help-0

[edgy cape]

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[formal fossil]

hi, need some help. i have difficult with sketching graphs .
Sketch the graph of a function that has the following properties:
f ″ ( x ) <0 for x <0 and f ″ ( x )> 0 for x > 0, f ′ ( x )> 0 for all x .

[hearty frost]

you cant graph function, the information is not enough, you can just predict if it will be positive and negative

and nature of the slope

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[wheat flint]

Guys I needed help with matrices to form equations

[wheat flint]

How do I calc values for each of those v and u

[sharp storm]

cramer rule

[wheat flint]

Im attempting

So I’m starting like this

But how do I get the answer on the other side of the equal symbol

This is all I get I don’t kno what to do from here

Anyone got an idea?

[sharp storm]

Maybe you understand by looking at this example?

,rotate

[wheat flint]

I was considering making simultaneous equations and then solving

[wheat flint]

To be honest I don’t understand thing I’m sorry

Anyone still here?

[sharp storm]

for v1 you replace your first column vector with the resulting vector and then divide the determinant of this matrix by the determinant of your original matrix.

for u2 you replace the second column vector with the resulting vector and so on.

[wheat flint]

Wouldn’t this method take a lot longer than just simultaneous equations

That’s the only issue, is timing

[sharp storm]

I only know it this way. Sry.

[wheat flint]

May I get connected to potentially someone else, I really do appreciate the help and will consider it, but because I’m already half way doing this way maybe someone will be able to help with my method

I genuinely appreciate the help

May we end this chat and I find another I guess

.close

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[alpine sable]

if a store is gonna give the 500th person a gift card, what type of sampling would that be? also a population, sample and sampling frame is biggest to largest right? how can i make a two way table and find probabilities and associtations, how do i find the LSRL, and would a z score be useful for college admission committees as much as percentiles?

[alpine sable]

also whats the difference between a cluster sample and census

also how do you interpret output from a calculator

I can technically tag helpers rn

<@&286206848099549185>

alright holdup i gotta leave for a sec just explain for now

how do you make a regression line using the output of a calculator

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@alpine sable Has your question been resolved?

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@alpine sable Has your question been resolved?

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@alpine sable Has your question been resolved?

[remote heron]

a lot of questions but did you get this one?

[alpine sable]

yes i got it

[wintry lotus]

That would be systematic sampling.
Not sure you mean by "biggest to largest"? But no, Population > Sampling Frame > Sample (since population is "everything", the frame is the conditions of the population you are testing, and the sample is the observations in the frame).
As for a two-way table: you should list your population groupings on the left (like "Male", "Female") and your results across the top (like "Like", "Dislike", "No Opinion") and populate the table with the count of each relative observation ("Male&Like", "Male&Dislike", "Male&NoOpinion" - repeate with "Female"). For relative popabilitites, take the relative observation count and divide by its total relative count (so "Male&Like"/"TotalMale") - Each row % should = 100%
The others - not sure

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[pale kestrel]

Is that all to the question?

[topaz coyote]

yes

[pale kestrel]

No clue, sorry

I'm confused on what S C R are

[abstract fractal]

What's S? What's C? What's R?

[topaz coyote]

sexagesimal degrees, centesimals degrees, radians

[abstract fractal]

It'd be best to convert all the angles into one, such as radians

How many sexagesimal degrees are in a full rotation?

[topaz coyote]

360

[abstract fractal]

So that's just degrees? Nice. Okay, so how do we convert from S degrees to R radians?

[abstract fractal]

Can you see that S = 180R/π

And can you see that C = 200R/π?

@ me if you return

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@topaz coyote Has your question been resolved?

[topaz coyote]

No

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[fickle agate]

can i get help in this part

[pale kestrel]

all 12?

[fickle agate]

ig, im stuck

[pale kestrel]

What is a function

That's key to solving all of these

[fickle agate]

a relationship between one variable and another variable?

[pale kestrel]

not quite

Is there some page earlier that defines it

[fickle agate]

i dont have the book, my teacher sent it

[pale kestrel]

A function f : A -> B is a map from domain A to codomain B

Are you familiar with something like this?

In other words the function f assigns every element of A to a single element of B

[fickle agate]

ohhhhhh

.close

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[lost salmon]

Hello im trying to simplyfy the left side of the queation

[lost salmon]

i know its possible im so sure

but since there is an inequality and both sides will be tampered with idk what to do

[pale kestrel]

I have doubts about simplifying...

I'd approach the problem by squaring both sides (noting both sides are non-negative and x^2 is an increasing function for non-negative x)

[lost salmon]

Awesome

that wont change the inqeality right?

[pale kestrel]

'noting both sides are non-negative and x^2 is an increasing function for non-negative x'

[lost salmon]

if we squad both sides

10 bcomes 100

[pale kestrel]

You understand why we can square both sides?

[lost salmon]

give me some time

[lost salmon]

yes

[pale kestrel]

or in general when you can apply a function to both sides of the inequality

[lost salmon]

ok uhhh

2ab

where a is sqrt(2t+1)) and b is sqrt(2t-1)

since we multply...

[pale kestrel]

btw, this approach might not help, its just what I'd try

[lost salmon]

what should i do then?

[pale kestrel]

try it

[lost salmon]

ok

what happens when u multiply the middle terms?

idk how to multiply square roots

[pale kestrel]

$\sqrt{ab} = \sqrt{a}\sqrt{b}$ ?

[ocean seal]

Shuri2060

[pale kestrel]

I would avoid writing 'x' for 'times'

[lost salmon]

ok

give me some time...

sqrt(4t) isnt 2t

its 2sqrt(t)

but how does that work!!!!

[pale kestrel]

I don't think I agree

[lost salmon]

where did i go wrong then

[pale kestrel]

^

You added the terms inside the sqroots instead of multiplying

[lost salmon]

oosp

uno momento por favor

next is....

2t - 1 ?

[pale kestrel]

no, that isn't a square

check for yourself what 2t-1 squared is

Before you had 2 square roots, now you have 1 square root. Can you think of a way to get rid of the last one?

[lost salmon]

uhhh

sqare again???

[pale kestrel]

If you square again just like that, you will end up with roots still

[lost salmon]

Ahhhh

bro i give up

[frigid hatch]

you could simplify your inequality to see things better

[lost salmon]

i want to simplyfy

[pale kestrel]

divide by 2 is what they mean

[lost salmon]

Oh

[pale kestrel]

what I meant is to only have one square root on one side

so that when you square both sides, the root goes away

[lost salmon]

i only have a sqare root on one sid

2(sqrt(4t^2 -1))

[pale kestrel]

if you square that side as is, that 4t will get involved

[lost salmon]

lemme divide by 2 first

2t + sqrt(4t^2 -1)

still dont know how to get rid of the sqaure root

[pale kestrel]

$$2t + \sqrt{4t^2 -1} \leq 50$$

[ocean seal]

Shuri2060

[pale kestrel]

We have this yes?

[lost salmon]

yep

yes

[pale kestrel]

If you just square both sides like this

you will get more roots

[lost salmon]

OH I SEE

Ok ok i got it

it would be like (a+b)2

and i would have 2ab

ok uhhh

[pale kestrel]

ok, so you need to avoid that

[lost salmon]

do i have to move the 2t to one side

[pale kestrel]

👌

$$\sqrt{4t^2 -1} \leq 50 - 2t$$

[ocean seal]

Shuri2060

[pale kestrel]

But now you also have to be careful

Can you square both sides?

[lost salmon]

yes?

[pale kestrel]

because?

[lost salmon]

one the left the root will go

?

[pale kestrel]

no.

Think of this example

$$-4 \leq 3$$

[ocean seal]

Shuri2060

[pale kestrel]

You can't just square both sides right?

[lost salmon]

oh

becuz of the inequality?

[pale kestrel]

yes.

but there are cases where you can do it.

[lost salmon]

do i need to swithc it?

or i cant change it at all

[pale kestrel]

No, you need to realise when you are able to square both sides of an inequality (while preserving it)

there are 3 cases, really. Both sides are negative. Both positive. Or 1 positive, 1 negative

[lost salmon]

both positive

[pale kestrel]

You can also square when both are negative, but then you'd need to switch the sign

$$\sqrt{4t^2 -1} \leq 50 - 2t$$

[ocean seal]

Shuri2060

[pale kestrel]

^ so back to this

[lost salmon]

so we swap everything?????

[pale kestrel]

???

You need to figure out which case this is

[lost salmon]

-50+2t > -sqrt(4t^2 -1)

[pale kestrel]

no.

[lost salmon]

or multiply everything by -1

then switch the signs

[pale kestrel]

That's not what I meant

[lost salmon]

https://tenor.com/view/confusion-confused-look-questions-why-why-me-gif-17660966

[pale kestrel]

If I gave you the inequality $$x < y$$

[ocean seal]

Shuri2060

[pale kestrel]

You need to know about the signs of x and y

before trying to square both sides

[lost salmon]

they both positive

bro im getting so confused

[lost salmon]

What abt it!??!?!

[pale kestrel]

^ they're both non-negative because the left hand side is 0 or greater

you get that?

that's why you can square

if you weren't sure, then you'd have to split this inequality into multiple cases

The square root symbol always refers to the positive root, so $\sqrt{4t^2 - 1}$ can't be negative

[ocean seal]

Shuri2060

[lost salmon]

that's why you can square

so i do sqaure?

[pale kestrel]

Yes

[lost salmon]

-_-

ok....

im am stuck

[pale kestrel]

What do you get

[pale kestrel]

You can take the next step?

what's left after simplifying

$$4t^2-1 \leq 2500 - 200t + 4t^2$$

[ocean seal]

Shuri2060

[pale kestrel]

👌

[lost salmon]

HOWWW

[glass lichen]

it's a linear inequality

[lost salmon]

Ok so i keep simplifiing

[glass lichen]

you solve for t.

[lost salmon]

200t<2501

t > 2501/200

[pale kestrel]

$$t\leq\frac{2501}{200}$$

[ocean seal]

Shuri2060

[lost salmon]

when u divide u need to switch the ineqality?

[pale kestrel]

I didn't, but you did for some reason

[lost salmon]

I THOUGH UR SUPPOSED TO

[pale kestrel]

If you divide by a negative number

[lost salmon]

Bru

ok

we keep going

t > 2501/200

[pale kestrel]

You're done?

no, its t <= 2501/200

[lost salmon]

t> 12.505

t<12.505

Ok let me check with desmos

WAIT

@pale kestrel

THERE MUST A MINIUM

Since we cant get a negative

Ok ur gone

[pale kestrel]

Hmm somethings wrong somewhere, I'll hunt

[lost salmon]

no no

no

its simple i got it

must be 0.5

since if its below o.5

then u get the sqrt of a - number

i got it

[pale kestrel]

Yes you're right

my bad

[lost salmon]

thanks alot

np np

my brain overheating

but im so board without computer

Ok thats it for now.

[pale kestrel]

1/2 <= t <= 2501/200

[lost salmon]

tysm!!

[pale kestrel]

👌

[lost salmon]

Woooo

byeeeee

.close

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[frosty gorge]

grade 11 functions, know clue where to start, been a long time since i last did this 😅

[echo socket]

Just instead of x plug in -x^2

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[tepid zodiac]

Hii guys

[tepid zodiac]

What's wrong with my method!

I try to find volume of cone with triple integral

And I do z first

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@tepid zodiac Has your question been resolved?

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[torpid turret]

Hi can someone check to see if I solved this question correctly?

I’m very confused if I did whether or not

[gray isle]

error in the last line / order of steps

missing the
(f + g)(5) = (5-5) + 2*5^2
which should be the second step leading to the conclusion of
(f + g)(5) = 50

[torpid turret]

Wait which one?

I think I did it like that.

Ohhh

Wait I see it now

My apologies

And finally is this answer correct or did I have errors anywhere?

[gray isle]

bad notation in multiple places

you should be writing those () around f+g and f-g

also don't write stuff like
$$5x-(-2x-3) = 2x+3$$

[ocean seal]

ℝamonov

[gray isle]

the notation for what question c) is asking is ambiguous

and i have no idea what you were doing for d)

actually there are even more issues i spotted in A

you multiplied f(x) with g(x) instead of adding them

5x+2x isn't 7x+2x either

[torpid turret]

Okay I’ll fix these immediately!

Thank u

[gray isle]

do you have an image of how c) was originally given?

[torpid turret]

Umm I don’t think so I think it was in the directions next to number 17

[gray isle]

based on context it seems its supposed to be
$$(f\cdot g)(x)$$

[ocean seal]

ℝamonov

[torpid turret]

I think so

I fixed the mistakes btw

At least I think I did

[gray isle]

also don't write stuff like
5x-(-2x-3) = 2x+3

[torpid turret]

Oh

Okay

[gray isle]

d) is still a bit messed up
you're writing on paper and not typing,
you have the advantage of horizontal fraction lines so that you can clearly indicate numerators and denominators

(otherwise use additional parentheses as needed)

(and you also wrote -2x - 1)

[torpid turret]

I think I accidentally put one instead of three

Oh

Yes

I just saw that 😂

[gray isle]

write it like $\frac{5x}{-2x-3}$ (which can be simplified a little by factoring out the -1)

[ocean seal]

ℝamonov

[torpid turret]

Okay will do

I’m a bit confused on how to factor however

Would I do it by the -3

[gray isle]

consider
-(a+b) = -a - b

[torpid turret]

-x(x+3)?

[gray isle]

no

[torpid turret]

Hmm

I’m lost

[gray isle]

do you have any issue with

-(a+b) = -a - b

[torpid turret]

I don’t rlly know what that is tbh 😅😅

[gray isle]

basic application of the distributive property

[torpid turret]

Oh

[gray isle]

pretty much what you applied in Qc)

factoring is just going in the other direction

[torpid turret]

Okay

So would it start at the -3?

[gray isle]

wdym

[torpid turret]

Ummm

Nvm

I’m not quite sure on how to like factor the fraction tbh 😅

[gray isle]

focus on the denominator

are you able to factor the -(1) out of
-2x - 3

[torpid turret]

Yes

I think?

[lone heart]

@torpid turret Has your question been resolved?

[lone heart]

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[silver bay]

how do you do this

[hearty frost]

do you know how to calculate slope of a line?

[silver bay]

f(a) - f(b)/ a - b

[hearty frost]

yes

just substitute x = 2.9 on point Q

you will get coordinates of Q

and you have coordinates of P

then apply slope formula

[silver bay]

p - q?

[hearty frost]

apply slope formula on PQ you have both the points ??

[silver bay]

could you show me this

i tried it but i mightve done something wrong

[hearty frost]

in Q(x, 2/(x-2) first we put x = 2.9

you get Q?

and P is given as (3,-2)

[silver bay]

yeah i got Q

-2.22 repeating

[hearty frost]

Q is a coordinate ?

[silver bay]

2.9,-2.22

oh

[hearty frost]

no

sorr

you are right

[hearty frost]

this is correct

now you have P(3,-2) and Q(2.9,-22) so apply slope formula

[silver bay]

f(p) - f(q)/p - q?

would f(p) = -2, f(q) = -2.22, p = 3, q = 2.9?

[hearty frost]

yes

[silver bay]

i got -2.826666

but it said incorrect

[hearty frost]

it is right

[silver bay]

😭

[hearty frost]

check your calculation on the last part

your calculation is wrong

[silver bay]

which part

[hearty frost]

(-2)-(-2.2222)/ 3- 2.9

did you get this?

[silver bay]

-4.159259

[hearty frost]

no

0.22222/0.1 ???

did you get this

[silver bay]

i got that answer before but it wasnt correct

2.2222

[hearty frost]

it should be the correct answer lol

2.222222

six decimal places?

[silver bay]

got it

thank you

.close

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[dusky quest]

I just need a little help in algebra
I did not understood the black part. ( how 1/RS become 1 )

[raw shard]

pretty sure those aren’t equal

wait actually

[royal meadow]

the whole bracket is squared

[raw shard]

oh darn i didn’t see that

[dusky quest]

yes but squaring 1/Rs becomes one ?

[royal meadow]

?

[raw shard]

a^2*b^2 = (ab)^2

[royal meadow]

so you basically have r^2 * (1/r + B)^2, which is the same as (r * (1/r + B))^2, which is the same as (1 + rB)^2

[dusky quest]

wait wait

[dusky quest]

Ohh yes yes I understood, thankyou very much I was really helpful, I have been scratching my head 20 mins,

why I can't see the question like you guys can
thankyou again very much

[royal meadow]

why I can't the like you guys can
it's all experience, we've seen this stuff a lot, nothing mad

perseverance

[lone heart]

@dusky quest Has your question been resolved?

[rough gale]

the number of students in a school is betwen 1200 and 1300 if we group them into groups of 12,20, and 36, 7 students are always left over how many students are there in the school?

[marsh rapids]

So 12n+7=20m+7=36l+7, i.e. 12n=20m=36l, so (students - 7) is a multiple of LCM(12,20,36). This leaves a unique answer.@rough gale

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[dire moat]

Need help in solid geometry

[dire moat]

A right circular cone with top width 24cm and altitude 8cm is filled with water. A spherical steel ball with radius 3.0cm is submerged in the cone. Find the volume of water below the sphere.

[feral moth]

Volume of cone - volume of sphere

@dire moat

[lone heart]

@dire moat Has your question been resolved?

[remote heron]

its more complicated than this i think

but reducing the problem to 2d will probably help

a triangle for a cone and a semi circle for a sphere

[dire moat]

It says find the volume of the water below the sphere so I tried Volume of cone at radius 3cm - volume of the hemisphere but I got a negative value

I don't know if this is right

[remote heron]

chr

a picture like this might help

lemme see if i can get an answer

heh

well i figured out at least the uhh

how do you call it

i guess you have it there, it's just 2

where the sphere makes contact with the cone

using the volume of this cone, less the spherical cap, gives the answer

idk if youre allowed to use formulas for that

that cap has height 5 less sqrt 11

,w volume spherical cap

[ocean seal]

Results provided by WolframAlpha

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[hybrid heath]

this is apparently achieved via polynomial division, but how?

[dire moat]

@remote heron thanks for the time and effort

[remote heron]

did you get it?

[lone heart]

@hybrid heath Has your question been resolved?

[hybrid heath]

This is as far as I've gotten; no idea what the next step needs to be

[gray isle]

well you have the quotient and remainder already

[hybrid heath]

really?

[gray isle]

yes

well 10/4 can be simplified further and all you need is to write it in the required form

= q(x) + r(x)/d(x)

[hybrid heath]

ooooh

no wonder. I always get confused by fractions dividing fractions :/

now I see how they got that answer

guess I need to practice a bunch of these problems now. thanks for your help!

.close

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[harsh ocean]

Having a function like $f(\varphi (t))$, if we take its derivative wrt time or varphi would it be total or partial? Like $\partial_{\varphi} f(\varphi (t))$ and $\frac{d}{dt} f(\varphi (t))

[ocean seal]

JSGF
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

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[blazing thunder]

I’m unsure on how to answer c and d, here is my working

(Btw in case you fall for it too, it’s not a quadratic)

Please ping me if you are able to help

[pale kestrel]

draw a picture for c

theres the original curve, and the equation 4g(x) = k
@blazing thunder

you can draw another graph that helps

for d, as u said, its not a quadratic, so you shouldnt get a straight line

[lone heart]

@blazing thunder Has your question been resolved?

[blazing thunder]

But how do I find out what it is

Well not the answer but how do I find the equation of g(x)

[pale kestrel]

Ok, first part c. did you make progress?

[pale kestrel]

Also, you don't. The equation of g(x) is irrelevant to the question

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[blazing thunder]

.reopen

[lone heart]

✅

[blazing thunder]

bruh moment

thanks shuri, im doing it rn

[pale kestrel]

what did you draw for c

[blazing thunder]

i drew 4g(x)

i am kind of confused on what it would do if it equals k

[pale kestrel]

its perhaps easier if you rearrange

so you have just g(x) on one side

[blazing thunder]

ohh

[pale kestrel]

but if u already drew 4g(x) you should also be good

[pale kestrel]

You have a graph of y = 4g(x).

You are interested in the equation 4g(x) = k

Does this hint at what you should draw?

[blazing thunder]

What about this?

It’s sending

[pale kestrel]

ok

y = 4g(x)

Then the question asks about
4g(x) = k

[blazing thunder]

But wouldn't that be linear

[pale kestrel]

What you've written in the top right... I don't get what it is

[blazing thunder]

Oh

[pale kestrel]

would what be linear

[blazing thunder]

Well I know you can use | _ | for matrices and vectors for the discriminant

I thought you could use it for the discriminant of a line too

b^2-4ac

That one

[pale kestrel]

i think youre confusing terms

thats discriminant of quadratic

and only applies to quadratics

[blazing thunder]

Oh ok

But if I had x^2 = 9 then you would just get 2 lines at y=-3 and y=3

[pale kestrel]

and the determinant is a different thing entirely

[blazing thunder]

So would it even have 2 roots

[pale kestrel]

go back to what i said

y = 4g(x)
4g(x) = k

[blazing thunder]

Yeah

[pale kestrel]

drawing the line y = k would help right?

[blazing thunder]

Ok I'll do that

[pale kestrel]

except youre trying to find k

[blazing thunder]

Wait but that is just x = 0

[pale kestrel]

no

lets say k = 2

draw that on the graph (as an example)

[blazing thunder]

just 2 lines going down the side

[pale kestrel]

no

what youve drawn there is

x = 1

and x = 4

[blazing thunder]

i am so confused

sorry

[pale kestrel]

try to draw y = k for some examples of k

[blazing thunder]

would it just be points?

[pale kestrel]

so draw y = -10, y = 2, y = 10

[blazing thunder]

and then i see a line form?

[pale kestrel]

lets say

points?

no, the equation y = -10 is going to be a straight line

[blazing thunder]

oh so was i meant to do a horizontal line at y = 2

[pale kestrel]

👌

where y = k and y = 4g(x) intersect

those are the solutions (or roots) of your equation k = 4g(x)

now you need to figure out which k give you 2 roots

[blazing thunder]

k > -8

because if its below -8 there are no roots

if it = -8 one root

is that right?

[pale kestrel]

right

[blazing thunder]

😄

ok now for d...

hopefully it wont be as hard

idk how i got stuck on something like this lol

[pale kestrel]

the question tells you the y axis is an asymptote

[blazing thunder]

ohhh

[pale kestrel]

in terms of gradient, what does that mean for the curve

[blazing thunder]

is it just upside down for the sketch

it never touches y i think

even on g'(x)\

[pale kestrel]

uhh

if you mean the y-axis, thats right

there is nothing on the left hand aide of the graph for the gradient

[blazing thunder]

Yeah

[pale kestrel]

an asymptote means the slope goes to infinity (plus or minus)

so with that in mind, figure out how the graph of the g' starts

[blazing thunder]

would i get a cubic sort of look

[pale kestrel]

let me see

wouldnt call it cubic

[blazing thunder]

well yeah one side is more stretched

[pale kestrel]

i think all theyre looking for

is that the curve goes to minus infinity

asymptotically at the y axis like youve done

and it passes through 2, 0

like youve done

after that, it goes to positive infinity

You didnt have to change the direction of the curve after it goes above the x axis

so it didnt have to look like a cubic

[blazing thunder]

but the rate of the gradient increasing increases

anyway

thanks for helping me shuri

very much appreciated

[pale kestrel]

👌

[blazing thunder]

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[alpine zephyr]

how m i supposed to solve this?

[charred osprey]

take your calculate find the value of x by solving x2 + x +1 = 0

then just replace the x

in (x2 + 1/x2)2

[alpine zephyr]

i cant
look it has no real solutions

[charred osprey]

oh

i didn't see it lol

:))

[wispy matrix]

since the left handed side is always positive, the statement is false for any value of x. so, i think its 0

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[lone heart]

@violet lichen Has your question been resolved?

[pale kestrel]

What defn of compact are you given

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[misty bobcat]

does function have inverse if is increasing (not strictly increasing ) ?

[violet lichen]

.reopen

[violet lichen]

Every open cover contains a finite open cover or equivalently we need to show that M is bounded and closed, since it's a subset of R.

[misty bobcat]

.close

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[misty bobcat]

.reopen

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✅

[misty bobcat]

.close

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[alpine sable]

tried doing lots of stuff

dont really know what else to do

[lone heart]

@alpine sable Has your question been resolved?

[pale kestrel]

can u share a picture

[velvet sapphire]

I think it is looks like this

[pale kestrel]

I think I know this from origami 😂

[velvet sapphire]

Lol😂

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@alpine sable Has your question been resolved?

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@alpine sable Has your question been resolved?

[royal meadow]

clearly:

1. A+B+C+D+E+F = LW
2. A+D = LW/4
3. C+F = LW/4

and then
4. B+E = (A+B+C+D+E+F) - (A+D) - (C+F) = LW - LW/4 - LW/4 = LW/2

also:
5: A+B+C = LW/2
6: D+E+F = LW/2

less obviously, however, A+B is similar to F. the vertical base of A+B is twice that of F, so the horizontal length of A+B is twice that of F.

but the horizontal length of A+B plus the horizontal length of F is just L, so horizontal length of A+B = (2/3)L, horizontal length of F = L/3

then:
A+B+F = 1/2 * (W) * (2L/3) + 1/2 * (W/2) * (L/3) = LW/3 + LW/12 = (5/12)LW

ie.
7. A+B+F = (5/12)LW

but:
5. A+B+C = (1/2)LW

combining [5] and [7] gives:
8. C-F = (1/12)LW

now we combine [8] with [3]:
3. C+F = (1/4)LW

to get:
9. 2C = (1/3)LW, ie. C = (1/6)LW
10. 2F = (1/6)LW. ie. F = (1/12)LW

we can repeat this entire process by noting, similarly to [7], that:
11. B+C+D = (5/12)LW

combine with [6]:
6. A+B+C = (1/2)LW

and
12. A-D = (1/12)LW

combining with [2]:
2. A+D = (1/4)LW

and we see again
13. 2A = (1/3)LW, ie. A = (1/6)LW
14. 2F = (1/6)LW, ie. F = (1/12)LW

now we just use [9], [13] and [5] again:
5. A+B+C = (1/2)LW
9. C = (1/6)LW
13. A = (1/6)LW

to see finally:
15. B = (1/6)LW

so:
16. A = B = C = (1/6)LW

now, view A, B and C's bases as being the sides of them that are on the diagonal of the rectangle. they all have the same perpendicular height from this diagonal to the bottom-left corner.

but if they all have the same areas, and they all have the same perpendicular heights, then they must have the same base lengths. so the three sides on the diagonal of the rectangle are equal.

_ _
fun problem

[alpine sable]

Woah

Did you do this with areas??

Whaaaaaaaaaa

It was meant to be a vector problem I believe

I'll check this out shortly thanks

[pale kestrel]

wow

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[inner sequoia]

how do i simplify this

[pliant zephyr]

75/3=25

[inner sequoia]

this is wht i got

[pliant zephyr]

sqrt(25)=5

[inner sequoia]

wtf shit ur right

[pliant zephyr]

noice

[raw shard]

sqrt(xy/z) = sqrt(x)sqrt(y)/sqrt(z)

[inner sequoia]

yeah

[inner sequoia]

what did i do wrong here

[pliant zephyr]

ig u didn't do 75/3

[raw shard]

well you certainly shouldn’t have an x with a positive exponent at the end

assuming the very bottom of that page is your final answer

[inner sequoia]

yeah

[inner sequoia]

i redid it, what do i do from here

[pliant zephyr]

yeah am getting the same

[inner sequoia]

bruh

.close

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[warped phoenix]

how is "the function is of at least degree: 2" incorrect?

there are 2 zeroes, so shouldnt the degree be 2?

[jagged imp]

a function of degree 2 will always have exactly one vertex/turning point, and the graph shown has 3

[warped phoenix]

im still not sure what it would be

[jagged imp]

The strongest constraint on the graph is that it has 3 turning points. A function with n turning points has degree at least n+1. The other thing you may have to consider is that the end behaviour shows that the function must have even degree.

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[alpine sable]

What's 9+10?so sorry oh gosh bad attention I hate this aaaa

[jagged imp]

good one !

[echo socket]

No trolling please

[fathom mantle]

what

[alpine sable]

Am sorry

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[raw shard]

please immediately close the channels when you see stupid stuff like this being asked

i’m minimodding i know you don’t have to say it

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[misty bobcat]

how to prove this using differentation ?

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[potent stream]

it’s not in English so I can’t rlly help u

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[earnest osprey]

I forgot how to solve ratios and rate

[earnest osprey]

can someone help me

nvm

.close

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.reopen

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✅

[earnest osprey]

nvm I need help 🤩🤩

nvm I don't need any help now.

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[rancid karma]

Hello i need help with a qyestion

[noble sinew]

have you tried anything?

[rancid karma]

no i am new to this

[noble sinew]

do you understand what it is asking?

[rancid karma]

probability theory if I'm correct???

[noble sinew]

do you understand what it is asking?

what exactly is it asking for?

[rancid karma]

No not really

[noble sinew]

so its asking given we observed a 6 what is the highest x can be such that the prob we threw with one of the weighted dices is over 50%

[rancid karma]

okay

[noble sinew]

so its conditional probability, so using bayes theorem for example is probably a good idea

and then you need to solve an equation

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[rancid karma]

okay thx

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[peak knoll]

hi i am currently stuck on a min cut max flow problem
the min cut of this graph is clearly 9 (a, b), (b, d) (d, t)
and yet the max flow answer given is 7
i know that the min cut capacity is equal to the max flow
am i misunderstanding something?

<@&286206848099549185>

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@peak knoll Has your question been resolved?

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@peak knoll Has your question been resolved?

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@peak knoll Has your question been resolved?

[primal berry]

You were probably waiting for someone to finally come around and answer your min-cut max-flow issue
From the graph that you've sent the min cut is actually 8 from what I've gathered.
Looking at (a,b) you get a flow of 1
Looking at (a,d) you get a flow of 4
Looking at (c,d) you get a flor of 3
But the max flow is indeed 7 simply because of the edge (c,d)
As if you push 5 units of flow through (s,c) then you get a problem. (c,d) is the only edge that can acompany any flow and even then it can only take 3 units.
(s,a) can take all 4 units of flow and send 1 unit across edge (a,b) and then 3 units across edge (a,d)
Finally resulting in a flow of 1 along edge (b,t) and 6 across edge (d,t)

Hopefully that's helpful

[primal berry]

@peak knoll, Was this helpful?

[peak knoll]

yeah thanks i simply didnt see the actual min cut which is (s, c) and (a, b, d, t)

i asked my ta after a long day so its been resolved

thanks for the help

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[stray mesa]

yo this is kind of easy i just want to verify

[stray mesa]

i have a batch of 6 parts in which 3 are defective and 3 are non-defective

how many different samples can i have with 3 parts

and how many of these samples have exactly 3 non-defective parts

and how many of these samples have atleast one non-defective part

[stray mesa]

i found 8 for this one

[stray mesa]

1 for this

[stray mesa]

and 7 for this one

[wintry lotus]

Not sure "8" is the answer for the first one. Does order matter?

[rocky atlas]

I don't think so

It only asks for how many he can "have" not the arrangements

Plus it didn't add "in how many ways"

Usually order related questions come in that format

[wintry lotus]

Good point. I believe that for the first question, the answer would be "4" then

[alpine sable]

Hello,
Can we encode memory spaces with quantum calculations that would allow us to know with certainty in which memory space the series of natural numbers are stored?
I would like to do it to 1 to 10.

[rocky atlas]

You need to create new channel for asking question

[alpine sable]

Sorry

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[bleak ridge]

Do you know how to set up any of the formulas

From the context of the problem

Well say x is parts per hour before

And y is parts per hour after

What's the first thing you could write

Based on the first piece of information they give

[pale kestrel]

The approach is to pick some unknowns in the question

and call them something

like x, y

and form information from there

[bleak ridge]

So y=x+6 is your first one yes

The second one is a bit more involved but

[summer sail]

0.2*x=6

[bleak ridge]

I'm not sure

What I had in mind was something else

[summer sail]

Yes just solve it

[pale kestrel]

stop trolling

[bleak ridge]

If you produced parts for 5 hours with 3 parts per hour how many parts would you make?

[summer sail]

0.2 *x = 6 |*5
x = 30

[bleak ridge]

Yeah

[summer sail]

There you go

[bleak ridge]

The point is also not to give the answer away

And the second part of the formula

If something's 120% higher how do you write that

Well not 120% higher

But 120% of the old value, 20% higher

Yeah pretty much

You just multiply by 1.2

So putting both of those things together how would you write a second equation using the second set of info they give

How would you write the amount of parts they produced before in 8 hours in terms of x

[summer sail]

Oh shit my bad its 30/8

[bleak ridge]

Thinking back to the 3*5 example

8 hours in this case

Cause it was before the new tech

And how about the new?

Yeah exactly

Ye

And that's 120% higher

How do you write that

Other way

[summer sail]

Im not joking it should be correct

[bleak ridge]

8x * 1.2

[summer sail]

Parts produced per hoir before rhe new tech right ?

That was the question

[bleak ridge]

Cause the 6y is 120% higher than the 8x

The 8x isn't 120% higher than the 6y

What's it equal to

I mean the 6y

Yes

[summer sail]

They produce 6 parts per hour. After 6 jours they reached 120% of their previous production. 6*6 =36 = 120%
100% = 30
30/8 = parts per hour before switching to the new technology therefore the awnser is 3.75

Why ???

[bleak ridge]

Try solving the system

Ye

Si

[lone heart]

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[bleak ridge]

[lone heart]

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[clever tapir]

<@&286206848099549185>

[hearty frost]

So

It makes one rotation every 24 minutes

How much does it travel in 24 min then

I mean

What does it imply to do one rotation

Of a circle

[hearty frost]

Do you know distance traveled in one rotation of a circle?

[lone heart]

@clever tapir Has your question been resolved?

[clever tapir]

is that circumfrance

[hearty frost]

Yes

So find the circumference

[lone heart]

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[peak cloud]

Can someone help me with this topic?

About laws of indices.

[peak cloud]

I wanted to ask that if the root is on 4 divided by 2 then it's on 2⁰ as well so we'll have to mulitiply 2⁰ with 1/2.

[peak cloud]

Except that is not what is happening here.

[pale kestrel]

rewrite root as 'to the power of a half'

and any fractions

as to the power of -1

so $\frac{a}{b} = ab^{-1}$

$\sqrt{a} = a^{\frac{1}{2}}$

[ocean seal]

Shuri2060

[peak cloud]

I don't really get it lol.Can you simplify it somewhat?

[pale kestrel]

what part

[thorny patio]

That does happen in that example

2^(0*1/2) = 2^0 = 1

Oh wait

You start with

2

Not 2^0

In that example you can simplify inside that fraction

Before using the exponent properties

Simplifying first will usually clean things up for the final answer

[peak cloud]

Ok.And also I wanted to ask that this will be solved with law 5 right?

[thorny patio]

Yes it would be

[lone heart]

@peak cloud Has your question been resolved?

[lone heart]

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[nocturne gazelle]

How come Z_+ and Z_0>=0 have the same cardinality

[nocturne gazelle]

arent they defined

1,2,3...

and

0,1,2,3....

so wont we have one more element in Z_0>=0

so it cant be one-t-one

[ancient saddle]

They are infinite sets, so we can't say that one set has one more element than the other. These two sets have the same cardinality because you can find a one-to-one relation between them

[nocturne gazelle]

so what is an example wheere there isnt a one-to=one

of an infinite set

@ancient saddle

[ancient saddle]

Integers and real numbers. There are many videos on youtube about the cardinality of the real numbers, it's a very interesting topic

[nocturne gazelle]

what about rationals and integers

shouldnt they have diff cardinalities too

[noble sinew]

Its the same reason

You can construct a bijective function so they have the same cardinality

[wary gale]

lmao im in grade 8 and they gave me a decimal review

[next basalt]

decimals ez

u take advanced

[lone heart]

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[alpine sable]

How did he get -sqrt2 from -8?

[glass lichen]

they didnt

x^2=2 iff x=+-sqrt(2)

x^2=-8 has no solutions in R

[alpine sable]

Ah nvm, it looked like because it's below it

[lone heart]

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[charred heron]

ive got an answer but it says its wrong

ive checked it multiple ways and all the values work out

.close

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[valid pecan]

Guys

[valid pecan]

Sorry sami

[deep rain]

😄

[valid pecan]

How to solve this

How am i supposed to find the value of n?

Or x

[lone heart]

@valid pecan Has your question been resolved?

[valid pecan]

.close

[lone heart]

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[remote heron]

did you get it?

[valid pecan]

no

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[remote heron]

i think i can help

[remote heron]

if you want

[valid pecan]

yes

how do you solve

[remote heron]

try writing $8^n = 2^{3n}$

[ocean seal]

jan Niku

[remote heron]

see if you can find a similar way to rewrite $20^n = $?

it leaves you with a common factor

[valid pecan]

what is this

oh

2^3 is 8

[remote heron]

like what are the prime factors of 20

yea

$20 = 2 ^2 \cdot 5$, yea?

[ocean seal]

jan Niku

[valid pecan]

yes

[remote heron]

so $20^n = 2^{2n} \cdot 5^n$

[ocean seal]

jan Niku

[remote heron]

then we have $\frac{ 2^{3n} + 2^n }{ 2^{2n}5^n + 5^n }$

[ocean seal]

jan Niku

[remote heron]

looks ripe for factorin

[valid pecan]

oh

then i can make n root of the equation?

[remote heron]

no

factor

[valid pecan]

after factorizing

[remote heron]

oh

yea

what do you get

[valid pecan]

oh

[remote heron]

it shouldnt be necessary

[valid pecan]

lemme calculate

it

[remote heron]

should be solveable by inspection

it simplifies greatly

x should be rational

[valid pecan]

x = 0.4?

[remote heron]

yea

[valid pecan]

thxxx

[remote heron]

ezpz 😄

.close

[lone heart]

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[valid pecan]

👍

i am go solve it on paper and submit

[pale kestrel]

@valid pecan u need to consider if n = 0

[remote heron]

o

.reopen

[lone heart]

✅

[remote heron]

true

is it special