quotient rule
f(x)/g(x) = ( f'(x)g(x) - f(x)g'(x) )/ (g(x))^2

[thorn kestrel]

Ouhhhh okieee

Many big thanks

[scenic mirage]

Just don't overthink it and follow the rules

[thorn kestrel]

Sorry this is my first time learn it. I will try ma best

[scenic mirage]

Yeah during my first time working with them, I keep thinking about mixing the rules or moving stuff around but it's very straightforward

[thorn kestrel]

Aahhh alrrr

Thank you for your helpp

[scenic mirage]

.close

I guess the person who opened it has to type it

[thorn kestrel]

Aahh alr i will

.close

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[strange lantern]

How would we go about doing this?

[strange lantern]

I keep thinking that its a full rectangle (Cause the half got doubled) + a quarter of a rectangle (cause the half got reduced by a quarter)

so its 1 + 1/4

but its not

[winter patrol]

a quarter of a rectangle (cause the half got reduced by a quarter)
is flawed

reduced by a quarter of the square

[devout snow]

@strange lantern Has your question been resolved?

[strange lantern]

but the rectangle got halfed, and then subtracted by a quarter

so is it not 1/2 - 1/4?

[winter patrol]

no

area of the second square is reduced by a quarter of its area (it referring to the area of a quarter of the second square and not of the original rectangle)

[strange lantern]

so 1/2 - 1/8?

or 1/2 - 1/16

[winter patrol]

first one

how'd you suddenly get 1/16

[strange lantern]

ok ty for the help

[strange lantern]

just added that in case i mentally calculated it wrong

the quarter of 1/2

but yeah its 1/8

.close

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[coarse abyss]

How do you do this

im stuck here

I think this is wrong anyway

[devout snow]

@coarse abyss Has your question been resolved?

[devout snow]

@coarse abyss Has your question been resolved?

[thorny lily]

r u sure u wrote the q correctly

I put it in integral calculator and none of the techniques worked

If the second square root was x^4+2x^2+1 it would be possible with u sub

[coarse abyss]

trig sub?

Calculators cant do every integral

[devout snow]

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[coarse abyss]

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[waxen shell]

help pls

[viscid ivy]

Hii

@waxen shell There

[waxen shell]

hello

[viscid ivy]

So bro

Start from considering the eaual angles x

Okk

Equal*

Now 2x+k = 180

Three angles of triangle

Again 81 + k = 180 - x since the lines are parallel

Your question will be solved using the equationz

@waxen shell got it ?

[waxen shell]

So is k 99?

[viscid ivy]

calculated ?

[waxen shell]

oh wait no

[viscid ivy]

Okk

[waxen shell]

how is x worked out

[viscid ivy]

K.= 18

You have two linear equations

Solve for x.and k

[waxen shell]

I understand now

thank you

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[fervent ledge]

which condition is necessary for valid expansion of given expression, a or b?

<@&286206848099549185>

[viscid ivy]

Bro

[fervent ledge]

!15m

[devout snow]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[viscid ivy]

Mod.x < 3/5

Coz if x greater than that

[fervent ledge]

y

[viscid ivy]

You will get complex number

√-ve

Got it.?

5x < 3

[fervent ledge]

heart

[viscid ivy]

Or x < 3/5

[viscid ivy]

Mistake huh

[fervent ledge]

i did this and then selected the other option

cuz i saw 5/3 in this epression and in the options too

lol

@viscid ivy is it inverse of this term

like I'll take a number common and then the term i get, I'll invert it

[viscid ivy]

Okk

[fervent ledge]

correct method?

[viscid ivy]

But you need the term inside to be greater than 0

Yes 1-5/3x > 0

Solve this to get x<3/5

[fervent ledge]

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[analog badge]

how can i implement the simpson rule computacionally

[analog badge]

with a given error i know how to do it , but i want the user to specify the error he wants so then i can aproximate the integral based on that

[devout snow]

@analog badge Has your question been resolved?

[devout snow]

@analog badge Has your question been resolved?

[devout snow]

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[prisma frost]

how do i answer this question

[prisma frost]

i did the first 2 bits

its just c im confused about

[lunar harbor]

$2a(1+\cos \alpha)=2a \sec \alpha \implies 1+\cos \alpha=\sec \alpha$

[woven radish]

Civil Service Pigeon

[lunar harbor]

Now, ||multiply both sides by sec alpha||

You should observe that you get ||a quadratic in cos(alpha)||

[devout snow]

@prisma frost Has your question been resolved?

[prisma frost]

why did you make them equal to each others?

[prisma frost]

i get they intesect but how does that help find where where the half line meets them

[lunar harbor]

You don’t need to

You just need cos(alpha)

[lunar harbor]

B/c it says OB=2OA

[prisma frost]

oh ok

thank you

[devout snow]

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[mild basin]

please help with this question:

[mild basin]

are both of these sets considered Row Space Basis?
the first set is after doing full RREF
the second is going back to original rows (being careful to track row swap during RREF)

IT WORKS!

SAME EITHER WAY

AMAZING

does that mean this is not correct?

i took that from the row space basis after doing RREF

<@&286206848099549185> anybody available today?

[mild basin]

would really like to know what these 2 vectors represent

[devout snow]

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[vast quiver]

In a televised game, three boys independently each choose their favorite girl from among three girls, and the three girls simultaneously choose their favorite boy from among the three boys. If a boy and a girl choose each other, they win a trip. What is, to the nearest 0.1%, the probability of winning three trips?

[devout snow]

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

[vast quiver]

It’s wrong

[patent grove]

,rccw

[patent grove]

what was the answer

[vast quiver]

0.8%

[patent grove]

like i have one but im not sure if what i did was correct

hm

uh so we could start by

finding the total number of ways

which would be 729

[vast quiver]

yh i noticed that mistake too

[patent grove]

uh to be completely honest i cant fucking read what you've written

[vast quiver]

its combinations from counting principles

maybe u use a diff notation

but its the same as 3C1 for the first one for example

[patent grove]

no i got that i meant like its too light and shit but its fine ill manage

[vast quiver]

ah

3.3C1.3C1.2C1.2C1.1C1.1C1/729

[patent grove]

then we could find the favourable outcomes

[patent grove]

yep thanks

lemme think

[vast quiver]

theyre asking the chance that we get the 3 trips so i thought we only pick that outcome

[patent grove]

hm

[vast quiver]

i suck in counting principles though so im not expecting anything i did to be slightly right

[patent grove]

well same tbh

[vast quiver]

😭

its the bane of my existence

[patent grove]

im getting like

11.1%

so lets not go there

[patent grove]

fr

[vast quiver]

the options r 0.2 0.8 2.5 4 and 16.7

and this book has a history of always being wrong but the solutions said 0.8

[patent grove]

its wrong then

trust

[vast quiver]

i can never see what i do wrong

[patent grove]

what was the question again

[vast quiver]

In a televised game, three boys independently each choose their favorite girl from among three girls, and the three girls simultaneously choose their favorite boy from among the three boys. If a boy and a girl choose each other, they win a trip. What is, to the nearest 0.1%, the probability of winning three trips?

[patent grove]

whatever im doing im getting like

1/729

[vast quiver]

what ru thinking

[patent grove]

so

basically

for each pair

the probability of them choosing each other is 1/9

and since there are three trips

that would be 1/729

and as a percentage that's like 0.14%

rounding off to 0.8

if that makes sense

@vast quiver did i confuse you

[vast quiver]

yes

[patent grove]

how much

[viscid ivy]

Very much

[patent grove]

yep someone else take over

im probably gonna go sleep for like 8 hours now

[viscid ivy]

Coz theres 2 boys in your image and 2 girls in her img

So she cant get the 3 thing

[patent grove]

and then if your doubt's uncleared then ill help you

[vast quiver]

what do i do then

[patent grove]

well im gonna go bye

[vast quiver]

@viscid ivy

[viscid ivy]

Hii

[vast quiver]

can u help pls

[viscid ivy]

Yeah whats the question but

[patent grove]

In a televised game, three boys independently each choose their favorite girl from among three girls, and the three girls simultaneously choose their favorite boy from among the three boys. If a boy and a girl choose each other, they win a trip. What is, to the nearest 0.1%, the probability of winning three trips?

[viscid ivy]

Okk

Total ways boys can choose girl is 27 right then

And total way girls choose boys is also 27

So the total set is( 27*27 ) elements

[vast quiver]

yes

[viscid ivy]

We need winning three trips

ok

Now

Do you have the answer ?

Just asking

[vast quiver]

0.8%

[viscid ivy]

Ok

So now lets consider only girls are choosing

So 1st girl 3 choices 2nd girl 2 choices and 3 rd one only 1 choice

Now choices of boys are fixed and i think only these possible ways 3 tickets can be won

[vast quiver]

that would be 2.5% and thats one of the options

[viscid ivy]

no

[vast quiver]

oh wait

[viscid ivy]

6/(27*27)

[vast quiver]

no ur right

[viscid ivy]

*100

Percent

[viscid ivy]

?

[vast quiver]

ok ty

i get it

[viscid ivy]

Is it the correct answer ?

[vast quiver]

yes

[viscid ivy]

Ok nice !

[vast quiver]

can u help w someone else

i have the solution but i just dont understand it

[patent grove]

wait the answer was 3!/729 * 100 right

[vast quiver]

ur throwing 3 dices and theyre asking the chance that the product of the eyes of the dice is equal to 6 and we did (P3 + 2C3)/6^3

but where does the P3 come from

[viscid ivy]

Yeahh

Can you clearly say the question

Product of what number comes on die equals 6 right ?

[vast quiver]

We are rolling 3 dice. What is the probability that the product of the pips equals 6?

[viscid ivy]

Okk got it

So 1,2,3 or 6,1,1

2 combinations right ?

[vast quiver]

ohh wait i get it

[viscid ivy]

okk

[vast quiver]

because 1,2,3 is equal to the permutation of 3

[viscid ivy]

Yeah

[vast quiver]

haha okk

tysmmm

[viscid ivy]

Anytime !

[vast quiver]

.close

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[steel pagoda]

hi. Can i ask here how to solve some maths for computer science?

[steel pagoda]

This is a worksheet for a class called Problems and Solutions. I am struggling to find a tutorial on YouTube which explains how to do this worksheet.
The closest I have found is from Abdul Bari. Explanations on youtube I have found so far don't satisfy the nature of the questions.

[analog wedge]

@steel pagoda

i need help!!

[steel pagoda]

im asking for help

[analog wedge]

o

[viscid ivy]

Haha

Ayden broo

[devout snow]

@steel pagoda Has your question been resolved?

[steel pagoda]

<@&286206848099549185>

[orchid charm]

have patience

[devout snow]

@steel pagoda Has your question been resolved?

[devout snow]

@steel pagoda Has your question been resolved?

[steel pagoda]

oki

[devout snow]

@steel pagoda Has your question been resolved?

[devout snow]

@steel pagoda Has your question been resolved?

[devout snow]

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[rocky scroll]

hi

[rocky scroll]

so i got a question which ive like forgotten how to do and im kinda embarrased lol

could anyone let me know if im on the right track?

[rigid pewter]

no way😱😱nick eh 30 in mathematics discord yeah that looks perfect assuming your simplification is right

[rocky scroll]

oh alr thanks

ill make sure to get a vic roy for u

.close

[devout snow]

Channel closed

Closed by @rocky scroll

Use .reopen if this was a mistake.

[rigid pewter]

why banhammer react 💀

[rocky scroll]

mods ban him

[wicked badger]

Lol

[rocky scroll]

.reopen

[devout snow]

✅

[rocky scroll]

sorry just a follow up question

if i were to find a rule for the Area only in terms of x, how would i do it?

oh the 2y + 12 = 180

simplify it further then sub it in

?

thanks bro

.close

[devout snow]

Channel closed

Closed by @rocky scroll

Use .reopen if this was a mistake.

[rocky scroll]

.reopen

[devout snow]

✅

[rocky scroll]

sorry guys too much streaming

theres a question which says to state the domain, if we were considering both xy-12y-264 and 79x-1212 (the one i got from subbing in), it would just be all real values right? Also it then says to sketch the graph of A against x and to state the max possible area of the enclosure and so im gettign the feeling that its actually a quadratic and ive done something wrong?

[sage acorn]

yoo bro

ik where you get this

[rocky scroll]

is it from a tuition?

[sage acorn]

yes

lol

[rocky scroll]

no way

[sage acorn]

ik

LOL

victoria?

[rocky scroll]

yea

[sage acorn]

alright

does he start with m

[rocky scroll]

yep

[sage acorn]

madira?

lol

[rocky scroll]

lmao

[sage acorn]

what a coincidence

do u go narre warren

[rocky scroll]

nah

[sage acorn]

oh so mount wavery

k

[rocky scroll]

yea

[rocky scroll]

btw i still need help with this if theres anyone

[sand isle]

NICKEH30 ?!

[rocky scroll]

ik bro its me

[sand isle]

woah

[rocky scroll]

original question

[sand isle]

how does domain and range

apply here

[rocky scroll]

theres a question which says "State a domain of function A(x)"

on the next page

<@&286206848099549185>

if someone is kind enough to help nick eh 30 with his question please ping me and ill be here 🙏

[devout snow]

@rocky scroll Has your question been resolved?

[rocky scroll]

guys its been 40 minutes 😭

oh so just all real numbers for that one?

so the graph would be linear

what about the max possible area of the enclosure

differentiate?

no

[rocky ice]

do u have a function for A(x)

[rocky scroll]

it said tofind the rule for A which i got xy-12y-264

then with only x terms i got 79x-1212

[rocky ice]

what did u change y to?

[rocky scroll]

i got y = 79

oh wait mb its meant to be 84

i messed up 180 - 12 omg bro

alr so with that

i got A = 84x - 1272

instead of 79x-1212

[rocky ice]

mistake when finding perimeter

its x - 12 not 12 - x

[rocky ice]

it shouldnt be linear so yeah theres a mistake

it should be a quadratic

[rocky scroll]

ohhhh

[rocky ice]

see what u get now

[rocky scroll]

alr thanks

ill see

y = x-90?

90-x mb

y = 90-x

[rocky ice]

show the working for me nick

[rocky scroll]

hold on give me 5

[rocky ice]

ping me when ur done

[rocky scroll]

im back

ill type out my working out

[rocky ice]

sure

[rocky scroll]

x + y + x - 12 + y - 22 + 12 + 22= 180

[rocky ice]

yup

[rocky scroll]

x + y + x - 12 + y - 22 + 12 + 22 = 180

[rocky ice]

yeah

[rocky scroll]

then 2x+2y = 180

[rocky ice]

yea

simplify

[rocky scroll]

x+y=90

y = 90-x

[rocky ice]

y =…

alr

what u think u should do now

[rocky scroll]

sub that in for the equation before

[rocky ice]

sweet

[rocky scroll]

then after i should get a quadratic right?

[rocky ice]

yea

so first get the quadratic

it should be a negative one

then we’ll figure out how to go

[rocky scroll]

alr

let me do that real quick

wait

i didnt get a negative quadratic

i got x^2 -102x -1344

oh my

nvm i know what i ddi

[rocky ice]

lol good

cus if its positive

then theres no good answer lol

[rocky scroll]

alr i got -x^2 + 102x + 1344

so i can just sketch it and find out everything

ill quickly do that

[rocky ice]

yeah

[rocky scroll]

bro

[rocky ice]

yo

[rocky scroll]

i got (51,1257) as the tp

is that right?

[rocky ice]

idk lol ill check for u tho

[rocky ice]

as long as this is correct

then yes

(51, 1257)

so what is the max area?

[rocky scroll]

would it be 51m?

[rocky ice]

51 is x

[rocky scroll]

oh wait i have to sub it in

[rocky ice]

x is a length

you dont have to sub lol

(51, 1257)

you have it right there

[rocky scroll]

1257?

[rocky ice]

at x = 51, A = 1257

[rocky scroll]

ohhh

[rocky ice]

yeah

[rocky scroll]

ok

[rocky ice]

so thats the maximum possible area for that question

[rocky scroll]

i understand now

yeah

[rocky ice]

sweet bro

[rocky scroll]

thank you bro

[rocky ice]

no problem nick eh

[rocky scroll]

that waiting for 40 mins was worth it

also nice beserk pfp

[rocky ice]

cant believe i met the real nick eh

[rocky scroll]

thats what they all say

[rocky ice]

W for recognising it

[rocky scroll]

alright thanks bro

cya

.close

[rocky ice]

laters

[devout snow]

Channel closed

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Send your question here to claim the channel.

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.

[restive river]

what is the difference betweeb question 1 and 3?

[trail eagle]

They want you to swap the order of integration

That will mean redefining the bounds accordingly

[restive river]

yes but whats the difference between them

like in q2 i have reversed the order and changed the boundaries

what am i supposed to do in q4

q3*

[trail eagle]

It's just having you compute it by changing the order. Notice that if you didn't change the order you'd have to integrate something like arctan(sqrt(x)), and that's not possible.

Changing the order actually makes the integral doable

[restive river]

i know i did that in q2 😭

[trail eagle]

Q2 lays the groundwork by having you describe the domain both ways

Then you compute in Q3

[restive river]

in q2 they said evaluate

evaluate the integral by changing the order

so i have already evaluated

[trail eagle]

It's just breaking down the question in two parts

Evaluate the integral by

1. sketching the domain of both types
2. actually computing the type II

[restive river]

ohhhhh

[trail eagle]

That's what's it's asking

[restive river]

wth

you saved my life

[trail eagle]

It's the same question

[restive river]

thank you sm 👍👏

[trail eagle]

No worries!

[restive river]

.close

[devout snow]

Channel closed

Closed by @plain idol

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[devout snow]

Available help channel!

Send your question here to claim the channel.

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

[neat oasis]

Someone had a lifetime batting avg of 0.305 at the beginning of the 2007 season. He had 2067 hits out 6767 at vats. During the 2007 season, he had 183
a. write an equation describing his batting avg at the end of 2007 season using x for number of at bats he had during the season
b. determine the HA and VA
c. what is the meaning of horizontal asmp for the graph of this equation

[devout snow]

@neat oasis Has your question been resolved?

[devout snow]

@neat oasis Has your question been resolved?

[devout snow]

Channel closed

Closed due to timeout

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Available help channel!

Send your question here to claim the channel.

Remember:
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• Show your work, and if possible, explain where you are stuck.
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• 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.

[unreal schooner]

how to simplify this cos4a+2sin^2 2a

[sonic smelt]

Use one of the double angle identities for cosine

[unreal schooner]

i used this one cos^2-sin^2a

[sonic smelt]

There is a better one

[sonic smelt]

Rewrite cos^2 as 1 - sin^2 in that

[rocky ice]

1 - 2 sin^2 a

[unreal schooner]

ok and 2sin^2 2a like that 8sin^2 a cos^2 a

?

[sonic smelt]

Rewriting 2sin^2(2a) will make the simplification harder

This channel is taken

[rocky ice]

just leave that term

rewriting cos(4a) will allow you to simplify with the 2nd term

[unreal schooner]

ok

and answer will be cos2a?

1

yes

thanks

.close

[devout snow]

Channel closed

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[devout snow]

Available help channel!

Send your question here to claim the channel.

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.

[feral cairn]

Let A be a real 2 × 2 matrix and L : R^2 → R^2 : v→ A * v the corresponding linear mapping. We call L conformal if L is injective and
for all v, w ∈ R^2 with v, w != 0 it holds that (Screenshot)
L is conformal. Show that ||L(v)|| = r*||v|| if r> 0 and not depends on v ∈ R^2.
Tip: First consider the basis vectors e1 = (1,0) and e2 = (0,1) and the vector e1+e2