help-13

[young flume]

u just don't include the 1 because it makes the equation easier to read and anything multiplied by 1 is itself either way

[regal marlin]

i think this is right

then simplify everything in the Sqrt

[strong prairie]

ok i get that

[young flume]

Okay

[strong prairie]

im just tryna show everything

[young flume]

then u start with the square root

simplify that and then u continue with the fraction

[regal marlin]

and just solve it then you can find x on the quadrants

@strong prairie can you try to use this

[strong prairie]

do i combine everything in the top?

[regal marlin]

wait no

[strong prairie]

so i have 7 + (26)

or do i combine them

is what i mean

[regal marlin]

why that shi so small

[young flume]

no

[regal marlin]

do 4(1^2)(-26) which is -104 so

11 - 104 which becomes 115

[young flume]

its positive

[upper ruin]

Why do you keep writing 1² instead of 1, though?

[young flume]

its 104

[regal marlin]

so sqrt(115)

[young flume]

its sqrt 225

-4 * -26 = 104

[regal marlin]

ahh rihgt

mb

[upper ruin]

And also do not forget the ² on the 11 @strong prairie

[young flume]

• 121 = 225

sqrt = 15

-11 +- 15

    2

sorry idk latex thats teh best i can do man

[regal marlin]

actually you are wrong because the constant is negative because of the - sign

x^2 + 11x - 26

lol

im right

its -26

[young flume]

what

[regal marlin]

you said the constant was positive right

[young flume]

no

[regal marlin]

or did you mean to say something else

[young flume]

i said the constant is negative

[regal marlin]

oh

[young flume]

u multipied a positive constant by a negative

and i said it was pos dood

🥹

[regal marlin]

ok

[regal marlin]

oh

[strong prairie]

where did the ^2 on the 11 come from?

[young flume]

its in the formula

b^2

11 is the b

[strong prairie]

ah ok

[young flume]

when plugging in also make sure you parenthesis your a,b, and c

because -11^2 and (-11)^2 are different

no parenthesis itll only square the term its connected to, 11

and you end with a negative

lmk if ur confused any where else ill try my best to explain

If hes having trouble with the quadratic formula I dont think hes gonna like factoring 💔

ah

i didnt even see that

its a diff of squares

(x-sqrt15)(x+sqrt15)

or am i wrong

broooo what

really

[strong prairie]

the question says to solve it using factoring, but if there is a easier way then idc

[young flume]

i never learned that

no

maybe

idk

im very caffeinated right now

how would u factor it

because i did

hold on

[upper ruin]

Hint: -2 and 13

[young flume]

holy fuck im stupid

hey mine kinda works also

[upper ruin]

You forgot the x 😬

[young flume]

huh

[upper ruin]

So it doesn't work

[young flume]

where

did i forget an x

[upper ruin]

It's 11x, not 11

[young flume]

bruh

ok enough coffee for me

im forgetting basic algebra

[strong prairie]

this only week 2 of my class why this shi so complicated

im watching the video rn

yes

like 1x or 2x 1 or 2 being the coefficient

5?

a?

or 1?

no

a

this

il put it again so we can look

11

1

becuase x^2 is 1

-26

and i got this far

121

-4

-104

17

225

is this supposed to be -4?

if not where did the - go in the formula

i did that on the paper that makes sense to me

and i have a question about the order of operations rq

mb

how do you know that its (b)^2 and -4 x26 and they are separate

why doesnt it fallow like how its written?

like b^2 -4 * A * C

or is the asnwer to that, its just how you solve it

and not b^2 -4 then *a then *c i did that first and it was like 3000 and i knew that was wrong but idk

thats multiply

[wraith dagger]

mq in his algebra/stats arc

[strong prairie]

i see, thats still confusing to me but i guess that's just how u solve it

ok so i have 225

ad the sqrt is 15

/2?

even the -11?

gotcha

-5.5 +- 7.5

2 and -13

nicee

thank you

i see

oh yea to not work with .5s

ok gn

.close

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[pearl prairie]

could someone help me understand what i did wrong on my assignment 😅😅

[digital bane]

which one shall we start with?

[pearl prairie]

2

[digital bane]

sure

[pearl prairie]

i did everything right

i think

[left warren]

Anyone know statistics?

[hollow trail]

the graph is not correct on 2

[digital bane]

!occupied

[cedar kiln]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[digital bane]

please grab an available channel, like #help-36

[left warren]

What should I do
I am new here 😭

[hollow trail]

when you have two inequalities that have to be satisfied at the same time you should only draw between the two boundaries

[pearl prairie]

ohhh

[digital bane]

much the same issue for 3

for 4, you ate a negative sign by accident on top of the same issue

[pearl prairie]

so like this

[digital bane]

correct. no arrows

[hollow trail]

yes, that's the correct graph

[pearl prairie]

bro the teacher never told me this 😡😡

[digital bane]

drawing an arrow implies that the inequality is without bound in that direction

which is not what you mean here

[last apex]

Don't expect to be taught everything

[pearl prairie]

yes yes i’ll keep that in mind

this is for 3 right

[digital bane]

looks good

[pearl prairie]

since i got six incorrect

would this be correct

[digital bane]

no

you divided by -4

guess what you should do when you divide by a negative number?

your graph is right though

[pearl prairie]

flip the sign

right

[digital bane]

correct

because as written, your inequality is impossible

x has to be greater than -9 and less than -12 at the same time

which isn't happening

[pearl prairie]

ohhh i seee

thank you

[digital bane]

7 looks like the same issue again

as is 9

and 10 too from the looks of it

[pearl prairie]

so like this

[digital bane]

if these match your original ranges, yeah

[pearl prairie]

yes

wait i’ll do number 9

would this be two equations or just one

[digital bane]

you might wanna redo 9 actually

because i noticed in your original working you forgot about the - sign in -3x

[pearl prairie]

yes i’m redoing it

was i doing the equation kinda right?

[digital bane]

the idea is there, but you forgot the - sign in -3x and the whole thing kinda crumbles there

[pearl prairie]

would this be correct then

[digital bane]

looks good

[pearl prairie]

the graph would look like this

[digital bane]

yup

[pearl prairie]

okayoaky

thank you for the help 🫰🏽

[digital bane]

nps

!done

[cedar kiln]

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

[pearl prairie]

.close

[cedar kiln]

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[green drum]

Why does the x on the bottom have absolute value? I understand all of it until there and I'm stuck where it comes from

[tropic oxide]

sqrt(x^2) = |x| because sqrt(anything) is positive

sqrt(x^2)=x would be wrong if x is less than 0

[lyric plank]

this is kind of strange though, presumably x is positive here?

[tropic oxide]

maybe the next step is stripping the absolute value bars? idk

[green drum]

but In most of my classes, they never do absolute value of x?

[tropic oxide]

but this is def the rule they used here

[green drum]

is it just assumed always?

[lyric plank]

sqrt(x^2) = |x| is a true statement regardless

[tropic oxide]

i think you may be running into a silent assumption of x>0

[pulsar lily]

well no wait, this ought to be sqrt(x)^2, not sqrt(x^2)

[lyric plank]

that's probably more accurate yeah, i think the work here is somewhat flawed

or at least unnecessarily adding steps

[green drum]

wait I still dont understand why it cant be negative

cause square root of 49 is -7 and 7?

[pulsar lily]

no, the square root function isn't multi-valued; it always takes the positive one

[lyric plank]

okay that's like a whole separate thing

the square root of a positive number is defined to be the positive root, we just define one to be default

what i'm saying at least is that if x is negative, then sqrt(x) isn't defined unless you extend to the complex numbers

and at that point the rule that

sqrt(a) * sqrt(b) = sqrt(ab)

doesn't really translate

so it seems a bit pointless

[green drum]

so I ignore the negative answers?

[lyric plank]

i would just think of sqrt(x) * sqrt(x) as = x

bc sqrt(x) is generally defined as "whatever number, such that squaring it gets me x"

i would not do the |x| thing that they're doing there

[pulsar lily]

in a vacuum, i.e. without the context of this particular problem, sqrt(x^2) = |x| for all real x

[green drum]

I still don't quite get it

[pulsar lily]

but because there is a "sqrt(x)" involved in your expression, we are to believe that x is nonnegative (indeed, nonzero, to avoid division by 0)

[green drum]

doesn't the square root and square cancel out and then its just x?

[pulsar lily]

no, because sqrt((-7)^2) is not -7

[green drum]

oh wait

I get it now

thanks!

.close

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[lost wigeon]

Help

[digital bane]

question please

[lost wigeon]

I tried to make a 4-bit subtractor

And i faild

[prisma pike]

Rip

It's ok man I don't even know what that is

[lyric plank]

if you can make a 4-bit adder, subtractors are really easy with 2's complement

[lost wigeon]

I alredy made one

[lyric plank]

great

now

a - b = a + (~b) + 1

(but your leading bit will have to flip meaning from being 2^n to -2^n)

[lost wigeon]

I think got it you need to invert a and resoult like:
not(c)=not(a)+b?

[lyric plank]

is that supposed to be

c = b - a

[lost wigeon]

Yes

[lyric plank]

that won't work exactly

a - b = a + not(b) + 1

this is the formula

[lost wigeon]

Is +1 jus +not(forrow_in)?

[lyric plank]

+1 is just adding the number 1

[prisma pike]

Oh I thought you were making ts with logic gates

[lyric plank]

i assume they are

but if they already have an adder, a subtractor doesn't need a new circuit beyond inverters i guess

[prisma pike]

I agree with your magic words magic man

[lost wigeon]

Ok bye

.close

[cedar kiln]

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[lyric plank]

4 bit subtraction

let's say i want to do 5 - 3

that would be

0101 - 0011

for the algorithm, just turn 0011 into 1100, and then do

0101 + 1100 + 1

that gets us

0010

which is 2, exactly what we want

:/ okay

[prisma pike]

Twos complement core frfr

[lyric plank]

yup

[prisma pike]

My computing syllabus actually taught me something

This is unprecedented

[lost wigeon]

Cool

.close

[lyric plank]

you already closed it

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[coral cobalt]

this is question

[coral cobalt]

this is answer, i dont know how they eliminated 3/7

i dont understand that part

i got the rest right

[upper laurel]

if you had something like -x^2 - 2x - 1,

[coral cobalt]

yes

[upper laurel]

that couldnt be written as a perfect square

however thatd be -(x + 1)^2

and so would have a discriminant of 0

[coral cobalt]

why couldnt that be written as a perfect square

i dont think i understand what a perfect square means

[upper laurel]

-(x + 1)^2 is not a square

[coral cobalt]

can u explain sorry

[mental trail]

If the discriminant is 0, then the polynomial can be factored as p(x) = a(x-b)^2

[upper laurel]

a square is a number that can be written as a square of other numbers

[jagged tide]

try plugging m=3/7 here ig

[mental trail]

but if a < 0, that can't be a perfect square

[upper laurel]

-(x + 1)^2 is not the same thing as (-(x + 1))^2

-(x + 1)^2 would be like -1

[coral cobalt]

this makes sense

[coral cobalt]

o

[upper laurel]

here they wanted m - 4 to be at least 0

but ideally you check for 2m - 1 instead

[mental trail]

both are ok

[upper laurel]

in either case, m - 4 and 2m - 1 must both be at least 0

[coral cobalt]

so basically

is that just a rule i can remember

or is it only for this case

[upper laurel]

its an extra condition, you should remember it

I wouldnt have seen this coming

[coral cobalt]

to be a perfect square, m-4 and 2m-1 must both be atleast 0?

[coral cobalt]

yeahh i thought i aced it with those two answers and thought so easy

[upper laurel]

not every problem is going to have an m - 4 and an 2m - 1

[coral cobalt]

OH FLip thats from the question

[upper laurel]

for ax^2 + bx + c, in general a and c have to both be at least 0

[coral cobalt]

so A and C

yeahhh

[upper laurel]

yep

for example for 2x^2 + 4x + 2,

thats 2(x + 1)^2

but you can put the 2 inside:

[coral cobalt]

a is > 0

c is > 0

[upper laurel]

(sqrt(2) x + sqrt(2))^2

and so 2(x + 1)^2 is also a perfect square, it just takes some work

[coral cobalt]

so i can jsut remember the condition for a quadratic in the form ax^2 + bx + c to be perfect square is a > 0 and c > 0

[upper laurel]

sure

[coral cobalt]

ok

that makes the most sense

thanks all of you for helping

.close

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[manic kelp]

I don't understand how we did part a)

Shouldn't the second part (after -3 times the determinant) with -1 be +1?

I mean even the formula (Let's decompose the determinant into the elements of the first row) has only multiplication and addition? Or am I missing something

[tropic oxide]

remember that A_ij also incorporates the sign alternation as (-1)^(i+j)

and the sign for the entry in row 1, col 2 is negative

that's why they put minus like that

[manic kelp]

I'm new to this whole topic so I don't fully understand yet

[manic kelp]

Alr I think I get this

[tropic oxide]

the 3x3 dets are the minors while the A_ij are the algebraic complements

[manic kelp]

Oh

Alright hold on

So to find the algebraic complements I need to refer back to task 1?

[tropic oxide]

no, in 1 you found two minors

the M's

[manic kelp]

And A12

And the other one

A32

So to find A11=(-1)^1+1 times M11

In my case my determinat is
0 2 2 4
2 5 1 -3
1 0 -1 2
-3 4 5 1

So the first thing would be 0 times whatever turns out to be 0

[tropic oxide]

M11*

[manic kelp]

M is the minor?

Oh

Yes

M11

[manic kelp]

I know that the second one comes out to be -2 times
0 2 4
1 0 2
-3 4 1
?

And the third is 4 times whatever, the 4 won't have a -
Right?

[cedar kiln]

@manic kelp Has your question been resolved?

[manic kelp]

I just wanna know if I'm thinking right^

[empty tulip]

Hii fellas

I'm new to the world of math

I want to start from scratch

Any recommendations would be appreciated

[dense lotus]

Practice, Practice, Practice

[empty tulip]

Thank you,any book recommendations?

[manic kelp]

This channel is still occupied by me

Please take this conversation elsewhere

[empty tulip]

Oh okay

My bad

I'm sorry

[manic kelp]

My question is still here if anyone could help

[manic kelp]

No worries

[manic kelp]

<@&286206848099549185>

[supple patrol]

yes

[cedar kiln]

@manic kelp Has your question been resolved?

[cedar kiln]

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[crimson sedge]

I want some help

[azure apex]

https://dontasktoask.com

[azure apex]

,rotate

[azure apex]

which one

[crimson sedge]

All

Anyone here

Hello

Please help

[cedar kiln]

@crimson sedge Has your question been resolved?

[sullen cipher]

Which one

[wicked mantle]

He said all 🙂

[sullen cipher]

I thought all as in yall

[tropic nova]

ok so

[sullen cipher]

And i remember helping him solve one of these

[tropic nova]

same

so you see, what is AGE? hint: GED = 126 degrees. think of alternate angles.

Lets go through this one by one:

finding GEF is easy, right?

whats GEF?

[ancient iris]

i dont think bros listening

[crimson sedge]

I am here

Can we move forward

Everytime this happens to me

[sullen cipher]

U can start by replying to Uzu M

That way he gets notified that u r here too

[crimson sedge]

So can we start

@tropic nova

[tropic nova]

so what do you think is GEF

[crimson sedge]

?

[tropic nova]

what is angle GEF?

[crimson sedge]

Idk

[tropic nova]

what is angle FED?

since we know GEF = GED - FED, we can find GEF by finding FED since we already know GED.

[crimson sedge]

Fed=90 degree

So it's 126-90

= chattis

Am I right

[tropic nova]

yes

now, we can find angle FGE अब, हम पा सकते हैं angle FGE

[crimson sedge]

Ok move forward

@tropic nova

Koi ho

Anyone

[cedar kiln]

@crimson sedge Has your question been resolved?

[cedar kiln]

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[neon wyvern]

Can someone help me draw this I’m so confused

[dreamy void]

,rccw

[neon wyvern]

Ah sorry shoulda rotated it

[dreamy void]

It's good to draw an example of what increasing/decreasing looks like as well concave up/down

[dreamy void]

So then we can get from the text that there are two turning points, in x=3 and x=6

In (-4,3) it's concave down and we know it's increasing on (-4,1) so we can draw on (-4,1) that is like -e^-x

[neon wyvern]

?

[dreamy void]

yes but until 1 not -1

[dreamy void]

yea

[neon wyvern]

Man I really hope this isn’t on the test lmao

[dreamy void]

now next it's decreasing on (1,5) and still concave down on (-4,3) so we draw a function on (1,3) similar to 1/x

[neon wyvern]

Would it look like this?

[dreamy void]

more like a curve L

[neon wyvern]

So the curve L is still concave down?

[dreamy void]

Oh wait my bad

[dreamy void]

it should look like this

[neon wyvern]

Oh

[dreamy void]

I thought for a moment concave up

[neon wyvern]

Lolll

[dreamy void]

Too much informationa at once

[neon wyvern]

Fr I’m so lost 😭

[dreamy void]

just connect this nicely to your first function on (1,3)

[neon wyvern]

???

[dreamy void]

yea

[neon wyvern]

I don’t understand where it’s supposed to end tho

[dreamy void]

i think it's up to you

[neon wyvern]

Ope

[dreamy void]

what matters is that you make sure the properties are right

[neon wyvern]

Oki

So is that it or is there more,

[dreamy void]

so at x=3 we have a turning point

so we have now concave up on (3,6)

[neon wyvern]

Oh

[neon wyvern]

WAIT

[dreamy void]

and we know it's decreasing on (1,5)

so from (3,5) we can draw a function that is still decreasing but concave up

that would be now a curly L

[neon wyvern]

Where would I connect it to?

[dreamy void]

to your current graph

[dreamy void]

like on the right you continue to go down and to the right until x=5

[dreamy void]

yes

so the graph is still concave up on (3,6) and increasing on (5,7) so we draw a graph on (5,6) that increases but is still concave up

like a U basically

[neon wyvern]

Uh

[dreamy void]

yeah...

[neon wyvern]

Is it done?

[dreamy void]

the thing is you drew it too high

[neon wyvern]

Ope

[dreamy void]

so the last piece won't be visble

unless you extend the graph over the text

[neon wyvern]

I’ll erase

[dreamy void]

yeah just up until 3 or 4 is fine

[neon wyvern]

6,7

[dreamy void]

because the last piece must be increasing on (5,7) and concave down on (6,7)

[neon wyvern]

https://tenor.com/view/67-gif-8575841764206736991

So okay for (5,7) 5 is the x and 7 is the y right

Cuz it’s not making sense

[dreamy void]

something like this

[neon wyvern]

So purple concave up

Blue concave down

[dreamy void]

yes and incr

and incr

yea

[neon wyvern]

Okay thank you so much ima go back and look over to make sure understand what we did🙏🙏

[dreamy void]

I would color the different function parts

[neon wyvern]

Good idea

[dreamy void]

and write what they are and do

[neon wyvern]

Tyyyy

.close

[cedar kiln]

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[exotic sonnet]

Okay so, in desmos when I plug in x to the power of x, it gives me a graph that only goes to the right, it doesn't have any negative values, but you can also just plug in something like -3 to the power of -3 and get a value that would be negative, why does desmos do this?

[ancient lodge]

negative exponents of negative numbers are not well defined for non integers

you could go into complex world

https://math.stackexchange.com/questions/1211/non-integer-powers-of-negative-numbers

but the graph is over the reals anyway

technically you could draw a bunch of discrete dots at x=-1, x=-2, ...

but with how desmos works, you won't see those

[exotic sonnet]

okay

reading that it seems a bit over my head but i think i understand

for non interger negative values we don't rly have the numbers

[ancient lodge]

sure

it's not well defined what number you would assign to those

anyway imma go in a little so any other questions

[cedar kiln]

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[exotic sonnet]

.close

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[plush blade]

how does this become -1/3*x^5 and not -2x^5

[slate lintel]

it's -2/6 x^5

[plush blade]

wait but we get rid of the x^5 and that leaves us with -2/6

but why is there still x^5?

[slate lintel]

how are you getting rid of x^5

[bright fiber]

1 apple - 3 apples is -2 apples

you still have apples

(err, negative apples, anti apples)

[slate lintel]

if you have 3 chickens and you eat 1 chicken yeah that

[plush blade]

yes i get that but

see the example i draw

[bright fiber]

my girl went for chicke straight away

[plush blade]

why is there still x^5

[slate lintel]

why did you cross those out

idgi

[plush blade]

because they cancel out eachother?

[slate lintel]

what

how

[cyan pebble]

its still 2 apples, not just 2

[bright fiber]

2 antimatter apples to be exact

[slate lintel]

you're subtracting here

[plush blade]

yes

[cyan pebble]

pure energy

if u were given x - 3x

would that be -2?

[plush blade]

yes ofcourse

[cyan pebble]

or -2 x

[plush blade]

-2x

[slate lintel]

if you have 3 chickens and you eat 1 chicken you're left with 2 bloodstained chickens, not just the physical number 2

[cyan pebble]

well then, why would it be different here

[slate lintel]

if u were given y - 3y i suppose you'd also have -2y?

[plush blade]

yes

[cyan pebble]

think substitution is too much for this

[slate lintel]

replace y with x^5

[buoyant sand]

nah

it's a valid explanation

he understands this concept

but not this concept

so bridge the gap

[plush blade]

okay

i got it now

thanks

.close

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[fiery valley]

hello there,

i dont get it in a sense that im still piecing out how each concept is related to each other

this gets me into questions like:

1. how did we change the inequality symbol in the end to somehow x <= -3? is it because the product rule in the number line shows positive? is that the requirement that it needs to be positive?

[buoyant sand]

so we want the positive product, right?

that occurs when x<= -3 and x>=5

[fiery valley]

same thing with 5 <= x at the end

[fiery valley]

is that the end goal basically?

[buoyant sand]

the question asks us

to find

(x+3)(x-5) >= 0

and this occurs when

x <= -3 or when x >= 5

[fiery valley]

okay i think it clicked-- somehow

thanks my dude

[fiery valley]

but if we wanted the negative product

ie. (x+3)(x-5) <= 0

it would be x >= -3 or x <=5

[buoyant sand]

yep

but

put it together

-3 <= x <= 5

[fiery valley]

in betweeners

yeah

thanks my dude 🫶

[buoyant sand]

np

[fiery valley]

how do you end this LOL

!end

i forgot 😭

[buoyant sand]

.close

[fiery valley]

danke

[buoyant sand]

np

[fiery valley]

!close

[buoyant sand]

.close 😭 🙏

[fiery valley]

.close

[buoyant sand]

like

[cedar kiln]

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[buoyant sand]

verbatim

yeye

[fiery valley]

HAHAHAHAH

[livid hound]

and, not or

[cedar kiln]

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[naive hornet]

In Triangle ABC, orthocentre is (1,2), circumcenter is (4,5). If the equation of side BC is 2x+2y=3, then find the circumradius of the Triangle.

[naive hornet]

Help guys

[tropic oxide]

could help to at least put all these things down on a graph, right?

[naive hornet]

yeah

I put on Desmos

I assumed B to be like (x,y) and then tried to form like a circumcircle equation with it

[misty anvil]

Find reflection of orthocentre about the side BC

[naive hornet]

I don't get the intension

[misty anvil]

It will lie on the circumcircle

Then use distance formula between that reflection point the circumcentre to find the radius

[naive hornet]

what how? 💀

[misty anvil]

Oh damn

We were taught that

[naive hornet]

I don't know this theorem

[misty anvil]

Lemme find proof for you

[naive hornet]

thanks

@misty anvil Dude, please share the proof

[misty anvil]

Yea but it's not the one my teacher showed

[naive hornet]

if I understand it, then its fine

[misty anvil]

He did it by contradiction

[misty anvil]

Okk

[naive hornet]

Proof by Contradiction in Co-ordinate 💀 . Another level of stuff here

[misty anvil]

Fr man

He showed us 2 cases

First told us that it won't come on circumvented

*circumcentre

[naive hornet]

close call

[misty anvil]

Then said wow magic it is on circumcentre

[naive hornet]

please share

I'm curious now

[misty anvil]

Here

https://math.stackexchange.com/questions/589877/why-would-the-reflections-of-the-orthocentre-lie-on-the-circumcircle

Ig this is correct proof

I have one video

But it's in hindi

[naive hornet]

no problem

[misty anvil]

In tht he first assumes a point on the circle then proves that it is the reflection of the orthocentre

So basically reverse engineering

https://youtu.be/LeUvHd0hb_Q?si=DuQ-1KbVoqqHTGoB

[naive hornet]

ok. got it.

.close

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[swift carbon]

Helloo

[swift carbon]

My sister needs hello

Help

It says “a rocket is scheduled to launch from a command center in 3.75 hours. What time is it now? It says the launch time is 11:20

Helloo

[split ice]

essentially, this question is asking "what time is it now, if it will be 11:20 in 3.75 hours?"

[swift carbon]

Yes

[split ice]

for an elapsed time problem, you need to do 11:20 - (3.75 hours), essentially

but one is in hours and minutes, the other is just in hours

[swift carbon]

Oh okay

Thank you

.close

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[split ice]

well you still need to convert one to the other

but if you got that then

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[pine swift]

is it even possible to solve this with kvl? Vx is the objective

[pine swift]

urgent pls help

[hollow trail]

not entirely clear what voltage Vx is suppused to be based on the diagram

[cedar kiln]

@pine swift Has your question been resolved?

[pine swift]

Yes, that's the point

It's 4Vx

[hollow trail]

well we can't solve the circuit unless we know what Vx is supposed to refer to on it (like which two points are we taking the voltage between)

[pine swift]

The question is like that bro 😭

Idek how we're supposed to solve this

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[stoic crystal]

how to prove using induction

[cedar kiln]

@stoic crystal Has your question been resolved?

[spiral orbit]

What have you done so far?

[stoic crystal]

i showed it for the base case n = 1

[spiral orbit]

alright, what's next?

[stoic crystal]

idk

[spiral orbit]

well you need to carry out the inductive step

assume that the statement is true for i=n-1

and show it is true for i=n

Let's tackle iv) first

$\prod_{i=1}^n \left( 1 + a^{2^{i-1}} \right) = \left( \prod_{i=1}^{n-1} \left( 1 + a^{2^{i-1}} \right) \right) \cdot \left( 1 + a^{2^{n-1}} \right)$

[wraith dagger]

Peter

[spiral orbit]

can you see how this is true?

[stoic crystal]

I prefer using n + 1

[spiral orbit]

no biggie

$\prod_{i=1}^{n+1} \left( 1 + a^{2^{i-1}} \right) = \left( \prod_{i=1}^{n} \left( 1 + a^{2^{i-1}} \right) \right) \cdot \left( 1 + a^{2^{n}} \right)$

[wraith dagger]

Peter

[spiral orbit]

@stoic crystal this makes sense though, right?

we just split the product of n+1 terms by considering the product of the first n terms and multiplying that with the last term

[stoic crystal]

yes

[spiral orbit]

perfect, now what can you say about the product from 1 to n from the induction hypothesis

what would its value be

[spiral orbit]

great, sub that in and continue the arithmetic

[stoic crystal]

,, \prod_{i=1}^{n+1} (1 + a^{2i - 1}) = \frac{1 - a^{2^n}}{1 - a} \cdot (1 + a^{2n})

[wraith dagger]

Renato

[stoic crystal]

@spiral orbit

are you here?

[spiral orbit]

yeah, that looks good

either multiply the top row out, or notice it is a difference of cubes and use the formula

anyway you should be really close to the solution at this point

[stoic crystal]

help

[spiral orbit]

?

[stoic crystal]

difference of squares, no?

[spiral orbit]

sure

[stoic crystal]

how to use it?

@spiral orbit

[spiral orbit]

you don't have to, just multiply the terms out

$(1-a^{2^n})(1 + a^{2^n})$

[wraith dagger]

Peter

[spiral orbit]

multiply these out

[stoic crystal]

dude help

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

2^(n+1)

[spiral orbit]

great, you know the formula, a=1 and b=a^(2^n)

what do you get when you plug in those values

[stoic crystal]

I mean

2^(n+1)

[spiral orbit]

ok, I thought this would be straightforward but this is what you should obtain

$(1-a^{2^n})(1 + a^{2^n}) = 1^2 - \left( a^{2^n} \right)^2 = 1 - a^{2^{n} \cdot 2} = 1 - a^{2^{n+1}}$

[wraith dagger]

Peter

[spiral orbit]

is any step in the above equality confusing you?

[cedar kiln]

@stoic crystal Has your question been resolved?

[stoic crystal]

ye

[stoic crystal]

yes its straight forward, right.?

,, \prod_{i=1}^{n+1} (1 + a^{2i - 1}) = \frac{1 - a^{2^{n+1}}}{1 - a}

[wraith dagger]

Renato

[stoic crystal]

@spiral orbit

like this my dude?

[stoic crystal]

.close

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[last laurel]

y < –3x + 5. graph

[last laurel]

my question is how do you get x

[digital bane]

you don't need to get x. do you know how to graph y = -3x + 5?

[last laurel]

yeah

so thats it

oh my

okay thank you

[digital bane]

mhm

but remember to graph that line as dotted

[last laurel]

yeah I got that

[stoic vapor]

Just in case:
$$y < -3x+5 \iff y-5 < -3x \iff \frac{y-5}{-3} > x$$

[wraith dagger]

Sam

[last laurel]

yeah I understand this as well

thanks guys

.close

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[hushed belfry]

is this correct?, took me some time

[stoic vapor]

No

[austere hull]

use a calculator

[cedar kiln]

@hushed belfry Has your question been resolved?

[cedar kiln]

@hushed belfry Has your question been resolved?

[latent bloom]

[wicked mantle]

No, is there anything else you wanna ask aside from this? 🙂

[wicked mantle]

.solved

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[distant delta]

how do i do this

[hollow trail]

looks separable

[distant delta]

yea but its not a linear equation

[hollow trail]

separable equations don't have to be linear

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[shrewd eagle]

please help please

[cedar kiln]

Please don't occupy multiple help channels.

[dull oxide]

!1c

[cedar kiln]

Please stick to your channel.

[shrewd eagle]

hello?

.close

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[balmy prawn]

i completed the question

but i wanna double check the answer

[wicked mantle]

Alright

[balmy prawn]

i got- maya: 379.9, jake: 389.3, difference:9.4

is that right?

uhm ...

[cedar kiln]

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[balmy prawn]

.end

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[young summit]

hu

[young summit]

hi

Calculate the diagonal length of a 1×1
square. Enter the first three digits of the decimal expansion of the result

is the answer
1.41
or
141
what is correct?

i don't know what does the question mean by (Enter the first three digits of the decimal expansion of the result)

[indigo lagoon]

it means omit the rest of them

$\sqrt2 = 1.414\dots$

[wraith dagger]

This is sad 😢

[young summit]

so 1.414 would be the answer ?

[indigo lagoon]

Enter the first three digits of the decimal expansion of the result

[dry bluff]

Yeah if it's worded like that it's weird

[stiff brook]

huh it seems to ask the digits

[dry bluff]

Then it's like competition math

[stiff brook]

id wager 141

[indigo lagoon]

If I weren't mistaken, you're supposed to enter 141

[dry bluff]

If it's just a school assignment it's probably like a mistake

[young summit]

ok

414 or 141

[dry bluff]

@young summit what is this for?

[indigo lagoon]

141, 414 was my horrendous typo

[young summit]

it's training exam

after 1 hour is my exam real on

one *

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[faint temple]

I feel like I kind of understand the question but I'm not sure how to answer it

[faint temple]

ive heard of 2 factor and factorable so I'm assuming its just talking about 2 factors

from what ive seen there could be 1. two squares 2. a triangle and a 5 vertex shape 3. maybe just the whole thing?

what i think im really struggling with the most is b

[cedar kiln]

@faint temple Has your question been resolved?

[faint temple]

<@&286206848099549185> could i please get some help

[fathom bridge]

Any probability masters here 😁💀

[indigo lagoon]

might considered claiming another channel, this one is currently occuiped

[faint temple]

If anyone has the time to help please ping me so I don't miss it!!

[faint temple]

I have been thinking for an hour and still not entirely sure what im doing 😔 if no ones available i might try asking at another time

[floral arrow]

I just looked up the definition of a 2-factorization so bear with me

It seems there are at least two different factorizations with two 4-cycles

[faint temple]

omg nel its you again

[floral arrow]

And given the questions a,b,c, I assume there's a third I can't find

(and question d would be about the 3-cycle + 5-cycle one)

[faint temple]

but theyre rotations of eachother right

[floral arrow]

No

[faint temple]

yeah thats what i thought too

oh

[floral arrow]

Also you can rearrange the graph like this, not sure if it's useful at all

[faint temple]

im also considering whether a graph is a 2 factorisation of itself

[faint temple]

ooh

[floral arrow]

From what I've read, no; a 2-factorization needs 2 cycles that, combined, span the graph

[faint temple]

wait which are they

[floral arrow]

You found the two squares already, try finding another

Just try some 4-cycles

[faint temple]

oh wait yeah i see it

[faint temple]

its like a bow

wait no

[floral arrow]

Yeah

[faint temple]

wait yeah

its like a bow

[floral arrow]

Which vertices?

[faint temple]

with this one itd just be like 4 "adjacent" ones

[floral arrow]

RIght exactly

[faint temple]

maybe b is just the strategy and c is the factorisation lmao

[floral arrow]

Hm maybe, honestly I have no clue what "strategy" they want

[faint temple]

i dont really understand what it means by strategy

yeah

ive got to leave thanks for helping though!

ill try my best to come up with some strategy lmao

[faint temple]

ur actually my saviour ngl 😌😌

.close

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[quartz salmon]

How should I approach this problem?

Are the parameters indicating from minute 0 to minute 4 for the first r.v., and 0 to 6 for the other?

I am not sure how to interpret it

[tropic oxide]

think of their arrival times as being uniformly distributed over a rectangle in the xy plane

[tropic oxide]

U(a,b) means a uniform distribution over the interval [a,b]. thats what the params mean

[quartz salmon]

yeah i know this part but i am trying to interpret it in the context of the problem

[high coyote]

So the time starts at 20:00

[quartz salmon]

that A has an equally probable likelihood of arriving at each part (how long?) between 0 to 4 minutes after 8?

[high coyote]

So, X comes at 20:03 ←→ X=3
Y comes at 20:05 ←→ Y=5

[tropic oxide]

yes, A arrives at a uniformly random time between 8:00 and 8:04

[high coyote]

X and Y being uniform

[quartz salmon]

okay so how should i translate the final sentence into P(•)?

i imagine there has to be some inequality

[high coyote]

Yess

[quartz salmon]

for A to wait for B, it would have to be the sum of probabibilities on the other side of the bigger sample space(?)

[high coyote]

If A has to wait to B means that A arrives earlier than B

[tropic oxide]

if you have to wait for your friend how does that translate into you and your friend's arrival times

[quartz salmon]

yes that makes sense

so does it make sense to write Ω = {0, 1, 2, 3, 4} x {0, 1, 2, 3, 4, 5, 6} (our sample space), giving us an area that is the shape of a 4 by 6 rectangle?

and since we want to find out how high the likelihood it is for A to arrive earlier, we want to know the area of the shaded rectangle, relative to the total outcomes (4*6)

[high coyote]

No

X and Y are uniform

Not discrete

Unform random variables are continous on intervals

[quartz salmon]

okay

[high coyote]

X could take value π

20:00+π

[quartz salmon]

yes

[high coyote]

So as Ann said, it is a rectangle on R²

[quartz salmon]

[f_{X}(x) = \frac{1}{4}, 0 < x < 4]
[f_{Y}(y) = \frac{1}{6}, 0 < y < 6]
\text{We want to find P(A arrives earlier), which translates to P(Y>X) if we let}
\text{Y = minutes in late arrival, and X = minutes in late arrival}
This is equivalent to finding the area over the diagonal relative to the area of the entire rectangle.

[wraith dagger]

dghf

[high coyote]

Yes

[quartz salmon]

the diagonal would be y = x since that means they arrive at the same time, and we want to find the other side, i.e. the pdf of y>x

is that correct

i think it's a joint pdf

[f_{X, Y}(x, y)=f_X(x) f_Y(y)=\frac{1}{24}, \quad 0<x<4,0<y<6]
[P(Y>X)=\iint_{y>x} f_{X, Y}(x, y) d y d x]
[P(Y>X)=\int_0^4 \int_x^6 \frac{1}{24} d y d x]

[wraith dagger]

dghf

[quartz salmon]

and then it's basically plug and chug

if the deduction was correct

[cedar kiln]

@quartz salmon Has your question been resolved?

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[cedar kiln]

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[blazing wraith]

Is there anything to do other than just integrate this? If so how do I know I can't do anything

[sullen cipher]

Direct integration is easier

Go for two terms separately

[azure apex]

what else are u gonna do 😭 if it is an int problem, you integrate

[blazing wraith]

https://tenor.com/view/lil-yachty-drake-laptop-duh-gif-8033838636860661307

[cursive tree]

mfs in calc do anything but the intended way

[azure apex]

😭

[random swift]

split it into one minus the other integral

[blazing wraith]

what is this called, its not integration by parts right?

[ancient lodge]

^^^^^^

[random swift]

It's using the linearity property of integrals

$$\int f(x) + g(x) \mbox{d}x = \int f(x) \mbox{d}x + \int g(x) \mbox{d}x$$

[wraith dagger]

Shuba

[blazing wraith]

I get that

i was just asking what its called

[random swift]

the linearity property

[blazing wraith]

what i struggle with is how to approach a problem, do i integrate by parts, u substitution, trig identities?

[azure apex]

in simple terms

ibp: when you have two functions being multiplied

[random swift]

For the second, use u ||= cos(x)|| substitution

[azure apex]

and:
the derivatives are really nice for one function(like x^2)
the derivative/int of one repeats itself after a few terms like e^x sinx
u can actually get something useful

u-sub is when

[blazing wraith]

like this?

[azure apex]

u can see the derivative of one function

in the integrand

[azure apex]

yes

the derivative of x is 1

so if we take x for D and cos(2-3x) for I

it will turn out pretty nice

[azure apex]

like 1/xlnx

$\int \frac{1}{x\ln x} , dx$

[wraith dagger]

mersenne primes

[azure apex]

do u see that subbing would actually cancel something

u = lnx

[blazing wraith]

x/x

= 1

[azure apex]

yep]

it turns out pretty nice

[blazing wraith]

for this what would u be?

2-3x?

[azure apex]

u do trig substitution whenever u see something which looks really close to an identity

[azure apex]

well we can substitute but would it give us something nice? try predicting and thinking abt it

[blazing wraith]

not really

[azure apex]

notice that we have xcos(2-3x) (4 is a const so doesnt matter)

[azure apex]

yeah so remove that from your list of techniques u can use

[azure apex]

now think abt ibp

[blazing wraith]

4x would be u no?

[azure apex]

think abt it

[azure apex]

(ibp = integration by parts if u didnt realize btw 💀)

[blazing wraith]

how does cos(2-3x) turn into this

nvrm i got it

.solved

[cedar kiln]

Channel closed

Closed by @blazing wraith

Use .reopen if this was a mistake.

[cedar kiln]

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Remember:
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• 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.

[quiet needle]

Why is the π constant the value where trigonometric functions shift, I mean why does the series x - x³/3! + x⁵/5!... Become 0 at nπ?

[dire geode]

those both are true yes

why do you think they can't be true?

[quiet needle]

???

Wdym

[dire geode]

pi is constant yes

[buoyant sand]

what 😭

he's js asking for an explanation

[dire geode]

and sin(n pi) = 0 yes

[dire geode]

if you want to ask your own question, open your own channel