help-49

[broken anchor]

Yeah the smaller exponent is negligible

[gusty trellis]

it is negligible only in the case of dividing right ?

negligible to the other one

[broken anchor]

Well dividing is when you'd need something like this

If a term is going to 0 then that only causes problems if it's being divided by another term that goes to 0

For limits that is

[midnight plank]

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[frank grotto]

I need help doing a transformation for a linear function. The problem is f(x) = 1/2x ; it wants a reflection across the x axis, to be translated down 4 units and left 6 units

[frank grotto]

I am mainly stuck on the part where I have to translate it horizontally

[wanton belfry]

to shift the graph to the right you change the input from x to x-a to shift a units

and x+a to shift a units to the left

[frank grotto]

So if I were to do g(x) = (-1/2x+6)-4 would that be correct based on what the problem wants?

[wanton belfry]

can you use less ambiguous notation lol

be careful with the parentheses

[frank grotto]

Yeah I think I’m still lost

Wait no I’m not

I think I got it now thanks!

.close

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[proper wadi]

https://cdn.discordapp.com/attachments/813800596116471839/1036317309096165516/unknown.png

[proper wadi]

im stuck on this question

this is what ive done so far

[tardy zephyr]

Surface area is the added up area of all the faces

[proper wadi]

yeh ik that

1500= h * x^2

SA = x^2 +4hx

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[candid sail]

OK so my problem here is that I have to show thhe equation above equals the equation below by integrating by parts

Because it has to work with all values of n i examine it with n=2
Now I got to the part where my equation is
int ln^2(x) = x(lnx)^2 - 2* int (lnx)

posting an image please wait

where did i go wrong, that should equate to 1 if In = (formula)

[midnight plank]

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@candid sail Has your question been resolved?

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@candid sail Has your question been resolved?

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@candid sail Has your question been resolved?

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[ebon nest]

b

[frank marsh]

I might be mistaken but i dont believe that is the amplitude

huh

Interesting

Oh i see nvm

No idea the answer t your q tho sry

[midnight plank]

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[jade flicker]

Can someone help me with these questions

[brittle rampart]

is there more to this?

like an image

[mild lagoon]

send the entire image

[tropic nexus]

just conservation of mechanical energy?

with 1/2kx^2 for E_spring

[midnight plank]

@jade flicker Has your question been resolved?

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[coarse ruin]

How to solve this problem
What is the scalar product, in meters, of A.B if the magnitudes of A = 20m and B = 15m? The angle between the two vectors is 75*

[brittle rampart]

$a\cdot b = |a||b|\cos(\theta)$

[grand pond]

maximo

[coarse ruin]

so should I multiply 20 and 15?

[brittle rampart]

and multiply by cos(75)

[coarse ruin]

oh wait lemme try to solve it

is it 77.645?

Am I correct sir?

[brittle rampart]

meters, yes

[coarse ruin]

okay thank you

.close

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[coarse ruin]

.reopen

[midnight plank]

✅

[coarse ruin]

Now i am confused

What is the magnitude of the vector product B x A if the similar values from Item no.3 (A = 20m and B= 15m) are given? The angle between the two vector is 75*

[brittle rampart]

$|a\times b| = |a||b|\sin(\theta)$

[grand pond]

maximo

[coarse ruin]

so its sin now not cos?

[brittle rampart]

the magnitude of the cross product uses sin, yes

[coarse ruin]

so is it 20m x 15m sin 75?

i get 289.777 and its not in the choices

[brittle rampart]

can you send a picture of the question?

[spiral monolith]

Round

[coarse ruin]

ohh so I need to round it up

thank you very much

.close

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[last slate]

can someone help me, is it JI = IU

[velvet oar]

yep

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[last slate]

These are not congruent right? Because there is not enough information given. Only an angle and 1 side.

[frank creek]

Right. Those triangles aren't neccesarily congruents

You would need more info such as if the top is parallel to the bottom

Or another angle

But that isn't the case

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[neon locust]

Is one of these answers wrong? Why do both end with - c even though one has + c and the other has - c?

[last slate]

because c-b^2/4a<0

https://www.mathsisfun.com/algebra/completing-square.html

[neon locust]

im familiar with (-b ± √b^2 - 4ac) / 2a, is c-b^2/4a another form of that

[last slate]

probably

oh wait

you said the quadratic formula lol

its related

but we dont have to go that far

c-b^2/4a is the left over term after completing the square

[last slate]

see the derivation here

[neon locust]

does that mean c will always be negative?

[last slate]

no

its has the opposite sign to the discriminant

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[flint bane]

can someone help me please?

[midnight plank]

@flint bane Has your question been resolved?

[flint bane]

yes

please

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[placid badge]

how do i get started on this question?

[placid badge]

well i would derive them but what then

[velvet compass]

think about slope

[placid badge]

2

[velvet compass]

slope is f'(1) and it need to be 2

[placid badge]

oh so once i derive the equation, i need to see if f'(1) is 2

[velvet compass]

ye

[placid badge]

ok ok thanks

when i derive c and d and do f'(1) i get a different number

is it cuz i derived wrong

c would be 4(1/2root(f(x)) - 3 right

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[unique radish]

Hint: Use the quadratic formula.

[midnight plank]

@sleek niche Has your question been resolved?

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[sleek niche]

.reopen

[midnight plank]

✅

[sleek niche]

i meant to click no

it hasnt been resolved

[fallow scarab]

did you use the quadratic formula yet?

[sleek niche]

i just need the answer

i dont care how its done just need the answer

respectfully

sorry if that comes off as rude

[last slate]

https://www.wolframalpha.com/

[sleek cloud]

#help-9

Close one

[sleek niche]

close 9

[sleek cloud]

Go there and type ".close"

[sleek niche]

i still need help with my question 😔

i cant find the answer

[sleek cloud]

But you have multiple channels open

[sleek niche]

i legit closed 9?

[sleek cloud]

Which violates the rules and can get you banned

Good

Also asking for direct answers is forbidden

Respectfully, this is not the right place

My recommendation: go to the Symbolab website

And type your equation

[fallow scarab]

go pay for a tutor if you want an answer. help channels aren't for giving away answers

[sleek niche]

.close

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[versed ermine]

Can someone help me with this? I need help with the equation.

[midnight plank]

@versed ermine Has your question been resolved?

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[old sapphire]

Is the following relation reflexive?
R1 = {(a, b), (a, c), (a, a), (b, a), (c, a)}
And
A = {a,b,c,d}
its not right? because it's missing (b,b) and (c,c)?

[old sapphire]

This is discrete math related

[visual tiger]

And (d,d) as well

But yes it isn't reflexive !

[old sapphire]

Awesome, thanks, I was just clarifying because when it comes to relations, it would make sense if (a,b) and (b,a) somehow made 'a' relate to itself.

.close

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[velvet compass]

by factor theorem you have f(3) = 0

[last slate]

^ just do the long algebra and solve for m

[earnest dagger]

10(0)^3-39(0)^2+m(0)+30 like this?

[velvet compass]

why x = 0 there

[earnest dagger]

bc you said f(3)=0

[velvet compass]

it means its value is 0 when x is 3

[earnest dagger]

oh ok

maybe its the wording of the question bc im still stuck

[midnight plank]

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@earnest dagger Has your question been resolved?

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[river night]

yalls

yo boy needs help

i dont know how

i need a step by step

way

to get it

[terse zephyr]

u see how Y is always 3 times bigger than X

[river night]

yes

OH

thats what it means?

[terse zephyr]

This means the rate of change is 3

[river night]

this was an easy one btw

lemme show you the ones

idk

[terse zephyr]

And since this is true for every X and Y it is also linear

[river night]

wait

then is it linear?

idk what linear and non linear is

could you explain

[terse zephyr]

linear is that it increases with the same every time

so every Y in that table is 3 times bigger than X

[ebon nest]

if the difference between each value for every increase in x is the same its linear

[terse spear]

Linear rate of change is when between every x, it changes by the same value and between every y it changes by the same value

[river night]

ok si si

lemme get another problem

ok

dont mind the lines

i made

ok can someone explain thos

[ebon nest]

what is the difference between each y term

[river night]

is it 2

[ebon nest]

you need to look at all of them

[river night]

oki

[ebon nest]

and then look at the differences in the x values

[river night]

ok

so i got

y
-2
-8
-2
-8

what does this mean?

[ebon nest]

ok so what are hte differences in the x values

[river night]

ok let me do

x
+3
+12
+3
+12

now whats

[ebon nest]

ok so if the x values increased at the same rate

so like +3 +3 +3 +3

and y values where -2 8 -2 8 would it be linear or non-linear ?

[river night]

non linear

[ebon nest]

no....

[ebon nest]

^

[river night]

ok ok

so

something linear would be like 2+2+2 x

and y 4+4+4

[ebon nest]

something linear would be

x: 1,2,3,4

y: 3,5,7,9

because the y values increase by the same value, +2

[river night]

ohhh

[ebon nest]

something like

x: 1,2,3,4

[river night]

am gets

[ebon nest]

y: 1, 1034, 1, 348, 2

would not be linear

because the y values dont increase by the same value

[ebon nest]

here the y values dont increase by the same value BUT the x values arent 1,2,3,4

they change so you need to do some more math to tell

[river night]

so how do i know fond the rate of change

[ebon nest]

have you done rate of change = change in y / change in x?

[river night]

no

is it like

x/y

[ebon nest]

well what have u learnt in class

no its y2 - y1 / x2 - x1

[river night]

that we divide y by x

[ebon nest]

no

its change in y divided by chagne in x

not y/x

[river night]

yah i mean that

[ebon nest]

what have u done in ur class?

[river night]

idk man

been absent

[ebon nest]

oh

[river night]

thats why am in need of help

buy we just got in this unit

so were in the beginning

[ebon nest]

so we can call
3 = y1
-9 = x1

5 = y2
-12 = x2

[terse spear]

Maybe looking at the material you missed helps

[river night]

ok

can you simplify

like

i still dont know the rate of change

cus my teacher ik she said

you divide something by something

[terse spear]

Yes that's valid too

[river night]

but what do i divide?

[terse spear]

One of the values by the previous one

[river night]

OHH

OHHH

[terse spear]

And if all of them result in the same value, it has the same rate of change

[river night]

that makes sense

lemme do it

and see if i get it right

[river night]

like the difference?

or just the value

[terse spear]

The values in the table

[river night]

oh

so

x=-12
y=5

how do i divide that

[terse spear]

Consecutive x values

[river night]

oh

what

[terse spear]

Not division between x and y values

[river night]

like

-12 to -9

[terse spear]

Take some x value from that table, divide it by the x value previous

[river night]

can you do that

so i can see

[terse spear]

No

[river night]

why bro

[terse spear]

I told you what to do

Take some x value from that table, divide it by the x value previous

What's one of the x values?

[river night]

-12

and then what

[terse spear]

Does that have another x value previous to it?

[river night]

oh

can i do

3

no

6

and 3

[terse spear]

If you did 6, what's the x value previous?

[river night]

3

[terse spear]

Then apply this

Take some x value from that table, divide it by the x value previous

[river night]

ok

[terse spear]

And you do that process for all of the x values

Then apply that to the y values

[river night]

so

3 divided

-9

[terse spear]

Yes

[river night]

and then repeat it?

[terse spear]

Yes

[river night]

ok i confused

what should i do now

like

[terse spear]

And if the division answer is all the same when you do that to all the x values, it has the same rate of change for x

Then you apply it to the y values

[river night]

would rate of change be 3

[terse spear]

What's 3/-9?

What?

[river night]

o.3

[terse spear]

What is that in simplified fraction form?

[river night]

9 divide$ by 3

i think you ragged

ima go ask my teacher

tomorrow when i come back

she gotta deal with it

at leasts she gets paid for doing so

lol

[midnight plank]

@river night Has your question been resolved?

[river night]

yes

[midnight plank]

@river night Has your question been resolved?

[midnight plank]

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[fierce mesa]

on #7, i don’t understand what it’s asking us to do

[fierce mesa]

you would think that it’s just asking you to multiply the outputs you get for both functions when the input is 1

so for a) it should be 3•0 right?

but in the back of the book the answer is 1

and i’m really confused on how they got that

con someone help pls

[last slate]

okay okay @fierce mesa

so are you familiar with **composition **

[fierce mesa]

?

[last slate]

function composition

what this symbol ∘ means

[fierce mesa]

ohh

yeah

[last slate]

okay, so you know how a function is basically just like a machine, kind of

or more analogously, think of it as your keyboard

[fierce mesa]

yeah

[last slate]

you press a button on your keyboard (input) and it prints out something on your screen (output)

[fierce mesa]

yeah

[last slate]

so it kind of goes like this x (input) ----> function ------> f(x) (output)

with composition, imagine if the process went through multiple "machines" if that makes sense

so

[fierce mesa]

i think i get it

it would be a new function altogether right

like h(x)?

[last slate]

x (input) ----> function of x ------> f(x) (output of x) ------> function of f(x) ------> g(f(x)) (output of f(x)

if that makes sense

[fierce mesa]

yeah it does

[last slate]

its like imagine the f(x) as the x you are started with

but you are kind of adding it to a new function

[fierce mesa]

mhm

[last slate]

yeah, so knowing that, let's go back to your question

[last slate]

lets start with number 1

we have f(g(1)), with x = 1

[fierce mesa]

a)?

[last slate]

yes, apologies

[fierce mesa]

nw

[last slate]

so 1 is our first 'input', we send it through our fancy machine for g to give us g(1)

[fierce mesa]

alr

[last slate]

we notice how when x = 1, our fancy machine converts it to a 0

so g(1) is actually equal to 0

but now, we have to find f(g(1))

but what did we get g(1) as? @fierce mesa

[fierce mesa]

sorry i’m back

[last slate]

its fine!

[fierce mesa]

0

[last slate]

yeah

so what is f(g(1)) really if g(1) = 0?

[fierce mesa]

so it would just 0

[last slate]

0 of?

[fierce mesa]

3•0?

[last slate]

no! there is no multiplication in this

[fierce mesa]

😭

[last slate]

remember this is just composition, we are just inputting inputs into functions

[last slate]

remember this

[fierce mesa]

f(0)?

[last slate]

yes!

exactly!

[fierce mesa]

oh

[last slate]

so what is f(0) in the picture?

it is when x = 0

[fierce mesa]

-1?

[last slate]

yep!

[fierce mesa]

ohhhh

[last slate]

so overall, f(g(1)) = -1

can you do part b for me now?

[fierce mesa]

THTA MAKES SO MUCH SENSE

[last slate]

yepp!

its like, we are basically sending the stuff through a lot of processing machines, and turning them into different stuff

[fierce mesa]

(f•g)(-1)
g(x)=0
f(0)=-1

?

[last slate]

we can have something like t(r(y(i(u(k(h(j(g(f(x))))))) going through multiple (you won't see something like that ever dont worry haha)

[fierce mesa]

lol yeah

[last slate]

yeppie!

[fierce mesa]

YAYY

thank you so much for your help

[last slate]

you get it. Good job!!

[fierce mesa]

c:

[last slate]

of course, ask away if there is any more questions/confusion

[fierce mesa]

i think i’m good for now, but i will def come back if i have anymore questions

thank you so much again!!

[last slate]

sounds good to me! Good luck with your studies 😊

[fierce mesa]

thank you :))

have a great rest of your day/night!!

[midnight plank]

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[cyan nymph]

hello I do not understand b I know that you have to plug in the values into the formula I just don't understand plugging in part ig

[cyan nymph]

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[normal plover]

how do you state the domain for a question like this

[noble eagle]

is it not just $$xe\mathbb{R}$$

[normal plover]

how did u know ?

[grand pond]

Bestower

[normal plover]

or this one

Is there a trick im missing or something cause im so confused

They use number lines and everything and i just dont get it

[noble eagle]

because at the core it doesn't really matter

whether it has a x intercept or not

[normal plover]

oh

[noble eagle]

x^2 will always be Xer

[normal plover]

okay

So if it has one x intercept would you always do it like this for example

-12 < x < 12

and if it has two intercepts would u always do it like x < -4, x > 4

[river night]

k

[noble eagle]

so long as its x^2 there it will always be xer

regardless of its x intercepts

so long as theres no horizontal reflection or transformation

[normal plover]

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[finite sphinx]

.reopen

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✅

[finite sphinx]

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[kind zealot]

<@&268886789983436800> this guy is reopening all channels making it look like they are all occupied

[finite sphinx]

a test 🤦‍♂️

[analog vine]

please dont "test" things

and also stop closing other peoples' channels "Due to inactiveness"

the bot will do it automatically

its like youre more interested in being a procedural heckler than in actually helping

[analog vine]

fyi your "test" was quite disruptive, there are now no more available channels.

[finite sphinx]

wont it go back

[analog vine]

yes, but you aren't so important that the rest of the server should collectively move aside to satisfy your "tests"

[finite sphinx]

oh ok

my bad

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[prime crystal]

Let θ : G → H be a group isomorphism. Then ord(θ(g)) = ord(g) for all g ∈ G.
how to show ord(θ(g)) = ord(g) ?

[midnight plank]

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[prime crystal]

<@&286206848099549185>

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[woeful ibex]

https://cdn.discordapp.com/attachments/903463355619110912/1037798709624316005/16675008698587824421353184085953.jpg

[woeful ibex]

How to solve number 1?

[dark kayak]

there are two approaches

the first one would be to solve it as a quadratic equation (which would be the long, but always working approach)

and the second one would be to recognize that you can factor out 5 and x

[pallid remnant]

try adding and subtracting 25 * 5
then factor 5 and solve the perfect square in the brackets

then diff of squares

with sqrt 5

if you really wanna

[dark kayak]

or just factor out 5x to get 5x * (x-10)

which is the factored form

[pallid remnant]

oh right

yeah i was too exited i didnt see that

[dark kayak]

5 * (x - 0) * (x - 10)

[pallid remnant]

😭

[dark kayak]

although the quadratic equation method always works

[pallid remnant]

they ask for the discrmininant if factoring doesnt work so i guess they wanted the quadratic method as a fall back method

[woeful ibex]

I gtg but thz

@woeful ibex

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[graceful siren]

how do i find the minimum value of a function

[graceful siren]

i use c - (b^2/4a) but i don’t understand this method

and where tey got 2x-6 from

[dull yoke]

Do u know what it means to take the derivative of a function

Calculus

[graceful siren]

i’ve studied derivatives yes but this is supposed to be basic algebra

[dull yoke]

Well that’s how they got the min

[graceful siren]

oh

[dull yoke]

They found the derivative and set = 0 to find the critical value, which is where the min is

[graceful siren]

o

okay thank you🙏

[dull yoke]

Np

[graceful siren]

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[sleek cloud]

ABC and DEC are similar?

Circle theorem

Are you given any other info? The question is asking to find the area of DEC right?

Can you post the original question just in case?

Can't seem to find the solution

I can't find a way

So far I know that ratio of the sides between the triangles is 2/5 and ratio of areas is 4/25 but that's all I got

[midnight plank]

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[drifting mesa]

how would i go about solving this?

[charred onyx]

Did you try something ?

@drifting mesa

[drifting mesa]

i tried this, but i don’t think i achieved anything by it.

[charred onyx]

wow how do you get rid of the modulus ? @drifting mesa

I think it's wrong

Do you know that | a+ib | = sqrt(a^2 + b^2) ?

[drifting mesa]

nah, surprisingly we have never learnt how to do this algebra.

[charred onyx]

never ?

[drifting mesa]

never

[charred onyx]

that's weird

did you do the complex plane ?

[drifting mesa]

yep

funnily enough, a question like this hasnt come up lol

[charred onyx]

well basically for z a complex number, | z | is the distance from point z to the origin of the axis

[drifting mesa]

yep

[charred onyx]

So you can use the pythagorean theorem

| z | = sqrt( Re(z)^2 + Im(z)^2 )

Got this ?

[drifting mesa]

yep

[charred onyx]

So in your case

Let z = x + iy

and then, | x+yi -9i | = sqrt(x^2 + (y-9)^2 )

...

do this on the right hand side

you'll get an equation between x and y

Maybe it'll look like a circle equation

[drifting mesa]

would this be correct?

just need to tidy up after

[charred onyx]

yep i think so

[drifting mesa]

okay, cheers mate 👍

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[edgy parrot]

Can someone tell me what's wrong with this answer? ("Appoint each nodes their degree. Write the answer as a set of pairs ["N", deg("N")]")

[midnight plank]

@edgy parrot Has your question been resolved?

[wet pollen]

@edgy parrot I would ask your teacher. It is an undirected graph so everything appears correct to me. It may be the formatting. 🤷‍♂️

[midnight plank]

@edgy parrot Has your question been resolved?

[edgy parrot]

So it's actually correct then?

[wet pollen]

It would appear so to me. As I said, you should ask your teacher for clarification.

[edgy parrot]

Oh I just forgot the quotation marks nvm

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[sweet niche]

can I have help for you or might not be that hard but I don’t get it I’m only in 7th

[sweet niche]

I’m lost on this

[pallid remnant]

the area of a triangle is?
(base * height)/2

[sweet niche]

yea but I’m trying to find h

[pallid remnant]

its dotted

its outside the triangoe

triangle

[sweet niche]

I tried this stuff before on a different one and it didn’t work

but ok

[pallid remnant]

12 + 8 = 20 cm
(20 × 12) / 2 = 120 cm²

[sweet niche]

thank you 🙏🏽

[pallid remnant]

no problem

[sweet niche]

I got another theres no way, I never struggle this bad

[pallid remnant]

do the 2 areas separately

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[floral apex]

Im just trying to make progress on the first part

it doesnt seem like theres anything to be done in the transform?

we have no idea what u is so its not clear how you can apply anything

this is the result from 1 but it doesnt seem helpful

[midnight plank]

@floral apex Has your question been resolved?

[open hatch]

What's 1DHE

[floral apex]

one dimensional heat equation

sorry, i could have included that

[open hatch]

Can you show the equation

[floral apex]

sure

$\pdv[2]{u}{x} = \frac 1 k \pdv{u}{t}$

[grand pond]

jan Niku

[floral apex]

.

[open hatch]

Take the ft of both sides?

[open hatch]

Use the ft of a derivative

[floral apex]

trying to do that now

you do mean like $\mathscr F {u _{xx} }$ right

[grand pond]

jan Niku

[open hatch]

Yes

[floral apex]

okay, i will try to figure it out

it doesnt really make sense though like

im assuming you do ipb?

but the evaluation doesnt seem to work out

[open hatch]

You could start with single derivatives first

[floral apex]

like $\int _{-\infty} ^\infty \pdv[2]{u}{x} e^{ikx} \dd x = e^{ikx} \pdv{u}{x} \bigg\vert _{-\infty} ^\infty - ik \int _{-\infty} ^\infty \pdv{u}{x} e^{ikx} \dd x$

[open hatch]

I think you would have to handle derivatives wrt x and t differently

[grand pond]

jan Niku

[floral apex]

or maybe this is not how it works

[floral apex]

i guess i can figure out t when i get to that side

[floral apex]

i mean the t partial just comes out right?

if youre transforming in the x

its the x partials that are in the way

[open hatch]

Yea

[floral apex]

since this is an exponential with imaginary parrt you cant say anything about its behavior at infinity right

do you assume you know something about u at infinity?

[open hatch]

Probably, I haven't studied ft's rigorously

I think what you did is fine tho

[floral apex]

you cannot progress from where i am though

[open hatch]

You can do the same thing again

To get it in terms of the ft of u

[floral apex]

i mean you cant do anything with that piece thats evaluated

[floral apex]

im not sure what you mean

[open hatch]

I think you just say that's 0

[open hatch]

For the new intrgral

Notice that the new integral is the ft of du/dx

[floral apex]

ah

i still have a lot of doubts about saying its 0

[open hatch]

The result you get tho is correct I'm p sure

I've seen it before

Taking the ft of a derivative basically multiplies the ft by ik (or -ik)

You should probably use K instead of k

[floral apex]

his suggestion is bad

but sure

[open hatch]

k already appears here

[floral apex]

i just changed it there

im still not sure i follow but

[floral apex]

can i ask just for guidance on uhh

piecing it together after the transform?

i think it turns your pde into

$\pdv t U(k,t) + k^2 c U(k,t) = 0$

[open hatch]

This is now a linear first order ODE

[grand pond]

jan Niku

[floral apex]

should be a plus

[floral apex]

we dont care about k?

[open hatch]

Yea there are no derivatives wrt k

[floral apex]

and we dont care the t is a partial?

[open hatch]

Doesn't really matter

[floral apex]

ah, okay

well i still have a lot of questions but at least i got the answer

thank you @open hatch

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[nimble copper]

,rotate ccw

[nimble copper]

[last slate]

How do I do this question

<@&286206848099549185>

[hot totem]

If you can, draw.

If you can't draw, describe your issue

describe your problem more to get more help

[last slate]

I don't know how to find C

This is what I did

[vague lantern]

okay sure

solve simultaneous

allow C(p,q)

substitute into its own line

and into line L

[last slate]

what do you mean by that?

[vague lantern]

okay so

let the coordinates

of C

be (p,q)

u found the eqn of the line

parallel to AB

yes?

so

[last slate]

Yes

[vague lantern]

u know C lies on that line

so u can plug the coordinates

of C

into that eqn

they also said

it intersects line L

at C

so point C

lies on line L as well

so plug C coords

into line L

after doing those steps

you’d have 2 equations

solve them simultaneously

[last slate]

But I don't know the coordinates of C

[vague lantern]

that’s why

we let C be (p,q)

we are going to solve

for p and Q

[last slate]

is this right?

[last slate]

.

[vague lantern]

yes sure :)

solve for x now

[last slate]

Ohh thank you

[vague lantern]

my pleasure

[last slate]

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[stray hawk]

Help

[fallow scarab]

didn't you get help already

or are you doing Q3

[midnight plank]

@stray hawk Has your question been resolved?

[stray hawk]

No I didn’t

All I was told was “graph”

[fallow scarab]

Oh your work was fine from what I saw

[stray hawk]

Then why she told me it wasn’t I needed to graph

Can u double check please before I submit

[fallow scarab]

no she didn't. she said your question asks for you to graph

which is correct, but not absolutely necessary.

hints are meant to help you if you're stuck

i can't see anything wrong with your work

[midnight plank]

@stray hawk Has your question been resolved?

[stray hawk]

So short it down right?

[fallow scarab]

Short?

[midnight plank]

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[frail jacinth]

help i dont understand any of this

[nova phoenix]

you have to make a "4-number" parallelogram (4 triangles in a row/column) such that you get the highest possible value

[frail jacinth]

ohh at least i understand kind of what it is its actually asking me to do now

[nova phoenix]

Here's a hint:
There are 3 "Directions" the parallelogram can go in:
Left leaning, right leaning and flat.
Theres only 4 "left-leaning" parallelograms (bottom - 20 to the 5 in the middle, bottom -7 to the top 6, bottom 18 to top -15, middle 10 to top 35)
Theres 9 right-leaning parallelograms (you count them) and 12 horizontal ones.
Method of exhaustion: do all 25 calculations and you can determine which is best

[frail jacinth]

alright tysm

this helped a lot

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[twin monolith]

i'm trying to figure out the simplest and naturally correct way to do some calculations for explaining videogame content.

the actual numbers are a bit more complicated but follow the same format

as an example, if you have a set of 10 marbles with 1 red and 1 blue with the rest black, what is the probability of 1 person drawing the red marble and putting it back and another drawing the blue marble if the red is given 2 draws and the blue 3 draws?

what I end up with is

10^5 permutations total

then I have

(1)(9) * (2 choose 1) * (1)(9)(9) * (3 choose 1)

(10)(10) * (10)(10)(10

[twin monolith]

in order to clarify, they're only drawn once each but whatever is drawn is put back in the pool

is this correct?

10 marbles, 1 blue, 1 red, put back after each draw
one person draws twice, the other three times
one gets the red, one gets the blue

and only once each

[next rover]

you;re saying they both have to draw 2 black as well?

[twin monolith]

example:
B X ; R X X

because it's no more than once

[next rover]

yes, but what about blue and red

[twin monolith]

basically, one person draws twice and draws a 1 in 10 chance of their 2 draws; the other draws 3 times and draws a different 1 in 10 chance

[next rover]

if i'm red, I'm allowed to draw black-red-black, that's clear, but am i allowed to draw blue-red-black, and am i allowed to draw red-red-black

[twin monolith]

yes

wait

in that example, no

[next rover]

yes, i;m allowed two draws, ignoring that

[twin monolith]

hmm, now i'm not sure. it's a reference to our conversation of 5 choose 2 and 24 choose 3 from the other day

[next rover]

i don;t remember it

[twin monolith]

ah, might've been someone else, just you're almost always the person to respond to me

I get confused because you have to switch between using permutations and using combinations

why? because
RX is the same as
XR in terms of the probability from 2 draws

so in the above equation, a 1 in 10 event then has 9 in 10 other events that can happen to fit the same result

great, now i'm wondering if you have to subtract the other marble from the 9 in order to exclude it

with would be
( 1 ) ( 8)

( 9 ) ( 9 )

still ends up multiplied by ( 2 choose 1 ) though

R = red X = filler

for now, I have to write everything out because i'm not familiar enough with the processes

or is it
( 1 ) ( 8 )

( 10 ) ( 9) because the successful draw does not have an exclusion?

or
( 1 ) ( 8 )

(10 ) ( 10 )

in the case of the marbles a total of

(2 choose 1 times 3 choose 1)
times

(1 ) ( 8 ) ( 1 ) ( 8 ) ( 8 )

(10^ 5 )

would that be right for both players to have 1 but neither have the other?

[midnight plank]

@twin monolith Has your question been resolved?

[midnight plank]

@twin monolith Has your question been resolved?

[midnight plank]

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[obtuse basin]

Notice that x dy/dx + y is the derivative of xy and 1 + dy/dx is the derivative of x + y

I'd rewrite this as 1/xy * d/dx(xy) = 1/(x + y)^2 * d/dx(x + y)

Do you see anything familiar?

It's as if chain rule has been applied, isn't it?

Yup, the left hand side is now the derivative of ln(xy) where as the right hand side is the derivative of -1/(x + y)

Meaning that ln(xy) = c - 1/(x + y) for some constant c

Now really sure how to solve for y here tho lol since we get it inside log and inside a denominator

Of solving the differential equation?

Yeah not sure, all I did was notice that x dy/dx + y is the derivative of xy

And everything else became clear

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[raw smelt]

The yearbook club had a meeting. The meeting had people 12 , which is one-fourth of the club. How many people are in the club?

[obtuse basin]

Just multiply 12 by 4?

[warm magnet]

I mean yeah you have 1/4

And you wanna get 1

So multiply by 4

[raw smelt]

Suppose a charity received a donation of 17.6 million. If this represents 39% of the charity's donated funds, what is the total amount of its donated funds?
Round your answer to the nearest million dollars.

<@&286206848099549185>

[midnight plank]

@raw smelt Has your question been resolved?

[last slate]

into eq

X * 0.39 = 17.6 Million

if this doesn't make sense ping

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[exotic kelp]

Need help factoring

[exotic kelp]

x^7 + x^4

[indigo sentinel]

There has to be more to the equation

you cant factorize that

[exotic kelp]

that's the whole equation

I just can't find out how can I factorize it

[indigo sentinel]

oh lmao

im silly

wait no

you cant

7 is a prime number

you'd have to multiply until they have a common... I dont know what its called in english

[exotic kelp]

I have the answer but I just can't find out how do I get there

[indigo sentinel]

Send the answer

yeah but their equation has +

[exotic kelp]

x^4 (x +1) ( x^2 -x +1 )

[indigo sentinel]

Akren see if you can help, im lost

[exotic kelp]

I'm sorry haha

I think i need to have ^3 on both terms because "(x +1) ( x^2 -x +1 )" it's the addiction cubique rule a^3 +b^3 = ( a +b) (a^2 - ab + b^2)

im sorry

i was looking at the paper feeling dumb

haha

ohh

i got it

thank you

❤️

.close

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[dusky thunder]

hello! i'm watching a tutorial on how to code tetris and I'm struggling to understand the system they are using to represent the different rotations for pieces.
I was hoping this might make sense to someone else who would be kind enough to explain to me? much appreciate it!

Kind::O => &[(0, 0), (0, 1), (1, 0), (1, 1)],
Kind::I => &[(-1, 0), (0, 0), (1, 0), (2, 0)],
Kind::T => &[(-1, 0), (0, 0), (1, 0), (0, 1)],
Kind::L => &[(-1, 0), (0, 0), (1, 0), (1, 1)],
Kind::J => &[(-1, 1), (-1, 0), (0, 0), (1, 0)],
Kind::S => &[(-1, 0), (0, 0), (0, 1), (1, 1)],
Kind::Z => &[(-1, 1), (0, 1), (0, 0), (1, 0)],

[midnight plank]

@dusky thunder Has your question been resolved?

[dusky thunder]

<@&286206848099549185>

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@dusky thunder Has your question been resolved?

[hot totem]

Looks like comparison against right turns and left turns. I can't see the relation to a rotation matrix which is how I think it should be done
https://math.stackexchange.com/questions/1676441/how-to-rotate-the-positions-of-a-matrix-by-90-degrees

On the 4x4 and 3x3 grids you can figure out the right and left turns from the (0,0) reference points

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[gentle sentinel]

can som eone PLEASE help with this one

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@gentle sentinel Has your question been resolved?

[gentle sentinel]

what do you think you neanderthal

why even ask if there clearly hasent been any messages

[gentle sentinel]

.close

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[thin pond]

Can someone help with b?

[thin pond]

The solutions on the back of the textbook say that <4=2x and <5=3x but I'm confused why

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[digital badger]

I'm familiar with how to take a definite integral but a bit confused as to how to work this application.

[vale willow]

well we have a system of equations

[digital badger]

right

[vale willow]

F(b) - F(a) = 4
F(b)- F(c)=-2

[digital badger]

mhm

[vale willow]

sorry corrected mistake

[digital badger]

haha no worries, my tired brain didn't even notice

[vale willow]

if we subract the systems we get
-F(a)+F(c) =6

[digital badger]

ok

[vale willow]

which is the integration range of the first integral

if we work it out it makes ((x^2)/2)*F(c) +2x - ((x^2)/2)*F(a) +2x

which is ((x^2)/2)(F(c)-F(a) +(4x)/((x^2)/2)) or
((x^2)/2)(6+(4x)/((x^2)/2))

[digital badger]

Ok that makes some sense, I'm going to work on simplifying that

[vale willow]

yeah lol im too lazy but i think it shold be ez

[digital badger]

wait isn't that just 6+4x?

[vale willow]

6*((x^2)/2)+4x

but close enough

[digital badger]

oh so 3x^2 + 4x

[vale willow]

uhhhh yes

[digital badger]

why does it say I'm wrong then

[vale willow]

either site is bad or try
3(x^2) + 4x

[digital badger]

it's not that

huh

oh well then

perhaps I was supposed to plug something in

[vale willow]

how😭😭😭😭

oh maybe

it very wierdly says "exact" answer so deff smthing scethy

[digital badger]

yeah, it suggests that my answer is supposed to be some kind of integer

nope, the program is just a jerk and didn't like the use of "x" and wanted (c-a)

[vale willow]

oh yeah totaly forgot that f(x) and x use the same variable

cuz like 99% of the cases it isnt like that and my brain tuned it out

[digital badger]

yup lol

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[last slate]

i'm supposed to derive the first four terms of the sequence that this creates. I don't know how to get a though?

[subtle blaze]

Doesn’t matter

[last slate]

first term is n = 1

[subtle blaze]

Then (a-1)/(a-1) is 1

First term

2nd term is just a+1 if you do difference of squares

3rd term you can difference of cubes as well

4th I’m sure you can figure out

[last slate]

mk tnx

c.lose

.close

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[rugged sage]

I am trying to solve for X

but its not correct

what am i doing wrong

i multiplied A^-1 to both sides

giving me

BXA^-1B^-1 = A^-1 + I

then i multiplied by B^-1

giving me XA^-1B^-1 = AB^-1 + B^-1

thenby A

= A(AB^-1) + A(B^-1)

then B

BA(AB^-1) + BA(B^-1)

so that would give BA(AB^-1) + A

oh fuck me thats the answer

😭

sorry is my procedure correct?

<@&286206848099549185>

the answer key is AB^-1 (BA) + A

they have it flipped

[last slate]

!15m